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Curriculum Standards: Create and use rules, tables, spreadsheets and graphs to describe patterns of change and solve problems. - 5.2.1.1 Understand how fractions are related to division. - 5.NC.9.1 Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems. - MAFS.6.G.1.1 Implement division of fractions to show quotients as fractions and mixed numbers. - 5.NC.9.2 Use multiplication to divide a whole number by a unit fraction. - 5.NC.9.3 Use models, such as pictorial models or a number line, to show dividing a whole number by a unit fraction. - 5.NC.9.4 Use place value to compare decimals through thousandths. - 5.NC.1.5 Use place value to round decimals to different places. - 5.NC.1.6 Use the structure of the decimal place-value system to solve problems involving patterns. - 5.NC.1.7 Write a simple expression for a calculation. - MAFS.5.OA.1.AP.2a Use patterns and the properties of multiplication to calculate a product when multiplying by a power of 10; use whole-number exponents to write powers of 10. - 5.NC.1.1 Recognize properties of simple plane figures using polygon-shaped manipulatives. - MAFS.5.G.2.AP.3a Read and write whole numbers using standard form, expanded form, and number names. - 5.NC.1.2 Represent decimals to thousandths as fractions and fraction with denominators of 1,000 as decimals. - 5.NC.1.3 Read and write numbers with decimals through thousandths using standard form, expanded form, and number names; identify equivalent decimals. - 5.NC.1.4 Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y-coordinate). - 5.G.1 Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. - 5.G.2 Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates. Recognize opposite signs of numbers as indicating locations on opposite sides of 0 on the number line; recognize that the opposite of the opposite of a number is the number itself, e.g., -(-3) = 3, and that 0 is its own opposite. - 6.NS.C.6a Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles. - 5.G.3 Add and subtract fractions (including mixed numbers) with unlike denominators. (May include multiple methods and representations.) - M05.A-F.1.1.1 Classify two-dimensional figures in a hierarchy based on properties. - 5.G.4 Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates. Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane. - 6.NS.C.6c Read, write, or select a decimal to the hundredths place. - MAFS.5.NBT.1.AP.3a Compare two decimals to the hundredths place, whose values are less than 1. - MAFS.5.NBT.1.AP.3b Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates. Understand signs of numbers in ordered pairs as indicating locations in quadrants of the coordinate plane; recognize that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes. - 6.NS.C.6b Evaluate a simple expression involving one set of parenthesis. - MAFS.5.OA.1.AP.1a Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. - MAFS.5.NF.2.6 Interpret multiplication as scaling (resizing), by: - MAFS.5.NF.2.5 Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction. - MAFS.5.NF.2.4 Solve problems involving computation of fractions by using information presented in line plots. - M05.D- M.2.1.1 Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. For example, interpret 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3, and that when 3 wholes are shared equally among 4 people each person has a share of size 3/4. If 9 people want to share a 50-pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie? - MAFS.5.NF.2.3 Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and <, symbols to record the results of comparisons. - 5.NBT.3b Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 x 100 + 4 x 10 + 7 x 1 + 3 x (1/10) + 9 x (1/100) + 2 x (1/1000). - 5.NBT.3a Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. - 5.NF.B.6 Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. For example, interpret 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3, and that when 3 wholes are shared equally among 4 people each person has a share of size 3/4. If 9 people want to share a 50-pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie? - 5.NF.B.3 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. For example, 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. - 5.OA.3 Use polygon-shaped manipulatives to classify and organize two-dimensional figures into Venn diagrams based on the attributes of the figures. - MAFS.5.G.2.AP.4a 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. For example, 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. - 5.OA.B.3 Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. For example, 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. - 5.OA.2 Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. - 5.OA.1 English language learners communicate information, ideas and concepts necessary for academic success in the content area of Mathematics. - ELD.K12.ELL.MA.1 Construct viable arguments and critique the reasoning of others. - MAFS.K12.MP.3.1 Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. - MAFS.5.MD.2.2 Round decimals to the next whole number. - MAFS.5.NBT.1.AP.4a Round decimals to the tenths place. - MAFS.5.NBT.1.AP.4b Use models to divide unit fractions by non-zero whole numbers. - 5.NC.9.5 Use models to divide whole numbers and unit fractions. Check your answer using multiplication. - 5.NC.9.6 Round decimals to the hundredths place. - MAFS.5.NBT.1.AP.4c Solve multi-step problems involving division with unit fractions. - 5.NC.9.7 Apply the commutative, associative and distributive properties and order of operations to generate equivalent numerical expressions and to solve problems involving whole numbers. - 5.2.2.1 Notice repetition in calculations and generalize about how to divide whole numbers and unit fractions. - 5.NC.9.8 Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles. - 5.G.B.3 Add decimals to hundredths using familiar strategies, such as partial sums. - 5.NC.2.4 Subtract decimals to hundredths familiar strategies, such as partial differences. - 5.NC.2.5 Use prior math knowledge and equations or bar diagrams to solve problems. - 5.NC.2.6 Identify parts of the coordinate plane (x-axis, y-axis, and the origin) and the ordered pair (x-coordinate and y-coordinate). Limit the coordinate plane to quadrant I. - M05.C-G.1.1.1 Represent real-world and mathematical problems by plotting points in quadrant I of the coordinate plane and interpret coordinate values of points in the context of the situation. - M05.C-G.1.1.2 Use properties of addition and strategies to solve problems mentally. - 5.NC.2.1 Use rounding or compatible numbers to estimate sums and differences. - 5.NC.2.2 Model sums and differences of decimals. - 5.NC.2.3 Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. For example, create a story context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi?. - 6.NS.A.1 Classify two-dimensional figures in a hierarchy based on properties. - 5.G.B.4 Write and evaluate numerical expressions involving whole-number exponents. - 6.EE.A.1 Compare the value of a number when it is represented in different place values of two three-digit numbers. - MAFS.5.NBT.1.AP.1a Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). - M05.A-T.2.1.3 Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) - 5.NF.A.1 Solve real-world problems with measurement conversions. - 5.MD.12.8 Use multiple grouping symbols (parentheses, brackets, or braces) in numerical expressions and evaluate expressions containing these symbols. - M05.B-O.1.1.1 Convert units of time. - 5.MD.12.7 Write simple expressions that model calculations with numbers and interpret numerical expressions without evaluating them. - M05.B-O.1.1.2 Be precise when solving measurement problems. - 5.MD.12.9 Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y-coordinate). - MAFS.5.G.1.1 Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. - MAFS.5.NF.1.2 Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. - MAFS.5.G.1.2 Convert customary units of capacity. - 5.MD.12.2 Convert customary units of length. - 5.MD.12.1 Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. - MAFS.5.NF.1.1 Convert metric units of length. - 5.MD.12.4 Convert customary units of weight. - 5.MD.12.3 Multiply multi-digit whole numbers (not to exceed three-digit by three-digit). - M05.A-T.2.1.1 Convert metric units of mass. - 5.MD.12.6 Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. - 5.NF.A.2 Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors. - M05.A-T.2.1.2 Convert metric units of capacity. - 5.MD.12.5 Reason abstractly and quantitatively. - MAFS.K12.MP.2.1 Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units. - MAFS.5.MD.3.4 Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 x 100 + 4 x 10 + 7 x 1 + 3 x (1/10) + 9 x (1/100) + 2 x (1/1000). - 5.NBT.A.3a Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume. - MAFS.5.MD.3.5 Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and <, symbols to record the results of comparisons. - 5.NBT.A.3b Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. For example, create a story context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi? - MAFS.6.NS.1.1 Use reasoning to solve problems by making sense of quantities and relationships in the situation. - 5.OA.13.4 Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates. Understand signs of numbers in ordered pairs as indicating locations in quadrants of the coordinate plane; recognize that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes. - 6.NS.6b Evaluate expressions and solve equations involving variables when values for the variables are given. - 5.2.3.3 Identify what an exponent represents (e.g., 10³= 10X10X10). - MAFS.5.NBT.1.AP.2a Represent real-world situations using equations and inequalities involving variables. Create real-world situations corresponding to equations and inequalities. - 5.2.3.2 Interpret numerical expressions without evaluating them. - 5.OA.13.3 Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units. - 5.MD.C.4 Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates. Recognize opposite signs of numbers as indicating locations on opposite sides of 0 on the number line; recognize that the opposite of the opposite of a number is the number itself, e.g., -(-3) = 3, and that 0 is its own opposite. - 6.NS.6a Determine whether an equation or inequality involving a variable is true or false for a given value of the variable. - 5.2.3.1 Write simple expressions that show calculations with numbers. - 5.OA.13.2 Identify the direction the decimal point will move when multiplying or dividing by a multiple of 10. - MAFS.5.NBT.1.AP.2b Use the order of operations to evaluate expressions. - 5.OA.13.1 Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates. Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane. - 6.NS.6c Use properties and the standard algorithm for multiplication to find the product of multi-digit numbers. - 5.NC.3.7 Use models and strategies to solve word problems. - 5.NC.3.8 Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. - 5.G.A.2 Make sense of problems and persevere in solving them. - MP.1 Locate points on a coordinate grid. - 5.G.14.1 Critique the reasoning of others by asking questions, looking for flaws, and using prior knowledge of estimating products. - 5.NC.3.9 Reason abstractly and quantitatively. - MP.2 Graph points on a coordinate grid. - 5.G.14.2 Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y-coordinate). - 5.G.A.1 Find a location on a map using given coordinates. - MAFS.5.G.1.AP.2a Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. - 5.NF.6 Use place-value strategies and the standard algorithm to multiply multi-digit numbers by 1-digit numbers. - 5.NC.3.3 Use the expanded and the standard algorithm to multiply 2-digit by 2-digit numbers. Estimate to check if products are reasonable. - 5.NC.3.4 Multiply 3-digit by 2-digit numbers by adding partial products or by using the standard algorithm. - 5.NC.3.5 Use knowledge about place value and multiplying with 2-digit and 3-digit numbers to multiply with zeros. - 5.NC.3.6 Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. - 5.NF.2 Look for and make use of structure. - MP.7 Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) - 5.NF.1 Look for and express regularity in repeated reasoning. - MP.8 Use place-value understandings and patterns to mentally multiply whole numbers and powers of 10. - 5.NC.3.1 Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. For example, interpret 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3, and that when 3 wholes are shared equally among 4 people each person has a share of size 3/4. If 9 people want to share a 50-pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie? - 5.NF.3 Use rounding and compatible numbers to estimate products. - 5.NC.3.2 Solve real-world problems by graphing points. - 5.G.14.3 Construct viable arguments and critique the reasoning of others. - MP.3 Model with mathematics. - MP.4 Use reasoning to solve problems by making sense of quantities and relationships in the situation. - 5.G.14.4 Use appropriate tools strategically. - MP.5 Attend to precision. - MP.6 Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. For example, create a story context for (1/3) ÷ 4, and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that (1/3) ÷ 4 = 1/12 because (1/12) × 4 = 1/3. - 5.NF.7a Convert standard measurements of length to solve real-world problems. - MAFS.5.MD.1.AP.1b Convert standard measurements of mass to solve real-world problems. - MAFS.5.MD.1.AP.1c Convert standard measurements of time to solve real-world problems. - MAFS.5.MD.1.AP.1a Solve unit rate problems including those involving unit pricing and constant speed. For example, if it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed? - 6.RP.A.3b 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. Formulas will be provided. - M05.D-M.3.1.1 Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent. - 6.RP.A.3c Find volumes of solid figures composed of two nonoverlapping right rectangular prisms. - M05.D- M.3.1.2 Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for 4 ÷ (1/5), and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 × (1/5) = 4. - 5.NF.7b Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins? - 5.NF.7c Make tables of equivalent ratios relating quantities with whole-number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios. - 6.RP.A.3a Graph ordered pairs (coordinates). - MAFS.5.G.1.AP.1c Locate points on a coordinate plane. - MAFS.5.G.1.AP.1b Locate the x- and y-axis on a coordinate plane. - MAFS.5.G.1.AP.1a Represent a problem situation with a mathematical model. - 5.NC.7.12 Make a line plot to display a data set of measurements in fractions of a unit (1/2 , 1/4 , 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally. - 5.MD.2 Add and subtract mixed numbers using equivalent fractions and a common denominator. - 5.NC.7.11 Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units. - 5.MD.4 Subtract mixed numbers using equivalent fractions and a common denominator. - 5.NC.7.10 Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. - 5.MD.1 Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. - MAFS.5.NBT.1.3.b Use appropriate tools strategically. - MAFS.K12.MP.5.1 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). - MAFS.5.NBT.1.3.a Given two pattern descriptions involving the same context (e.g., collecting marbles), determine the first five terms and compare the values. - MAFS.5.OA.2.AP.3a 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. - MAFS.5.OA.2.3 Make a line plot to display a data set of measurements in fractions of a unit (1/2 , 1/4 , 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally. - 5.MD.B.2 Graph ordered pairs on a coordinate plane when given a table that follows patterns rules. - MAFS.5.OA.2.AP.3b Multiply decimals using partial products and models. - 5.NC.4.6 Use properties to multiply decimals. - 5.NC.4.7 Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. - MAFS.5.OA.1.2 A solid figure which can be packed without gaps or overlaps using n unit cubes is said to have a volume of n cubic units. - MAFS.5.MD.3.3.b Use number sense and reasoning to place the decimal point in a product. - 5.NC.4.8 Use previously learned concepts and skills to represent and solve problems. - 5.NC.4.9 A cube with side length 1 unit, called a “unit cube,” is said to have “one cubic unit” of volume, and can be used to measure volume. - MAFS.5.MD.3.3.a Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. - MAFS.5.OA.1.1 Use rounding and compatible numbers to estimate the product of a decimal and a whole number. - 5.NC.4.2 Use models to represent multiplying a decimal and a whole number. - 5.NC.4.3 Use place-value understanding and an algorithm for multiplying whole numbers to multiply a decimal and a whole number. - 5.NC.4.4 Understand that positive and negative numbers are used together to describe quantities having opposite directions or values (e.g., temperature above/below zero, elevation above/below sea level, credits/debits, positive/negative electric charge); use positive and negative numbers to represent quantities in real-world contexts, explaining the meaning of 0 in each situation. - 6.NS.C.5 Use grids to model decimals and find the product of a decimal and a decimal. - 5.NC.4.5 Use knowledge about place value and patterns to find the product of a decimal number and a power of 10. - 5.NC.4.1 Classify two-dimensional figures in a hierarchy based on properties. - M05.C-G.2.1.1 Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems. - 6.G.A.1 Generate two numerical patterns using two given rules. - M05.B-O.2.1.1 Identify apparent relationships between corresponding terms of two patterns with the same starting numbers that follow different rules. - M05.B-O.2.1.2 Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. - 5.MD.A.1 Understand that positive and negative numbers are used together to describe quantities having opposite directions or values (e.g., temperature above/below zero, elevation above/below sea level, credits/debits, positive/negative electric charge); use positive and negative numbers to represent quantities in real-world contexts, explaining the meaning of 0 in each situation. - MAFS.6.NS.3.5 Compare two decimals to thousandths based on meanings of the digits in each place using >, =, and < symbols. - M05.A-T.1.1.4 Round decimals to any place (limit rounding to ones, tenths, hundredths, or thousandths place). - M05.A-T.1.1.5 Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. - 5.OA.A.1 Model with mathematics. - MAFS.K12.MP.4.1 Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. For example, 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. - 5.OA.A.2 Explain patterns in the number of zeros of the product when multiplying a number by powers of 10 and 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. - M05.A-T.1.1.2 Read and write decimals to thousandths using base-ten numerals, word form, and expanded form. - M05.A-T.1.1.3 Convert among different-sized standard measurement units (i.e., km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec) within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. - MAFS.5.MD.1.1 Demonstrate an understanding that in a multi-digit number, a digit in one place represents 1/10 of what it represents in the place to its left. - M05.A-T.1.1.1 Use place value and sharing to divide by 2-digit divisors. - 5.NC.5.5 Use place value and sharing to divide greater dividends. - 5.NC.5.6 Select from different strategies to divide 3-and 4-digit numbers by 2-digit numbers. - 5.NC.5.7 Make sense of problems and keep working. - 5.NC.5.8 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. - 5.MD.C.5a Use place-value patterns and mental math to find quotients. - 5.NC.5.1 Use compatible numbers and place-value patterns to estimate quotients. - 5.NC.5.2 Recognize volume as additive. 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. - 5.MD.C.5c Interpret division of a whole number by a unit fraction, and compute such quotients. - MAFS.5.NF.2.7.b Use models to find quotients. - 5.NC.5.3 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. - 5.MD.C.5b Solve division problems using partial quotients. - 5.NC.5.4 Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. - MAFS.5.NF.2.7.a Recognize volume as additive. 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. - 5.MD.5c Classify triangles by their angles and sides. - 5.G.16.1 Classify quadrilaterals by their properties. - 5.G.16.2 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. - 5.MD.5b Classify quadrilaterals using a hierarchy. - 5.G.16.3 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. - 5.MD.5a Construct arguments about geometric figures. - 5.G.16.4 Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. For example, create a story context for (1/3) ÷ 4, and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that (1/3) ÷ 4 = 1/12 because (1/12) × 4 = 1/3. - 5.NF.B.7a Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins? - 5.NF.B.7c Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for 4 ÷ (1/5), and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 × (1/5) = 4. - 5.NF.B.7b Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. - 5.NBT.B.7 Write, interpret, and explain statements of order for rational numbers in real-world contexts. For example, write –3 ºC > –7 ºC to express the fact that –3 ºC is warmer than –7 ºC. - MAFS.6.NS.3.7b 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 Interpret statements of inequality as statements about the relative position of two numbers on a number line diagram. For example, interpret –3 > –7 as a statement that –3 is located to the right of –7 on a number line oriented from left to right. - MAFS.6.NS.3.7a Know and use the definitions of the mean, median and range of a set of data. Know how to use a spreadsheet to find the mean, median and range of a data set. Understand that the mean is a “leveling out” of data. - 5.4.1.1 Collect and graph fractional data on a line plot (e.g., length of each person’s pencil in classroom, hours of exercise each week). - MAFS.5.MD.2.AP.2a Fluently multiply multi-digit whole numbers using the standard algorithm. - 5.NBT.B.5 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. - 5.NBT.B.6 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. - 5.NBT.A.1 Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. - 5.NBT.A.2 Write informative/explanatory texts to examine a topic and convey ideas and information clearly. (a) Introduce a topic clearly, provide a general observation and focus, and group related information logically; include formatting (e.g., headings), illustrations, and multimedia when useful to aiding comprehension. (b) Develop the topic with facts, definitions, concrete details, quotations, or other information and examples related to the topic. (c) Link ideas within and across categories of information using words, phrases, and clauses (e.g., in contrast, especially). (d) Use precise language and domain- specific vocabulary to inform about or explain the topic. (e) Provide a concluding statement or section related to the information or explanation presented. - LAFS.5.W.1.2 Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent. - 6.RP.3c Look for and make use of structure. - MAFS.K12.MP.7.1 Understand signs of numbers in ordered pairs as indicating locations in quadrants of the coordinate plane; recognize that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes. - MAFS.6.NS.3.6b Recognize opposite signs of numbers as indicating locations on opposite sides of 0 on the number line; recognize that the opposite of the opposite of a number is the number itself, e.g., –(–3) = 3, and that 0 is its own opposite. - MAFS.6.NS.3.6a Make tables of equivalent ratios relating quantities with whole-number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios. - 6.RP.3a Interpret the product a/b x q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = (ac)/(bd). - 5.NF.4a Solve unit rate problems including those involving unit pricing and constant speed. For example, if it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed? - 6.RP.3b Solve one-step problems using decimals. - MAFS.5.NBT.2.AP.7a Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side lengths, and show that the area is the same as would be found by multiplying the side lengths. Multiply fractional side lengths to find areas of rectangles, and represent fraction products as rectangular areas. - 5.NF.4b Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane. - MAFS.6.NS.3.6c Use models to visualize the relationship between division and multiplication to divide decimals by 2-digit whole numbers. - 5.NC.6.4 Use models to divide a decimal by a decimal. - 5.NC.6.5 Use reasoning to solve problems by making sense of quantities and relationships in problem situations. - 5.NC.6.6 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. - MAFS.5.MD.3.5.b 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. - MAFS.5.MD.3.5.a Use mental math and place-value patterns to divide a decimal by a power of 10. - 5.NC.6.1 Use reasoning and strategies such as rounding and compatible numbers to estimate quotients in problems with decimals. - 5.NC.6.2 Recognize volume as additive. 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. - MAFS.5.MD.3.5.c Use models to help find quotients in problems involving decimals. - 5.NC.6.3 Develop and use the formulas V = ?wh and V = Bh to determine the volume of rectangular prisms. Justify why base area B and height h are multiplied to find the volume of a ectangular prism by breaking the prism into layers of unit cubes. - 5.3.2.4 Add or subtract fractions with unlike denominators within one whole unit on a number line. - MAFS.5.NF.1.AP.1b Add and subtract fractions with like denominators with sums greater than 1 represented by mixed numbers using visual fraction models. - MAFS.5.NF.1.AP.1a Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations). For example, use the formulas V = s3 and A = 6 s2 to find the volume and surface area of a cube with sides of length s = 1/2. - 6.EE.A.2c Develop and use formulas to determine the area of triangles, parallelograms and figures that can be decomposed into triangles. - 5.3.2.1 Understand that the volume of a three dimensional figure can be found by counting the total number of same-sized cubic units that fill a shape without gaps or overlaps. Use cubic units to label volume measurements. - 5.3.2.3 Use various tools and strategies to measure the volume and surface area of objects that are shaped like rectangular prisms. - 5.3.2.2 Comparing the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication. - 5.NF.B.5a Explaining why multiplying a given number by a fraction greater than 1 results in a product greater than the given number (recognizing multiplication by whole numbers greater than 1 as a familiar case); explaining why multiplying a given number by a fraction less than 1 results in a product smaller than the given number; and relating the principle of fraction equivalence a/b = (n × a)/(n × b) to the effect of multiplying a/b by 1. - 5.NF.B.5b Use place value understanding to round decimals to any place. - 5.NBT.A.4 Comparing the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication. - 5.NF.5a Explaining why multiplying a given number by a fraction greater than 1 results in a product greater than the given number (recognizing multiplication by whole numbers greater than 1 as a familiar case); explaining why multiplying a given number by a fraction less than 1 results in a product smaller than the given number; and relating the principle of fraction equivalence a/b = (n × a)/(n × b) to the effect of multiplying a/b by 1. - 5.NF.5b Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. - 5.NBT.7 Multiply a fraction (including mixed numbers) by a fraction. - M05.A-F.2.1.2 Solve word problems involving the addition and subtraction of fractions using visual fraction models. - MAFS.5.NF.1.AP.2a Solve word problems involving division of whole numbers leading to answers in the form of fractions (including mixed numbers). - M05.A-F.2.1.1 Divide unit fractions by whole numbers and whole numbers by unit fractions. - M05.A-F.2.1.4 Demonstrate an understanding of multiplication as scaling (resizing). - M05.A-F.2.1.3 Summarize a written text read aloud or information presented in diverse media and formats, including visually, quantitatively, and orally. - LAFS.5.SL.1.2 Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 5 topics and texts, building on others’ ideas and expressing their own clearly. (a) Come to discussions prepared, having read or studied required material; explicitly draw on that preparation and other information known about the topic to explore ideas under discussion. (b) Follow agreed-upon rules for discussions and carry out assigned roles. (c) Pose and respond to specific questions by making comments that contribute to the discussion and elaborate on the remarks of others. (d) Review the key ideas expressed and draw conclusions in light of information and knowledge gained from the discussions. - LAFS.5.SL.1.1 Summarize the points a speaker makes and explain how each claim is supported by reasons and evidence. - LAFS.5.SL.1.3 Solve real-world and mathematical problems requiring addition, subtraction, multiplication and division of multi-digit whole numbers. Use various strategies, including the inverse relationships between operations, the use of technology, and the context of the problem to assess the reasonableness of results. - 5.1.1.4 Estimate solutions to arithmetic problems in order to assess the reasonableness of results. - 5.1.1.3 Attend to precision. - MAFS.K12.MP.6.1 Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side lengths, and show that the area is the same as would be found by multiplying the side lengths. Multiply fractional side lengths to find areas of rectangles, and represent fraction products as rectangular areas. - 5.NF.B.4b Interpret the product a/b x q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = (ac)/(bd). - 5.NF.B.4a Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. - 5.NBT.2 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. - 5.NBT.1 Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. - MAFS.5.NF.2.7.c 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. - 5.NBT.6 Fluently multiply multi-digit whole numbers using the standard algorithm. - 5.NBT.5 Use place value understanding to round decimals to any place. - 5.NBT.4 Add fractions with unlike denominators using equivalent fractions with a common denominator. - 5.NC.7.3 Subtract fractions with unlike denominators. - 5.NC.7.4 Write equivalent fractions to add and subtract fractions with unlike denominators. - 5.NC.7.5 Estimate sums and differences of fractions and mixed numbers. - 5.NC.7.6 Determine the volume of a rectangular prism built by “unit cubes.” - MAFS.5.MD.3.AP.4a Explaining why multiplying a given number by a fraction greater than 1 results in a product greater than the given number (recognizing multiplication by whole numbers greater than 1 as a familiar case); explaining why multiplying a given number by a fraction less than 1 results in a product smaller than the given number; and relating the principle of fraction equivalence a/b = (n × a)/(n × b) to the effect of multiplying a/b by 1. - MAFS.5.NF.2.5.b Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. For example, "The ratio of wings to beaks in the bird house at the zoo was 2:1, because for every 2 wings there was 1 beak." "For every vote candidate A received, candidate C received nearly three votes." - 6.RP.A.1 Comparing the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication. - MAFS.5.NF.2.5.a Understand the concept of a unit rate a/b associated with a ratio a:b with b ? 0, and use rate language in the context of a ratio relationship. For example, "This recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there is 3/4 cup of flour for each cup of sugar." "We paid $75 for 15 hamburgers, which is a rate of $5 per hamburger." - 6.RP.A.2 Estimate sums and differences of fractions by using the nearest half or whole number. - 5.NC.7.1 Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations. - 6.RP.A.3 Find common denominators for fractions with unlike denominators. - 5.NC.7.2 Recognize and draw a net for a three-dimensional figure. - 5.3.1.2 Describe and classify three-dimensional figures including cubes, prisms and pyramids by the number of edges, faces or vertices as well as the types of faces. - 5.3.1.1 Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true. - 6.EE.B.5 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 Multiply a fraction by a whole or mixed number using visual fraction models. - MAFS.5.NF.2.AP.4a Determine whether the product will increase or decrease based on the multiple using visual fraction models. - MAFS.5.NF.2.AP.5a Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems. - 6.G.1 Use multiplication to represent each layer of the rectangular prism. - MAFS.5.MD.3.AP.5a Make sense of problems and persevere in solving them. - 5.MP.1 Connect the layers to the dimensions and multiply to find the volume of the rectangular prism. - MAFS.5.MD.3.AP.5c Use addition to determine the length, width, and height. - MAFS.5.MD.3.AP.5b 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. - MAFS.5.NBT.2.6 Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. - MAFS.5.NBT.2.7 Fluently multiply multi-digit whole numbers using the standard algorithm. - MAFS.5.NBT.2.5 Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. - MAFS.5.G.2.3 Find the volume of solid figures. - 5.MD.11.1 Classify and organize two-dimensional figures into Venn diagrams based on the attributes of the figures. - MAFS.5.G.2.4 Find the volume of a solid figure that is the combination of two or more rectangular prisms. - 5.MD.11.3 Find the volume of rectangular prisms using a formula. - 5.MD.11.2 Use previously learned knowledge about volume to choose the appropriate tools to solve volume problems. - 5.MD.11.5 Use models, prior knowledge of volume and previously learned strategies to solve word problems involving volume. - 5.MD.11.4 Divide unit fractions by whole numbers and whole numbers by unit fractions using visual fraction models. - MAFS.5.NF.2.AP.3a Order fractions and decimals, including mixed numbers and improper fractions, and locate on a number line. - 5.1.2.3 Find 0.1 more than a number and 0.1 less than a number. Find 0.01 more than a number and 0.01 less than a number. Find 0.001 more than a number and 0.001 less than a number. - 5.1.2.2 Round numbers to the nearest 0.1, 0.01 and 0.001. - 5.1.2.5 Recognize and generate equivalent decimals, fractions, mixed numbers and improper fractions in various contexts. - 5.1.2.4 Make sense of problems and persevere in solving them. - MAFS.K12.MP.1.1 Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent. - MAFS.6.RP.1.3c Add mixed numbers using models. - 5.NC.7.7 Convert between different-sized measurement units within a given measurement system. A table of equivalencies will be provided. - M05.D-M.1.1.1 Add mixed numbers using equivalent fractions and a common denominator. - 5.NC.7.8 Use models to subtract mixed numbers. - 5.NC.7.9 Multiply a whole number by a fraction. - 5.NC.8.2 Multiply fractions and whole numbers. - 5.NC.8.3 Interpret the product (a/b) × q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. - MAFS.5.NF.2.4.a Use models to multiply two fractions. - 5.NC.8.4 Multiply two fractions. - 5.NC.8.5 Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side lengths, and show that the area is the same as would be found by multiplying the side lengths. Multiply fractional side lengths to find areas of rectangles, and represent fraction products as rectangular areas. - MAFS.5.NF.2.4.b A cube with side length 1 unit, called a unit cube, is said to have one cubic unit of volume, and can be used to measure volume. - 5.MD.C.3a Multiply a fraction by a whole number. - 5.NC.8.1 A solid figure that can be packed without gaps or overlaps using n unit cubes is said to have a volume of n cubic units. - 5.MD.3b A cube with side length 1 unit, called a "unit cube," is said to have "one cubic unit" of volume, and can be used to measure volume. - 5.MD.3a A solid figure that can be packed without gaps or overlaps using n unit cubes is said to have a volume of n cubic units. - 5.MD.C.3b Read and write decimals using place value to describe decimals in terms of groups from millionths to millions. - 5.1.2.1 Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true. - 6.EE.5 Divide unit fractions by whole numbers and whole numbers by unit fractions using visual fraction models. - MAFS.5.NF.2.AP.7a Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. For example, create a story context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi? - 6.NS.1 Write and evaluate numerical expressions involving whole-number exponents. - 6.EE.1 Understand that positive and negative numbers are used together to describe quantities having opposite directions or values (e.g., temperature above/below zero, elevation above/below sea level, credits/debits, positive/negative electric charge); use positive and negative numbers to represent quantities in real-world contexts, explaining the meaning of 0 in each situation. - 6.NS.5 Look for and make use of structure. - 5.MP.7 Attend to precision. - 5.MP.6 Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. For example, “The ratio of wings to beaks in the bird house at the zoo was 2:1, because for every 2 wings there was 1 beak.” “For every vote candidate A received, candidate C received nearly three votes.” - MAFS.6.RP.1.1 Understand the concept of a unit rate a/b associated with a ratio a:b with b ? 0, and use rate language in the context of a ratio relationship. For example, “This recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there is 3/4 cup of flour for each cup of sugar.” “We paid $75 for 15 hamburgers, which is a rate of $5 per hamburger.” - MAFS.6.RP.1.2 Look for and express regularity in repeated reasoning. - 5.MP.8 Construct viable arguments and critique the reasoning of others. - 5.MP.3 Find whole number quotients up to two dividends and two divisors. - MAFS.5.NBT.2.AP.6a Reason abstractly and quantitatively. - 5.MP.2 Find whole number quotients of whole numbers with up to two-digit dividends and two-digit divisors. - MAFS.5.NBT.2.AP.6b Use appropriate tools strategically. - 5.MP.5 Model with mathematics. - 5.MP.4 Use place value understanding to round decimals to any place. - MAFS.5.NBT.1.4 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. - MAFS.5.NBT.1.1 Use packing to recognize volume of a solid figure. - MAFS.5.MD.3.AP.3a Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. - MAFS.5.NBT.1.2 Organize and display data in a line plot. - 5.MD.10.2 Read and analyze line plots. - 5.MD.10.1 Critique the reasoning of others using understanding of line plots and fractions. - 5.MD.10.4 Solve problems using data in a line plot. - 5.MD.10.3 Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. For example, “The ratio of wings to beaks in the bird house at the zoo was 2:1, because for every 2 wings there was 1 beak.” “For every vote candidate A received, candidate C received nearly three votes.” - 6.RP.1 Understand the concept of a unit rate a/b associated with a ratio a:b with b z 0, and use rate language in the context of a ratio relationship. For example, “This recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there is 3/4 cup of flour for each cup of sugar.” “We paid $75 for 15 hamburgers, which is a rate of $5 per hamburger.” - 6.RP.2 Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations. - 6.RP.3 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 Multiply a fraction by a whole or mixed number using visual fraction models. - MAFS.5.NF.2.AP.6a 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 Look for and express regularity in repeated reasoning. - MAFS.K12.MP.8.1 Make sense of problems and persevere in solving them. - 5.OA.15.4 Analyze patterns and graph ordered pairs generated from number sequences. - 5.OA.15.3 Use tables to identify relationships between patterns. - 5.OA.15.2 Find the area of a rectangle using fractions and diagrams. - 5.NC.8.6 English language learners communicate for social and instructional purposes within the school setting. - ELD.K12.ELL.SI.1 Use models, equations and previously learned strategies to multiply mixed numbers. - 5.NC.8.7 Analyze numerical relationships. - 5.OA.15.1 Fluently multiply two-digit numbers. - MAFS.5.NBT.2.AP.5a Compare the size of the product to the size of one factor without multiplying to consider multiplication as scaling. - 5.NC.8.8 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 Use previously learned 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I_ff977ee4-33fe-3b81-955e-6d3afb1e26ee_R/BasicLTI.xml I_ffa429f3-985b-3de2-a046-f20ce1875a45_1_R/BasicLTI.xml I_ffa979e6-1061-3766-876b-8568be7a450c_R/BasicLTI.xml I_ffb146b8-7e38-3d01-bcc5-f532b7ee41cc_R/BasicLTI.xml I_ffb27137-ef09-35c5-8fe2-bba52f727e5f_1_R/BasicLTI.xml I_ffb8aade-7802-3fa9-a99f-1dd11bd00c2c_R/BasicLTI.xml I_ffc19b05-12f3-3f9b-b3ef-666e2e29bdd6_1_R/BasicLTI.xml I_ffc5211c-8a6c-3be1-ae9a-4b8b30bd46ff_1_R/BasicLTI.xml I_ffc89128-7205-3e96-82fc-7bf7aadd9257_1_R/BasicLTI.xml I_ffd26ebf-6a78-3429-ad8f-5a1c6a582be7_R/BasicLTI.xml I_ffd5b790-69a2-3d1c-8d63-2f3a2c2f5252_R/BasicLTI.xml I_fff00d8a-cf36-3618-8726-474c071b66c1_R/BasicLTI.xml I_fff779c8-fe97-3564-8f79-e0cc4414eb6d_R/BasicLTI.xml I_fffd6430-84b1-3a5d-8857-282f28f2e4de_R/BasicLTI.xml Title: enVision Mathematics 2020 Grade 5 Description: enVision Mathematics 2020 Grade 5 Academic Vocabulary Academic Vocabulary: Accurate Academic Vocabulary: Approach Academic Vocabulary: Appropriate Academic Vocabulary: Approximate Academic Vocabulary: Argument Academic Vocabulary: Arrange Academic Vocabulary: Calculate Academic Vocabulary: Conjecture Academic Vocabulary: Construct Academic Vocabulary: Context Academic Vocabulary: Contrast Academic Vocabulary: Demonstrate Academic Vocabulary: Describe Academic Vocabulary: Develop Academic Vocabulary: Diagram Academic Vocabulary: Distribute Academic Vocabulary: Establish Academic Vocabulary: Evaluate Academic Vocabulary: Examine Academic Vocabulary: Example Academic Vocabulary: Experience Academic Vocabulary: Experiment Academic Vocabulary: Explain Academic Vocabulary: Express Academic Vocabulary: Extend Academic Vocabulary: Frequent Academic Vocabulary: Horizontal Academic Vocabulary: Identify Academic Vocabulary: Infer Academic Vocabulary: Justify Academic Vocabulary: Opposite Academic Vocabulary: Organize Academic Vocabulary: Persuade Academic Vocabulary: Predict Academic Vocabulary: Recognize Academic Vocabulary: Region Academic Vocabulary: Relationship Academic Vocabulary: Simplify Academic Vocabulary: Support Academic Vocabulary: Vertical Grade 5 Readiness Tests Grade 5 Readiness Test Grade 5 Online Readiness Test Math Practices Animations Math Practice 1 Animation Math Practice 2 Animation Math Practice 3 Animation Math Practice 4 Animation Math Practice 5 Animation Math Practice 6 Animation Math Practice 7 Animation Math Practice 8 Animation Math Practices Animations (Spanish) Animaciones de Prácticas matemáticas 1 Animaciones de Prácticas matemáticas 2 Animaciones de Prácticas matemáticas 3 Animaciones de Prácticas matemáticas 4 Animaciones de Prácticas matemáticas 5 Animaciones de Prácticas matemáticas 6 Animaciones de Prácticas matemáticas 7 Animaciones de Prácticas matemáticas 8 Topic 1: Understand Place Value Topic 1: Today's Challenge Topic 1: Beginning of Topic Interactive Student Edition: Beginning of Topic 1 Topic 1: enVision STEM Activity Grade 5 Topic 1: Review What You Know Topic 1: Vocabulary Cards 1-1: Patterns with Exponents and Powers of 10 Interactive Student Edition: Grade 5 Lesson 1-1 Math Anytime 1-1: Daily Review Topic 1: Today's Challenge Step 1: Problem-Based Learning 1-1: Solve & Share Curriculum Standards: Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. English language learners communicate for social and instructional purposes within the school setting. Write informative/explanatory texts to examine a topic and convey ideas and information clearly. (a) Introduce a topic clearly, provide a general observation and focus, and group related information logically; include formatting (e.g., headings), illustrations, and multimedia when useful to aiding comprehension. (b) Develop the topic with facts, definitions, concrete details, quotations, or other information and examples related to the topic. (c) Link ideas within and across categories of information using words, phrases, and clauses (e.g., in contrast, especially). (d) Use precise language and domain-specific vocabulary to inform about or explain the topic. (e) Provide a concluding statement or section related to the information or explanation presented. English language learners communicate information, ideas and concepts necessary for academic success in the content area of Mathematics. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. Use patterns and the properties of multiplication to calculate a product when multiplying by a power of 10; use whole-number exponents to write powers of 10. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10 and 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. Read and write decimals using place value to describe decimals in terms of groups from millionths to millions. Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 5 topics and texts, building on others’ ideas and expressing their own clearly. (a) Come to discussions prepared, having read or studied required material; explicitly draw on that preparation and other information known about the topic to explore ideas under discussion. (b) Follow agreed-upon rules for discussions and carry out assigned roles. (c) Pose and respond to specific questions by making comments that contribute to the discussion and elaborate on the remarks of others. (d) Review the key ideas expressed and draw conclusions in light of information and knowledge gained from the discussions. Summarize a written text read aloud or information presented in diverse media and formats, including visually, quantitatively, and orally. Summarize the points a speaker makes and explain how each claim is supported by reasons and evidence. Step 2: Visual Learning 1-1: Visual Learning Curriculum Standards: Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. Use patterns and the properties of multiplication to calculate a product when multiplying by a power of 10; use whole-number exponents to write powers of 10. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10 and 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. Read and write decimals using place value to describe decimals in terms of groups from millionths to millions. Identify what an exponent represents (e.g., 10³= 10X10X10). 1-1: Convince Me! Curriculum Standards: Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. Use patterns and the properties of multiplication to calculate a product when multiplying by a power of 10; use whole-number exponents to write powers of 10. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10 and 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. Read and write decimals using place value to describe decimals in terms of groups from millionths to millions. Practice and Problem Solving 1-1: Student Edition Practice Curriculum Standards: Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. Use patterns and the properties of multiplication to calculate a product when multiplying by a power of 10; use whole-number exponents to write powers of 10. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10 and 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. Read and write decimals using place value to describe decimals in terms of groups from millionths to millions. 1-1: Practice Buddy: Independent Practice; Problem Solving Curriculum Standards: Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. Use patterns and the properties of multiplication to calculate a product when multiplying by a power of 10; use whole-number exponents to write powers of 10. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10 and 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. Read and write decimals using place value to describe decimals in terms of groups from millionths to millions. 1-1: Practice Buddy: Additional Practice Curriculum Standards: Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. Use patterns and the properties of multiplication to calculate a product when multiplying by a power of 10; use whole-number exponents to write powers of 10. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10 and 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. Read and write decimals using place value to describe decimals in terms of groups from millionths to millions. 1-1: Interactive Additional Practice Step 3: Assess & Differentiate 1-1: Practice Buddy: Additional Practice Curriculum Standards: Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. Use patterns and the properties of multiplication to calculate a product when multiplying by a power of 10; use whole-number exponents to write powers of 10. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10 and 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. Read and write decimals using place value to describe decimals in terms of groups from millionths to millions. 1-1: Enrichment Curriculum Standards: Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. Use patterns and the properties of multiplication to calculate a product when multiplying by a power of 10; use whole-number exponents to write powers of 10. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10 and 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. Read and write decimals using place value to describe decimals in terms of groups from millionths to millions. 1-1: Quick Check Curriculum Standards: Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. Use patterns and the properties of multiplication to calculate a product when multiplying by a power of 10; use whole-number exponents to write powers of 10. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10 and 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. Read and write decimals using place value to describe decimals in terms of groups from millionths to millions. 1-1: Lesson Self-Assessment 1-1: Reteach to Build Understanding Curriculum Standards: Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. Use patterns and the properties of multiplication to calculate a product when multiplying by a power of 10; use whole-number exponents to write powers of 10. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10 and 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. Read and write decimals using place value to describe decimals in terms of groups from millionths to millions. Identify what an exponent represents (e.g., 10³= 10X10X10). 1-1: Build Mathematical Literacy Curriculum Standards: Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 5 topics and texts, building on others’ ideas and expressing their own clearly. (a) Come to discussions prepared, having read or studied required material; explicitly draw on that preparation and other information known about the topic to explore ideas under discussion. (b) Follow agreed-upon rules for discussions and carry out assigned roles. (c) Pose and respond to specific questions by making comments that contribute to the discussion and elaborate on the remarks of others. (d) Review the key ideas expressed and draw conclusions in light of information and knowledge gained from the discussions. English language learners communicate for social and instructional purposes within the school setting. Summarize a written text read aloud or information presented in diverse media and formats, including visually, quantitatively, and orally. Summarize the points a speaker makes and explain how each claim is supported by reasons and evidence. Write informative/explanatory texts to examine a topic and convey ideas and information clearly. (a) Introduce a topic clearly, provide a general observation and focus, and group related information logically; include formatting (e.g., headings), illustrations, and multimedia when useful to aiding comprehension. (b) Develop the topic with facts, definitions, concrete details, quotations, or other information and examples related to the topic. (c) Link ideas within and across categories of information using words, phrases, and clauses (e.g., in contrast, especially). (d) Use precise language and domain-specific vocabulary to inform about or explain the topic. (e) Provide a concluding statement or section related to the information or explanation presented. English language learners communicate information, ideas and concepts necessary for academic success in the content area of Mathematics. 1-1: Enrichment Game: Galaxy Hunt - Millions 1-1: enVision STEM Activity Curriculum Standards: Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. Use patterns and the properties of multiplication to calculate a product when multiplying by a power of 10; use whole-number exponents to write powers of 10. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10 and 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. Read and write decimals using place value to describe decimals in terms of groups from millionths to millions. 1-1: Another Look Curriculum Standards: Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. Use patterns and the properties of multiplication to calculate a product when multiplying by a power of 10; use whole-number exponents to write powers of 10. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10 and 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. Read and write decimals using place value to describe decimals in terms of groups from millionths to millions. Identify what an exponent represents (e.g., 10³= 10X10X10). Spanish Resources 1-1: eText del Libro del estudiante 1-1: Repaso diario 1-1: Aprendizaje visual 1-1: Amigo de práctica: Práctica adicional 1-1: Práctica adicional interactiva 1-1: Refuerzo para mejorar la comprensión 1-1: Desarrollar la competencia matemática 1-1: Ampliación 1-2: Understand Whole-Number Place Value Interactive Student Edition: Grade 5 Lesson 1-2 Math Anytime 1-2: Daily Review Topic 1: Today's Challenge Step 1: Problem-Based Learning 1-2: Solve & Share Curriculum Standards: 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. English language learners communicate for social and instructional purposes within the school setting. Write informative/explanatory texts to examine a topic and convey ideas and information clearly. (a) Introduce a topic clearly, provide a general observation and focus, and group related information logically; include formatting (e.g., headings), illustrations, and multimedia when useful to aiding comprehension. (b) Develop the topic with facts, definitions, concrete details, quotations, or other information and examples related to the topic. (c) Link ideas within and across categories of information using words, phrases, and clauses (e.g., in contrast, especially). (d) Use precise language and domain-specific vocabulary to inform about or explain the topic. (e) Provide a concluding statement or section related to the information or explanation presented. English language learners communicate information, ideas and concepts necessary for academic success in the content area of Mathematics. 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. Recognize that in a multi- digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left. Read and write whole numbers using standard form, expanded form, and number names. Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left. Demonstrate an understanding that in a multi-digit number, a digit in one place represents 1/10 of what it represents in the place to its left. Read and write decimals using place value to describe decimals in terms of groups from millionths to millions. Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 5 topics and texts, building on others’ ideas and expressing their own clearly. (a) Come to discussions prepared, having read or studied required material; explicitly draw on that preparation and other information known about the topic to explore ideas under discussion. (b) Follow agreed-upon rules for discussions and carry out assigned roles. (c) Pose and respond to specific questions by making comments that contribute to the discussion and elaborate on the remarks of others. (d) Review the key ideas expressed and draw conclusions in light of information and knowledge gained from the discussions. Summarize a written text read aloud or information presented in diverse media and formats, including visually, quantitatively, and orally. Summarize the points a speaker makes and explain how each claim is supported by reasons and evidence. Step 2: Visual Learning 1-2: Visual Learning Curriculum Standards: 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. 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. Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left. Read and write whole numbers using standard form, expanded form, and number names. Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left. Demonstrate an understanding that in a multi-digit number, a digit in one place represents 1/10 of what it represents in the place to its left. Read and write decimals using place value to describe decimals in terms of groups from millionths to millions. Compare the value of a number when it is represented in different place values of two three-digit numbers. 1-2: Convince Me! Curriculum Standards: 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. 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. Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left. Read and write whole numbers using standard form, expanded form, and number names. Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left. Demonstrate an understanding that in a multi-digit number, a digit in one place represents 1/10 of what it represents in the place to its left. Read and write decimals using place value to describe decimals in terms of groups from millionths to millions. Practice and Problem Solving 1-2: Student Edition Practice Curriculum Standards: 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. 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. Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left. Read and write whole numbers using standard form, expanded form, and number names. Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left. Demonstrate an understanding that in a multi-digit number, a digit in one place represents 1/10 of what it represents in the place to its left. Read and write decimals using place value to describe decimals in terms of groups from millionths to millions. 1-2: Practice Buddy: Independent Practice; Problem Solving Curriculum Standards: 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. 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. Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left. Read and write whole numbers using standard form, expanded form, and number names. Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left. Demonstrate an understanding that in a multi-digit number, a digit in one place represents 1/10 of what it represents in the place to its left. Read and write decimals using place value to describe decimals in terms of groups from millionths to millions. 1-2: Practice Buddy: Additional Practice Curriculum Standards: 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. 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. Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left. Read and write whole numbers using standard form, expanded form, and number names. Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left. Demonstrate an understanding that in a multi-digit number, a digit in one place represents 1/10 of what it represents in the place to its left. Read and write decimals using place value to describe decimals in terms of groups from millionths to millions. 1-2: Interactive Additional Practice Step 3: Assess & Differentiate 1-2: Practice Buddy: Additional Practice Curriculum Standards: 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. 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. Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left. Read and write whole numbers using standard form, expanded form, and number names. Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left. Demonstrate an understanding that in a multi-digit number, a digit in one place represents 1/10 of what it represents in the place to its left. Read and write decimals using place value to describe decimals in terms of groups from millionths to millions. 1-2: Enrichment Curriculum Standards: 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. 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. Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left. Read and write whole numbers using standard form, expanded form, and number names. Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left. Demonstrate an understanding that in a multi-digit number, a digit in one place represents 1/10 of what it represents in the place to its left. Read and write decimals using place value to describe decimals in terms of groups from millionths to millions. 1-2: Quick Check Curriculum Standards: 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. 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. Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left. Read and write whole numbers using standard form, expanded form, and number names. Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left. Demonstrate an understanding that in a multi-digit number, a digit in one place represents 1/10 of what it represents in the place to its left. Read and write decimals using place value to describe decimals in terms of groups from millionths to millions. 1-2: Lesson Self-Assessment 1-2: Reteach to Build Understanding Curriculum Standards: 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. 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. Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left. Read and write whole numbers using standard form, expanded form, and number names. Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left. Demonstrate an understanding that in a multi-digit number, a digit in one place represents 1/10 of what it represents in the place to its left. Read and write decimals using place value to describe decimals in terms of groups from millionths to millions. Compare the value of a number when it is represented in different place values of two three-digit numbers. 1-2: Build Mathematical Literacy Curriculum Standards: Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 5 topics and texts, building on others’ ideas and expressing their own clearly. (a) Come to discussions prepared, having read or studied required material; explicitly draw on that preparation and other information known about the topic to explore ideas under discussion. (b) Follow agreed-upon rules for discussions and carry out assigned roles. (c) Pose and respond to specific questions by making comments that contribute to the discussion and elaborate on the remarks of others. (d) Review the key ideas expressed and draw conclusions in light of information and knowledge gained from the discussions. English language learners communicate for social and instructional purposes within the school setting. Summarize a written text read aloud or information presented in diverse media and formats, including visually, quantitatively, and orally. Summarize the points a speaker makes and explain how each claim is supported by reasons and evidence. Write informative/explanatory texts to examine a topic and convey ideas and information clearly. (a) Introduce a topic clearly, provide a general observation and focus, and group related information logically; include formatting (e.g., headings), illustrations, and multimedia when useful to aiding comprehension. (b) Develop the topic with facts, definitions, concrete details, quotations, or other information and examples related to the topic. (c) Link ideas within and across categories of information using words, phrases, and clauses (e.g., in contrast, especially). (d) Use precise language and domain-specific vocabulary to inform about or explain the topic. (e) Provide a concluding statement or section related to the information or explanation presented. English language learners communicate information, ideas and concepts necessary for academic success in the content area of Mathematics. 1-2: Enrichment Game: Galaxy Hunt - Millions 1-2: Pick a Project 1-2: Another Look Curriculum Standards: 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. 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. Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left. Read and write whole numbers using standard form, expanded form, and number names. Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left. Demonstrate an understanding that in a multi-digit number, a digit in one place represents 1/10 of what it represents in the place to its left. Read and write decimals using place value to describe decimals in terms of groups from millionths to millions. Compare the value of a number when it is represented in different place values of two three-digit numbers. Spanish Resources 1-2: eText del Libro del estudiante 1-2: Repaso diario 1-2: Aprendizaje visual 1-2: Amigo de práctica: Práctica adicional 1-2: Práctica adicional interactiva 1-2: Refuerzo para mejorar la comprensión 1-2: Desarrollar la competencia matemática 1-2: Ampliación 1-3: Decimals to Thousandths Interactive Student Edition: Grade 5 Lesson 1-3 Math Anytime 1-3: Daily Review Topic 1: Today's Challenge Step 1: Problem-Based Learning 1-3: Solve & Share Curriculum Standards: Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left. Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 x 100 + 4 x 10 + 7 x 1 + 3 x (1/10) + 9 x (1/100) + 2 x (1/1000). English language learners communicate for social and instructional purposes within the school setting. Write informative/explanatory texts to examine a topic and convey ideas and information clearly. (a) Introduce a topic clearly, provide a general observation and focus, and group related information logically; include formatting (e.g., headings), illustrations, and multimedia when useful to aiding comprehension. (b) Develop the topic with facts, definitions, concrete details, quotations, or other information and examples related to the topic. (c) Link ideas within and across categories of information using words, phrases, and clauses (e.g., in contrast, especially). (d) Use precise language and domain- specific vocabulary to inform about or explain the topic. (e) Provide a concluding statement or section related to the information or explanation presented. English language learners communicate information, ideas and concepts necessary for academic success in the content area of Mathematics. Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left. Read 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). Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left. Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 × 100 + 4 × 10 + 7 × 1 + 3 × (1/10) + 9 × (1/100) + 2 × (1/1000). Read and write decimals 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). Represent decimals to thousandths as fractions and fraction with denominators of 1,000 as decimals. Recognize that in a multi- digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left. Read and write decimals to thousandths using base-ten numerals, word form, and expanded form. Read and write decimals using place value to describe decimals in terms of groups from millionths to millions. Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 5 topics and texts, building on others’ ideas and expressing their own clearly. (a) Come to discussions prepared, having read or studied required material; explicitly draw on that preparation and other information known about the topic to explore ideas under discussion. (b) Follow agreed-upon rules for discussions and carry out assigned roles. (c) Pose and respond to specific questions by making comments that contribute to the discussion and elaborate on the remarks of others. (d) Review the key ideas expressed and draw conclusions in light of information and knowledge gained from the discussions. Summarize a written text read aloud or information presented in diverse media and formats, including visually, quantitatively, and orally. Summarize the points a speaker makes and explain how each claim is supported by reasons and evidence. Step 2: Visual Learning 1-3: Visual Learning Curriculum Standards: Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left. Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 x 100 + 4 x 10 + 7 x 1 + 3 x (1/10) + 9 x (1/100) + 2 x (1/1000). Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left. Read 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). Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left. Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 × 100 + 4 × 10 + 7 × 1 + 3 × (1/10) + 9 × (1/100) + 2 × (1/1000). Read and write decimals 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). Represent decimals to thousandths as fractions and fraction with denominators of 1,000 as decimals. Recognize that in a multi- digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left. Read and write decimals to thousandths using base-ten numerals, word form, and expanded form. Read and write decimals using place value to describe decimals in terms of groups from millionths to millions. 1-3: Convince Me! Curriculum Standards: Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left. Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 x 100 + 4 x 10 + 7 x 1 + 3 x (1/10) + 9 x (1/100) + 2 x (1/1000). Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left. Read 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). Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left. Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 × 100 + 4 × 10 + 7 × 1 + 3 × (1/10) + 9 × (1/100) + 2 × (1/1000). Read and write decimals 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). Represent decimals to thousandths as fractions and fraction with denominators of 1,000 as decimals. Recognize that in a multi- digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left. Read and write decimals to thousandths using base-ten numerals, word form, and expanded form. Read and write decimals using place value to describe decimals in terms of groups from millionths to millions. Practice and Problem Solving 1-3: Student Edition Practice Curriculum Standards: Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left. Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 x 100 + 4 x 10 + 7 x 1 + 3 x (1/10) + 9 x (1/100) + 2 x (1/1000). Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left. Read 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). Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left. Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 × 100 + 4 × 10 + 7 × 1 + 3 × (1/10) + 9 × (1/100) + 2 × (1/1000). Read and write decimals 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). Represent decimals to thousandths as fractions and fraction with denominators of 1,000 as decimals. Recognize that in a multi- digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left. Read and write decimals to thousandths using base-ten numerals, word form, and expanded form. Read and write decimals using place value to describe decimals in terms of groups from millionths to millions. 1-3: Practice Buddy: Independent Practice; Problem Solving Curriculum Standards: Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left. Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 x 100 + 4 x 10 + 7 x 1 + 3 x (1/10) + 9 x (1/100) + 2 x (1/1000). Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left. Read 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). Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left. Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 × 100 + 4 × 10 + 7 × 1 + 3 × (1/10) + 9 × (1/100) + 2 × (1/1000). Read and write decimals 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). Represent decimals to thousandths as fractions and fraction with denominators of 1,000 as decimals. Recognize that in a multi- digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left. Read and write decimals to thousandths using base-ten numerals, word form, and expanded form. Read and write decimals using place value to describe decimals in terms of groups from millionths to millions. 1-3: Practice Buddy: Additional Practice Curriculum Standards: Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left. Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 x 100 + 4 x 10 + 7 x 1 + 3 x (1/10) + 9 x (1/100) + 2 x (1/1000). Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left. Read 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). Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left. Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 × 100 + 4 × 10 + 7 × 1 + 3 × (1/10) + 9 × (1/100) + 2 × (1/1000). Read and write decimals 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). Represent decimals to thousandths as fractions and fraction with denominators of 1,000 as decimals. Recognize that in a multi- digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left. Read and write decimals to thousandths using base-ten numerals, word form, and expanded form. Read and write decimals using place value to describe decimals in terms of groups from millionths to millions. 1-3: Interactive Additional Practice Step 3: Assess & Differentiate 1-3: Practice Buddy: Additional Practice Curriculum Standards: Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left. Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 x 100 + 4 x 10 + 7 x 1 + 3 x (1/10) + 9 x (1/100) + 2 x (1/1000). Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left. Read 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). Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left. Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 × 100 + 4 × 10 + 7 × 1 + 3 × (1/10) + 9 × (1/100) + 2 × (1/1000). Read and write decimals 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). Represent decimals to thousandths as fractions and fraction with denominators of 1,000 as decimals. Recognize that in a multi- digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left. Read and write decimals to thousandths using base-ten numerals, word form, and expanded form. Read and write decimals using place value to describe decimals in terms of groups from millionths to millions. 1-3: Enrichment Curriculum Standards: Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left. Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 x 100 + 4 x 10 + 7 x 1 + 3 x (1/10) + 9 x (1/100) + 2 x (1/1000). Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left. Read 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). Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left. Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 × 100 + 4 × 10 + 7 × 1 + 3 × (1/10) + 9 × (1/100) + 2 × (1/1000). Read and write decimals 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). Represent decimals to thousandths as fractions and fraction with denominators of 1,000 as decimals. Recognize that in a multi- digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left. Read and write decimals to thousandths using base-ten numerals, word form, and expanded form. Read and write decimals using place value to describe decimals in terms of groups from millionths to millions. 1-3: Quick Check Curriculum Standards: Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left. Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 x 100 + 4 x 10 + 7 x 1 + 3 x (1/10) + 9 x (1/100) + 2 x (1/1000). Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left. Read 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). Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left. Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 × 100 + 4 × 10 + 7 × 1 + 3 × (1/10) + 9 × (1/100) + 2 × (1/1000). Read and write decimals 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). Represent decimals to thousandths as fractions and fraction with denominators of 1,000 as decimals. Recognize that in a multi- digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left. Read and write decimals to thousandths using base-ten numerals, word form, and expanded form. Read and write decimals using place value to describe decimals in terms of groups from millionths to millions. 1-3: Lesson Self-Assessment 1-3: Reteach to Build Understanding Curriculum Standards: Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left. Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 x 100 + 4 x 10 + 7 x 1 + 3 x (1/10) + 9 x (1/100) + 2 x (1/1000). Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left. Read 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). Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left. Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 × 100 + 4 × 10 + 7 × 1 + 3 × (1/10) + 9 × (1/100) + 2 × (1/1000). Read and write decimals 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). Represent decimals to thousandths as fractions and fraction with denominators of 1,000 as decimals. Recognize that in a multi- digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left. Read and write decimals to thousandths using base-ten numerals, word form, and expanded form. Read and write decimals using place value to describe decimals in terms of groups from millionths to millions. 1-3: Build Mathematical Literacy Curriculum Standards: Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 5 topics and texts, building on others’ ideas and expressing their own clearly. (a) Come to discussions prepared, having read or studied required material; explicitly draw on that preparation and other information known about the topic to explore ideas under discussion. (b) Follow agreed-upon rules for discussions and carry out assigned roles. (c) Pose and respond to specific questions by making comments that contribute to the discussion and elaborate on the remarks of others. (d) Review the key ideas expressed and draw conclusions in light of information and knowledge gained from the discussions. English language learners communicate for social and instructional purposes within the school setting. Summarize a written text read aloud or information presented in diverse media and formats, including visually, quantitatively, and orally. Summarize the points a speaker makes and explain how each claim is supported by reasons and evidence. Write informative/explanatory texts to examine a topic and convey ideas and information clearly. (a) Introduce a topic clearly, provide a general observation and focus, and group related information logically; include formatting (e.g., headings), illustrations, and multimedia when useful to aiding comprehension. (b) Develop the topic with facts, definitions, concrete details, quotations, or other information and examples related to the topic. (c) Link ideas within and across categories of information using words, phrases, and clauses (e.g., in contrast, especially). (d) Use precise language and domain-specific vocabulary to inform about or explain the topic. (e) Provide a concluding statement or section related to the information or explanation presented. English language learners communicate information, ideas and concepts necessary for academic success in the content area of Mathematics. 1-3: Enrichment 1-3: Digital Math Tool Activity 1-3: Pick a Project 1-3: Another Look Curriculum Standards: Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left. Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 x 100 + 4 x 10 + 7 x 1 + 3 x (1/10) + 9 x (1/100) + 2 x (1/1000). Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left. Read 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). Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left. Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 × 100 + 4 × 10 + 7 × 1 + 3 × (1/10) + 9 × (1/100) + 2 × (1/1000). Read and write decimals 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). Represent decimals to thousandths as fractions and fraction with denominators of 1,000 as decimals. Recognize that in a multi- digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left. Read and write decimals to thousandths using base-ten numerals, word form, and expanded form. Read and write decimals using place value to describe decimals in terms of groups from millionths to millions. Spanish Resources 1-3: eText del Libro del estudiante 1-3: Repaso diario 1-3: Aprendizaje visual 1-3: Amigo de práctica: Práctica adicional 1-3: Práctica adicional interactiva 1-3: Refuerzo para mejorar la comprensión 1-3: Desarrollar la competencia matemática 1-3: Ampliación 1-4: Understand Decimal Place Value Interactive Student Edition: Grade 5 Lesson 1-4 Math Anytime 1-4: Daily Review Topic 1: Today's Challenge Step 1: Problem-Based Learning 1-4: Solve & Share Curriculum Standards: Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 x 100 + 4 x 10 + 7 x 1 + 3 x (1/10) + 9 x (1/100) + 2 x (1/1000). English language learners communicate for social and instructional purposes within the school setting. Write informative/explanatory texts to examine a topic and convey ideas and information clearly. (a) Introduce a topic clearly, provide a general observation and focus, and group related information logically; include formatting (e.g., headings), illustrations, and multimedia when useful to aiding comprehension. (b) Develop the topic with facts, definitions, concrete details, quotations, or other information and examples related to the topic. (c) Link ideas within and across categories of information using words, phrases, and clauses (e.g., in contrast, especially). (d) Use precise language and domain-specific vocabulary to inform about or explain the topic. (e) Provide a concluding statement or section related to the information or explanation presented. English language learners communicate information, ideas and concepts necessary for academic success in the content area of Mathematics. Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 × 100 + 4 × 10 + 7 × 1 + 3 × (1/10) + 9 × (1/100) + 2 × (1/1000). Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 × 100 + 4 × 10 + 7 × 1 + 3 × (1/10) + 9 × (1/100) + 2 × (1/1000). Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 × 100 + 4 × 10 + 7 × 1 + 3 × (1/10) + 9 × (1/100) + 2 × (1/1000). Read and write numbers with decimals through thousandths using standard form, expanded form, and number names; identify equivalent decimals. Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 x 100 + 4 x 10 + 7 x 1 + 3 x (1/10) + 9 x (1/100) + 2 x (1/1000). Read and write decimals to thousandths using base-ten numerals, word form, and expanded form. Read and write decimals using place value to describe decimals in terms of groups from millionths to millions. Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 5 topics and texts, building on others’ ideas and expressing their own clearly. (a) Come to discussions prepared, having read or studied required material; explicitly draw on that preparation and other information known about the topic to explore ideas under discussion. (b) Follow agreed-upon rules for discussions and carry out assigned roles. (c) Pose and respond to specific questions by making comments that contribute to the discussion and elaborate on the remarks of others. (d) Review the key ideas expressed and draw conclusions in light of information and knowledge gained from the discussions. Summarize a written text read aloud or information presented in diverse media and formats, including visually, quantitatively, and orally. Summarize the points a speaker makes and explain how each claim is supported by reasons and evidence. Step 2: Visual Learning 1-4: Visual Learning Curriculum Standards: Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 x 100 + 4 x 10 + 7 x 1 + 3 x (1/10) + 9 x (1/100) + 2 x (1/1000). Read, write, or select a decimal to the hundredths place. Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 × 100 + 4 × 10 + 7 × 1 + 3 × (1/10) + 9 × (1/100) + 2 × (1/1000). Read and write decimals to thousandths using base- ten numerals, number names, and expanded form, e.g., 347.392 = 3 × 100 + 4 × 10 + 7 × 1 + 3 × (1/10) + 9 × (1/100) + 2 × (1/1000). Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 × 100 + 4 × 10 + 7 × 1 + 3 × (1/10) + 9 × (1/100) + 2 × (1/1000). Read and write numbers with decimals through thousandths using standard form, expanded form, and number names; identify equivalent decimals. Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 x 100 + 4 x 10 + 7 x 1 + 3 x (1/10) + 9 x (1/100) + 2 x (1/1000). Read and write decimals to thousandths using base-ten numerals, word form, and expanded form. Read and write decimals using place value to describe decimals in terms of groups from millionths to millions. 1-4: Convince Me! Curriculum Standards: Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 x 100 + 4 x 10 + 7 x 1 + 3 x (1/10) + 9 x (1/100) + 2 x (1/1000). Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 × 100 + 4 × 10 + 7 × 1 + 3 × (1/10) + 9 × (1/100) + 2 × (1/1000). Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 × 100 + 4 × 10 + 7 × 1 + 3 × (1/10) + 9 × (1/100) + 2 × (1/1000). Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 × 100 + 4 × 10 + 7 × 1 + 3 × (1/10) + 9 × (1/100) + 2 × (1/1000). Read and write numbers with decimals through thousandths using standard form, expanded form, and number names; identify equivalent decimals. Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 x 100 + 4 x 10 + 7 x 1 + 3 x (1/10) + 9 x (1/100) + 2 x (1/1000). Read and write decimals to thousandths using base-ten numerals, word form, and expanded form. Read and write decimals using place value to describe decimals in terms of groups from millionths to millions. Practice and Problem Solving 1-4: Student Edition Practice Curriculum Standards: Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 x 100 + 4 x 10 + 7 x 1 + 3 x (1/10) + 9 x (1/100) + 2 x (1/1000). Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 × 100 + 4 × 10 + 7 × 1 + 3 × (1/10) + 9 × (1/100) + 2 × (1/1000). Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 × 100 + 4 × 10 + 7 × 1 + 3 × (1/10) + 9 × (1/100) + 2 × (1/1000). Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 × 100 + 4 × 10 + 7 × 1 + 3 × (1/10) + 9 × (1/100) + 2 × (1/1000). Read and write numbers with decimals through thousandths using standard form, expanded form, and number names; identify equivalent decimals. Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 x 100 + 4 x 10 + 7 x 1 + 3 x (1/10) + 9 x (1/100) + 2 x (1/1000). Read and write decimals to thousandths using base-ten numerals, word form, and expanded form. Read and write decimals using place value to describe decimals in terms of groups from millionths to millions. 1-4: Practice Buddy: Independent Practice; Problem Solving Curriculum Standards: Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 x 100 + 4 x 10 + 7 x 1 + 3 x (1/10) + 9 x (1/100) + 2 x (1/1000). Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 × 100 + 4 × 10 + 7 × 1 + 3 × (1/10) + 9 × (1/100) + 2 × (1/1000). Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 × 100 + 4 × 10 + 7 × 1 + 3 × (1/10) + 9 × (1/100) + 2 × (1/1000). Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 × 100 + 4 × 10 + 7 × 1 + 3 × (1/10) + 9 × (1/100) + 2 × (1/1000). Read and write numbers with decimals through thousandths using standard form, expanded form, and number names; identify equivalent decimals. Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 x 100 + 4 x 10 + 7 x 1 + 3 x (1/10) + 9 x (1/100) + 2 x (1/1000). Read and write decimals to thousandths using base-ten numerals, word form, and expanded form. Read and write decimals using place value to describe decimals in terms of groups from millionths to millions. 1-4: Practice Buddy: Additional Practice Curriculum Standards: Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 x 100 + 4 x 10 + 7 x 1 + 3 x (1/10) + 9 x (1/100) + 2 x (1/1000). Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 × 100 + 4 × 10 + 7 × 1 + 3 × (1/10) + 9 × (1/100) + 2 × (1/1000). Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 × 100 + 4 × 10 + 7 × 1 + 3 × (1/10) + 9 × (1/100) + 2 × (1/1000). Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 × 100 + 4 × 10 + 7 × 1 + 3 × (1/10) + 9 × (1/100) + 2 × (1/1000). Read and write numbers with decimals through thousandths using standard form, expanded form, and number names; identify equivalent decimals. Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 x 100 + 4 x 10 + 7 x 1 + 3 x (1/10) + 9 x (1/100) + 2 x (1/1000). Read and write decimals to thousandths using base-ten numerals, word form, and expanded form. Read and write decimals using place value to describe decimals in terms of groups from millionths to millions. 1-4: Interactive Additional Practice Step 3: Assess & Differentiate 1-4: Practice Buddy: Additional Practice Curriculum Standards: Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 x 100 + 4 x 10 + 7 x 1 + 3 x (1/10) + 9 x (1/100) + 2 x (1/1000). Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 × 100 + 4 × 10 + 7 × 1 + 3 × (1/10) + 9 × (1/100) + 2 × (1/1000). Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 × 100 + 4 × 10 + 7 × 1 + 3 × (1/10) + 9 × (1/100) + 2 × (1/1000). Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 × 100 + 4 × 10 + 7 × 1 + 3 × (1/10) + 9 × (1/100) + 2 × (1/1000). Read and write numbers with decimals through thousandths using standard form, expanded form, and number names; identify equivalent decimals. Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 x 100 + 4 x 10 + 7 x 1 + 3 x (1/10) + 9 x (1/100) + 2 x (1/1000). Read and write decimals to thousandths using base-ten numerals, word form, and expanded form. Read and write decimals using place value to describe decimals in terms of groups from millionths to millions. 1-4: Enrichment Curriculum Standards: Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 x 100 + 4 x 10 + 7 x 1 + 3 x (1/10) + 9 x (1/100) + 2 x (1/1000). Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 × 100 + 4 × 10 + 7 × 1 + 3 × (1/10) + 9 × (1/100) + 2 × (1/1000). Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 × 100 + 4 × 10 + 7 × 1 + 3 × (1/10) + 9 × (1/100) + 2 × (1/1000). Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 × 100 + 4 × 10 + 7 × 1 + 3 × (1/10) + 9 × (1/100) + 2 × (1/1000). Read and write numbers with decimals through thousandths using standard form, expanded form, and number names; identify equivalent decimals. Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 x 100 + 4 x 10 + 7 x 1 + 3 x (1/10) + 9 x (1/100) + 2 x (1/1000). Read and write decimals to thousandths using base-ten numerals, word form, and expanded form. Read and write decimals using place value to describe decimals in terms of groups from millionths to millions. 1-4: Quick Check Curriculum Standards: Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 x 100 + 4 x 10 + 7 x 1 + 3 x (1/10) + 9 x (1/100) + 2 x (1/1000). Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 × 100 + 4 × 10 + 7 × 1 + 3 × (1/10) + 9 × (1/100) + 2 × (1/1000). Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 × 100 + 4 × 10 + 7 × 1 + 3 × (1/10) + 9 × (1/100) + 2 × (1/1000). Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 × 100 + 4 × 10 + 7 × 1 + 3 × (1/10) + 9 × (1/100) + 2 × (1/1000). Read and write numbers with decimals through thousandths using standard form, expanded form, and number names; identify equivalent decimals. Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 x 100 + 4 x 10 + 7 x 1 + 3 x (1/10) + 9 x (1/100) + 2 x (1/1000). Read and write decimals to thousandths using base-ten numerals, word form, and expanded form. Read and write decimals using place value to describe decimals in terms of groups from millionths to millions. 1-4: Lesson Self-Assessment 1-4: Reteach to Build Understanding Curriculum Standards: Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 x 100 + 4 x 10 + 7 x 1 + 3 x (1/10) + 9 x (1/100) + 2 x (1/1000). Read, write, or select a decimal to the hundredths place. Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 × 100 + 4 × 10 + 7 × 1 + 3 × (1/10) + 9 × (1/100) + 2 × (1/1000). Read and write decimals to thousandths using base- ten numerals, number names, and expanded form, e.g., 347.392 = 3 × 100 + 4 × 10 + 7 × 1 + 3 × (1/10) + 9 × (1/100) + 2 × (1/1000). Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 × 100 + 4 × 10 + 7 × 1 + 3 × (1/10) + 9 × (1/100) + 2 × (1/1000). Read and write numbers with decimals through thousandths using standard form, expanded form, and number names; identify equivalent decimals. Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 x 100 + 4 x 10 + 7 x 1 + 3 x (1/10) + 9 x (1/100) + 2 x (1/1000). Read and write decimals to thousandths using base-ten numerals, word form, and expanded form. Read and write decimals using place value to describe decimals in terms of groups from millionths to millions. 1-4: Build Mathematical Literacy Curriculum Standards: Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 5 topics and texts, building on others’ ideas and expressing their own clearly. (a) Come to discussions prepared, having read or studied required material; explicitly draw on that preparation and other information known about the topic to explore ideas under discussion. (b) Follow agreed-upon rules for discussions and carry out assigned roles. (c) Pose and respond to specific questions by making comments that contribute to the discussion and elaborate on the remarks of others. (d) Review the key ideas expressed and draw conclusions in light of information and knowledge gained from the discussions. English language learners communicate for social and instructional purposes within the school setting. Summarize a written text read aloud or information presented in diverse media and formats, including visually, quantitatively, and orally. Summarize the points a speaker makes and explain how each claim is supported by reasons and evidence. Write informative/explanatory texts to examine a topic and convey ideas and information clearly. (a) Introduce a topic clearly, provide a general observation and focus, and group related information logically; include formatting (e.g., headings), illustrations, and multimedia when useful to aiding comprehension. (b) Develop the topic with facts, definitions, concrete details, quotations, or other information and examples related to the topic. (c) Link ideas within and across categories of information using words, phrases, and clauses (e.g., in contrast, especially). (d) Use precise language and domain-specific vocabulary to inform about or explain the topic. (e) Provide a concluding statement or section related to the information or explanation presented. English language learners communicate information, ideas and concepts necessary for academic success in the content area of Mathematics. 1-4: Enrichment 1-4: Digital Math Tool Activity 1-4: Problem-Solving Reading Activity Curriculum Standards: Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 x 100 + 4 x 10 + 7 x 1 + 3 x (1/10) + 9 x (1/100) + 2 x (1/1000). Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 × 100 + 4 × 10 + 7 × 1 + 3 × (1/10) + 9 × (1/100) + 2 × (1/1000). Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 × 100 + 4 × 10 + 7 × 1 + 3 × (1/10) + 9 × (1/100) + 2 × (1/1000). Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 × 100 + 4 × 10 + 7 × 1 + 3 × (1/10) + 9 × (1/100) + 2 × (1/1000). Read and write numbers with decimals through thousandths using standard form, expanded form, and number names; identify equivalent decimals. Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 x 100 + 4 x 10 + 7 x 1 + 3 x (1/10) + 9 x (1/100) + 2 x (1/1000). Read and write decimals to thousandths using base-ten numerals, word form, and expanded form. Read and write decimals using place value to describe decimals in terms of groups from millionths to millions. 1-4: Another Look Curriculum Standards: Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 x 100 + 4 x 10 + 7 x 1 + 3 x (1/10) + 9 x (1/100) + 2 x (1/1000). Read, write, or select a decimal to the hundredths place. Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 × 100 + 4 × 10 + 7 × 1 + 3 × (1/10) + 9 × (1/100) + 2 × (1/1000). Read and write decimals to thousandths using base- ten numerals, number names, and expanded form, e.g., 347.392 = 3 × 100 + 4 × 10 + 7 × 1 + 3 × (1/10) + 9 × (1/100) + 2 × (1/1000). Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 × 100 + 4 × 10 + 7 × 1 + 3 × (1/10) + 9 × (1/100) + 2 × (1/1000). Read and write numbers with decimals through thousandths using standard form, expanded form, and number names; identify equivalent decimals. Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 x 100 + 4 x 10 + 7 x 1 + 3 x (1/10) + 9 x (1/100) + 2 x (1/1000). Read and write decimals to thousandths using base-ten numerals, word form, and expanded form. Read and write decimals using place value to describe decimals in terms of groups from millionths to millions. Spanish Resources 1-4: eText del Libro del estudiante 1-4: Repaso diario 1-4: Aprendizaje visual 1-4: Amigo de práctica: Práctica adicional 1-4: Práctica adicional interactiva 1-4: Refuerzo para mejorar la comprensión 1-4: Desarrollar la competencia matemática 1-4: Ampliación 1-5: Compare Decimals Interactive Student Edition: Grade 5 Lesson 1-5 Math Anytime 1-5: Daily Review Topic 1: Today's Challenge Step 1: Problem-Based Learning 1-5: Solve & Share Curriculum Standards: Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and <, symbols to record the results of comparisons. English language learners communicate for social and instructional purposes within the school setting. Write informative/explanatory texts to examine a topic and convey ideas and information clearly. (a) Introduce a topic clearly, provide a general observation and focus, and group related information logically; include formatting (e.g., headings), illustrations, and multimedia when useful to aiding comprehension. (b) Develop the topic with facts, definitions, concrete details, quotations, or other information and examples related to the topic. (c) Link ideas within and across categories of information using words, phrases, and clauses (e.g., in contrast, especially). (d) Use precise language and domain- specific vocabulary to inform about or explain the topic. (e) Provide a concluding statement or section related to the information or explanation presented. English language learners communicate information, ideas and concepts necessary for academic success in the content area of Mathematics. Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 5 topics and texts, building on others’ ideas and expressing their own clearly. (a) Come to discussions prepared, having read or studied required material; explicitly draw on that preparation and other information known about the topic to explore ideas under discussion. (b) Follow agreed-upon rules for discussions and carry out assigned roles. (c) Pose and respond to specific questions by making comments that contribute to the discussion and elaborate on the remarks of others. (d) Review the key ideas expressed and draw conclusions in light of information and knowledge gained from the discussions. Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. Use place value to compare decimals through thousandths. Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and <, symbols to record the results of comparisons. Compare two decimals to thousandths based on meanings of the digits in each place using >, =, and < symbols. Order fractions and decimals, including mixed numbers and improper fractions, and locate on a number line. Summarize a written text read aloud or information presented in diverse media and formats, including visually, quantitatively, and orally. Summarize the points a speaker makes and explain how each claim is supported by reasons and evidence. Step 2: Visual Learning 1-5: Visual Learning Curriculum Standards: Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and <, symbols to record the results of comparisons. Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. Use place value to compare decimals through thousandths. Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and <, symbols to record the results of comparisons. Compare two decimals to thousandths based on meanings of the digits in each place using >, =, and < symbols. Order fractions and decimals, including mixed numbers and improper fractions, and locate on a number line. Compare two decimals to the hundredths place, whose values are less than 1. 1-5: Convince Me! Curriculum Standards: Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and <, symbols to record the results of comparisons. Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. Use place value to compare decimals through thousandths. Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and <, symbols to record the results of comparisons. Compare two decimals to thousandths based on meanings of the digits in each place using >, =, and < symbols. Order fractions and decimals, including mixed numbers and improper fractions, and locate on a number line. Practice and Problem Solving 1-5: Student Edition Practice Curriculum Standards: Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and <, symbols to record the results of comparisons. Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. Use place value to compare decimals through thousandths. Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and <, symbols to record the results of comparisons. Compare two decimals to thousandths based on meanings of the digits in each place using >, =, and < symbols. Order fractions and decimals, including mixed numbers and improper fractions, and locate on a number line. 1-5: Practice Buddy: Independent Practice; Problem Solving Curriculum Standards: Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and <, symbols to record the results of comparisons. Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. Use place value to compare decimals through thousandths. Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and <, symbols to record the results of comparisons. Compare two decimals to thousandths based on meanings of the digits in each place using >, =, and < symbols. Order fractions and decimals, including mixed numbers and improper fractions, and locate on a number line. 1-5: Practice Buddy: Additional Practice Curriculum Standards: Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and <, symbols to record the results of comparisons. Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. Use place value to compare decimals through thousandths. Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and <, symbols to record the results of comparisons. Compare two decimals to thousandths based on meanings of the digits in each place using >, =, and < symbols. Order fractions and decimals, including mixed numbers and improper fractions, and locate on a number line. 1-5: Interactive Additional Practice Step 3: Assess & Differentiate 1-5: Practice Buddy: Additional Practice Curriculum Standards: Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and <, symbols to record the results of comparisons. Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. Use place value to compare decimals through thousandths. Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and <, symbols to record the results of comparisons. Compare two decimals to thousandths based on meanings of the digits in each place using >, =, and < symbols. Order fractions and decimals, including mixed numbers and improper fractions, and locate on a number line. 1-5: Enrichment Curriculum Standards: Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and <, symbols to record the results of comparisons. Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. Use place value to compare decimals through thousandths. Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and <, symbols to record the results of comparisons. Compare two decimals to thousandths based on meanings of the digits in each place using >, =, and < symbols. Order fractions and decimals, including mixed numbers and improper fractions, and locate on a number line. 1-5: Quick Check Curriculum Standards: Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and <, symbols to record the results of comparisons. Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. Use place value to compare decimals through thousandths. Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and <, symbols to record the results of comparisons. Compare two decimals to thousandths based on meanings of the digits in each place using >, =, and < symbols. Order fractions and decimals, including mixed numbers and improper fractions, and locate on a number line. 1-5: Lesson Self-Assessment 1-5: Reteach to Build Understanding Curriculum Standards: Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and <, symbols to record the results of comparisons. Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. Use place value to compare decimals through thousandths. Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and <, symbols to record the results of comparisons. Compare two decimals to thousandths based on meanings of the digits in each place using >, =, and < symbols. Order fractions and decimals, including mixed numbers and improper fractions, and locate on a number line. Compare two decimals to the hundredths place, whose values are less than 1. 1-5: Build Mathematical Literacy Curriculum Standards: Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 5 topics and texts, building on others’ ideas and expressing their own clearly. (a) Come to discussions prepared, having read or studied required material; explicitly draw on that preparation and other information known about the topic to explore ideas under discussion. (b) Follow agreed-upon rules for discussions and carry out assigned roles. (c) Pose and respond to specific questions by making comments that contribute to the discussion and elaborate on the remarks of others. (d) Review the key ideas expressed and draw conclusions in light of information and knowledge gained from the discussions. English language learners communicate for social and instructional purposes within the school setting. Summarize a written text read aloud or information presented in diverse media and formats, including visually, quantitatively, and orally. Summarize the points a speaker makes and explain how each claim is supported by reasons and evidence. Write informative/explanatory texts to examine a topic and convey ideas and information clearly. (a) Introduce a topic clearly, provide a general observation and focus, and group related information logically; include formatting (e.g., headings), illustrations, and multimedia when useful to aiding comprehension. (b) Develop the topic with facts, definitions, concrete details, quotations, or other information and examples related to the topic. (c) Link ideas within and across categories of information using words, phrases, and clauses (e.g., in contrast, especially). (d) Use precise language and domain-specific vocabulary to inform about or explain the topic. (e) Provide a concluding statement or section related to the information or explanation presented. English language learners communicate information, ideas and concepts necessary for academic success in the content area of Mathematics. 1-5: Enrichment 1-5: Digital Math Tool Activity 1-5: enVision STEM Activity Curriculum Standards: Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and <, symbols to record the results of comparisons. Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. Use place value to compare decimals through thousandths. Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and <, symbols to record the results of comparisons. Compare two decimals to thousandths based on meanings of the digits in each place using >, =, and < symbols. Order fractions and decimals, including mixed numbers and improper fractions, and locate on a number line. 1-5: Another Look Curriculum Standards: Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and <, symbols to record the results of comparisons. Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. Use place value to compare decimals through thousandths. Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and <, symbols to record the results of comparisons. Compare two decimals to thousandths based on meanings of the digits in each place using >, =, and < symbols. Order fractions and decimals, including mixed numbers and improper fractions, and locate on a number line. Compare two decimals to the hundredths place, whose values are less than 1. Spanish Resources 1-5: eText del Libro del estudiante 1-5: Repaso diario 1-5: Aprendizaje visual 1-5: Amigo de práctica: Práctica adicional 1-5: Práctica adicional interactiva 1-5: Refuerzo para mejorar la comprensión 1-5: Desarrollar la competencia matemática 1-5: Ampliación 1-6: Round Decimals Interactive Student Edition: Grade 5 Lesson 1-6 Math Anytime 1-6: Daily Review Topic 1: Today's Challenge Step 1: Problem-Based Learning 1-6: Solve & Share Curriculum Standards: Use place value understanding to round decimals to any place. English language learners communicate for social and instructional purposes within the school setting. Write informative/explanatory texts to examine a topic and convey ideas and information clearly. (a) Introduce a topic clearly, provide a general observation and focus, and group related information logically; include formatting (e.g., headings), illustrations, and multimedia when useful to aiding comprehension. (b) Develop the topic with facts, definitions, concrete details, quotations, or other information and examples related to the topic. (c) Link ideas within and across categories of information using words, phrases, and clauses (e.g., in contrast, especially). (d) Use precise language and domain- specific vocabulary to inform about or explain the topic. (e) Provide a concluding statement or section related to the information or explanation presented. English language learners communicate information, ideas and concepts necessary for academic success in the content area of Mathematics. Use place value understanding to round decimals to any place. Use place value understanding to round decimals to any place. Use place value to round decimals to different places. Use place value understanding to round decimals to any place. Round decimals to any place (limit rounding to ones, tenths, hundredths, or thousandths place). Round numbers to the nearest 0.1, 0.01 and 0.001. Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 5 topics and texts, building on others’ ideas and expressing their own clearly. (a) Come to discussions prepared, having read or studied required material; explicitly draw on that preparation and other information known about the topic to explore ideas under discussion. (b) Follow agreed-upon rules for discussions and carry out assigned roles. (c) Pose and respond to specific questions by making comments that contribute to the discussion and elaborate on the remarks of others. (d) Review the key ideas expressed and draw conclusions in light of information and knowledge gained from the discussions. Summarize a written text read aloud or information presented in diverse media and formats, including visually, quantitatively, and orally. Summarize the points a speaker makes and explain how each claim is supported by reasons and evidence. Step 2: Visual Learning 1-6: Visual Learning Curriculum Standards: Use place value understanding to round decimals to any place. Use place value understanding to round decimals to any place. Use place value understanding to round decimals to any place. Use place value to round decimals to different places. Use place value understanding to round decimals to any place. Round decimals to any place (limit rounding to ones, tenths, hundredths, or thousandths place). Round numbers to the nearest 0.1, 0.01 and 0.001. Round decimals to the next whole number. Round decimals to the tenths place. Round decimals to the hundredths place. 1-6: Convince Me! Curriculum Standards: Use place value understanding to round decimals to any place. Use place value understanding to round decimals to any place. Use place value understanding to round decimals to any place. Use place value to round decimals to different places. Use place value understanding to round decimals to any place. Round decimals to any place (limit rounding to ones, tenths, hundredths, or thousandths place). Round numbers to the nearest 0.1, 0.01 and 0.001. Practice and Problem Solving 1-6: Student Edition Practice Curriculum Standards: Use place value understanding to round decimals to any place. Use place value understanding to round decimals to any place. Use place value understanding to round decimals to any place. Use place value to round decimals to different places. Use place value understanding to round decimals to any place. Round decimals to any place (limit rounding to ones, tenths, hundredths, or thousandths place). Round numbers to the nearest 0.1, 0.01 and 0.001. 1-6: Practice Buddy: Independent Practice; Problem Solving Curriculum Standards: Use place value understanding to round decimals to any place. Use place value understanding to round decimals to any place. Use place value understanding to round decimals to any place. Use place value to round decimals to different places. Use place value understanding to round decimals to any place. Round decimals to any place (limit rounding to ones, tenths, hundredths, or thousandths place). Round numbers to the nearest 0.1, 0.01 and 0.001. 1-6: Practice Buddy: Additional Practice Curriculum Standards: Use place value understanding to round decimals to any place. Use place value understanding to round decimals to any place. Use place value understanding to round decimals to any place. Use place value to round decimals to different places. Use place value understanding to round decimals to any place. Round decimals to any place (limit rounding to ones, tenths, hundredths, or thousandths place). Round numbers to the nearest 0.1, 0.01 and 0.001. 1-6: Interactive Additional Practice Step 3: Assess & Differentiate 1-6: Practice Buddy: Additional Practice Curriculum Standards: Use place value understanding to round decimals to any place. Use place value understanding to round decimals to any place. Use place value understanding to round decimals to any place. Use place value to round decimals to different places. Use place value understanding to round decimals to any place. Round decimals to any place (limit rounding to ones, tenths, hundredths, or thousandths place). Round numbers to the nearest 0.1, 0.01 and 0.001. 1-6: Enrichment Curriculum Standards: Use place value understanding to round decimals to any place. Use place value understanding to round decimals to any place. Use place value understanding to round decimals to any place. Use place value to round decimals to different places. Use place value understanding to round decimals to any place. Round decimals to any place (limit rounding to ones, tenths, hundredths, or thousandths place). Round numbers to the nearest 0.1, 0.01 and 0.001. 1-6: Quick Check Curriculum Standards: Use place value understanding to round decimals to any place. Use place value understanding to round decimals to any place. Use place value understanding to round decimals to any place. Use place value to round decimals to different places. Use place value understanding to round decimals to any place. Round decimals to any place (limit rounding to ones, tenths, hundredths, or thousandths place). Round numbers to the nearest 0.1, 0.01 and 0.001. 1-6: Lesson Self-Assessment 1-6: Reteach to Build Understanding Curriculum Standards: Use place value understanding to round decimals to any place. Use place value understanding to round decimals to any place. Use place value understanding to round decimals to any place. Use place value to round decimals to different places. Use place value understanding to round decimals to any place. Round decimals to any place (limit rounding to ones, tenths, hundredths, or thousandths place). Round numbers to the nearest 0.1, 0.01 and 0.001. Round decimals to the next whole number. Round decimals to the tenths place. Round decimals to the hundredths place. 1-6: Build Mathematical Literacy Curriculum Standards: Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 5 topics and texts, building on others’ ideas and expressing their own clearly. (a) Come to discussions prepared, having read or studied required material; explicitly draw on that preparation and other information known about the topic to explore ideas under discussion. (b) Follow agreed-upon rules for discussions and carry out assigned roles. (c) Pose and respond to specific questions by making comments that contribute to the discussion and elaborate on the remarks of others. (d) Review the key ideas expressed and draw conclusions in light of information and knowledge gained from the discussions. English language learners communicate for social and instructional purposes within the school setting. Summarize a written text read aloud or information presented in diverse media and formats, including visually, quantitatively, and orally. Summarize the points a speaker makes and explain how each claim is supported by reasons and evidence. Write informative/explanatory texts to examine a topic and convey ideas and information clearly. (a) Introduce a topic clearly, provide a general observation and focus, and group related information logically; include formatting (e.g., headings), illustrations, and multimedia when useful to aiding comprehension. (b) Develop the topic with facts, definitions, concrete details, quotations, or other information and examples related to the topic. (c) Link ideas within and across categories of information using words, phrases, and clauses (e.g., in contrast, especially). (d) Use precise language and domain-specific vocabulary to inform about or explain the topic. (e) Provide a concluding statement or section related to the information or explanation presented. English language learners communicate information, ideas and concepts necessary for academic success in the content area of Mathematics. 1-6: Enrichment 1-6: Digital Math Tool Activity 1-6: Problem-Solving Reading Activity Curriculum Standards: Use place value understanding to round decimals to any place. Use place value understanding to round decimals to any place. Use place value understanding to round decimals to any place. Use place value to round decimals to different places. Use place value understanding to round decimals to any place. Round decimals to any place (limit rounding to ones, tenths, hundredths, or thousandths place). Round numbers to the nearest 0.1, 0.01 and 0.001. 1-6: Another Look Curriculum Standards: Use place value understanding to round decimals to any place. Use place value understanding to round decimals to any place. Use place value understanding to round decimals to any place. Use place value to round decimals to different places. Use place value understanding to round decimals to any place. Round decimals to any place (limit rounding to ones, tenths, hundredths, or thousandths place). Round numbers to the nearest 0.1, 0.01 and 0.001. Round decimals to the next whole number. Round decimals to the tenths place. Round decimals to the hundredths place. Spanish Resources 1-6: eText del Libro del estudiante 1-6: Repaso diario 1-6: Aprendizaje visual 1-6: Amigo de práctica: Práctica adicional 1-6: Práctica adicional interactiva 1-6: Refuerzo para mejorar la comprensión 1-6: Desarrollar la competencia matemática 1-6: Ampliación 1-7: Problem Solving: Look For and Use Structure Interactive Student Edition: Grade 5 Lesson 1-7 Math Anytime 1-7: Daily Review Topic 1: Today's Challenge Step 1: Problem-Based Learning 1-7: Solve & Share Curriculum Standards: Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 x 100 + 4 x 10 + 7 x 1 + 3 x (1/10) + 9 x (1/100) + 2 x (1/1000). Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and <, symbols to record the results of comparisons. Look for and make use of structure. English language learners communicate for social and instructional purposes within the school setting. Write informative/explanatory texts to examine a topic and convey ideas and information clearly. (a) Introduce a topic clearly, provide a general observation and focus, and group related information logically; include formatting (e.g., headings), illustrations, and multimedia when useful to aiding comprehension. (b) Develop the topic with facts, definitions, concrete details, quotations, or other information and examples related to the topic. (c) Link ideas within and across categories of information using words, phrases, and clauses (e.g., in contrast, especially). (d) Use precise language and domain- specific vocabulary to inform about or explain the topic. (e) Provide a concluding statement or section related to the information or explanation presented. English language learners communicate information, ideas and concepts necessary for academic success in the content area of Mathematics. Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 5 topics and texts, building on others’ ideas and expressing their own clearly. (a) Come to discussions prepared, having read or studied required material; explicitly draw on that preparation and other information known about the topic to explore ideas under discussion. (b) Follow agreed-upon rules for discussions and carry out assigned roles. (c) Pose and respond to specific questions by making comments that contribute to the discussion and elaborate on the remarks of others. (d) Review the key ideas expressed and draw conclusions in light of information and knowledge gained from the discussions. Summarize a written text read aloud or information presented in diverse media and formats, including visually, quantitatively, and orally. Summarize the points a speaker makes and explain how each claim is supported by reasons and evidence. 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). Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. Look for and make use of structure. 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). Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. Look for and make use of structure. Mathematically proficient students look closely to discern a pattern or structure. Young students, for example, might notice that three and seven more is the same amount as seven and three more, or they may sort a collection of shapes according to how many sides the shapes have. Later, students will see 7 × 8 equals the well remembered 7 × 5 + 7 × 3, in preparation for learning about the distributive property. In the expression x² + 9x + 14, older students can see the 14 as 2 × 7 and the 9 as 2 + 7. They recognize the significance of an existing line in a geometric figure and can use the strategy of drawing an auxiliary line for solving problems. They also can step back for an overview and shift perspective. They can see complicated things, such as some algebraic expressions, as single objects or as being composed of several objects. For example, they can see 5 – 3(x – y)² as 5 minus a positive number times a square and use that to realize that its value cannot be more than 5 for any real numbers x and y. 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). Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. Use the structure of the decimal place-value system to solve problems involving patterns. Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 x 100 + 4 x 10 + 7 x 1 + 3 x (1/10) + 9 x (1/100) + 2 x (1/1000). Look for and make use of structure. Look for and make Use of structure. Read and write decimals to thousandths using base-ten numerals, word form, and expanded form. Look for and make use of structure. Read and write decimals using place value to describe decimals in terms of groups from millionths to millions. Step 2: Visual Learning 1-7: Visual Learning Curriculum Standards: Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 x 100 + 4 x 10 + 7 x 1 + 3 x (1/10) + 9 x (1/100) + 2 x (1/1000). Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and <, symbols to record the results of comparisons. Look for and make use of structure. 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). Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. Look for and make use of structure. 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). Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. Look for and make use of structure. Mathematically proficient students look closely to discern a pattern or structure. Young students, for example, might notice that three and seven more is the same amount as seven and three more, or they may sort a collection of shapes according to how many sides the shapes have. Later, students will see 7 × 8 equals the well remembered 7 × 5 + 7 × 3, in preparation for learning about the distributive property. In the expression x² + 9x + 14, older students can see the 14 as 2 × 7 and the 9 as 2 + 7. They recognize the significance of an existing line in a geometric figure and can use the strategy of drawing an auxiliary line for solving problems. They also can step back for an overview and shift perspective. They can see complicated things, such as some algebraic expressions, as single objects or as being composed of several objects. For example, they can see 5 – 3(x – y)² as 5 minus a positive number times a square and use that to realize that its value cannot be more than 5 for any real numbers x and y. 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). Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. Use the structure of the decimal place-value system to solve problems involving patterns. Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 x 100 + 4 x 10 + 7 x 1 + 3 x (1/10) + 9 x (1/100) + 2 x (1/1000). Look for and make use of structure. Look for and make Use of structure. Read and write decimals to thousandths using base-ten numerals, word form, and expanded form. Look for and make use of structure. Read and write decimals using place value to describe decimals in terms of groups from millionths to millions. 1-7: Convince Me! Curriculum Standards: Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 x 100 + 4 x 10 + 7 x 1 + 3 x (1/10) + 9 x (1/100) + 2 x (1/1000). Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and <, symbols to record the results of comparisons. Look for and make use of structure. 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). Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. Look for and make use of structure. 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). Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. Look for and make use of structure. Mathematically proficient students look closely to discern a pattern or structure. Young students, for example, might notice that three and seven more is the same amount as seven and three more, or they may sort a collection of shapes according to how many sides the shapes have. Later, students will see 7 × 8 equals the well remembered 7 × 5 + 7 × 3, in preparation for learning about the distributive property. In the expression x² + 9x + 14, older students can see the 14 as 2 × 7 and the 9 as 2 + 7. They recognize the significance of an existing line in a geometric figure and can use the strategy of drawing an auxiliary line for solving problems. They also can step back for an overview and shift perspective. They can see complicated things, such as some algebraic expressions, as single objects or as being composed of several objects. For example, they can see 5 – 3(x – y)² as 5 minus a positive number times a square and use that to realize that its value cannot be more than 5 for any real numbers x and y. 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). Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. Use the structure of the decimal place-value system to solve problems involving patterns. Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 x 100 + 4 x 10 + 7 x 1 + 3 x (1/10) + 9 x (1/100) + 2 x (1/1000). Look for and make use of structure. Look for and make Use of structure. Read and write decimals to thousandths using base-ten numerals, word form, and expanded form. Look for and make use of structure. Read and write decimals using place value to describe decimals in terms of groups from millionths to millions. Practice and Problem Solving 1-7: Student Edition Practice Curriculum Standards: Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 x 100 + 4 x 10 + 7 x 1 + 3 x (1/10) + 9 x (1/100) + 2 x (1/1000). Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and <, symbols to record the results of comparisons. Look for and make use of structure. 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). Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. Look for and make use of structure. 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). Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. Look for and make use of structure. Mathematically proficient students look closely to discern a pattern or structure. Young students, for example, might notice that three and seven more is the same amount as seven and three more, or they may sort a collection of shapes according to how many sides the shapes have. Later, students will see 7 × 8 equals the well remembered 7 × 5 + 7 × 3, in preparation for learning about the distributive property. In the expression x² + 9x + 14, older students can see the 14 as 2 × 7 and the 9 as 2 + 7. They recognize the significance of an existing line in a geometric figure and can use the strategy of drawing an auxiliary line for solving problems. They also can step back for an overview and shift perspective. They can see complicated things, such as some algebraic expressions, as single objects or as being composed of several objects. For example, they can see 5 – 3(x – y)² as 5 minus a positive number times a square and use that to realize that its value cannot be more than 5 for any real numbers x and y. 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). Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. Use the structure of the decimal place-value system to solve problems involving patterns. Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 x 100 + 4 x 10 + 7 x 1 + 3 x (1/10) + 9 x (1/100) + 2 x (1/1000). Look for and make use of structure. Look for and make Use of structure. Read and write decimals to thousandths using base-ten numerals, word form, and expanded form. Look for and make use of structure. Read and write decimals using place value to describe decimals in terms of groups from millionths to millions. 1-7: Practice Buddy: Independent Practice; Problem Solving Curriculum Standards: Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 x 100 + 4 x 10 + 7 x 1 + 3 x (1/10) + 9 x (1/100) + 2 x (1/1000). Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and <, symbols to record the results of comparisons. Look for and make use of structure. 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). Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. Look for and make use of structure. 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). Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. Look for and make use of structure. Mathematically proficient students look closely to discern a pattern or structure. Young students, for example, might notice that three and seven more is the same amount as seven and three more, or they may sort a collection of shapes according to how many sides the shapes have. Later, students will see 7 × 8 equals the well remembered 7 × 5 + 7 × 3, in preparation for learning about the distributive property. In the expression x² + 9x + 14, older students can see the 14 as 2 × 7 and the 9 as 2 + 7. They recognize the significance of an existing line in a geometric figure and can use the strategy of drawing an auxiliary line for solving problems. They also can step back for an overview and shift perspective. They can see complicated things, such as some algebraic expressions, as single objects or as being composed of several objects. For example, they can see 5 – 3(x – y)² as 5 minus a positive number times a square and use that to realize that its value cannot be more than 5 for any real numbers x and y. 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). Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. Use the structure of the decimal place-value system to solve problems involving patterns. Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 x 100 + 4 x 10 + 7 x 1 + 3 x (1/10) + 9 x (1/100) + 2 x (1/1000). Look for and make use of structure. Look for and make Use of structure. Read and write decimals to thousandths using base-ten numerals, word form, and expanded form. Look for and make use of structure. Read and write decimals using place value to describe decimals in terms of groups from millionths to millions. 1-7: Practice Buddy: Additional Practice Curriculum Standards: Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 x 100 + 4 x 10 + 7 x 1 + 3 x (1/10) + 9 x (1/100) + 2 x (1/1000). Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and <, symbols to record the results of comparisons. Look for and make use of structure. 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). Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. Look for and make use of structure. 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). Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. Look for and make use of structure. Mathematically proficient students look closely to discern a pattern or structure. Young students, for example, might notice that three and seven more is the same amount as seven and three more, or they may sort a collection of shapes according to how many sides the shapes have. Later, students will see 7 × 8 equals the well remembered 7 × 5 + 7 × 3, in preparation for learning about the distributive property. In the expression x² + 9x + 14, older students can see the 14 as 2 × 7 and the 9 as 2 + 7. They recognize the significance of an existing line in a geometric figure and can use the strategy of drawing an auxiliary line for solving problems. They also can step back for an overview and shift perspective. They can see complicated things, such as some algebraic expressions, as single objects or as being composed of several objects. For example, they can see 5 – 3(x – y)² as 5 minus a positive number times a square and use that to realize that its value cannot be more than 5 for any real numbers x and y. 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). Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. Use the structure of the decimal place-value system to solve problems involving patterns. Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 x 100 + 4 x 10 + 7 x 1 + 3 x (1/10) + 9 x (1/100) + 2 x (1/1000). Look for and make use of structure. Look for and make Use of structure. Read and write decimals to thousandths using base-ten numerals, word form, and expanded form. Look for and make use of structure. Read and write decimals using place value to describe decimals in terms of groups from millionths to millions. 1-7: Interactive Additional Practice Step 3: Assess & Differentiate 1-7: Practice Buddy: Additional Practice Curriculum Standards: Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 x 100 + 4 x 10 + 7 x 1 + 3 x (1/10) + 9 x (1/100) + 2 x (1/1000). Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and <, symbols to record the results of comparisons. Look for and make use of structure. 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). Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. Look for and make use of structure. 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). Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. Look for and make use of structure. Mathematically proficient students look closely to discern a pattern or structure. Young students, for example, might notice that three and seven more is the same amount as seven and three more, or they may sort a collection of shapes according to how many sides the shapes have. Later, students will see 7 × 8 equals the well remembered 7 × 5 + 7 × 3, in preparation for learning about the distributive property. In the expression x² + 9x + 14, older students can see the 14 as 2 × 7 and the 9 as 2 + 7. They recognize the significance of an existing line in a geometric figure and can use the strategy of drawing an auxiliary line for solving problems. They also can step back for an overview and shift perspective. They can see complicated things, such as some algebraic expressions, as single objects or as being composed of several objects. For example, they can see 5 – 3(x – y)² as 5 minus a positive number times a square and use that to realize that its value cannot be more than 5 for any real numbers x and y. 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). Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. Use the structure of the decimal place-value system to solve problems involving patterns. Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 x 100 + 4 x 10 + 7 x 1 + 3 x (1/10) + 9 x (1/100) + 2 x (1/1000). Look for and make use of structure. Look for and make Use of structure. Read and write decimals to thousandths using base-ten numerals, word form, and expanded form. Look for and make use of structure. Read and write decimals using place value to describe decimals in terms of groups from millionths to millions. 1-7: Enrichment Curriculum Standards: Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 x 100 + 4 x 10 + 7 x 1 + 3 x (1/10) + 9 x (1/100) + 2 x (1/1000). Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and <, symbols to record the results of comparisons. Look for and make use of structure. 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). Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. Look for and make use of structure. 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). Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. Look for and make use of structure. Mathematically proficient students look closely to discern a pattern or structure. Young students, for example, might notice that three and seven more is the same amount as seven and three more, or they may sort a collection of shapes according to how many sides the shapes have. Later, students will see 7 × 8 equals the well remembered 7 × 5 + 7 × 3, in preparation for learning about the distributive property. In the expression x² + 9x + 14, older students can see the 14 as 2 × 7 and the 9 as 2 + 7. They recognize the significance of an existing line in a geometric figure and can use the strategy of drawing an auxiliary line for solving problems. They also can step back for an overview and shift perspective. They can see complicated things, such as some algebraic expressions, as single objects or as being composed of several objects. For example, they can see 5 – 3(x – y)² as 5 minus a positive number times a square and use that to realize that its value cannot be more than 5 for any real numbers x and y. 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). Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. Use the structure of the decimal place-value system to solve problems involving patterns. Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 x 100 + 4 x 10 + 7 x 1 + 3 x (1/10) + 9 x (1/100) + 2 x (1/1000). Look for and make use of structure. Look for and make Use of structure. Read and write decimals to thousandths using base-ten numerals, word form, and expanded form. Look for and make use of structure. Read and write decimals using place value to describe decimals in terms of groups from millionths to millions. 1-7: Quick Check Curriculum Standards: Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 x 100 + 4 x 10 + 7 x 1 + 3 x (1/10) + 9 x (1/100) + 2 x (1/1000). Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and <, symbols to record the results of comparisons. Look for and make use of structure. 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). Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. Look for and make use of structure. 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). Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. Look for and make use of structure. Mathematically proficient students look closely to discern a pattern or structure. Young students, for example, might notice that three and seven more is the same amount as seven and three more, or they may sort a collection of shapes according to how many sides the shapes have. Later, students will see 7 × 8 equals the well remembered 7 × 5 + 7 × 3, in preparation for learning about the distributive property. In the expression x² + 9x + 14, older students can see the 14 as 2 × 7 and the 9 as 2 + 7. They recognize the significance of an existing line in a geometric figure and can use the strategy of drawing an auxiliary line for solving problems. They also can step back for an overview and shift perspective. They can see complicated things, such as some algebraic expressions, as single objects or as being composed of several objects. For example, they can see 5 – 3(x – y)² as 5 minus a positive number times a square and use that to realize that its value cannot be more than 5 for any real numbers x and y. 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). Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. Use the structure of the decimal place-value system to solve problems involving patterns. Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 x 100 + 4 x 10 + 7 x 1 + 3 x (1/10) + 9 x (1/100) + 2 x (1/1000). Look for and make use of structure. Look for and make Use of structure. Read and write decimals to thousandths using base-ten numerals, word form, and expanded form. Look for and make use of structure. Read and write decimals using place value to describe decimals in terms of groups from millionths to millions. 1-7: Lesson Self-Assessment 1-7: Reteach to Build Understanding Curriculum Standards: Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 x 100 + 4 x 10 + 7 x 1 + 3 x (1/10) + 9 x (1/100) + 2 x (1/1000). Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and <, symbols to record the results of comparisons. Look for and make use of structure. 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). Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. Look for and make use of structure. 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). Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. Look for and make use of structure. Mathematically proficient students look closely to discern a pattern or structure. Young students, for example, might notice that three and seven more is the same amount as seven and three more, or they may sort a collection of shapes according to how many sides the shapes have. Later, students will see 7 × 8 equals the well remembered 7 × 5 + 7 × 3, in preparation for learning about the distributive property. In the expression x² + 9x + 14, older students can see the 14 as 2 × 7 and the 9 as 2 + 7. They recognize the significance of an existing line in a geometric figure and can use the strategy of drawing an auxiliary line for solving problems. They also can step back for an overview and shift perspective. They can see complicated things, such as some algebraic expressions, as single objects or as being composed of several objects. For example, they can see 5 – 3(x – y)² as 5 minus a positive number times a square and use that to realize that its value cannot be more than 5 for any real numbers x and y. 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). Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. Use the structure of the decimal place-value system to solve problems involving patterns. Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 x 100 + 4 x 10 + 7 x 1 + 3 x (1/10) + 9 x (1/100) + 2 x (1/1000). Look for and make use of structure. Look for and make Use of structure. Read and write decimals to thousandths using base-ten numerals, word form, and expanded form. Look for and make use of structure. Read and write decimals using place value to describe decimals in terms of groups from millionths to millions. 1-7: Build Mathematical Literacy Curriculum Standards: Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 5 topics and texts, building on others’ ideas and expressing their own clearly. (a) Come to discussions prepared, having read or studied required material; explicitly draw on that preparation and other information known about the topic to explore ideas under discussion. (b) Follow agreed-upon rules for discussions and carry out assigned roles. (c) Pose and respond to specific questions by making comments that contribute to the discussion and elaborate on the remarks of others. (d) Review the key ideas expressed and draw conclusions in light of information and knowledge gained from the discussions. English language learners communicate for social and instructional purposes within the school setting. Summarize a written text read aloud or information presented in diverse media and formats, including visually, quantitatively, and orally. Summarize the points a speaker makes and explain how each claim is supported by reasons and evidence. Write informative/explanatory texts to examine a topic and convey ideas and information clearly. (a) Introduce a topic clearly, provide a general observation and focus, and group related information logically; include formatting (e.g., headings), illustrations, and multimedia when useful to aiding comprehension. (b) Develop the topic with facts, definitions, concrete details, quotations, or other information and examples related to the topic. (c) Link ideas within and across categories of information using words, phrases, and clauses (e.g., in contrast, especially). (d) Use precise language and domain-specific vocabulary to inform about or explain the topic. (e) Provide a concluding statement or section related to the information or explanation presented. English language learners communicate information, ideas and concepts necessary for academic success in the content area of Mathematics. 1-7: Enrichment Game: Gobbling Gobs - Hundred Thousands and Millions 1-7: Pick a Project 1-7: Another Look Curriculum Standards: Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 x 100 + 4 x 10 + 7 x 1 + 3 x (1/10) + 9 x (1/100) + 2 x (1/1000). Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and <, symbols to record the results of comparisons. Look for and make use of structure. 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). Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. Look for and make use of structure. 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). Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. Look for and make use of structure. Mathematically proficient students look closely to discern a pattern or structure. Young students, for example, might notice that three and seven more is the same amount as seven and three more, or they may sort a collection of shapes according to how many sides the shapes have. Later, students will see 7 × 8 equals the well remembered 7 × 5 + 7 × 3, in preparation for learning about the distributive property. In the expression x² + 9x + 14, older students can see the 14 as 2 × 7 and the 9 as 2 + 7. They recognize the significance of an existing line in a geometric figure and can use the strategy of drawing an auxiliary line for solving problems. They also can step back for an overview and shift perspective. They can see complicated things, such as some algebraic expressions, as single objects or as being composed of several objects. For example, they can see 5 – 3(x – y)² as 5 minus a positive number times a square and use that to realize that its value cannot be more than 5 for any real numbers x and y. 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). Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. Use the structure of the decimal place-value system to solve problems involving patterns. Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 x 100 + 4 x 10 + 7 x 1 + 3 x (1/10) + 9 x (1/100) + 2 x (1/1000). Look for and make use of structure. Look for and make Use of structure. Read and write decimals to thousandths using base-ten numerals, word form, and expanded form. Look for and make use of structure. Read and write decimals using place value to describe decimals in terms of groups from millionths to millions. Spanish Resources 1-7: eText del Libro del estudiante 1-7: Repaso diario 1-7: Aprendizaje visual 1-7: Amigo de práctica: Práctica adicional 1-7: Práctica adicional interactiva 1-7: Refuerzo para mejorar la comprensión 1-7: Desarrollar la competencia matemática 1-7: Ampliación Topic 1: 3-Act Math: Buzz In Interactive Student Edition: Grade 5, Topic 1: 3-Act Math Mathematical Modeling Topic 1: 3-Act Math: Buzz In, Act 1 Topic 1: 3-Act Math: Buzz In, Act 2 Topic 1: 3-Act Math: Buzz In, Act 3 Topic 1: 3-Act Math: Buzz In, Sequel Topic 1: End of Topic Interactive Student Edition: End of Topic 1 Topic 1: Fluency Practice Activity Interactive Student Edition: Topic 1 Assessment Practice Interactive Student Edition: Topic 1 Performance Task Topic 1 Performance Task Topic 1 Assessment 1-1: Visual Learning Curriculum Standards: Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. Use patterns and the properties of multiplication to calculate a product when multiplying by a power of 10; use whole-number exponents to write powers of 10. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10 and 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. Read and write decimals using place value to describe decimals in terms of groups from millionths to millions. 1-2: Visual Learning Curriculum Standards: 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. 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. Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left. Read and write whole numbers using standard form, expanded form, and number names. Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left. Demonstrate an understanding that in a multi-digit number, a digit in one place represents 1/10 of what it represents in the place to its left. Read and write decimals using place value to describe decimals in terms of groups from millionths to millions. 1-3: Visual Learning Curriculum Standards: Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left. Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 x 100 + 4 x 10 + 7 x 1 + 3 x (1/10) + 9 x (1/100) + 2 x (1/1000). Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left. Read 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). Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left. Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 × 100 + 4 × 10 + 7 × 1 + 3 × (1/10) + 9 × (1/100) + 2 × (1/1000). Read and write decimals 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). Represent decimals to thousandths as fractions and fraction with denominators of 1,000 as decimals. Recognize that in a multi- digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left. Read and write decimals to thousandths using base-ten numerals, word form, and expanded form. Read and write decimals using place value to describe decimals in terms of groups from millionths to millions. 1-4: Visual Learning Curriculum Standards: Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 x 100 + 4 x 10 + 7 x 1 + 3 x (1/10) + 9 x (1/100) + 2 x (1/1000). Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 × 100 + 4 × 10 + 7 × 1 + 3 × (1/10) + 9 × (1/100) + 2 × (1/1000). Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 × 100 + 4 × 10 + 7 × 1 + 3 × (1/10) + 9 × (1/100) + 2 × (1/1000). Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 × 100 + 4 × 10 + 7 × 1 + 3 × (1/10) + 9 × (1/100) + 2 × (1/1000). Read and write numbers with decimals through thousandths using standard form, expanded form, and number names; identify equivalent decimals. Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 x 100 + 4 x 10 + 7 x 1 + 3 x (1/10) + 9 x (1/100) + 2 x (1/1000). Read and write decimals to thousandths using base-ten numerals, word form, and expanded form. Read and write decimals using place value to describe decimals in terms of groups from millionths to millions. 1-5: Visual Learning Curriculum Standards: Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and <, symbols to record the results of comparisons. Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. Use place value to compare decimals through thousandths. Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and <, symbols to record the results of comparisons. Compare two decimals to thousandths based on meanings of the digits in each place using >, =, and < symbols. Order fractions and decimals, including mixed numbers and improper fractions, and locate on a number line. 1-6: Visual Learning Curriculum Standards: Use place value understanding to round decimals to any place. Use place value understanding to round decimals to any place. Use place value understanding to round decimals to any place. Use place value to round decimals to different places. Use place value understanding to round decimals to any place. Round decimals to any place (limit rounding to ones, tenths, hundredths, or thousandths place). Round numbers to the nearest 0.1, 0.01 and 0.001. Game: Factory Frenzy - Decimals Topic 1 Online Assessment Curriculum Standards: Use place value understanding to round decimals to any place. Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and <, symbols to record the results of comparisons. 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. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 x 100 + 4 x 10 + 7 x 1 + 3 x (1/10) + 9 x (1/100) + 2 x (1/1000). Use place value understanding to round decimals to any place. Use place value understanding to round decimals to any place. Use place value to round decimals to different places. Use place value understanding to round decimals to any place. Round decimals to any place (limit rounding to ones, tenths, hundredths, or thousandths place). Round numbers to the nearest 0.1, 0.01 and 0.001. Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. Use place value to compare decimals through thousandths. Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and <, symbols to record the results of comparisons. Compare two decimals to thousandths based on meanings of the digits in each place using >, =, and < symbols. Order fractions and decimals, including mixed numbers and improper fractions, and locate on a number line. 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. Recognize that in a multi- digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left. Read and write whole numbers using standard form, expanded form, and number names. Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left. Demonstrate an understanding that in a multi-digit number, a digit in one place represents 1/10 of what it represents in the place to its left. Read and write decimals using place value to describe decimals in terms of groups from millionths to millions. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. Use patterns and the properties of multiplication to calculate a product when multiplying by a power of 10; use whole-number exponents to write powers of 10. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10 and 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. Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 × 100 + 4 × 10 + 7 × 1 + 3 × (1/10) + 9 × (1/100) + 2 × (1/1000). Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 × 100 + 4 × 10 + 7 × 1 + 3 × (1/10) + 9 × (1/100) + 2 × (1/1000). Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 × 100 + 4 × 10 + 7 × 1 + 3 × (1/10) + 9 × (1/100) + 2 × (1/1000). Read and write numbers with decimals through thousandths using standard form, expanded form, and number names; identify equivalent decimals. Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 x 100 + 4 x 10 + 7 x 1 + 3 x (1/10) + 9 x (1/100) + 2 x (1/1000). Read and write decimals to thousandths using base-ten numerals, word form, and expanded form. Represent decimals to thousandths as fractions and fraction with denominators of 1,000 as decimals. Topic 1 Spanish Assessments Tema 1: Tarea de rendimento Tema 1: Evaluación Topic 2: Use Models and Strategies to Add and Subtract Decimals Topic 2: Today's Challenge Topic 2: Beginning of Topic Interactive Student Edition: Beginning of Topic 2 Topic 2: enVision STEM Activity Grade 5 Topic 2: Review What You Know Topic 2: Vocabulary Cards 2-1: Mental Math Interactive Student Edition: Grade 5 Lesson 2-1 Math Anytime 2-1: Daily Review Topic 2: Today's Challenge Step 1: Problem-Based Learning 2-1: Solve & Share Curriculum Standards: Use place value understanding to round decimals to any place. Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. English language learners communicate for social and instructional purposes within the school setting. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Use properties of addition and strategies to solve problems mentally. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). Add and subtract decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. Apply the commutative, associative and distributive properties and order of operations to generate equivalent numerical expressions and to solve problems involving whole numbers. Write informative/explanatory texts to examine a topic and convey ideas and information clearly. (a) Introduce a topic clearly, provide a general observation and focus, and group related information logically; include formatting (e.g., headings), illustrations, and multimedia when useful to aiding comprehension. (b) Develop the topic with facts, definitions, concrete details, quotations, or other information and examples related to the topic. (c) Link ideas within and across categories of information using words, phrases, and clauses (e.g., in contrast, especially). (d) Use precise language and domain-specific vocabulary to inform about or explain the topic. (e) Provide a concluding statement or section related to the information or explanation presented. English language learners communicate information, ideas and concepts necessary for academic success in the content area of Mathematics. Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 5 topics and texts, building on others’ ideas and expressing their own clearly. (a) Come to discussions prepared, having read or studied required material; explicitly draw on that preparation and other information known about the topic to explore ideas under discussion. (b) Follow agreed-upon rules for discussions and carry out assigned roles. (c) Pose and respond to specific questions by making comments that contribute to the discussion and elaborate on the remarks of others. (d) Review the key ideas expressed and draw conclusions in light of information and knowledge gained from the discussions. Summarize a written text read aloud or information presented in diverse media and formats, including visually, quantitatively, and orally. Summarize the points a speaker makes and explain how each claim is supported by reasons and evidence. Step 2: Visual Learning 2-1: Visual Learning Curriculum Standards: Use place value understanding to round decimals to any place. Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Use properties of addition and strategies to solve problems mentally. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). Add and subtract decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. Apply the commutative, associative and distributive properties and order of operations to generate equivalent numerical expressions and to solve problems involving whole numbers. 2-1: Convince Me! Curriculum Standards: Use place value understanding to round decimals to any place. Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Use properties of addition and strategies to solve problems mentally. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). Add and subtract decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. Apply the commutative, associative and distributive properties and order of operations to generate equivalent numerical expressions and to solve problems involving whole numbers. Practice and Problem Solving 2-1: Student Edition Practice Curriculum Standards: Use place value understanding to round decimals to any place. Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Use properties of addition and strategies to solve problems mentally. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). Add and subtract decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. Apply the commutative, associative and distributive properties and order of operations to generate equivalent numerical expressions and to solve problems involving whole numbers. 2-1: Practice Buddy: Independent Practice; Problem Solving Curriculum Standards: Use place value understanding to round decimals to any place. Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Use properties of addition and strategies to solve problems mentally. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). Add and subtract decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. Apply the commutative, associative and distributive properties and order of operations to generate equivalent numerical expressions and to solve problems involving whole numbers. 2-1: Practice Buddy: Additional Practice Curriculum Standards: Use place value understanding to round decimals to any place. Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Use properties of addition and strategies to solve problems mentally. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). Add and subtract decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. Apply the commutative, associative and distributive properties and order of operations to generate equivalent numerical expressions and to solve problems involving whole numbers. 2-1: Interactive Additional Practice Step 3: Assess & Differentiate 2-1: Practice Buddy: Additional Practice Curriculum Standards: Use place value understanding to round decimals to any place. Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Use properties of addition and strategies to solve problems mentally. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). Add and subtract decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. Apply the commutative, associative and distributive properties and order of operations to generate equivalent numerical expressions and to solve problems involving whole numbers. 2-1: Enrichment Curriculum Standards: Use place value understanding to round decimals to any place. Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Use properties of addition and strategies to solve problems mentally. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). Add and subtract decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. Apply the commutative, associative and distributive properties and order of operations to generate equivalent numerical expressions and to solve problems involving whole numbers. 2-1: Quick Check Curriculum Standards: Use place value understanding to round decimals to any place. Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Use properties of addition and strategies to solve problems mentally. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). Add and subtract decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. Apply the commutative, associative and distributive properties and order of operations to generate equivalent numerical expressions and to solve problems involving whole numbers. 2-1: Lesson Self-Assessment 2-1: Reteach to Build Understanding Curriculum Standards: Use place value understanding to round decimals to any place. Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Use properties of addition and strategies to solve problems mentally. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). Add and subtract decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. Apply the commutative, associative and distributive properties and order of operations to generate equivalent numerical expressions and to solve problems involving whole numbers. 2-1: Build Mathematical Literacy Curriculum Standards: Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 5 topics and texts, building on others’ ideas and expressing their own clearly. (a) Come to discussions prepared, having read or studied required material; explicitly draw on that preparation and other information known about the topic to explore ideas under discussion. (b) Follow agreed-upon rules for discussions and carry out assigned roles. (c) Pose and respond to specific questions by making comments that contribute to the discussion and elaborate on the remarks of others. (d) Review the key ideas expressed and draw conclusions in light of information and knowledge gained from the discussions. English language learners communicate for social and instructional purposes within the school setting. Summarize a written text read aloud or information presented in diverse media and formats, including visually, quantitatively, and orally. Summarize the points a speaker makes and explain how each claim is supported by reasons and evidence. Write informative/explanatory texts to examine a topic and convey ideas and information clearly. (a) Introduce a topic clearly, provide a general observation and focus, and group related information logically; include formatting (e.g., headings), illustrations, and multimedia when useful to aiding comprehension. (b) Develop the topic with facts, definitions, concrete details, quotations, or other information and examples related to the topic. (c) Link ideas within and across categories of information using words, phrases, and clauses (e.g., in contrast, especially). (d) Use precise language and domain-specific vocabulary to inform about or explain the topic. (e) Provide a concluding statement or section related to the information or explanation presented. English language learners communicate information, ideas and concepts necessary for academic success in the content area of Mathematics. 2-1: Enrichment 2-1: Digital Math Tool Activity 2-1: Problem-Solving Reading Activity Curriculum Standards: Use place value understanding to round decimals to any place. Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Use properties of addition and strategies to solve problems mentally. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). Add and subtract decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. Apply the commutative, associative and distributive properties and order of operations to generate equivalent numerical expressions and to solve problems involving whole numbers. 2-1: Another Look Curriculum Standards: Use place value understanding to round decimals to any place. Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Use properties of addition and strategies to solve problems mentally. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). Add and subtract decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. Apply the commutative, associative and distributive properties and order of operations to generate equivalent numerical expressions and to solve problems involving whole numbers. Spanish Resources 2-1: eText del Libro del estudiante 2-1: Repaso diario 2-1: Aprendizaje visual 2-1: Amigo de práctica: Práctica adicional 2-1: Práctica adicional interactiva 2-1: Refuerzo para mejorar la comprensión 2-1: Desarrollar la competencia matemática 2-1: Ampliación 2-2: Estimate Sums and Differences of Decimals Interactive Student Edition: Grade 5 Lesson 2-2 Math Anytime 2-2: Daily Review Topic 2: Today's Challenge Step 1: Problem-Based Learning 2-2: Solve & Share Curriculum Standards: Use place value understanding to round decimals to any place. Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. English language learners communicate for social and instructional purposes within the school setting. Use place value understanding to round decimals to any place. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Use place value understanding to round decimals to any place. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Use rounding or compatible numbers to estimate sums and differences. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Round decimals to any place (limit rounding to ones, tenths, hundredths, or thousandths place). Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). Add and subtract decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Estimate sums and differences of decimals and fractions to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. Write informative/explanatory texts to examine a topic and convey ideas and information clearly. (a) Introduce a topic clearly, provide a general observation and focus, and group related information logically; include formatting (e.g., headings), illustrations, and multimedia when useful to aiding comprehension. (b) Develop the topic with facts, definitions, concrete details, quotations, or other information and examples related to the topic. (c) Link ideas within and across categories of information using words, phrases, and clauses (e.g., in contrast, especially). (d) Use precise language and domain-specific vocabulary to inform about or explain the topic. (e) Provide a concluding statement or section related to the information or explanation presented. English language learners communicate information, ideas and concepts necessary for academic success in the content area of Mathematics. Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 5 topics and texts, building on others’ ideas and expressing their own clearly. (a) Come to discussions prepared, having read or studied required material; explicitly draw on that preparation and other information known about the topic to explore ideas under discussion. (b) Follow agreed-upon rules for discussions and carry out assigned roles. (c) Pose and respond to specific questions by making comments that contribute to the discussion and elaborate on the remarks of others. (d) Review the key ideas expressed and draw conclusions in light of information and knowledge gained from the discussions. Summarize a written text read aloud or information presented in diverse media and formats, including visually, quantitatively, and orally. Summarize the points a speaker makes and explain how each claim is supported by reasons and evidence. Step 2: Visual Learning 2-2: Visual Learning Curriculum Standards: Use place value understanding to round decimals to any place. Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Use place value understanding to round decimals to any place. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Use place value understanding to round decimals to any place. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Use rounding or compatible numbers to estimate sums and differences. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Round decimals to any place (limit rounding to ones, tenths, hundredths, or thousandths place). Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). Add and subtract decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Estimate sums and differences of decimals and fractions to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. 2-2: Convince Me! Curriculum Standards: Use place value understanding to round decimals to any place. Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Use place value understanding to round decimals to any place. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Use place value understanding to round decimals to any place. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Use rounding or compatible numbers to estimate sums and differences. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Round decimals to any place (limit rounding to ones, tenths, hundredths, or thousandths place). Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). Add and subtract decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Estimate sums and differences of decimals and fractions to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. Practice and Problem Solving 2-2: Student Edition Practice Curriculum Standards: Use place value understanding to round decimals to any place. Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Use place value understanding to round decimals to any place. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Use place value understanding to round decimals to any place. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Use rounding or compatible numbers to estimate sums and differences. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Round decimals to any place (limit rounding to ones, tenths, hundredths, or thousandths place). Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). Add and subtract decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Estimate sums and differences of decimals and fractions to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. 2-2: Practice Buddy: Independent Practice; Problem Solving Curriculum Standards: Use place value understanding to round decimals to any place. Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Use place value understanding to round decimals to any place. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Use place value understanding to round decimals to any place. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Use rounding or compatible numbers to estimate sums and differences. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Round decimals to any place (limit rounding to ones, tenths, hundredths, or thousandths place). Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). Add and subtract decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Estimate sums and differences of decimals and fractions to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. 2-2: Practice Buddy: Additional Practice Curriculum Standards: Use place value understanding to round decimals to any place. Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Use place value understanding to round decimals to any place. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Use place value understanding to round decimals to any place. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Use rounding or compatible numbers to estimate sums and differences. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Round decimals to any place (limit rounding to ones, tenths, hundredths, or thousandths place). Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). Add and subtract decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Estimate sums and differences of decimals and fractions to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. 2-2: Interactive Additional Practice Step 3: Assess & Differentiate 2-2: Practice Buddy: Additional Practice Curriculum Standards: Use place value understanding to round decimals to any place. Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Use place value understanding to round decimals to any place. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Use place value understanding to round decimals to any place. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Use rounding or compatible numbers to estimate sums and differences. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Round decimals to any place (limit rounding to ones, tenths, hundredths, or thousandths place). Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). Add and subtract decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Estimate sums and differences of decimals and fractions to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. 2-2: Enrichment Curriculum Standards: Use place value understanding to round decimals to any place. Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Use place value understanding to round decimals to any place. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Use place value understanding to round decimals to any place. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Use rounding or compatible numbers to estimate sums and differences. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Round decimals to any place (limit rounding to ones, tenths, hundredths, or thousandths place). Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). Add and subtract decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Estimate sums and differences of decimals and fractions to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. 2-2: Quick Check Curriculum Standards: Use place value understanding to round decimals to any place. Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Use place value understanding to round decimals to any place. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Use place value understanding to round decimals to any place. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Use rounding or compatible numbers to estimate sums and differences. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Round decimals to any place (limit rounding to ones, tenths, hundredths, or thousandths place). Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). Add and subtract decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Estimate sums and differences of decimals and fractions to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. 2-2: Lesson Self-Assessment 2-2: Reteach to Build Understanding Curriculum Standards: Use place value understanding to round decimals to any place. Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Use place value understanding to round decimals to any place. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Use place value understanding to round decimals to any place. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Use rounding or compatible numbers to estimate sums and differences. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Round decimals to any place (limit rounding to ones, tenths, hundredths, or thousandths place). Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). Add and subtract decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Estimate sums and differences of decimals and fractions to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. 2-2: Build Mathematical Literacy Curriculum Standards: Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 5 topics and texts, building on others’ ideas and expressing their own clearly. (a) Come to discussions prepared, having read or studied required material; explicitly draw on that preparation and other information known about the topic to explore ideas under discussion. (b) Follow agreed-upon rules for discussions and carry out assigned roles. (c) Pose and respond to specific questions by making comments that contribute to the discussion and elaborate on the remarks of others. (d) Review the key ideas expressed and draw conclusions in light of information and knowledge gained from the discussions. English language learners communicate for social and instructional purposes within the school setting. Summarize a written text read aloud or information presented in diverse media and formats, including visually, quantitatively, and orally. Summarize the points a speaker makes and explain how each claim is supported by reasons and evidence. Write informative/explanatory texts to examine a topic and convey ideas and information clearly. (a) Introduce a topic clearly, provide a general observation and focus, and group related information logically; include formatting (e.g., headings), illustrations, and multimedia when useful to aiding comprehension. (b) Develop the topic with facts, definitions, concrete details, quotations, or other information and examples related to the topic. (c) Link ideas within and across categories of information using words, phrases, and clauses (e.g., in contrast, especially). (d) Use precise language and domain-specific vocabulary to inform about or explain the topic. (e) Provide a concluding statement or section related to the information or explanation presented. English language learners communicate information, ideas and concepts necessary for academic success in the content area of Mathematics. 2-2: Enrichment 2-2: Digital Math Tool Activity 2-2: enVision STEM Activity 2-2: Another Look Curriculum Standards: Use place value understanding to round decimals to any place. Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Use place value understanding to round decimals to any place. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Use place value understanding to round decimals to any place. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Use rounding or compatible numbers to estimate sums and differences. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Round decimals to any place (limit rounding to ones, tenths, hundredths, or thousandths place). Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). Add and subtract decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Estimate sums and differences of decimals and fractions to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. Spanish Resources 2-2: eText del Libro del estudiante 2-2: Repaso diario 2-2: Aprendizaje visual 2-2: Amigo de práctica: Práctica adicional 2-2: Práctica adicional interactiva 2-2: Refuerzo para mejorar la comprensión 2-2: Desarrollar la competencia matemática 2-2: Ampliación 2-3: Use Models to Add and Subtract Decimals Interactive Student Edition: Grade 5 Lesson 2-3 Math Anytime 2-3: Daily Review Topic 2: Today's Challenge Step 1: Problem-Based Learning 2-3: Solve & Share Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Model sums and differences of decimals. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). Add and subtract decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Model addition and subtraction of fractions and decimals using a variety of representations. Estimate sums and differences of decimals and fractions to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. English language learners communicate for social and instructional purposes within the school setting. Write informative/explanatory texts to examine a topic and convey ideas and information clearly. (a) Introduce a topic clearly, provide a general observation and focus, and group related information logically; include formatting (e.g., headings), illustrations, and multimedia when useful to aiding comprehension. (b) Develop the topic with facts, definitions, concrete details, quotations, or other information and examples related to the topic. (c) Link ideas within and across categories of information using words, phrases, and clauses (e.g., in contrast, especially). (d) Use precise language and domain-specific vocabulary to inform about or explain the topic. (e) Provide a concluding statement or section related to the information or explanation presented. English language learners communicate information, ideas and concepts necessary for academic success in the content area of Mathematics. Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 5 topics and texts, building on others’ ideas and expressing their own clearly. (a) Come to discussions prepared, having read or studied required material; explicitly draw on that preparation and other information known about the topic to explore ideas under discussion. (b) Follow agreed-upon rules for discussions and carry out assigned roles. (c) Pose and respond to specific questions by making comments that contribute to the discussion and elaborate on the remarks of others. (d) Review the key ideas expressed and draw conclusions in light of information and knowledge gained from the discussions. Summarize a written text read aloud or information presented in diverse media and formats, including visually, quantitatively, and orally. Summarize the points a speaker makes and explain how each claim is supported by reasons and evidence. Step 2: Visual Learning 2-3: Visual Learning Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Model sums and differences of decimals. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). Add and subtract decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Model addition and subtraction of fractions and decimals using a variety of representations. Estimate sums and differences of decimals and fractions to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. 2-3: Convince Me! Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Model sums and differences of decimals. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). Add and subtract decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Model addition and subtraction of fractions and decimals using a variety of representations. Estimate sums and differences of decimals and fractions to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. Practice and Problem Solving 2-3: Student Edition Practice Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Model sums and differences of decimals. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). Add and subtract decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Model addition and subtraction of fractions and decimals using a variety of representations. Estimate sums and differences of decimals and fractions to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. 2-3: Practice Buddy: Independent Practice; Problem Solving Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Model sums and differences of decimals. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). Add and subtract decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Model addition and subtraction of fractions and decimals using a variety of representations. Estimate sums and differences of decimals and fractions to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. 2-3: Practice Buddy: Additional Practice Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Model sums and differences of decimals. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). Add and subtract decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Model addition and subtraction of fractions and decimals using a variety of representations. Estimate sums and differences of decimals and fractions to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. 2-3: Interactive Additional Practice Step 3: Assess & Differentiate 2-3: Practice Buddy: Additional Practice Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Model sums and differences of decimals. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). Add and subtract decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Model addition and subtraction of fractions and decimals using a variety of representations. Estimate sums and differences of decimals and fractions to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. 2-3: Enrichment Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Model sums and differences of decimals. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). Add and subtract decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Model addition and subtraction of fractions and decimals using a variety of representations. Estimate sums and differences of decimals and fractions to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. 2-3: Quick Check Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Model sums and differences of decimals. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). Add and subtract decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Model addition and subtraction of fractions and decimals using a variety of representations. Estimate sums and differences of decimals and fractions to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. 2-3: Lesson Self-Assessment 2-3: Reteach to Build Understanding Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Model sums and differences of decimals. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). Add and subtract decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Model addition and subtraction of fractions and decimals using a variety of representations. Estimate sums and differences of decimals and fractions to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. 2-3: Build Mathematical Literacy Curriculum Standards: Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 5 topics and texts, building on others’ ideas and expressing their own clearly. (a) Come to discussions prepared, having read or studied required material; explicitly draw on that preparation and other information known about the topic to explore ideas under discussion. (b) Follow agreed-upon rules for discussions and carry out assigned roles. (c) Pose and respond to specific questions by making comments that contribute to the discussion and elaborate on the remarks of others. (d) Review the key ideas expressed and draw conclusions in light of information and knowledge gained from the discussions. English language learners communicate for social and instructional purposes within the school setting. Summarize a written text read aloud or information presented in diverse media and formats, including visually, quantitatively, and orally. Summarize the points a speaker makes and explain how each claim is supported by reasons and evidence. Write informative/explanatory texts to examine a topic and convey ideas and information clearly. (a) Introduce a topic clearly, provide a general observation and focus, and group related information logically; include formatting (e.g., headings), illustrations, and multimedia when useful to aiding comprehension. (b) Develop the topic with facts, definitions, concrete details, quotations, or other information and examples related to the topic. (c) Link ideas within and across categories of information using words, phrases, and clauses (e.g., in contrast, especially). (d) Use precise language and domain-specific vocabulary to inform about or explain the topic. (e) Provide a concluding statement or section related to the information or explanation presented. English language learners communicate information, ideas and concepts necessary for academic success in the content area of Mathematics. 2-3: Enrichment 2-3: Digital Math Tool Activity 2-3: Pick a Project Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Model sums and differences of decimals. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). Add and subtract decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Model addition and subtraction of fractions and decimals using a variety of representations. Estimate sums and differences of decimals and fractions to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. 2-3: Another Look Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Model sums and differences of decimals. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). Add and subtract decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Model addition and subtraction of fractions and decimals using a variety of representations. Estimate sums and differences of decimals and fractions to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. Spanish Resources 2-3: eText del Libro del estudiante 2-3: Repaso diario 2-3: Aprendizaje visual 2-3: Amigo de práctica: Práctica adicional 2-3: Práctica adicional interactiva 2-3: Refuerzo para mejorar la comprensión 2-3: Desarrollar la competencia matemática 2-3: Ampliación 2-4: Use Strategies to Add Decimals Interactive Student Edition: Grade 5 Lesson 2-4 Math Anytime 2-4: Daily Review Topic 2: Today's Challenge Step 1: Problem-Based Learning 2-4: Solve & Share Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add decimals to hundredths using familiar strategies, such as partial sums. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). Add and subtract decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Model addition and subtraction of fractions and decimals using a variety of representations. Estimate sums and differences of decimals and fractions to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. English language learners communicate for social and instructional purposes within the school setting. Write informative/explanatory texts to examine a topic and convey ideas and information clearly. (a) Introduce a topic clearly, provide a general observation and focus, and group related information logically; include formatting (e.g., headings), illustrations, and multimedia when useful to aiding comprehension. (b) Develop the topic with facts, definitions, concrete details, quotations, or other information and examples related to the topic. (c) Link ideas within and across categories of information using words, phrases, and clauses (e.g., in contrast, especially). (d) Use precise language and domain- specific vocabulary to inform about or explain the topic. (e) Provide a concluding statement or section related to the information or explanation presented. English language learners communicate information, ideas and concepts necessary for academic success in the content area of Mathematics. Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 5 topics and texts, building on others’ ideas and expressing their own clearly. (a) Come to discussions prepared, having read or studied required material; explicitly draw on that preparation and other information known about the topic to explore ideas under discussion. (b) Follow agreed-upon rules for discussions and carry out assigned roles. (c) Pose and respond to specific questions by making comments that contribute to the discussion and elaborate on the remarks of others. (d) Review the key ideas expressed and draw conclusions in light of information and knowledge gained from the discussions. Summarize a written text read aloud or information presented in diverse media and formats, including visually, quantitatively, and orally. Summarize the points a speaker makes and explain how each claim is supported by reasons and evidence. Step 2: Visual Learning 2-4: Visual Learning Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add decimals to hundredths using familiar strategies, such as partial sums. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). Add and subtract decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Model addition and subtraction of fractions and decimals using a variety of representations. Estimate sums and differences of decimals and fractions to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. 2-4: Convince Me! Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add decimals to hundredths using familiar strategies, such as partial sums. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). Add and subtract decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Model addition and subtraction of fractions and decimals using a variety of representations. Estimate sums and differences of decimals and fractions to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. Practice and Problem Solving 2-4: Student Edition Practice Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add decimals to hundredths using familiar strategies, such as partial sums. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). Add and subtract decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Model addition and subtraction of fractions and decimals using a variety of representations. Estimate sums and differences of decimals and fractions to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. 2-4: Practice Buddy: Independent Practice; Problem Solving Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add decimals to hundredths using familiar strategies, such as partial sums. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). Add and subtract decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Model addition and subtraction of fractions and decimals using a variety of representations. Estimate sums and differences of decimals and fractions to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. 2-4: Practice Buddy: Additional Practice Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add decimals to hundredths using familiar strategies, such as partial sums. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). Add and subtract decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Model addition and subtraction of fractions and decimals using a variety of representations. Estimate sums and differences of decimals and fractions to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. 2-4: Interactive Additional Practice Step 3: Assess & Differentiate 2-4: Practice Buddy: Additional Practice Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add decimals to hundredths using familiar strategies, such as partial sums. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). Add and subtract decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Model addition and subtraction of fractions and decimals using a variety of representations. Estimate sums and differences of decimals and fractions to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. 2-4: Enrichment Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add decimals to hundredths using familiar strategies, such as partial sums. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). Add and subtract decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Model addition and subtraction of fractions and decimals using a variety of representations. Estimate sums and differences of decimals and fractions to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. 2-4: Quick Check Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add decimals to hundredths using familiar strategies, such as partial sums. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). Add and subtract decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Model addition and subtraction of fractions and decimals using a variety of representations. Estimate sums and differences of decimals and fractions to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. 2-4: Lesson Self-Assessment 2-4: Reteach to Build Understanding Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add decimals to hundredths using familiar strategies, such as partial sums. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). Add and subtract decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Model addition and subtraction of fractions and decimals using a variety of representations. Estimate sums and differences of decimals and fractions to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. 2-4: Build Mathematical Literacy Curriculum Standards: Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 5 topics and texts, building on others’ ideas and expressing their own clearly. (a) Come to discussions prepared, having read or studied required material; explicitly draw on that preparation and other information known about the topic to explore ideas under discussion. (b) Follow agreed-upon rules for discussions and carry out assigned roles. (c) Pose and respond to specific questions by making comments that contribute to the discussion and elaborate on the remarks of others. (d) Review the key ideas expressed and draw conclusions in light of information and knowledge gained from the discussions. English language learners communicate for social and instructional purposes within the school setting. Summarize a written text read aloud or information presented in diverse media and formats, including visually, quantitatively, and orally. Summarize the points a speaker makes and explain how each claim is supported by reasons and evidence. Write informative/explanatory texts to examine a topic and convey ideas and information clearly. (a) Introduce a topic clearly, provide a general observation and focus, and group related information logically; include formatting (e.g., headings), illustrations, and multimedia when useful to aiding comprehension. (b) Develop the topic with facts, definitions, concrete details, quotations, or other information and examples related to the topic. (c) Link ideas within and across categories of information using words, phrases, and clauses (e.g., in contrast, especially). (d) Use precise language and domain-specific vocabulary to inform about or explain the topic. (e) Provide a concluding statement or section related to the information or explanation presented. English language learners communicate information, ideas and concepts necessary for academic success in the content area of Mathematics. 2-4: Enrichment Game: Factory Frenzy - Decimals 2-4: Pick a Project 2-4: Another Look Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add decimals to hundredths using familiar strategies, such as partial sums. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). Add and subtract decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Model addition and subtraction of fractions and decimals using a variety of representations. Estimate sums and differences of decimals and fractions to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. Spanish Resources 2-4: eText del Libro del estudiante 2-4: Repaso diario 2-4: Aprendizaje visual 2-4: Amigo de práctica: Práctica adicional 2-4: Práctica adicional interactiva 2-4: Refuerzo para mejorar la comprensión 2-4: Desarrollar la competencia matemática 2-4: Ampliación 2-5: Use Strategies to Subtract Decimals Interactive Student Edition: Grade 5 Lesson 2-5 Math Anytime 2-5: Daily Review Topic 2: Today's Challenge Step 1: Problem-Based Learning 2-5: Solve & Share Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. English language learners communicate for social and instructional purposes within the school setting. Write informative/explanatory texts to examine a topic and convey ideas and information clearly. (a) Introduce a topic clearly, provide a general observation and focus, and group related information logically; include formatting (e.g., headings), illustrations, and multimedia when useful to aiding comprehension. (b) Develop the topic with facts, definitions, concrete details, quotations, or other information and examples related to the topic. (c) Link ideas within and across categories of information using words, phrases, and clauses (e.g., in contrast, especially). (d) Use precise language and domain- specific vocabulary to inform about or explain the topic. (e) Provide a concluding statement or section related to the information or explanation presented. English language learners communicate information, ideas and concepts necessary for academic success in the content area of Mathematics. Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 5 topics and texts, building on others’ ideas and expressing their own clearly. (a) Come to discussions prepared, having read or studied required material; explicitly draw on that preparation and other information known about the topic to explore ideas under discussion. (b) Follow agreed-upon rules for discussions and carry out assigned roles. (c) Pose and respond to specific questions by making comments that contribute to the discussion and elaborate on the remarks of others. (d) Review the key ideas expressed and draw conclusions in light of information and knowledge gained from the discussions. Summarize a written text read aloud or information presented in diverse media and formats, including visually, quantitatively, and orally. Summarize the points a speaker makes and explain how each claim is supported by reasons and evidence. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Subtract decimals to hundredths familiar strategies, such as partial differences. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). Add and subtract decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Model addition and subtraction of fractions and decimals using a variety of representations. Solve real- world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. Step 2: Visual Learning 2-5: Visual Learning Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Subtract decimals to hundredths familiar strategies, such as partial differences. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). Add and subtract decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Model addition and subtraction of fractions and decimals using a variety of representations. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. 2-5: Convince Me! Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Subtract decimals to hundredths familiar strategies, such as partial differences. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). Add and subtract decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Model addition and subtraction of fractions and decimals using a variety of representations. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. Practice and Problem Solving 2-5: Student Edition Practice Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Subtract decimals to hundredths familiar strategies, such as partial differences. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). Add and subtract decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Model addition and subtraction of fractions and decimals using a variety of representations. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. 2-5: Practice Buddy: Independent Practice; Problem Solving Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Subtract decimals to hundredths familiar strategies, such as partial differences. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). Add and subtract decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Model addition and subtraction of fractions and decimals using a variety of representations. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. 2-5: Practice Buddy: Additional Practice Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Subtract decimals to hundredths familiar strategies, such as partial differences. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). Add and subtract decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Model addition and subtraction of fractions and decimals using a variety of representations. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. 2-5: Interactive Additional Practice Step 3: Assess & Differentiate 2-5: Practice Buddy: Additional Practice Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Subtract decimals to hundredths familiar strategies, such as partial differences. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). Add and subtract decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Model addition and subtraction of fractions and decimals using a variety of representations. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. 2-5: Enrichment Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Subtract decimals to hundredths familiar strategies, such as partial differences. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). Add and subtract decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Model addition and subtraction of fractions and decimals using a variety of representations. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. 2-5: Quick Check Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Subtract decimals to hundredths familiar strategies, such as partial differences. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). Add and subtract decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Model addition and subtraction of fractions and decimals using a variety of representations. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. 2-5: Lesson Self-Assessment 2-5: Reteach to Build Understanding Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Subtract decimals to hundredths familiar strategies, such as partial differences. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). Add and subtract decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Model addition and subtraction of fractions and decimals using a variety of representations. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. 2-5: Build Mathematical Literacy Curriculum Standards: Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 5 topics and texts, building on others’ ideas and expressing their own clearly. (a) Come to discussions prepared, having read or studied required material; explicitly draw on that preparation and other information known about the topic to explore ideas under discussion. (b) Follow agreed-upon rules for discussions and carry out assigned roles. (c) Pose and respond to specific questions by making comments that contribute to the discussion and elaborate on the remarks of others. (d) Review the key ideas expressed and draw conclusions in light of information and knowledge gained from the discussions. English language learners communicate for social and instructional purposes within the school setting. Summarize a written text read aloud or information presented in diverse media and formats, including visually, quantitatively, and orally. Summarize the points a speaker makes and explain how each claim is supported by reasons and evidence. Write informative/explanatory texts to examine a topic and convey ideas and information clearly. (a) Introduce a topic clearly, provide a general observation and focus, and group related information logically; include formatting (e.g., headings), illustrations, and multimedia when useful to aiding comprehension. (b) Develop the topic with facts, definitions, concrete details, quotations, or other information and examples related to the topic. (c) Link ideas within and across categories of information using words, phrases, and clauses (e.g., in contrast, especially). (d) Use precise language and domain-specific vocabulary to inform about or explain the topic. (e) Provide a concluding statement or section related to the information or explanation presented. English language learners communicate information, ideas and concepts necessary for academic success in the content area of Mathematics. 2-5: Enrichment Game: Factory Frenzy - Decimals 2-5: enVision STEM Activity Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Subtract decimals to hundredths familiar strategies, such as partial differences. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). Add and subtract decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Model addition and subtraction of fractions and decimals using a variety of representations. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. 2-5: Another Look Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Subtract decimals to hundredths familiar strategies, such as partial differences. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). Add and subtract decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Model addition and subtraction of fractions and decimals using a variety of representations. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. Spanish Resources 2-5: eText del Libro del estudiante 2-5: Repaso diario 2-5: Aprendizaje visual 2-5: Amigo de práctica: Práctica adicional 2-5: Práctica adicional interactiva 2-5: Refuerzo para mejorar la comprensión 2-5: Desarrollar la competencia matemática 2-5: Ampliación 2-6: Problem Solving: Model with Math Interactive Student Edition: Grade 5 Lesson 2-6 Math Anytime 2-6: Daily Review Topic 2: Today's Challenge Step 1: Problem-Based Learning 2-6: Solve & Share Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Model with mathematics. English language learners communicate for social and instructional purposes within the school setting. Write informative/explanatory texts to examine a topic and convey ideas and information clearly. (a) Introduce a topic clearly, provide a general observation and focus, and group related information logically; include formatting (e.g., headings), illustrations, and multimedia when useful to aiding comprehension. (b) Develop the topic with facts, definitions, concrete details, quotations, or other information and examples related to the topic. (c) Link ideas within and across categories of information using words, phrases, and clauses (e.g., in contrast, especially). (d) Use precise language and domain-specific vocabulary to inform about or explain the topic. (e) Provide a concluding statement or section related to the information or explanation presented. English language learners communicate information, ideas and concepts necessary for academic success in the content area of Mathematics. Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 5 topics and texts, building on others’ ideas and expressing their own clearly. (a) Come to discussions prepared, having read or studied required material; explicitly draw on that preparation and other information known about the topic to explore ideas under discussion. (b) Follow agreed-upon rules for discussions and carry out assigned roles. (c) Pose and respond to specific questions by making comments that contribute to the discussion and elaborate on the remarks of others. (d) Review the key ideas expressed and draw conclusions in light of information and knowledge gained from the discussions. Summarize a written text read aloud or information presented in diverse media and formats, including visually, quantitatively, and orally. Summarize the points a speaker makes and explain how each claim is supported by reasons and evidence. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Model with mathematics. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Model with mathematics. Mathematically proficient students can apply the mathematics they know to solve problems arising in everyday life, society, and the workplace. In early grades, this might be as simple as writing an addition equation to describe a situation. In middle grades, a student might apply proportional reasoning to plan a school event or analyze a problem in the community. By high school, a student might use geometry to solve a design problem or use a function to describe how one quantity of interest depends on another. Mathematically proficient students who can apply what they know are comfortable making assumptions and approximations to simplify a complicated situation, realizing that these may need revision later. They are able to identify important quantities in a practical situation and map their relationships using such tools as diagrams, two-way tables, graphs, flowcharts and formulas. They can analyze those relationships mathematically to draw conclusions. They routinely interpret their mathematical results in the context of the situation and reflect on whether the results make sense, possibly improving the model if it has not served its purpose. Use prior math knowledge and equations or bar diagrams to solve problems. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Model with mathematics. Model with mathematics. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). Model with mathematics. Add and subtract decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Model addition and subtraction of fractions and decimals using a variety of representations. Estimate sums and differences of decimals and fractions to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. Step 2: Visual Learning 2-6: Visual Learning Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Model with mathematics. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Model with mathematics. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Model with mathematics. Mathematically proficient students can apply the mathematics they know to solve problems arising in everyday life, society, and the workplace. In early grades, this might be as simple as writing an addition equation to describe a situation. In middle grades, a student might apply proportional reasoning to plan a school event or analyze a problem in the community. By high school, a student might use geometry to solve a design problem or use a function to describe how one quantity of interest depends on another. Mathematically proficient students who can apply what they know are comfortable making assumptions and approximations to simplify a complicated situation, realizing that these may need revision later. They are able to identify important quantities in a practical situation and map their relationships using such tools as diagrams, two-way tables, graphs, flowcharts and formulas. They can analyze those relationships mathematically to draw conclusions. They routinely interpret their mathematical results in the context of the situation and reflect on whether the results make sense, possibly improving the model if it has not served its purpose. Use prior math knowledge and equations or bar diagrams to solve problems. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Model with mathematics. Model with mathematics. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). Model with mathematics. Add and subtract decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Model addition and subtraction of fractions and decimals using a variety of representations. Estimate sums and differences of decimals and fractions to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. 2-6: Convince Me! Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Model with mathematics. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Model with mathematics. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Model with mathematics. Mathematically proficient students can apply the mathematics they know to solve problems arising in everyday life, society, and the workplace. In early grades, this might be as simple as writing an addition equation to describe a situation. In middle grades, a student might apply proportional reasoning to plan a school event or analyze a problem in the community. By high school, a student might use geometry to solve a design problem or use a function to describe how one quantity of interest depends on another. Mathematically proficient students who can apply what they know are comfortable making assumptions and approximations to simplify a complicated situation, realizing that these may need revision later. They are able to identify important quantities in a practical situation and map their relationships using such tools as diagrams, two-way tables, graphs, flowcharts and formulas. They can analyze those relationships mathematically to draw conclusions. They routinely interpret their mathematical results in the context of the situation and reflect on whether the results make sense, possibly improving the model if it has not served its purpose. Use prior math knowledge and equations or bar diagrams to solve problems. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Model with mathematics. Model with mathematics. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). Model with mathematics. Add and subtract decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Model addition and subtraction of fractions and decimals using a variety of representations. Estimate sums and differences of decimals and fractions to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. Practice and Problem Solving 2-6: Student Edition Practice Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Model with mathematics. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Model with mathematics. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Model with mathematics. Mathematically proficient students can apply the mathematics they know to solve problems arising in everyday life, society, and the workplace. In early grades, this might be as simple as writing an addition equation to describe a situation. In middle grades, a student might apply proportional reasoning to plan a school event or analyze a problem in the community. By high school, a student might use geometry to solve a design problem or use a function to describe how one quantity of interest depends on another. Mathematically proficient students who can apply what they know are comfortable making assumptions and approximations to simplify a complicated situation, realizing that these may need revision later. They are able to identify important quantities in a practical situation and map their relationships using such tools as diagrams, two-way tables, graphs, flowcharts and formulas. They can analyze those relationships mathematically to draw conclusions. They routinely interpret their mathematical results in the context of the situation and reflect on whether the results make sense, possibly improving the model if it has not served its purpose. Use prior math knowledge and equations or bar diagrams to solve problems. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Model with mathematics. Model with mathematics. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). Model with mathematics. Add and subtract decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Model addition and subtraction of fractions and decimals using a variety of representations. Estimate sums and differences of decimals and fractions to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. 2-6: Practice Buddy: Independent Practice; Problem Solving Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Model with mathematics. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Model with mathematics. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Model with mathematics. Mathematically proficient students can apply the mathematics they know to solve problems arising in everyday life, society, and the workplace. In early grades, this might be as simple as writing an addition equation to describe a situation. In middle grades, a student might apply proportional reasoning to plan a school event or analyze a problem in the community. By high school, a student might use geometry to solve a design problem or use a function to describe how one quantity of interest depends on another. Mathematically proficient students who can apply what they know are comfortable making assumptions and approximations to simplify a complicated situation, realizing that these may need revision later. They are able to identify important quantities in a practical situation and map their relationships using such tools as diagrams, two-way tables, graphs, flowcharts and formulas. They can analyze those relationships mathematically to draw conclusions. They routinely interpret their mathematical results in the context of the situation and reflect on whether the results make sense, possibly improving the model if it has not served its purpose. Use prior math knowledge and equations or bar diagrams to solve problems. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Model with mathematics. Model with mathematics. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). Model with mathematics. Add and subtract decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Model addition and subtraction of fractions and decimals using a variety of representations. Estimate sums and differences of decimals and fractions to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. 2-6: Practice Buddy: Additional Practice Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Model with mathematics. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Model with mathematics. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Model with mathematics. Mathematically proficient students can apply the mathematics they know to solve problems arising in everyday life, society, and the workplace. In early grades, this might be as simple as writing an addition equation to describe a situation. In middle grades, a student might apply proportional reasoning to plan a school event or analyze a problem in the community. By high school, a student might use geometry to solve a design problem or use a function to describe how one quantity of interest depends on another. Mathematically proficient students who can apply what they know are comfortable making assumptions and approximations to simplify a complicated situation, realizing that these may need revision later. They are able to identify important quantities in a practical situation and map their relationships using such tools as diagrams, two-way tables, graphs, flowcharts and formulas. They can analyze those relationships mathematically to draw conclusions. They routinely interpret their mathematical results in the context of the situation and reflect on whether the results make sense, possibly improving the model if it has not served its purpose. Use prior math knowledge and equations or bar diagrams to solve problems. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Model with mathematics. Model with mathematics. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). Model with mathematics. Add and subtract decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Model addition and subtraction of fractions and decimals using a variety of representations. Estimate sums and differences of decimals and fractions to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. 2-6: Interactive Additional Practice Step 3: Assess & Differentiate 2-6: Practice Buddy: Additional Practice Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Model with mathematics. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Model with mathematics. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Model with mathematics. Mathematically proficient students can apply the mathematics they know to solve problems arising in everyday life, society, and the workplace. In early grades, this might be as simple as writing an addition equation to describe a situation. In middle grades, a student might apply proportional reasoning to plan a school event or analyze a problem in the community. By high school, a student might use geometry to solve a design problem or use a function to describe how one quantity of interest depends on another. Mathematically proficient students who can apply what they know are comfortable making assumptions and approximations to simplify a complicated situation, realizing that these may need revision later. They are able to identify important quantities in a practical situation and map their relationships using such tools as diagrams, two-way tables, graphs, flowcharts and formulas. They can analyze those relationships mathematically to draw conclusions. They routinely interpret their mathematical results in the context of the situation and reflect on whether the results make sense, possibly improving the model if it has not served its purpose. Use prior math knowledge and equations or bar diagrams to solve problems. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Model with mathematics. Model with mathematics. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). Model with mathematics. Add and subtract decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Model addition and subtraction of fractions and decimals using a variety of representations. Estimate sums and differences of decimals and fractions to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. 2-6: Enrichment Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Model with mathematics. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Model with mathematics. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Model with mathematics. Mathematically proficient students can apply the mathematics they know to solve problems arising in everyday life, society, and the workplace. In early grades, this might be as simple as writing an addition equation to describe a situation. In middle grades, a student might apply proportional reasoning to plan a school event or analyze a problem in the community. By high school, a student might use geometry to solve a design problem or use a function to describe how one quantity of interest depends on another. Mathematically proficient students who can apply what they know are comfortable making assumptions and approximations to simplify a complicated situation, realizing that these may need revision later. They are able to identify important quantities in a practical situation and map their relationships using such tools as diagrams, two-way tables, graphs, flowcharts and formulas. They can analyze those relationships mathematically to draw conclusions. They routinely interpret their mathematical results in the context of the situation and reflect on whether the results make sense, possibly improving the model if it has not served its purpose. Use prior math knowledge and equations or bar diagrams to solve problems. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Model with mathematics. Model with mathematics. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). Model with mathematics. Add and subtract decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Model addition and subtraction of fractions and decimals using a variety of representations. Estimate sums and differences of decimals and fractions to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. 2-6: Quick Check Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Model with mathematics. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Model with mathematics. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Model with mathematics. Mathematically proficient students can apply the mathematics they know to solve problems arising in everyday life, society, and the workplace. In early grades, this might be as simple as writing an addition equation to describe a situation. In middle grades, a student might apply proportional reasoning to plan a school event or analyze a problem in the community. By high school, a student might use geometry to solve a design problem or use a function to describe how one quantity of interest depends on another. Mathematically proficient students who can apply what they know are comfortable making assumptions and approximations to simplify a complicated situation, realizing that these may need revision later. They are able to identify important quantities in a practical situation and map their relationships using such tools as diagrams, two-way tables, graphs, flowcharts and formulas. They can analyze those relationships mathematically to draw conclusions. They routinely interpret their mathematical results in the context of the situation and reflect on whether the results make sense, possibly improving the model if it has not served its purpose. Use prior math knowledge and equations or bar diagrams to solve problems. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Model with mathematics. Model with mathematics. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). Model with mathematics. Add and subtract decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Model addition and subtraction of fractions and decimals using a variety of representations. Estimate sums and differences of decimals and fractions to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. 2-6: Lesson Self-Assessment 2-6: Reteach to Build Understanding Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Model with mathematics. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Model with mathematics. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Model with mathematics. Mathematically proficient students can apply the mathematics they know to solve problems arising in everyday life, society, and the workplace. In early grades, this might be as simple as writing an addition equation to describe a situation. In middle grades, a student might apply proportional reasoning to plan a school event or analyze a problem in the community. By high school, a student might use geometry to solve a design problem or use a function to describe how one quantity of interest depends on another. Mathematically proficient students who can apply what they know are comfortable making assumptions and approximations to simplify a complicated situation, realizing that these may need revision later. They are able to identify important quantities in a practical situation and map their relationships using such tools as diagrams, two-way tables, graphs, flowcharts and formulas. They can analyze those relationships mathematically to draw conclusions. They routinely interpret their mathematical results in the context of the situation and reflect on whether the results make sense, possibly improving the model if it has not served its purpose. Use prior math knowledge and equations or bar diagrams to solve problems. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Model with mathematics. Model with mathematics. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). Model with mathematics. Add and subtract decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Model addition and subtraction of fractions and decimals using a variety of representations. Estimate sums and differences of decimals and fractions to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. 2-6: Build Mathematical Literacy Curriculum Standards: Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 5 topics and texts, building on others’ ideas and expressing their own clearly. (a) Come to discussions prepared, having read or studied required material; explicitly draw on that preparation and other information known about the topic to explore ideas under discussion. (b) Follow agreed-upon rules for discussions and carry out assigned roles. (c) Pose and respond to specific questions by making comments that contribute to the discussion and elaborate on the remarks of others. (d) Review the key ideas expressed and draw conclusions in light of information and knowledge gained from the discussions. English language learners communicate for social and instructional purposes within the school setting. Summarize a written text read aloud or information presented in diverse media and formats, including visually, quantitatively, and orally. Summarize the points a speaker makes and explain how each claim is supported by reasons and evidence. Write informative/explanatory texts to examine a topic and convey ideas and information clearly. (a) Introduce a topic clearly, provide a general observation and focus, and group related information logically; include formatting (e.g., headings), illustrations, and multimedia when useful to aiding comprehension. (b) Develop the topic with facts, definitions, concrete details, quotations, or other information and examples related to the topic. (c) Link ideas within and across categories of information using words, phrases, and clauses (e.g., in contrast, especially). (d) Use precise language and domain-specific vocabulary to inform about or explain the topic. (e) Provide a concluding statement or section related to the information or explanation presented. English language learners communicate information, ideas and concepts necessary for academic success in the content area of Mathematics. 2-6: Enrichment 2-6: Digital Math Tool Activity 2-6: Problem-Solving Reading Activity Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Model with mathematics. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Model with mathematics. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Model with mathematics. Mathematically proficient students can apply the mathematics they know to solve problems arising in everyday life, society, and the workplace. In early grades, this might be as simple as writing an addition equation to describe a situation. In middle grades, a student might apply proportional reasoning to plan a school event or analyze a problem in the community. By high school, a student might use geometry to solve a design problem or use a function to describe how one quantity of interest depends on another. Mathematically proficient students who can apply what they know are comfortable making assumptions and approximations to simplify a complicated situation, realizing that these may need revision later. They are able to identify important quantities in a practical situation and map their relationships using such tools as diagrams, two-way tables, graphs, flowcharts and formulas. They can analyze those relationships mathematically to draw conclusions. They routinely interpret their mathematical results in the context of the situation and reflect on whether the results make sense, possibly improving the model if it has not served its purpose. Use prior math knowledge and equations or bar diagrams to solve problems. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Model with mathematics. Model with mathematics. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). Model with mathematics. Add and subtract decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Model addition and subtraction of fractions and decimals using a variety of representations. Estimate sums and differences of decimals and fractions to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. 2-6: Another Look Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Model with mathematics. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Model with mathematics. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Model with mathematics. Mathematically proficient students can apply the mathematics they know to solve problems arising in everyday life, society, and the workplace. In early grades, this might be as simple as writing an addition equation to describe a situation. In middle grades, a student might apply proportional reasoning to plan a school event or analyze a problem in the community. By high school, a student might use geometry to solve a design problem or use a function to describe how one quantity of interest depends on another. Mathematically proficient students who can apply what they know are comfortable making assumptions and approximations to simplify a complicated situation, realizing that these may need revision later. They are able to identify important quantities in a practical situation and map their relationships using such tools as diagrams, two-way tables, graphs, flowcharts and formulas. They can analyze those relationships mathematically to draw conclusions. They routinely interpret their mathematical results in the context of the situation and reflect on whether the results make sense, possibly improving the model if it has not served its purpose. Use prior math knowledge and equations or bar diagrams to solve problems. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Model with mathematics. Model with mathematics. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). Model with mathematics. Add and subtract decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Model addition and subtraction of fractions and decimals using a variety of representations. Estimate sums and differences of decimals and fractions to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. Spanish Resources 2-6: eText del Libro del estudiante 2-6: Repaso diario 2-6: Aprendizaje visual 2-6: Amigo de práctica: Práctica adicional 2-6: Práctica adicional interactiva 2-6: Refuerzo para mejorar la comprensión 2-6: Desarrollar la competencia matemática 2-6: Ampliación Topic 2: End of Topic Interactive Student Edition: End of Topic 2 Topic 2: Fluency Practice Activity Interactive Student Edition: Topic 2 Assessment Practice Interactive Student Edition: Topic 2 Performance Task Topic 2 Performance Task Topic 2 Assessment 2-2: Visual Learning Curriculum Standards: Use place value understanding to round decimals to any place. Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Use place value understanding to round decimals to any place. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Use place value understanding to round decimals to any place. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Use rounding or compatible numbers to estimate sums and differences. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Round decimals to any place (limit rounding to ones, tenths, hundredths, or thousandths place). Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). Add and subtract decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Estimate sums and differences of decimals and fractions to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. 2-3: Visual Learning Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Model sums and differences of decimals. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). Add and subtract decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Model addition and subtraction of fractions and decimals using a variety of representations. Estimate sums and differences of decimals and fractions to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. 2-4: Visual Learning Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add decimals to hundredths using familiar strategies, such as partial sums. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). Add and subtract decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Model addition and subtraction of fractions and decimals using a variety of representations. Estimate sums and differences of decimals and fractions to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. 2-5: Visual Learning Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Subtract decimals to hundredths familiar strategies, such as partial differences. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). Add and subtract decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Model addition and subtraction of fractions and decimals using a variety of representations. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. 4-2: Center Games Topic 2 Online Assessment Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Use place value understanding to round decimals to any place. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Model sums and differences of decimals. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). Add and subtract decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Model addition and subtraction of fractions and decimals using a variety of representations. Estimate sums and differences of decimals and fractions to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. Add decimals to hundredths using familiar strategies, such as partial sums. Use place value understanding to round decimals to any place. Use place value understanding to round decimals to any place. Use rounding or compatible numbers to estimate sums and differences. Round decimals to any place (limit rounding to ones, tenths, hundredths, or thousandths place). Subtract decimals to hundredths familiar strategies, such as partial differences. Topic 2 Spanish Assessments Tema 2: Tarea de rendimento Tema 2: Evaluación Topic 3: Fluently Multiply Multi-Digit Whole Numbers Topic 3: Today's Challenge Topic 3: Beginning of Topic Interactive Student Edition_Beginning of Topic 3 Topic 3: enVision STEM Activity Grade 5 Topic 3: Review What You Know Topic 3: Vocabulary Cards 3-1: Multiply Greater Numbers by Powers of 10 Interactive Student Edition: Grade 5 Lesson 3-1 Math Anytime 3-1: Daily Review Topic 3: Today's Challenge Step 1: Problem-Based Learning 3-1: Solve & Share Curriculum Standards: 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. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. English language learners communicate for social and instructional purposes within the school setting. Write informative/explanatory texts to examine a topic and convey ideas and information clearly. (a) Introduce a topic clearly, provide a general observation and focus, and group related information logically; include formatting (e.g., headings), illustrations, and multimedia when useful to aiding comprehension. (b) Develop the topic with facts, definitions, concrete details, quotations, or other information and examples related to the topic. (c) Link ideas within and across categories of information using words, phrases, and clauses (e.g., in contrast, especially). (d) Use precise language and domain- specific vocabulary to inform about or explain the topic. (e) Provide a concluding statement or section related to the information or explanation presented. English language learners communicate information, ideas and concepts necessary for academic success in the content area of Mathematics. Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 5 topics and texts, building on others’ ideas and expressing their own clearly. (a) Come to discussions prepared, having read or studied required material; explicitly draw on that preparation and other information known about the topic to explore ideas under discussion. (b) Follow agreed-upon rules for discussions and carry out assigned roles. (c) Pose and respond to specific questions by making comments that contribute to the discussion and elaborate on the remarks of others. (d) Review the key ideas expressed and draw conclusions in light of information and knowledge gained from the discussions. Summarize a written text read aloud or information presented in diverse media and formats, including visually, quantitatively, and orally. Summarize the points a speaker makes and explain how each claim is supported by reasons and evidence. 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. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. 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. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. Use place-value understandings and patterns to mentally multiply whole numbers and powers of 10. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10 and 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. 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. Step 2: Visual Learning 3-1: Visual Learning Curriculum Standards: 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. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. 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. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. 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. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. Use place-value understandings and patterns to mentally multiply whole numbers and powers of 10. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10 and 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. 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. 3-1: Convince Me! Curriculum Standards: 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. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. 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. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. 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. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. Use place-value understandings and patterns to mentally multiply whole numbers and powers of 10. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10 and 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. 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. Practice and Problem Solving 3-1: Student Edition Practice Curriculum Standards: 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. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. 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. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. 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. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. Use place-value understandings and patterns to mentally multiply whole numbers and powers of 10. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10 and 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. 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. 3-1: Practice Buddy: Independent Practice; Problem Solving Curriculum Standards: 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. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. 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. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. 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. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. Use place-value understandings and patterns to mentally multiply whole numbers and powers of 10. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10 and 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. 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. 3-1: Practice Buddy: Additional Practice Curriculum Standards: 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. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. 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. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. 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. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. Use place-value understandings and patterns to mentally multiply whole numbers and powers of 10. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10 and 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. 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. 3-1: Interactive Additional Practice Step 3: Assess & Differentiate 3-1: Practice Buddy: Additional Practice Curriculum Standards: 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. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. 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. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. 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. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. Use place-value understandings and patterns to mentally multiply whole numbers and powers of 10. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10 and 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. 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. 3-1: Enrichment Curriculum Standards: 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. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. 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. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. 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. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. Use place-value understandings and patterns to mentally multiply whole numbers and powers of 10. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10 and 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. 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. 3-1: Quick Check Curriculum Standards: 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. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. 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. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. 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. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. Use place-value understandings and patterns to mentally multiply whole numbers and powers of 10. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10 and 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. 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. 3-1: Lesson Self-Assessment 3-1: Reteach to Build Understanding Curriculum Standards: 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. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. 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. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. 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. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. Use place-value understandings and patterns to mentally multiply whole numbers and powers of 10. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10 and 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. 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. 3-1: Build Mathematical Literacy Curriculum Standards: Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 5 topics and texts, building on others’ ideas and expressing their own clearly. (a) Come to discussions prepared, having read or studied required material; explicitly draw on that preparation and other information known about the topic to explore ideas under discussion. (b) Follow agreed-upon rules for discussions and carry out assigned roles. (c) Pose and respond to specific questions by making comments that contribute to the discussion and elaborate on the remarks of others. (d) Review the key ideas expressed and draw conclusions in light of information and knowledge gained from the discussions. English language learners communicate for social and instructional purposes within the school setting. Summarize a written text read aloud or information presented in diverse media and formats, including visually, quantitatively, and orally. Summarize the points a speaker makes and explain how each claim is supported by reasons and evidence. Write informative/explanatory texts to examine a topic and convey ideas and information clearly. (a) Introduce a topic clearly, provide a general observation and focus, and group related information logically; include formatting (e.g., headings), illustrations, and multimedia when useful to aiding comprehension. (b) Develop the topic with facts, definitions, concrete details, quotations, or other information and examples related to the topic. (c) Link ideas within and across categories of information using words, phrases, and clauses (e.g., in contrast, especially). (d) Use precise language and domain-specific vocabulary to inform about or explain the topic. (e) Provide a concluding statement or section related to the information or explanation presented. English language learners communicate information, ideas and concepts necessary for academic success in the content area of Mathematics. 3-1: Enrichment 3-1: Digital Math Tool Activity 3-1: enVision STEM Activity Curriculum Standards: 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. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. 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. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. 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. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. Use place-value understandings and patterns to mentally multiply whole numbers and powers of 10. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10 and 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. 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. 3-1: Another Look Curriculum Standards: 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. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. 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. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. 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. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. Use place-value understandings and patterns to mentally multiply whole numbers and powers of 10. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10 and 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. 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. Spanish Resources 3-1: eText del Libro del estudiante 3-1: Repaso diario 3-1: Aprendizaje visual 3-1: Amigo de práctica: Práctica adicional 3-1: Práctica adicional interactiva 3-1: Refuerzo para mejorar la comprensión 3-1: Desarrollar la competencia matemática 3-1: Ampliación 3-2: Estimate Products Interactive Student Edition: Grade 5 Lesson 3-2 Math Anytime 3-2: Daily Review Topic 3: Today's Challenge Step 1: Problem-Based Learning 3-2: Solve & Share Curriculum Standards: Fluently multiply multi-digit whole numbers using the standard algorithm. English language learners communicate for social and instructional purposes within the school setting. Write informative/explanatory texts to examine a topic and convey ideas and information clearly. (a) Introduce a topic clearly, provide a general observation and focus, and group related information logically; include formatting (e.g., headings), illustrations, and multimedia when useful to aiding comprehension. (b) Develop the topic with facts, definitions, concrete details, quotations, or other information and examples related to the topic. (c) Link ideas within and across categories of information using words, phrases, and clauses (e.g., in contrast, especially). (d) Use precise language and domain-specific vocabulary to inform about or explain the topic. (e) Provide a concluding statement or section related to the information or explanation presented. English language learners communicate information, ideas and concepts necessary for academic success in the content area of Mathematics. Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 5 topics and texts, building on others’ ideas and expressing their own clearly. (a) Come to discussions prepared, having read or studied required material; explicitly draw on that preparation and other information known about the topic to explore ideas under discussion. (b) Follow agreed-upon rules for discussions and carry out assigned roles. (c) Pose and respond to specific questions by making comments that contribute to the discussion and elaborate on the remarks of others. (d) Review the key ideas expressed and draw conclusions in light of information and knowledge gained from the discussions. Summarize a written text read aloud or information presented in diverse media and formats, including visually, quantitatively, and orally. Summarize the points a speaker makes and explain how each claim is supported by reasons and evidence. Fluently multiply multi-digit whole numbers using the standard algorithm. Fluently multiply multi-digit whole numbers using the standard algorithm. Use rounding and compatible numbers to estimate products. Fluently multiply multi-digit whole numbers using the standard algorithm. Multiply multi-digit whole numbers (not to exceed three-digit by three-digit). Estimate solutions to arithmetic problems in order to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition, subtraction, multiplication and division of multi-digit whole numbers. Use various strategies, including the inverse relationships between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Step 2: Visual Learning 3-2: Visual Learning Curriculum Standards: Fluently multiply multi-digit whole numbers using the standard algorithm. Fluently multiply multi-digit whole numbers using the standard algorithm. Fluently multiply multi-digit whole numbers using the standard algorithm. Use rounding and compatible numbers to estimate products. Fluently multiply multi-digit whole numbers using the standard algorithm. Multiply multi-digit whole numbers (not to exceed three-digit by three-digit). Estimate solutions to arithmetic problems in order to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition, subtraction, multiplication and division of multi-digit whole numbers. Use various strategies, including the inverse relationships between operations, the use of technology, and the context of the problem to assess the reasonableness of results. 3-2: Convince Me! Curriculum Standards: Fluently multiply multi-digit whole numbers using the standard algorithm. Fluently multiply multi-digit whole numbers using the standard algorithm. Fluently multiply multi-digit whole numbers using the standard algorithm. Use rounding and compatible numbers to estimate products. Fluently multiply multi-digit whole numbers using the standard algorithm. Multiply multi-digit whole numbers (not to exceed three-digit by three-digit). Estimate solutions to arithmetic problems in order to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition, subtraction, multiplication and division of multi-digit whole numbers. Use various strategies, including the inverse relationships between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Practice and Problem Solving 3-2: Student Edition Practice Curriculum Standards: Fluently multiply multi-digit whole numbers using the standard algorithm. Fluently multiply multi-digit whole numbers using the standard algorithm. Fluently multiply multi-digit whole numbers using the standard algorithm. Use rounding and compatible numbers to estimate products. Fluently multiply multi-digit whole numbers using the standard algorithm. Multiply multi-digit whole numbers (not to exceed three-digit by three-digit). Estimate solutions to arithmetic problems in order to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition, subtraction, multiplication and division of multi-digit whole numbers. Use various strategies, including the inverse relationships between operations, the use of technology, and the context of the problem to assess the reasonableness of results. 3-2: Practice Buddy: Independent Practice; Problem Solving Curriculum Standards: Fluently multiply multi-digit whole numbers using the standard algorithm. Fluently multiply multi-digit whole numbers using the standard algorithm. Fluently multiply multi-digit whole numbers using the standard algorithm. Use rounding and compatible numbers to estimate products. Fluently multiply multi-digit whole numbers using the standard algorithm. Multiply multi-digit whole numbers (not to exceed three-digit by three-digit). Estimate solutions to arithmetic problems in order to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition, subtraction, multiplication and division of multi-digit whole numbers. Use various strategies, including the inverse relationships between operations, the use of technology, and the context of the problem to assess the reasonableness of results. 3-2: Practice Buddy: Additional Practice Curriculum Standards: Fluently multiply multi-digit whole numbers using the standard algorithm. Fluently multiply multi-digit whole numbers using the standard algorithm. Fluently multiply multi-digit whole numbers using the standard algorithm. Use rounding and compatible numbers to estimate products. Fluently multiply multi-digit whole numbers using the standard algorithm. Multiply multi-digit whole numbers (not to exceed three-digit by three-digit). Estimate solutions to arithmetic problems in order to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition, subtraction, multiplication and division of multi-digit whole numbers. Use various strategies, including the inverse relationships between operations, the use of technology, and the context of the problem to assess the reasonableness of results. 3-2: Interactive Additional Practice Step 3: Assess & Differentiate 3-2: Practice Buddy: Additional Practice Curriculum Standards: Fluently multiply multi-digit whole numbers using the standard algorithm. Fluently multiply multi-digit whole numbers using the standard algorithm. Fluently multiply multi-digit whole numbers using the standard algorithm. Use rounding and compatible numbers to estimate products. Fluently multiply multi-digit whole numbers using the standard algorithm. Multiply multi-digit whole numbers (not to exceed three-digit by three-digit). Estimate solutions to arithmetic problems in order to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition, subtraction, multiplication and division of multi-digit whole numbers. Use various strategies, including the inverse relationships between operations, the use of technology, and the context of the problem to assess the reasonableness of results. 3-2: Enrichment Curriculum Standards: Fluently multiply multi-digit whole numbers using the standard algorithm. Fluently multiply multi-digit whole numbers using the standard algorithm. Fluently multiply multi-digit whole numbers using the standard algorithm. Use rounding and compatible numbers to estimate products. Fluently multiply multi-digit whole numbers using the standard algorithm. Multiply multi-digit whole numbers (not to exceed three-digit by three-digit). Estimate solutions to arithmetic problems in order to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition, subtraction, multiplication and division of multi-digit whole numbers. Use various strategies, including the inverse relationships between operations, the use of technology, and the context of the problem to assess the reasonableness of results. 3-2: Quick Check Curriculum Standards: Fluently multiply multi-digit whole numbers using the standard algorithm. Fluently multiply multi-digit whole numbers using the standard algorithm. Fluently multiply multi-digit whole numbers using the standard algorithm. Use rounding and compatible numbers to estimate products. Fluently multiply multi-digit whole numbers using the standard algorithm. Multiply multi-digit whole numbers (not to exceed three-digit by three-digit). Estimate solutions to arithmetic problems in order to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition, subtraction, multiplication and division of multi-digit whole numbers. Use various strategies, including the inverse relationships between operations, the use of technology, and the context of the problem to assess the reasonableness of results. 3-2: Lesson Self-Assessment 3-2: Reteach to Build Understanding Curriculum Standards: Fluently multiply multi-digit whole numbers using the standard algorithm. Fluently multiply multi-digit whole numbers using the standard algorithm. Fluently multiply multi-digit whole numbers using the standard algorithm. Use rounding and compatible numbers to estimate products. Fluently multiply multi-digit whole numbers using the standard algorithm. Multiply multi-digit whole numbers (not to exceed three-digit by three-digit). Estimate solutions to arithmetic problems in order to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition, subtraction, multiplication and division of multi-digit whole numbers. Use various strategies, including the inverse relationships between operations, the use of technology, and the context of the problem to assess the reasonableness of results. 3-2: Build Mathematical Literacy Curriculum Standards: Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 5 topics and texts, building on others’ ideas and expressing their own clearly. (a) Come to discussions prepared, having read or studied required material; explicitly draw on that preparation and other information known about the topic to explore ideas under discussion. (b) Follow agreed-upon rules for discussions and carry out assigned roles. (c) Pose and respond to specific questions by making comments that contribute to the discussion and elaborate on the remarks of others. (d) Review the key ideas expressed and draw conclusions in light of information and knowledge gained from the discussions. English language learners communicate for social and instructional purposes within the school setting. Summarize a written text read aloud or information presented in diverse media and formats, including visually, quantitatively, and orally. Summarize the points a speaker makes and explain how each claim is supported by reasons and evidence. Write informative/explanatory texts to examine a topic and convey ideas and information clearly. (a) Introduce a topic clearly, provide a general observation and focus, and group related information logically; include formatting (e.g., headings), illustrations, and multimedia when useful to aiding comprehension. (b) Develop the topic with facts, definitions, concrete details, quotations, or other information and examples related to the topic. (c) Link ideas within and across categories of information using words, phrases, and clauses (e.g., in contrast, especially). (d) Use precise language and domain-specific vocabulary to inform about or explain the topic. (e) Provide a concluding statement or section related to the information or explanation presented. English language learners communicate information, ideas and concepts necessary for academic success in the content area of Mathematics. 3-2: Enrichment Game: Cosmic Caravan - Arrays and Multiples of 10 3-2: Problem-Solving Reading Activity Curriculum Standards: Fluently multiply multi-digit whole numbers using the standard algorithm. Fluently multiply multi-digit whole numbers using the standard algorithm. Fluently multiply multi-digit whole numbers using the standard algorithm. Use rounding and compatible numbers to estimate products. Fluently multiply multi-digit whole numbers using the standard algorithm. Multiply multi-digit whole numbers (not to exceed three-digit by three-digit). Estimate solutions to arithmetic problems in order to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition, subtraction, multiplication and division of multi-digit whole numbers. Use various strategies, including the inverse relationships between operations, the use of technology, and the context of the problem to assess the reasonableness of results. 3-2: Another Look Curriculum Standards: Fluently multiply multi-digit whole numbers using the standard algorithm. Fluently multiply multi-digit whole numbers using the standard algorithm. Fluently multiply multi-digit whole numbers using the standard algorithm. Use rounding and compatible numbers to estimate products. Fluently multiply multi-digit whole numbers using the standard algorithm. Multiply multi-digit whole numbers (not to exceed three-digit by three-digit). Estimate solutions to arithmetic problems in order to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition, subtraction, multiplication and division of multi-digit whole numbers. Use various strategies, including the inverse relationships between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Spanish Resources 3-2: eText del Libro del estudiante 3-2: Repaso diario 3-2: Aprendizaje visual 3-2: Amigo de práctica: Práctica adicional 3-2: Práctica adicional interactiva 3-2: Refuerzo para mejorar la comprensión 3-2: Desarrollar la competencia matemática 3-2: Ampliación 3-3: Multiply by 1-Digit Numbers Interactive Student Edition: Grade 5 Lesson 3-3 Math Anytime 3-3: Daily Review Topic 3: Today's Challenge Step 1: Problem-Based Learning 3-3: Solve & Share Curriculum Standards: Fluently multiply multi-digit whole numbers using the standard algorithm. English language learners communicate for social and instructional purposes within the school setting. Write informative/explanatory texts to examine a topic and convey ideas and information clearly. (a) Introduce a topic clearly, provide a general observation and focus, and group related information logically; include formatting (e.g., headings), illustrations, and multimedia when useful to aiding comprehension. (b) Develop the topic with facts, definitions, concrete details, quotations, or other information and examples related to the topic. (c) Link ideas within and across categories of information using words, phrases, and clauses (e.g., in contrast, especially). (d) Use precise language and domain-specific vocabulary to inform about or explain the topic. (e) Provide a concluding statement or section related to the information or explanation presented. English language learners communicate information, ideas and concepts necessary for academic success in the content area of Mathematics. Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 5 topics and texts, building on others’ ideas and expressing their own clearly. (a) Come to discussions prepared, having read or studied required material; explicitly draw on that preparation and other information known about the topic to explore ideas under discussion. (b) Follow agreed-upon rules for discussions and carry out assigned roles. (c) Pose and respond to specific questions by making comments that contribute to the discussion and elaborate on the remarks of others. (d) Review the key ideas expressed and draw conclusions in light of information and knowledge gained from the discussions. Summarize a written text read aloud or information presented in diverse media and formats, including visually, quantitatively, and orally. Summarize the points a speaker makes and explain how each claim is supported by reasons and evidence. Fluently multiply multi-digit whole numbers using the standard algorithm. Fluently multiply multi-digit whole numbers using the standard algorithm. Use place-value strategies and the standard algorithm to multiply multi-digit numbers by 1-digit numbers. Fluently multiply multi-digit whole numbers using the standard algorithm. Multiply multi-digit whole numbers (not to exceed three-digit by three-digit). Estimate solutions to arithmetic problems in order to assess the reasonableness of results. Solve real- world and mathematical problems requiring addition, subtraction, multiplication and division of multi- digit whole numbers. Use various strategies, including the inverse relationships between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Step 2: Visual Learning 3-3: Visual Learning Curriculum Standards: Fluently multiply multi-digit whole numbers using the standard algorithm. Fluently multiply multi-digit whole numbers using the standard algorithm. Fluently multiply multi-digit whole numbers using the standard algorithm. Use place-value strategies and the standard algorithm to multiply multi-digit numbers by 1-digit numbers. Fluently multiply multi-digit whole numbers using the standard algorithm. Multiply multi-digit whole numbers (not to exceed three-digit by three-digit). Estimate solutions to arithmetic problems in order to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition, subtraction, multiplication and division of multi-digit whole numbers. Use various strategies, including the inverse relationships between operations, the use of technology, and the context of the problem to assess the reasonableness of results. 3-3: Convince Me! Curriculum Standards: Fluently multiply multi-digit whole numbers using the standard algorithm. Fluently multiply multi-digit whole numbers using the standard algorithm. Fluently multiply multi-digit whole numbers using the standard algorithm. Use place-value strategies and the standard algorithm to multiply multi-digit numbers by 1-digit numbers. Fluently multiply multi-digit whole numbers using the standard algorithm. Multiply multi-digit whole numbers (not to exceed three-digit by three-digit). Estimate solutions to arithmetic problems in order to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition, subtraction, multiplication and division of multi-digit whole numbers. Use various strategies, including the inverse relationships between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Practice and Problem Solving 3-3: Student Edition Practice Curriculum Standards: Fluently multiply multi-digit whole numbers using the standard algorithm. Fluently multiply multi-digit whole numbers using the standard algorithm. Fluently multiply multi-digit whole numbers using the standard algorithm. Use place-value strategies and the standard algorithm to multiply multi-digit numbers by 1-digit numbers. Fluently multiply multi-digit whole numbers using the standard algorithm. Multiply multi-digit whole numbers (not to exceed three-digit by three-digit). Estimate solutions to arithmetic problems in order to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition, subtraction, multiplication and division of multi-digit whole numbers. Use various strategies, including the inverse relationships between operations, the use of technology, and the context of the problem to assess the reasonableness of results. 3-3: Practice Buddy: Independent Practice; Problem Solving Curriculum Standards: Fluently multiply multi-digit whole numbers using the standard algorithm. Fluently multiply multi-digit whole numbers using the standard algorithm. Fluently multiply multi-digit whole numbers using the standard algorithm. Use place-value strategies and the standard algorithm to multiply multi-digit numbers by 1-digit numbers. Fluently multiply multi-digit whole numbers using the standard algorithm. Multiply multi-digit whole numbers (not to exceed three-digit by three-digit). Estimate solutions to arithmetic problems in order to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition, subtraction, multiplication and division of multi-digit whole numbers. Use various strategies, including the inverse relationships between operations, the use of technology, and the context of the problem to assess the reasonableness of results. 3-3: Practice Buddy: Additional Practice Curriculum Standards: Fluently multiply multi-digit whole numbers using the standard algorithm. Fluently multiply multi-digit whole numbers using the standard algorithm. Fluently multiply multi-digit whole numbers using the standard algorithm. Use place-value strategies and the standard algorithm to multiply multi-digit numbers by 1-digit numbers. Fluently multiply multi-digit whole numbers using the standard algorithm. Multiply multi-digit whole numbers (not to exceed three-digit by three-digit). Estimate solutions to arithmetic problems in order to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition, subtraction, multiplication and division of multi-digit whole numbers. Use various strategies, including the inverse relationships between operations, the use of technology, and the context of the problem to assess the reasonableness of results. 3-3: Interactive Additional Practice Step 3: Assess & Differentiate 3-3: Practice Buddy: Additional Practice Curriculum Standards: Fluently multiply multi-digit whole numbers using the standard algorithm. Fluently multiply multi-digit whole numbers using the standard algorithm. Fluently multiply multi-digit whole numbers using the standard algorithm. Use place-value strategies and the standard algorithm to multiply multi-digit numbers by 1-digit numbers. Fluently multiply multi-digit whole numbers using the standard algorithm. Multiply multi-digit whole numbers (not to exceed three-digit by three-digit). Estimate solutions to arithmetic problems in order to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition, subtraction, multiplication and division of multi-digit whole numbers. Use various strategies, including the inverse relationships between operations, the use of technology, and the context of the problem to assess the reasonableness of results. 3-3: Enrichment Curriculum Standards: Fluently multiply multi-digit whole numbers using the standard algorithm. Fluently multiply multi-digit whole numbers using the standard algorithm. Fluently multiply multi-digit whole numbers using the standard algorithm. Use place-value strategies and the standard algorithm to multiply multi-digit numbers by 1-digit numbers. Fluently multiply multi-digit whole numbers using the standard algorithm. Multiply multi-digit whole numbers (not to exceed three-digit by three-digit). Estimate solutions to arithmetic problems in order to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition, subtraction, multiplication and division of multi-digit whole numbers. Use various strategies, including the inverse relationships between operations, the use of technology, and the context of the problem to assess the reasonableness of results. 3-3: Quick Check Curriculum Standards: Fluently multiply multi-digit whole numbers using the standard algorithm. Fluently multiply multi-digit whole numbers using the standard algorithm. Fluently multiply multi-digit whole numbers using the standard algorithm. Use place-value strategies and the standard algorithm to multiply multi-digit numbers by 1-digit numbers. Fluently multiply multi-digit whole numbers using the standard algorithm. Multiply multi-digit whole numbers (not to exceed three-digit by three-digit). Estimate solutions to arithmetic problems in order to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition, subtraction, multiplication and division of multi-digit whole numbers. Use various strategies, including the inverse relationships between operations, the use of technology, and the context of the problem to assess the reasonableness of results. 3-3: Lesson Self-Assessment 3-3: Reteach to Build Understanding Curriculum Standards: Fluently multiply multi-digit whole numbers using the standard algorithm. Fluently multiply multi-digit whole numbers using the standard algorithm. Fluently multiply multi-digit whole numbers using the standard algorithm. Use place-value strategies and the standard algorithm to multiply multi-digit numbers by 1-digit numbers. Fluently multiply multi-digit whole numbers using the standard algorithm. Multiply multi-digit whole numbers (not to exceed three-digit by three-digit). Estimate solutions to arithmetic problems in order to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition, subtraction, multiplication and division of multi-digit whole numbers. Use various strategies, including the inverse relationships between operations, the use of technology, and the context of the problem to assess the reasonableness of results. 3-3: Build Mathematical Literacy Curriculum Standards: Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 5 topics and texts, building on others’ ideas and expressing their own clearly. (a) Come to discussions prepared, having read or studied required material; explicitly draw on that preparation and other information known about the topic to explore ideas under discussion. (b) Follow agreed-upon rules for discussions and carry out assigned roles. (c) Pose and respond to specific questions by making comments that contribute to the discussion and elaborate on the remarks of others. (d) Review the key ideas expressed and draw conclusions in light of information and knowledge gained from the discussions. English language learners communicate for social and instructional purposes within the school setting. Summarize a written text read aloud or information presented in diverse media and formats, including visually, quantitatively, and orally. Summarize the points a speaker makes and explain how each claim is supported by reasons and evidence. Write informative/explanatory texts to examine a topic and convey ideas and information clearly. (a) Introduce a topic clearly, provide a general observation and focus, and group related information logically; include formatting (e.g., headings), illustrations, and multimedia when useful to aiding comprehension. (b) Develop the topic with facts, definitions, concrete details, quotations, or other information and examples related to the topic. (c) Link ideas within and across categories of information using words, phrases, and clauses (e.g., in contrast, especially). (d) Use precise language and domain-specific vocabulary to inform about or explain the topic. (e) Provide a concluding statement or section related to the information or explanation presented. English language learners communicate information, ideas and concepts necessary for academic success in the content area of Mathematics. 3-3: Enrichment Game: Launch that Sheep - Multiply and Divide 1-Digit Numbers 3-3: Pick a Project 3-3: Another Look Curriculum Standards: Fluently multiply multi-digit whole numbers using the standard algorithm. Fluently multiply multi-digit whole numbers using the standard algorithm. Fluently multiply multi-digit whole numbers using the standard algorithm. Use place-value strategies and the standard algorithm to multiply multi-digit numbers by 1-digit numbers. Fluently multiply multi-digit whole numbers using the standard algorithm. Multiply multi-digit whole numbers (not to exceed three-digit by three-digit). Estimate solutions to arithmetic problems in order to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition, subtraction, multiplication and division of multi-digit whole numbers. Use various strategies, including the inverse relationships between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Spanish Resources 3-3: eText del Libro del estudiante 3-3: Repaso diario 3-3: Aprendizaje visual 3-3: Amigo de práctica: Práctica adicional 3-3: Práctica adicional interactiva 3-3: Refuerzo para mejorar la comprensión 3-3: Desarrollar la competencia matemática 3-3: Ampliación 3-4: Multiply 2-Digit by 2-DIgit Numbers Interactive Student Edition: Grade 5 Lesson 3-4 Math Anytime 3-4: Daily Review Topic 3: Today's Challenge Step 1: Problem-Based Learning 3-4: Solve & Share Curriculum Standards: Fluently multiply multi-digit whole numbers using the standard algorithm. English language learners communicate for social and instructional purposes within the school setting. Write informative/explanatory texts to examine a topic and convey ideas and information clearly. (a) Introduce a topic clearly, provide a general observation and focus, and group related information logically; include formatting (e.g., headings), illustrations, and multimedia when useful to aiding comprehension. (b) Develop the topic with facts, definitions, concrete details, quotations, or other information and examples related to the topic. (c) Link ideas within and across categories of information using words, phrases, and clauses (e.g., in contrast, especially). (d) Use precise language and domain-specific vocabulary to inform about or explain the topic. (e) Provide a concluding statement or section related to the information or explanation presented. English language learners communicate information, ideas and concepts necessary for academic success in the content area of Mathematics. Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 5 topics and texts, building on others’ ideas and expressing their own clearly. (a) Come to discussions prepared, having read or studied required material; explicitly draw on that preparation and other information known about the topic to explore ideas under discussion. (b) Follow agreed-upon rules for discussions and carry out assigned roles. (c) Pose and respond to specific questions by making comments that contribute to the discussion and elaborate on the remarks of others. (d) Review the key ideas expressed and draw conclusions in light of information and knowledge gained from the discussions. Summarize a written text read aloud or information presented in diverse media and formats, including visually, quantitatively, and orally. Summarize the points a speaker makes and explain how each claim is supported by reasons and evidence. Fluently multiply multi-digit whole numbers using the standard algorithm. Fluently multiply multi-digit whole numbers using the standard algorithm. Use the expanded and the standard algorithm to multiply 2-digit by 2-digit numbers. Estimate to check if products are reasonable. Fluently multiply multi-digit whole numbers using the standard algorithm. Multiply multi-digit whole numbers (not to exceed three-digit by three-digit). Estimate solutions to arithmetic problems in order to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition, subtraction, multiplication and division of multi-digit whole numbers. Use various strategies, including the inverse relationships between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Step 2: Visual Learning 3-4: Visual Learning Curriculum Standards: Fluently multiply multi-digit whole numbers using the standard algorithm. Fluently multiply multi-digit whole numbers using the standard algorithm. Fluently multiply multi-digit whole numbers using the standard algorithm. Use the expanded and the standard algorithm to multiply 2-digit by 2-digit numbers. Estimate to check if products are reasonable. Fluently multiply multi-digit whole numbers using the standard algorithm. Multiply multi-digit whole numbers (not to exceed three-digit by three-digit). Estimate solutions to arithmetic problems in order to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition, subtraction, multiplication and division of multi-digit whole numbers. Use various strategies, including the inverse relationships between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Fluently multiply two-digit numbers. 3-4: Convince Me! Curriculum Standards: Fluently multiply multi-digit whole numbers using the standard algorithm. Fluently multiply multi-digit whole numbers using the standard algorithm. Fluently multiply multi-digit whole numbers using the standard algorithm. Use the expanded and the standard algorithm to multiply 2-digit by 2-digit numbers. Estimate to check if products are reasonable. Fluently multiply multi-digit whole numbers using the standard algorithm. Multiply multi-digit whole numbers (not to exceed three-digit by three-digit). Estimate solutions to arithmetic problems in order to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition, subtraction, multiplication and division of multi-digit whole numbers. Use various strategies, including the inverse relationships between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Practice and Problem Solving 3-4: Student Edition Practice Curriculum Standards: Fluently multiply multi-digit whole numbers using the standard algorithm. Fluently multiply multi-digit whole numbers using the standard algorithm. Fluently multiply multi-digit whole numbers using the standard algorithm. Use the expanded and the standard algorithm to multiply 2-digit by 2-digit numbers. Estimate to check if products are reasonable. Fluently multiply multi-digit whole numbers using the standard algorithm. Multiply multi-digit whole numbers (not to exceed three-digit by three-digit). Estimate solutions to arithmetic problems in order to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition, subtraction, multiplication and division of multi-digit whole numbers. Use various strategies, including the inverse relationships between operations, the use of technology, and the context of the problem to assess the reasonableness of results. 3-4: Practice Buddy: Independent Practice; Problem Solving Curriculum Standards: Fluently multiply multi-digit whole numbers using the standard algorithm. Fluently multiply multi-digit whole numbers using the standard algorithm. Fluently multiply multi-digit whole numbers using the standard algorithm. Use the expanded and the standard algorithm to multiply 2-digit by 2-digit numbers. Estimate to check if products are reasonable. Fluently multiply multi-digit whole numbers using the standard algorithm. Multiply multi-digit whole numbers (not to exceed three-digit by three-digit). Estimate solutions to arithmetic problems in order to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition, subtraction, multiplication and division of multi-digit whole numbers. Use various strategies, including the inverse relationships between operations, the use of technology, and the context of the problem to assess the reasonableness of results. 3-4: Practice Buddy: Additional Practice Curriculum Standards: Fluently multiply multi-digit whole numbers using the standard algorithm. Fluently multiply multi-digit whole numbers using the standard algorithm. Fluently multiply multi-digit whole numbers using the standard algorithm. Use the expanded and the standard algorithm to multiply 2-digit by 2-digit numbers. Estimate to check if products are reasonable. Fluently multiply multi-digit whole numbers using the standard algorithm. Multiply multi-digit whole numbers (not to exceed three-digit by three-digit). Estimate solutions to arithmetic problems in order to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition, subtraction, multiplication and division of multi-digit whole numbers. Use various strategies, including the inverse relationships between operations, the use of technology, and the context of the problem to assess the reasonableness of results. 3-4: Interactive Additional Practice Step 3: Assess & Differentiate 3-4: Practice Buddy: Additional Practice Curriculum Standards: Fluently multiply multi-digit whole numbers using the standard algorithm. Fluently multiply multi-digit whole numbers using the standard algorithm. Fluently multiply multi-digit whole numbers using the standard algorithm. Use the expanded and the standard algorithm to multiply 2-digit by 2-digit numbers. Estimate to check if products are reasonable. Fluently multiply multi-digit whole numbers using the standard algorithm. Multiply multi-digit whole numbers (not to exceed three-digit by three-digit). Estimate solutions to arithmetic problems in order to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition, subtraction, multiplication and division of multi-digit whole numbers. Use various strategies, including the inverse relationships between operations, the use of technology, and the context of the problem to assess the reasonableness of results. 3-4: Enrichment Curriculum Standards: Fluently multiply multi-digit whole numbers using the standard algorithm. Fluently multiply multi-digit whole numbers using the standard algorithm. Fluently multiply multi-digit whole numbers using the standard algorithm. Use the expanded and the standard algorithm to multiply 2-digit by 2-digit numbers. Estimate to check if products are reasonable. Fluently multiply multi-digit whole numbers using the standard algorithm. Multiply multi-digit whole numbers (not to exceed three-digit by three-digit). Estimate solutions to arithmetic problems in order to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition, subtraction, multiplication and division of multi-digit whole numbers. Use various strategies, including the inverse relationships between operations, the use of technology, and the context of the problem to assess the reasonableness of results. 3-4: Quick Check Curriculum Standards: Fluently multiply multi-digit whole numbers using the standard algorithm. Fluently multiply multi-digit whole numbers using the standard algorithm. Fluently multiply multi-digit whole numbers using the standard algorithm. Use the expanded and the standard algorithm to multiply 2-digit by 2-digit numbers. Estimate to check if products are reasonable. Fluently multiply multi-digit whole numbers using the standard algorithm. Multiply multi-digit whole numbers (not to exceed three-digit by three-digit). Estimate solutions to arithmetic problems in order to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition, subtraction, multiplication and division of multi-digit whole numbers. Use various strategies, including the inverse relationships between operations, the use of technology, and the context of the problem to assess the reasonableness of results. 3-4: Lesson Self-Assessment 3-4: Reteach to Build Understanding Curriculum Standards: Fluently multiply multi-digit whole numbers using the standard algorithm. Fluently multiply multi-digit whole numbers using the standard algorithm. Fluently multiply multi-digit whole numbers using the standard algorithm. Use the expanded and the standard algorithm to multiply 2-digit by 2-digit numbers. Estimate to check if products are reasonable. Fluently multiply multi-digit whole numbers using the standard algorithm. Multiply multi-digit whole numbers (not to exceed three-digit by three-digit). Estimate solutions to arithmetic problems in order to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition, subtraction, multiplication and division of multi-digit whole numbers. Use various strategies, including the inverse relationships between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Fluently multiply two-digit numbers. 3-4: Build Mathematical Literacy Curriculum Standards: Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 5 topics and texts, building on others’ ideas and expressing their own clearly. (a) Come to discussions prepared, having read or studied required material; explicitly draw on that preparation and other information known about the topic to explore ideas under discussion. (b) Follow agreed-upon rules for discussions and carry out assigned roles. (c) Pose and respond to specific questions by making comments that contribute to the discussion and elaborate on the remarks of others. (d) Review the key ideas expressed and draw conclusions in light of information and knowledge gained from the discussions. English language learners communicate for social and instructional purposes within the school setting. Summarize a written text read aloud or information presented in diverse media and formats, including visually, quantitatively, and orally. Summarize the points a speaker makes and explain how each claim is supported by reasons and evidence. Write informative/explanatory texts to examine a topic and convey ideas and information clearly. (a) Introduce a topic clearly, provide a general observation and focus, and group related information logically; include formatting (e.g., headings), illustrations, and multimedia when useful to aiding comprehension. (b) Develop the topic with facts, definitions, concrete details, quotations, or other information and examples related to the topic. (c) Link ideas within and across categories of information using words, phrases, and clauses (e.g., in contrast, especially). (d) Use precise language and domain-specific vocabulary to inform about or explain the topic. (e) Provide a concluding statement or section related to the information or explanation presented. English language learners communicate information, ideas and concepts necessary for academic success in the content area of Mathematics. 3-4: Enrichment Game: Multo - 2-Digit Numbers 3-4: Pick a Project 3-4: Another Look Curriculum Standards: Fluently multiply multi-digit whole numbers using the standard algorithm. Fluently multiply multi-digit whole numbers using the standard algorithm. Fluently multiply multi-digit whole numbers using the standard algorithm. Use the expanded and the standard algorithm to multiply 2-digit by 2-digit numbers. Estimate to check if products are reasonable. Fluently multiply multi-digit whole numbers using the standard algorithm. Multiply multi-digit whole numbers (not to exceed three-digit by three-digit). Estimate solutions to arithmetic problems in order to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition, subtraction, multiplication and division of multi-digit whole numbers. Use various strategies, including the inverse relationships between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Fluently multiply two-digit numbers. Spanish Resources 3-4: eText del Libro del estudiante 3-4: Repaso diario 3-4: Aprendizaje visual 3-4: Amigo de práctica: Práctica adicional 3-4: Práctica adicional interactiva 3-4: Refuerzo para mejorar la comprensión 3-4: Desarrollar la competencia matemática 3-4: Ampliación 3-5: Multiply 3-Digit by 2-Digit Numbers Interactive Student Edition: Grade 5 Lesson 3-5 Math Anytime 3-5: Daily Review Topic 3: Today's Challenge Step 1: Problem-Based Learning 3-5: Solve & Share Curriculum Standards: Fluently multiply multi-digit whole numbers using the standard algorithm. English language learners communicate for social and instructional purposes within the school setting. Fluently multiply multi-digit whole numbers using the standard algorithm. Fluently multiply multi-digit whole numbers using the standard algorithm. Multiply 3-digit by 2-digit numbers by adding partial products or by using the standard algorithm. Fluently multiply multi-digit whole numbers using the standard algorithm. Multiply multi-digit whole numbers (not to exceed three-digit by three- digit). Estimate solutions to arithmetic problems in order to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition, subtraction, multiplication and division of multi-digit whole numbers. Use various strategies, including the inverse relationships between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Write informative/explanatory texts to examine a topic and convey ideas and information clearly. (a) Introduce a topic clearly, provide a general observation and focus, and group related information logically; include formatting (e.g., headings), illustrations, and multimedia when useful to aiding comprehension. (b) Develop the topic with facts, definitions, concrete details, quotations, or other information and examples related to the topic. (c) Link ideas within and across categories of information using words, phrases, and clauses (e.g., in contrast, especially). (d) Use precise language and domain-specific vocabulary to inform about or explain the topic. (e) Provide a concluding statement or section related to the information or explanation presented. English language learners communicate information, ideas and concepts necessary for academic success in the content area of Mathematics. Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 5 topics and texts, building on others’ ideas and expressing their own clearly. (a) Come to discussions prepared, having read or studied required material; explicitly draw on that preparation and other information known about the topic to explore ideas under discussion. (b) Follow agreed-upon rules for discussions and carry out assigned roles. (c) Pose and respond to specific questions by making comments that contribute to the discussion and elaborate on the remarks of others. (d) Review the key ideas expressed and draw conclusions in light of information and knowledge gained from the discussions. Summarize a written text read aloud or information presented in diverse media and formats, including visually, quantitatively, and orally. Summarize the points a speaker makes and explain how each claim is supported by reasons and evidence. Step 2: Visual Learning 3-5: Visual Learning Curriculum Standards: Fluently multiply multi-digit whole numbers using the standard algorithm. Fluently multiply multi-digit whole numbers using the standard algorithm. Fluently multiply multi-digit whole numbers using the standard algorithm. Multiply 3-digit by 2-digit numbers by adding partial products or by using the standard algorithm. Fluently multiply multi-digit whole numbers using the standard algorithm. Multiply multi-digit whole numbers (not to exceed three-digit by three-digit). Estimate solutions to arithmetic problems in order to assess the reasonableness of results. Solve real- world and mathematical problems requiring addition, subtraction, multiplication and division of multi- digit whole numbers. Use various strategies, including the inverse relationships between operations, the use of technology, and the context of the problem to assess the reasonableness of results. 3-5: Convince Me! Curriculum Standards: Fluently multiply multi-digit whole numbers using the standard algorithm. Fluently multiply multi-digit whole numbers using the standard algorithm. Fluently multiply multi-digit whole numbers using the standard algorithm. Multiply 3-digit by 2-digit numbers by adding partial products or by using the standard algorithm. Fluently multiply multi-digit whole numbers using the standard algorithm. Multiply multi-digit whole numbers (not to exceed three-digit by three-digit). Estimate solutions to arithmetic problems in order to assess the reasonableness of results. Solve real- world and mathematical problems requiring addition, subtraction, multiplication and division of multi- digit whole numbers. Use various strategies, including the inverse relationships between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Practice and Problem Solving 3-5: Student Edition Practice Curriculum Standards: Fluently multiply multi-digit whole numbers using the standard algorithm. Fluently multiply multi-digit whole numbers using the standard algorithm. Fluently multiply multi-digit whole numbers using the standard algorithm. Multiply 3-digit by 2-digit numbers by adding partial products or by using the standard algorithm. Fluently multiply multi-digit whole numbers using the standard algorithm. Multiply multi-digit whole numbers (not to exceed three-digit by three-digit). Estimate solutions to arithmetic problems in order to assess the reasonableness of results. Solve real- world and mathematical problems requiring addition, subtraction, multiplication and division of multi- digit whole numbers. Use various strategies, including the inverse relationships between operations, the use of technology, and the context of the problem to assess the reasonableness of results. 3-5: Practice Buddy: Independent Practice; Problem Solving Curriculum Standards: Fluently multiply multi-digit whole numbers using the standard algorithm. Fluently multiply multi-digit whole numbers using the standard algorithm. Fluently multiply multi-digit whole numbers using the standard algorithm. Multiply 3-digit by 2-digit numbers by adding partial products or by using the standard algorithm. Fluently multiply multi-digit whole numbers using the standard algorithm. Multiply multi-digit whole numbers (not to exceed three-digit by three-digit). Estimate solutions to arithmetic problems in order to assess the reasonableness of results. Solve real- world and mathematical problems requiring addition, subtraction, multiplication and division of multi- digit whole numbers. Use various strategies, including the inverse relationships between operations, the use of technology, and the context of the problem to assess the reasonableness of results. 3-5: Practice Buddy: Additional Practice Curriculum Standards: Fluently multiply multi-digit whole numbers using the standard algorithm. Fluently multiply multi-digit whole numbers using the standard algorithm. Fluently multiply multi-digit whole numbers using the standard algorithm. Multiply 3-digit by 2-digit numbers by adding partial products or by using the standard algorithm. Fluently multiply multi-digit whole numbers using the standard algorithm. Multiply multi-digit whole numbers (not to exceed three-digit by three-digit). Estimate solutions to arithmetic problems in order to assess the reasonableness of results. Solve real- world and mathematical problems requiring addition, subtraction, multiplication and division of multi- digit whole numbers. Use various strategies, including the inverse relationships between operations, the use of technology, and the context of the problem to assess the reasonableness of results. 3-5: Interactive Additional Practice Step 3: Assess & Differentiate 3-5: Practice Buddy: Additional Practice Curriculum Standards: Fluently multiply multi-digit whole numbers using the standard algorithm. Fluently multiply multi-digit whole numbers using the standard algorithm. Fluently multiply multi-digit whole numbers using the standard algorithm. Multiply 3-digit by 2-digit numbers by adding partial products or by using the standard algorithm. Fluently multiply multi-digit whole numbers using the standard algorithm. Multiply multi-digit whole numbers (not to exceed three-digit by three-digit). Estimate solutions to arithmetic problems in order to assess the reasonableness of results. Solve real- world and mathematical problems requiring addition, subtraction, multiplication and division of multi- digit whole numbers. Use various strategies, including the inverse relationships between operations, the use of technology, and the context of the problem to assess the reasonableness of results. 3-5: Enrichment Curriculum Standards: Fluently multiply multi-digit whole numbers using the standard algorithm. Fluently multiply multi-digit whole numbers using the standard algorithm. Fluently multiply multi-digit whole numbers using the standard algorithm. Multiply 3-digit by 2-digit numbers by adding partial products or by using the standard algorithm. Fluently multiply multi-digit whole numbers using the standard algorithm. Multiply multi-digit whole numbers (not to exceed three-digit by three-digit). Estimate solutions to arithmetic problems in order to assess the reasonableness of results. Solve real- world and mathematical problems requiring addition, subtraction, multiplication and division of multi- digit whole numbers. Use various strategies, including the inverse relationships between operations, the use of technology, and the context of the problem to assess the reasonableness of results. 3-5: Quick Check Curriculum Standards: Fluently multiply multi-digit whole numbers using the standard algorithm. Fluently multiply multi-digit whole numbers using the standard algorithm. Fluently multiply multi-digit whole numbers using the standard algorithm. Multiply 3-digit by 2-digit numbers by adding partial products or by using the standard algorithm. Fluently multiply multi-digit whole numbers using the standard algorithm. Multiply multi-digit whole numbers (not to exceed three-digit by three-digit). Estimate solutions to arithmetic problems in order to assess the reasonableness of results. Solve real- world and mathematical problems requiring addition, subtraction, multiplication and division of multi- digit whole numbers. Use various strategies, including the inverse relationships between operations, the use of technology, and the context of the problem to assess the reasonableness of results. 3-5: Lesson Self-Assessment 3-5: Reteach to Build Understanding Curriculum Standards: Fluently multiply multi-digit whole numbers using the standard algorithm. Fluently multiply multi-digit whole numbers using the standard algorithm. Fluently multiply multi-digit whole numbers using the standard algorithm. Multiply 3-digit by 2-digit numbers by adding partial products or by using the standard algorithm. Fluently multiply multi-digit whole numbers using the standard algorithm. Multiply multi-digit whole numbers (not to exceed three-digit by three-digit). Estimate solutions to arithmetic problems in order to assess the reasonableness of results. Solve real- world and mathematical problems requiring addition, subtraction, multiplication and division of multi- digit whole numbers. Use various strategies, including the inverse relationships between operations, the use of technology, and the context of the problem to assess the reasonableness of results. 3-5: Build Mathematical Literacy Curriculum Standards: Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 5 topics and texts, building on others’ ideas and expressing their own clearly. (a) Come to discussions prepared, having read or studied required material; explicitly draw on that preparation and other information known about the topic to explore ideas under discussion. (b) Follow agreed-upon rules for discussions and carry out assigned roles. (c) Pose and respond to specific questions by making comments that contribute to the discussion and elaborate on the remarks of others. (d) Review the key ideas expressed and draw conclusions in light of information and knowledge gained from the discussions. English language learners communicate for social and instructional purposes within the school setting. Summarize a written text read aloud or information presented in diverse media and formats, including visually, quantitatively, and orally. Summarize the points a speaker makes and explain how each claim is supported by reasons and evidence. Write informative/explanatory texts to examine a topic and convey ideas and information clearly. (a) Introduce a topic clearly, provide a general observation and focus, and group related information logically; include formatting (e.g., headings), illustrations, and multimedia when useful to aiding comprehension. (b) Develop the topic with facts, definitions, concrete details, quotations, or other information and examples related to the topic. (c) Link ideas within and across categories of information using words, phrases, and clauses (e.g., in contrast, especially). (d) Use precise language and domain-specific vocabulary to inform about or explain the topic. (e) Provide a concluding statement or section related to the information or explanation presented. English language learners communicate information, ideas and concepts necessary for academic success in the content area of Mathematics. 3-5: Enrichment Game: Multo - 2-Digit Numbers 3-5: Pick a Project 3-5: Another Look Curriculum Standards: Fluently multiply multi-digit whole numbers using the standard algorithm. Fluently multiply multi-digit whole numbers using the standard algorithm. Fluently multiply multi-digit whole numbers using the standard algorithm. Multiply 3-digit by 2-digit numbers by adding partial products or by using the standard algorithm. Fluently multiply multi-digit whole numbers using the standard algorithm. Multiply multi-digit whole numbers (not to exceed three-digit by three-digit). Estimate solutions to arithmetic problems in order to assess the reasonableness of results. Solve real- world and mathematical problems requiring addition, subtraction, multiplication and division of multi- digit whole numbers. Use various strategies, including the inverse relationships between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Spanish Resources 3-5: eText del Libro del estudiante 3-5: Repaso diario 3-5: Aprendizaje visual 3-5: Amigo de práctica: Práctica adicional 3-5: Práctica adicional interactiva 3-5: Refuerzo para mejorar la comprensión 3-5: Desarrollar la competencia matemática 3-5: Ampliación Topic 3: 3-Act Math: Morning Commute Interactive Student Edition: Grade 5, Topic 3: 3-Act Math Mathematical Modeling Topic 3: 3-Act Math: Morning Commute, Act 1 Topic 3: 3-Act Math: Morning Commute, Act 2 Topic 3: 3-Act Math: Morning Commute, Act 3 Topic 3: 3-Act Math: Morning Commute, Sequel 3-6: Multiply Whole Numbers with Zeros Interactive Student Edition: Grade 5 Lesson 3-6 Math Anytime 3-6: Daily Review Topic 3: Today's Challenge Step 1: Problem-Based Learning 3-6: Solve & Share Curriculum Standards: Fluently multiply multi-digit whole numbers using the standard algorithm. English language learners communicate for social and instructional purposes within the school setting. Fluently multiply multi-digit whole numbers using the standard algorithm. Fluently multiply multi-digit whole numbers using the standard algorithm. Use knowledge about place value and multiplying with 2-digit and 3-digit numbers to multiply with zeros. Fluently multiply multi-digit whole numbers using the standard algorithm. Multiply multi-digit whole numbers (not to exceed three-digit by three-digit). Estimate solutions to arithmetic problems in order to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition, subtraction, multiplication and division of multi-digit whole numbers. Use various strategies, including the inverse relationships between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Write informative/explanatory texts to examine a topic and convey ideas and information clearly. (a) Introduce a topic clearly, provide a general observation and focus, and group related information logically; include formatting (e.g., headings), illustrations, and multimedia when useful to aiding comprehension. (b) Develop the topic with facts, definitions, concrete details, quotations, or other information and examples related to the topic. (c) Link ideas within and across categories of information using words, phrases, and clauses (e.g., in contrast, especially). (d) Use precise language and domain-specific vocabulary to inform about or explain the topic. (e) Provide a concluding statement or section related to the information or explanation presented. English language learners communicate information, ideas and concepts necessary for academic success in the content area of Mathematics. Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 5 topics and texts, building on others’ ideas and expressing their own clearly. (a) Come to discussions prepared, having read or studied required material; explicitly draw on that preparation and other information known about the topic to explore ideas under discussion. (b) Follow agreed-upon rules for discussions and carry out assigned roles. (c) Pose and respond to specific questions by making comments that contribute to the discussion and elaborate on the remarks of others. (d) Review the key ideas expressed and draw conclusions in light of information and knowledge gained from the discussions. Summarize a written text read aloud or information presented in diverse media and formats, including visually, quantitatively, and orally. Summarize the points a speaker makes and explain how each claim is supported by reasons and evidence. Step 2: Visual Learning 3-6: Visual Learning Curriculum Standards: Fluently multiply multi-digit whole numbers using the standard algorithm. Fluently multiply multi-digit whole numbers using the standard algorithm. Fluently multiply multi-digit whole numbers using the standard algorithm. Use knowledge about place value and multiplying with 2-digit and 3-digit numbers to multiply with zeros. Fluently multiply multi-digit whole numbers using the standard algorithm. Multiply multi-digit whole numbers (not to exceed three-digit by three-digit). Estimate solutions to arithmetic problems in order to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition, subtraction, multiplication and division of multi-digit whole numbers. Use various strategies, including the inverse relationships between operations, the use of technology, and the context of the problem to assess the reasonableness of results. 3-6: Convince Me! Curriculum Standards: Fluently multiply multi-digit whole numbers using the standard algorithm. Fluently multiply multi-digit whole numbers using the standard algorithm. Fluently multiply multi-digit whole numbers using the standard algorithm. Use knowledge about place value and multiplying with 2-digit and 3-digit numbers to multiply with zeros. Fluently multiply multi-digit whole numbers using the standard algorithm. Multiply multi-digit whole numbers (not to exceed three-digit by three-digit). Estimate solutions to arithmetic problems in order to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition, subtraction, multiplication and division of multi-digit whole numbers. Use various strategies, including the inverse relationships between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Practice and Problem Solving 3-6: Student Edition Practice Curriculum Standards: Fluently multiply multi-digit whole numbers using the standard algorithm. Fluently multiply multi-digit whole numbers using the standard algorithm. Fluently multiply multi-digit whole numbers using the standard algorithm. Use knowledge about place value and multiplying with 2-digit and 3-digit numbers to multiply with zeros. Fluently multiply multi-digit whole numbers using the standard algorithm. Multiply multi-digit whole numbers (not to exceed three-digit by three-digit). Estimate solutions to arithmetic problems in order to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition, subtraction, multiplication and division of multi-digit whole numbers. Use various strategies, including the inverse relationships between operations, the use of technology, and the context of the problem to assess the reasonableness of results. 3-6: Practice Buddy: Independent Practice; Problem Solving Curriculum Standards: Fluently multiply multi-digit whole numbers using the standard algorithm. Fluently multiply multi-digit whole numbers using the standard algorithm. Fluently multiply multi-digit whole numbers using the standard algorithm. Use knowledge about place value and multiplying with 2-digit and 3-digit numbers to multiply with zeros. Fluently multiply multi-digit whole numbers using the standard algorithm. Multiply multi-digit whole numbers (not to exceed three-digit by three-digit). Estimate solutions to arithmetic problems in order to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition, subtraction, multiplication and division of multi-digit whole numbers. Use various strategies, including the inverse relationships between operations, the use of technology, and the context of the problem to assess the reasonableness of results. 3-6: Practice Buddy: Additional Practice Curriculum Standards: Fluently multiply multi-digit whole numbers using the standard algorithm. Fluently multiply multi-digit whole numbers using the standard algorithm. Fluently multiply multi-digit whole numbers using the standard algorithm. Use knowledge about place value and multiplying with 2-digit and 3-digit numbers to multiply with zeros. Fluently multiply multi-digit whole numbers using the standard algorithm. Multiply multi-digit whole numbers (not to exceed three-digit by three-digit). Estimate solutions to arithmetic problems in order to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition, subtraction, multiplication and division of multi-digit whole numbers. Use various strategies, including the inverse relationships between operations, the use of technology, and the context of the problem to assess the reasonableness of results. 3-6: Interactive Additional Practice Step 3: Assess & Differentiate 3-6: Practice Buddy: Additional Practice Curriculum Standards: Fluently multiply multi-digit whole numbers using the standard algorithm. Fluently multiply multi-digit whole numbers using the standard algorithm. Fluently multiply multi-digit whole numbers using the standard algorithm. Use knowledge about place value and multiplying with 2-digit and 3-digit numbers to multiply with zeros. Fluently multiply multi-digit whole numbers using the standard algorithm. Multiply multi-digit whole numbers (not to exceed three-digit by three-digit). Estimate solutions to arithmetic problems in order to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition, subtraction, multiplication and division of multi-digit whole numbers. Use various strategies, including the inverse relationships between operations, the use of technology, and the context of the problem to assess the reasonableness of results. 3-6: Enrichment Curriculum Standards: Fluently multiply multi-digit whole numbers using the standard algorithm. Fluently multiply multi-digit whole numbers using the standard algorithm. Fluently multiply multi-digit whole numbers using the standard algorithm. Use knowledge about place value and multiplying with 2-digit and 3-digit numbers to multiply with zeros. Fluently multiply multi-digit whole numbers using the standard algorithm. Multiply multi-digit whole numbers (not to exceed three-digit by three-digit). Estimate solutions to arithmetic problems in order to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition, subtraction, multiplication and division of multi-digit whole numbers. Use various strategies, including the inverse relationships between operations, the use of technology, and the context of the problem to assess the reasonableness of results. 3-6: Quick Check Curriculum Standards: Fluently multiply multi-digit whole numbers using the standard algorithm. Fluently multiply multi-digit whole numbers using the standard algorithm. Fluently multiply multi-digit whole numbers using the standard algorithm. Use knowledge about place value and multiplying with 2-digit and 3-digit numbers to multiply with zeros. Fluently multiply multi-digit whole numbers using the standard algorithm. Multiply multi-digit whole numbers (not to exceed three-digit by three-digit). Estimate solutions to arithmetic problems in order to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition, subtraction, multiplication and division of multi-digit whole numbers. Use various strategies, including the inverse relationships between operations, the use of technology, and the context of the problem to assess the reasonableness of results. 3-6: Lesson Self-Assessment 3-6: Reteach to Build Understanding Curriculum Standards: Fluently multiply multi-digit whole numbers using the standard algorithm. Fluently multiply multi-digit whole numbers using the standard algorithm. Fluently multiply multi-digit whole numbers using the standard algorithm. Use knowledge about place value and multiplying with 2-digit and 3-digit numbers to multiply with zeros. Fluently multiply multi-digit whole numbers using the standard algorithm. Multiply multi-digit whole numbers (not to exceed three-digit by three-digit). Estimate solutions to arithmetic problems in order to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition, subtraction, multiplication and division of multi-digit whole numbers. Use various strategies, including the inverse relationships between operations, the use of technology, and the context of the problem to assess the reasonableness of results. 3-6: Build Mathematical Literacy Curriculum Standards: Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 5 topics and texts, building on others’ ideas and expressing their own clearly. (a) Come to discussions prepared, having read or studied required material; explicitly draw on that preparation and other information known about the topic to explore ideas under discussion. (b) Follow agreed-upon rules for discussions and carry out assigned roles. (c) Pose and respond to specific questions by making comments that contribute to the discussion and elaborate on the remarks of others. (d) Review the key ideas expressed and draw conclusions in light of information and knowledge gained from the discussions. English language learners communicate for social and instructional purposes within the school setting. Summarize a written text read aloud or information presented in diverse media and formats, including visually, quantitatively, and orally. Summarize the points a speaker makes and explain how each claim is supported by reasons and evidence. Write informative/explanatory texts to examine a topic and convey ideas and information clearly. (a) Introduce a topic clearly, provide a general observation and focus, and group related information logically; include formatting (e.g., headings), illustrations, and multimedia when useful to aiding comprehension. (b) Develop the topic with facts, definitions, concrete details, quotations, or other information and examples related to the topic. (c) Link ideas within and across categories of information using words, phrases, and clauses (e.g., in contrast, especially). (d) Use precise language and domain-specific vocabulary to inform about or explain the topic. (e) Provide a concluding statement or section related to the information or explanation presented. English language learners communicate information, ideas and concepts necessary for academic success in the content area of Mathematics. 3-6: Enrichment Game: Multo - 2-Digit Numbers 3-6: Problem-Solving Reading Activity Curriculum Standards: Fluently multiply multi-digit whole numbers using the standard algorithm. Fluently multiply multi-digit whole numbers using the standard algorithm. Fluently multiply multi-digit whole numbers using the standard algorithm. Use knowledge about place value and multiplying with 2-digit and 3-digit numbers to multiply with zeros. Fluently multiply multi-digit whole numbers using the standard algorithm. Multiply multi-digit whole numbers (not to exceed three-digit by three-digit). Estimate solutions to arithmetic problems in order to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition, subtraction, multiplication and division of multi-digit whole numbers. Use various strategies, including the inverse relationships between operations, the use of technology, and the context of the problem to assess the reasonableness of results. 3-6: Another Look Curriculum Standards: Fluently multiply multi-digit whole numbers using the standard algorithm. Fluently multiply multi-digit whole numbers using the standard algorithm. Fluently multiply multi-digit whole numbers using the standard algorithm. Use knowledge about place value and multiplying with 2-digit and 3-digit numbers to multiply with zeros. Fluently multiply multi-digit whole numbers using the standard algorithm. Multiply multi-digit whole numbers (not to exceed three-digit by three-digit). Estimate solutions to arithmetic problems in order to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition, subtraction, multiplication and division of multi-digit whole numbers. Use various strategies, including the inverse relationships between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Spanish Resources 3-6: eText del Libro del estudiante 3-6: Repaso diario 3-6: Aprendizaje visual 3-6: Amigo de práctica: Práctica adicional 3-6: Práctica adicional interactiva 3-6: Refuerzo para mejorar la comprensión 3-6: Desarrollar la competencia matemática 3-6: Ampliación 3-7: Practice Multiplying Multi-Digit Numbers Interactive Student Edition: Grade 5 Lesson 3-7 Math Anytime 3-7: Daily Review Topic 3: Today's Challenge Step 1: Problem-Based Learning 3-7: Solve & Share Curriculum Standards: Fluently multiply multi-digit whole numbers using the standard algorithm. Fluently multiply multi-digit whole numbers using the standard algorithm. Fluently multiply multi-digit whole numbers using the standard algorithm. Use properties and the standard algorithm for multiplication to find the product of multi-digit numbers. Fluently multiply multi-digit whole numbers using the standard algorithm. Multiply multi-digit whole numbers (not to exceed three-digit by three- digit). Estimate solutions to arithmetic problems in order to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition, subtraction, multiplication and division of multi-digit whole numbers. Use various strategies, including the inverse relationships between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Apply the commutative, associative and distributive properties and order of operations to generate equivalent numerical expressions and to solve problems involving whole numbers. English language learners communicate for social and instructional purposes within the school setting. Write informative/explanatory texts to examine a topic and convey ideas and information clearly. (a) Introduce a topic clearly, provide a general observation and focus, and group related information logically; include formatting (e.g., headings), illustrations, and multimedia when useful to aiding comprehension. (b) Develop the topic with facts, definitions, concrete details, quotations, or other information and examples related to the topic. (c) Link ideas within and across categories of information using words, phrases, and clauses (e.g., in contrast, especially). (d) Use precise language and domain- specific vocabulary to inform about or explain the topic. (e) Provide a concluding statement or section related to the information or explanation presented. English language learners communicate information, ideas and concepts necessary for academic success in the content area of Mathematics. Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 5 topics and texts, building on others’ ideas and expressing their own clearly. (a) Come to discussions prepared, having read or studied required material; explicitly draw on that preparation and other information known about the topic to explore ideas under discussion. (b) Follow agreed-upon rules for discussions and carry out assigned roles. (c) Pose and respond to specific questions by making comments that contribute to the discussion and elaborate on the remarks of others. (d) Review the key ideas expressed and draw conclusions in light of information and knowledge gained from the discussions. Summarize a written text read aloud or information presented in diverse media and formats, including visually, quantitatively, and orally. Summarize the points a speaker makes and explain how each claim is supported by reasons and evidence. Step 2: Visual Learning 3-7: Visual Learning Curriculum Standards: Fluently multiply multi-digit whole numbers using the standard algorithm. Fluently multiply multi-digit whole numbers using the standard algorithm. Fluently multiply multi-digit whole numbers using the standard algorithm. Use properties and the standard algorithm for multiplication to find the product of multi-digit numbers. Fluently multiply multi-digit whole numbers using the standard algorithm. Multiply multi-digit whole numbers (not to exceed three-digit by three- digit). Estimate solutions to arithmetic problems in order to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition, subtraction, multiplication and division of multi-digit whole numbers. Use various strategies, including the inverse relationships between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Apply the commutative, associative and distributive properties and order of operations to generate equivalent numerical expressions and to solve problems involving whole numbers. 3-7: Convince Me! Curriculum Standards: Fluently multiply multi-digit whole numbers using the standard algorithm. Fluently multiply multi-digit whole numbers using the standard algorithm. Fluently multiply multi-digit whole numbers using the standard algorithm. Use properties and the standard algorithm for multiplication to find the product of multi-digit numbers. Fluently multiply multi-digit whole numbers using the standard algorithm. Multiply multi-digit whole numbers (not to exceed three-digit by three- digit). Estimate solutions to arithmetic problems in order to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition, subtraction, multiplication and division of multi-digit whole numbers. Use various strategies, including the inverse relationships between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Apply the commutative, associative and distributive properties and order of operations to generate equivalent numerical expressions and to solve problems involving whole numbers. Practice and Problem Solving 3-7: Student Edition Practice Curriculum Standards: Fluently multiply multi-digit whole numbers using the standard algorithm. Fluently multiply multi-digit whole numbers using the standard algorithm. Fluently multiply multi-digit whole numbers using the standard algorithm. Use properties and the standard algorithm for multiplication to find the product of multi-digit numbers. Fluently multiply multi-digit whole numbers using the standard algorithm. Multiply multi-digit whole numbers (not to exceed three-digit by three- digit). Estimate solutions to arithmetic problems in order to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition, subtraction, multiplication and division of multi-digit whole numbers. Use various strategies, including the inverse relationships between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Apply the commutative, associative and distributive properties and order of operations to generate equivalent numerical expressions and to solve problems involving whole numbers. 3-7: Practice Buddy: Independent Practice; Problem Solving Curriculum Standards: Fluently multiply multi-digit whole numbers using the standard algorithm. Fluently multiply multi-digit whole numbers using the standard algorithm. Fluently multiply multi-digit whole numbers using the standard algorithm. Use properties and the standard algorithm for multiplication to find the product of multi-digit numbers. Fluently multiply multi-digit whole numbers using the standard algorithm. Multiply multi-digit whole numbers (not to exceed three-digit by three- digit). Estimate solutions to arithmetic problems in order to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition, subtraction, multiplication and division of multi-digit whole numbers. Use various strategies, including the inverse relationships between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Apply the commutative, associative and distributive properties and order of operations to generate equivalent numerical expressions and to solve problems involving whole numbers. 3-7: Practice Buddy: Additional Practice Curriculum Standards: Fluently multiply multi-digit whole numbers using the standard algorithm. Fluently multiply multi-digit whole numbers using the standard algorithm. Fluently multiply multi-digit whole numbers using the standard algorithm. Use properties and the standard algorithm for multiplication to find the product of multi-digit numbers. Fluently multiply multi-digit whole numbers using the standard algorithm. Multiply multi-digit whole numbers (not to exceed three-digit by three- digit). Estimate solutions to arithmetic problems in order to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition, subtraction, multiplication and division of multi-digit whole numbers. Use various strategies, including the inverse relationships between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Apply the commutative, associative and distributive properties and order of operations to generate equivalent numerical expressions and to solve problems involving whole numbers. 3-7: Interactive Additional Practice Step 3: Assess & Differentiate 3-7: Practice Buddy: Additional Practice Curriculum Standards: Fluently multiply multi-digit whole numbers using the standard algorithm. Fluently multiply multi-digit whole numbers using the standard algorithm. Fluently multiply multi-digit whole numbers using the standard algorithm. Use properties and the standard algorithm for multiplication to find the product of multi-digit numbers. Fluently multiply multi-digit whole numbers using the standard algorithm. Multiply multi-digit whole numbers (not to exceed three-digit by three- digit). Estimate solutions to arithmetic problems in order to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition, subtraction, multiplication and division of multi-digit whole numbers. Use various strategies, including the inverse relationships between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Apply the commutative, associative and distributive properties and order of operations to generate equivalent numerical expressions and to solve problems involving whole numbers. 3-7: Enrichment Curriculum Standards: Fluently multiply multi-digit whole numbers using the standard algorithm. Fluently multiply multi-digit whole numbers using the standard algorithm. Fluently multiply multi-digit whole numbers using the standard algorithm. Use properties and the standard algorithm for multiplication to find the product of multi-digit numbers. Fluently multiply multi-digit whole numbers using the standard algorithm. Multiply multi-digit whole numbers (not to exceed three-digit by three- digit). Estimate solutions to arithmetic problems in order to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition, subtraction, multiplication and division of multi-digit whole numbers. Use various strategies, including the inverse relationships between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Apply the commutative, associative and distributive properties and order of operations to generate equivalent numerical expressions and to solve problems involving whole numbers. 3-7: Quick Check Curriculum Standards: Fluently multiply multi-digit whole numbers using the standard algorithm. Fluently multiply multi-digit whole numbers using the standard algorithm. Fluently multiply multi-digit whole numbers using the standard algorithm. Use properties and the standard algorithm for multiplication to find the product of multi-digit numbers. Fluently multiply multi-digit whole numbers using the standard algorithm. Multiply multi-digit whole numbers (not to exceed three-digit by three- digit). Estimate solutions to arithmetic problems in order to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition, subtraction, multiplication and division of multi-digit whole numbers. Use various strategies, including the inverse relationships between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Apply the commutative, associative and distributive properties and order of operations to generate equivalent numerical expressions and to solve problems involving whole numbers. 3-7: Lesson Self-Assessment 3-7: Reteach to Build Understanding Curriculum Standards: Fluently multiply multi-digit whole numbers using the standard algorithm. Fluently multiply multi-digit whole numbers using the standard algorithm. Fluently multiply multi-digit whole numbers using the standard algorithm. Use properties and the standard algorithm for multiplication to find the product of multi-digit numbers. Fluently multiply multi-digit whole numbers using the standard algorithm. Multiply multi-digit whole numbers (not to exceed three-digit by three- digit). Estimate solutions to arithmetic problems in order to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition, subtraction, multiplication and division of multi-digit whole numbers. Use various strategies, including the inverse relationships between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Apply the commutative, associative and distributive properties and order of operations to generate equivalent numerical expressions and to solve problems involving whole numbers. 3-7: Build Mathematical Literacy Curriculum Standards: Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 5 topics and texts, building on others’ ideas and expressing their own clearly. (a) Come to discussions prepared, having read or studied required material; explicitly draw on that preparation and other information known about the topic to explore ideas under discussion. (b) Follow agreed-upon rules for discussions and carry out assigned roles. (c) Pose and respond to specific questions by making comments that contribute to the discussion and elaborate on the remarks of others. (d) Review the key ideas expressed and draw conclusions in light of information and knowledge gained from the discussions. English language learners communicate for social and instructional purposes within the school setting. Summarize a written text read aloud or information presented in diverse media and formats, including visually, quantitatively, and orally. Summarize the points a speaker makes and explain how each claim is supported by reasons and evidence. Write informative/explanatory texts to examine a topic and convey ideas and information clearly. (a) Introduce a topic clearly, provide a general observation and focus, and group related information logically; include formatting (e.g., headings), illustrations, and multimedia when useful to aiding comprehension. (b) Develop the topic with facts, definitions, concrete details, quotations, or other information and examples related to the topic. (c) Link ideas within and across categories of information using words, phrases, and clauses (e.g., in contrast, especially). (d) Use precise language and domain-specific vocabulary to inform about or explain the topic. (e) Provide a concluding statement or section related to the information or explanation presented. English language learners communicate information, ideas and concepts necessary for academic success in the content area of Mathematics. 3-7: Enrichment Game: Multo - 2-Digit Numbers 3-7: Pick a Project 3-7: Another Look Curriculum Standards: Fluently multiply multi-digit whole numbers using the standard algorithm. Fluently multiply multi-digit whole numbers using the standard algorithm. Fluently multiply multi-digit whole numbers using the standard algorithm. Use properties and the standard algorithm for multiplication to find the product of multi-digit numbers. Fluently multiply multi-digit whole numbers using the standard algorithm. Multiply multi-digit whole numbers (not to exceed three-digit by three- digit). Estimate solutions to arithmetic problems in order to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition, subtraction, multiplication and division of multi-digit whole numbers. Use various strategies, including the inverse relationships between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Apply the commutative, associative and distributive properties and order of operations to generate equivalent numerical expressions and to solve problems involving whole numbers. Spanish Resources 3-7: eText del Libro del estudiante 3-7: Repaso diario 3-7: Aprendizaje visual 3-7: Amigo de práctica: Práctica adicional 3-7: Práctica adicional interactiva 3-7: Refuerzo para mejorar la comprensión 3-7: Desarrollar la competencia matemática 3-7: Ampliación 3-8: Solve Word Problems Interactive Student Edition: Grade 5 Lesson 3-8 Math Anytime 3-8: Daily Review Topic 3: Today's Challenge Step 1: Problem-Based Learning 3-8: Solve & Share Curriculum Standards: Fluently multiply multi-digit whole numbers using the standard algorithm. Fluently multiply multi-digit whole numbers using the standard algorithm. Fluently multiply multi-digit whole numbers using the standard algorithm. Use models and strategies to solve word problems. Fluently multiply multi-digit whole numbers using the standard algorithm. Multiply multi-digit whole numbers (not to exceed three-digit by three-digit). Estimate solutions to arithmetic problems in order to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition, subtraction, multiplication and division of multi-digit whole numbers. Use various strategies, including the inverse relationships between operations, the use of technology, and the context of the problem to assess the reasonableness of results. English language learners communicate for social and instructional purposes within the school setting. Write informative/explanatory texts to examine a topic and convey ideas and information clearly. (a) Introduce a topic clearly, provide a general observation and focus, and group related information logically; include formatting (e.g., headings), illustrations, and multimedia when useful to aiding comprehension. (b) Develop the topic with facts, definitions, concrete details, quotations, or other information and examples related to the topic. (c) Link ideas within and across categories of information using words, phrases, and clauses (e.g., in contrast, especially). (d) Use precise language and domain-specific vocabulary to inform about or explain the topic. (e) Provide a concluding statement or section related to the information or explanation presented. English language learners communicate information, ideas and concepts necessary for academic success in the content area of Mathematics. Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 5 topics and texts, building on others’ ideas and expressing their own clearly. (a) Come to discussions prepared, having read or studied required material; explicitly draw on that preparation and other information known about the topic to explore ideas under discussion. (b) Follow agreed-upon rules for discussions and carry out assigned roles. (c) Pose and respond to specific questions by making comments that contribute to the discussion and elaborate on the remarks of others. (d) Review the key ideas expressed and draw conclusions in light of information and knowledge gained from the discussions. Summarize a written text read aloud or information presented in diverse media and formats, including visually, quantitatively, and orally. Summarize the points a speaker makes and explain how each claim is supported by reasons and evidence. Step 2: Visual Learning 3-8: Visual Learning Curriculum Standards: Fluently multiply multi-digit whole numbers using the standard algorithm. Fluently multiply multi-digit whole numbers using the standard algorithm. Fluently multiply multi-digit whole numbers using the standard algorithm. Use models and strategies to solve word problems. Fluently multiply multi-digit whole numbers using the standard algorithm. Multiply multi-digit whole numbers (not to exceed three-digit by three-digit). Estimate solutions to arithmetic problems in order to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition, subtraction, multiplication and division of multi-digit whole numbers. Use various strategies, including the inverse relationships between operations, the use of technology, and the context of the problem to assess the reasonableness of results. 3-8: Convince Me! Curriculum Standards: Fluently multiply multi-digit whole numbers using the standard algorithm. Fluently multiply multi-digit whole numbers using the standard algorithm. Fluently multiply multi-digit whole numbers using the standard algorithm. Use models and strategies to solve word problems. Fluently multiply multi-digit whole numbers using the standard algorithm. Multiply multi-digit whole numbers (not to exceed three-digit by three-digit). Estimate solutions to arithmetic problems in order to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition, subtraction, multiplication and division of multi-digit whole numbers. Use various strategies, including the inverse relationships between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Practice and Problem Solving 3-8: Student Edition Practice Curriculum Standards: Fluently multiply multi-digit whole numbers using the standard algorithm. Fluently multiply multi-digit whole numbers using the standard algorithm. Fluently multiply multi-digit whole numbers using the standard algorithm. Use models and strategies to solve word problems. Fluently multiply multi-digit whole numbers using the standard algorithm. Multiply multi-digit whole numbers (not to exceed three-digit by three-digit). Estimate solutions to arithmetic problems in order to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition, subtraction, multiplication and division of multi-digit whole numbers. Use various strategies, including the inverse relationships between operations, the use of technology, and the context of the problem to assess the reasonableness of results. 3-8: Practice Buddy: Independent Practice; Problem Solving Curriculum Standards: Fluently multiply multi-digit whole numbers using the standard algorithm. Fluently multiply multi-digit whole numbers using the standard algorithm. Fluently multiply multi-digit whole numbers using the standard algorithm. Use models and strategies to solve word problems. Fluently multiply multi-digit whole numbers using the standard algorithm. Multiply multi-digit whole numbers (not to exceed three-digit by three-digit). Estimate solutions to arithmetic problems in order to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition, subtraction, multiplication and division of multi-digit whole numbers. Use various strategies, including the inverse relationships between operations, the use of technology, and the context of the problem to assess the reasonableness of results. 3-8: Practice Buddy: Additional Practice Curriculum Standards: Fluently multiply multi-digit whole numbers using the standard algorithm. Fluently multiply multi-digit whole numbers using the standard algorithm. Fluently multiply multi-digit whole numbers using the standard algorithm. Use models and strategies to solve word problems. Fluently multiply multi-digit whole numbers using the standard algorithm. Multiply multi-digit whole numbers (not to exceed three-digit by three-digit). Estimate solutions to arithmetic problems in order to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition, subtraction, multiplication and division of multi-digit whole numbers. Use various strategies, including the inverse relationships between operations, the use of technology, and the context of the problem to assess the reasonableness of results. 3-8: Interactive Additional Practice Step 3: Assess & Differentiate 3-8: Practice Buddy: Additional Practice Curriculum Standards: Fluently multiply multi-digit whole numbers using the standard algorithm. Fluently multiply multi-digit whole numbers using the standard algorithm. Fluently multiply multi-digit whole numbers using the standard algorithm. Use models and strategies to solve word problems. Fluently multiply multi-digit whole numbers using the standard algorithm. Multiply multi-digit whole numbers (not to exceed three-digit by three-digit). Estimate solutions to arithmetic problems in order to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition, subtraction, multiplication and division of multi-digit whole numbers. Use various strategies, including the inverse relationships between operations, the use of technology, and the context of the problem to assess the reasonableness of results. 3-8: Enrichment Curriculum Standards: Fluently multiply multi-digit whole numbers using the standard algorithm. Fluently multiply multi-digit whole numbers using the standard algorithm. Fluently multiply multi-digit whole numbers using the standard algorithm. Use models and strategies to solve word problems. Fluently multiply multi-digit whole numbers using the standard algorithm. Multiply multi-digit whole numbers (not to exceed three-digit by three-digit). Estimate solutions to arithmetic problems in order to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition, subtraction, multiplication and division of multi-digit whole numbers. Use various strategies, including the inverse relationships between operations, the use of technology, and the context of the problem to assess the reasonableness of results. 3-8: Quick Check Curriculum Standards: Fluently multiply multi-digit whole numbers using the standard algorithm. Fluently multiply multi-digit whole numbers using the standard algorithm. Fluently multiply multi-digit whole numbers using the standard algorithm. Use models and strategies to solve word problems. Fluently multiply multi-digit whole numbers using the standard algorithm. Multiply multi-digit whole numbers (not to exceed three-digit by three-digit). Estimate solutions to arithmetic problems in order to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition, subtraction, multiplication and division of multi-digit whole numbers. Use various strategies, including the inverse relationships between operations, the use of technology, and the context of the problem to assess the reasonableness of results. 3-8: Lesson Self-Assessment 3-8: Reteach to Build Understanding Curriculum Standards: Fluently multiply multi-digit whole numbers using the standard algorithm. Fluently multiply multi-digit whole numbers using the standard algorithm. Fluently multiply multi-digit whole numbers using the standard algorithm. Use models and strategies to solve word problems. Fluently multiply multi-digit whole numbers using the standard algorithm. Multiply multi-digit whole numbers (not to exceed three-digit by three-digit). Estimate solutions to arithmetic problems in order to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition, subtraction, multiplication and division of multi-digit whole numbers. Use various strategies, including the inverse relationships between operations, the use of technology, and the context of the problem to assess the reasonableness of results. 3-8: Build Mathematical Literacy Curriculum Standards: Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 5 topics and texts, building on others’ ideas and expressing their own clearly. (a) Come to discussions prepared, having read or studied required material; explicitly draw on that preparation and other information known about the topic to explore ideas under discussion. (b) Follow agreed-upon rules for discussions and carry out assigned roles. (c) Pose and respond to specific questions by making comments that contribute to the discussion and elaborate on the remarks of others. (d) Review the key ideas expressed and draw conclusions in light of information and knowledge gained from the discussions. English language learners communicate for social and instructional purposes within the school setting. Summarize a written text read aloud or information presented in diverse media and formats, including visually, quantitatively, and orally. Summarize the points a speaker makes and explain how each claim is supported by reasons and evidence. Write informative/explanatory texts to examine a topic and convey ideas and information clearly. (a) Introduce a topic clearly, provide a general observation and focus, and group related information logically; include formatting (e.g., headings), illustrations, and multimedia when useful to aiding comprehension. (b) Develop the topic with facts, definitions, concrete details, quotations, or other information and examples related to the topic. (c) Link ideas within and across categories of information using words, phrases, and clauses (e.g., in contrast, especially). (d) Use precise language and domain-specific vocabulary to inform about or explain the topic. (e) Provide a concluding statement or section related to the information or explanation presented. English language learners communicate information, ideas and concepts necessary for academic success in the content area of Mathematics. 3-8: Enrichment 3-8: Digital Math Tool Activity 3-8: Pick a Project 3-8: Another Look Curriculum Standards: Fluently multiply multi-digit whole numbers using the standard algorithm. Fluently multiply multi-digit whole numbers using the standard algorithm. Fluently multiply multi-digit whole numbers using the standard algorithm. Use models and strategies to solve word problems. Fluently multiply multi-digit whole numbers using the standard algorithm. Multiply multi-digit whole numbers (not to exceed three-digit by three-digit). Estimate solutions to arithmetic problems in order to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition, subtraction, multiplication and division of multi-digit whole numbers. Use various strategies, including the inverse relationships between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Spanish Resources 3-8: eText del Libro del estudiante 3-8: Repaso diario 3-8: Aprendizaje visual 3-8: Amigo de práctica: Práctica adicional 3-8: Práctica adicional interactiva 3-8: Refuerzo para mejorar la comprensión 3-8: Desarrollar la competencia matemática 3-8: Ampliación 3-9: Problem Solving: Critique Reasoning Interactive Student Edition: Grade 5 Lesson 3-9 Math Anytime 3-9: Daily Review Topic 3: Today's Challenge Step 1: Problem-Based Learning 3-9: Solve & Share Curriculum Standards: Fluently multiply multi-digit whole numbers using the standard algorithm. Construct viable arguments and critique the reasoning of others. English language learners communicate for social and instructional purposes within the school setting. Write informative/explanatory texts to examine a topic and convey ideas and information clearly. (a) Introduce a topic clearly, provide a general observation and focus, and group related information logically; include formatting (e.g., headings), illustrations, and multimedia when useful to aiding comprehension. (b) Develop the topic with facts, definitions, concrete details, quotations, or other information and examples related to the topic. (c) Link ideas within and across categories of information using words, phrases, and clauses (e.g., in contrast, especially). (d) Use precise language and domain- specific vocabulary to inform about or explain the topic. (e) Provide a concluding statement or section related to the information or explanation presented. English language learners communicate information, ideas and concepts necessary for academic success in the content area of Mathematics. Fluently multiply multi-digit whole numbers using the standard algorithm. Fluently multiply multi-digit whole numbers using the standard algorithm. Critique the reasoning of others by asking questions, looking for flaws, and using prior knowledge of estimating products. Fluently multiply multi-digit whole numbers using the standard algorithm. Construct viable arguments and critique the reasoning of others. Construct viable arguments and critique the reasoning of others. Multiply multi-digit whole numbers (not to exceed three-digit by three-digit). Construct viable arguments and critique the reasoning of others. Estimate solutions to arithmetic problems in order to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition, subtraction, multiplication and division of multi-digit whole numbers. Use various strategies, including the inverse relationships between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher- led) with diverse partners on grade 5 topics and texts, building on others’ ideas and expressing their own clearly. (a) Come to discussions prepared, having read or studied required material; explicitly draw on that preparation and other information known about the topic to explore ideas under discussion. (b) Follow agreed-upon rules for discussions and carry out assigned roles. (c) Pose and respond to specific questions by making comments that contribute to the discussion and elaborate on the remarks of others. (d) Review the key ideas expressed and draw conclusions in light of information and knowledge gained from the discussions. Summarize a written text read aloud or information presented in diverse media and formats, including visually, quantitatively, and orally. Summarize the points a speaker makes and explain how each claim is supported by reasons and evidence. Step 2: Visual Learning 3-9: Visual Learning Curriculum Standards: Fluently multiply multi-digit whole numbers using the standard algorithm. Construct viable arguments and critique the reasoning of others. Fluently multiply multi-digit whole numbers using the standard algorithm. Fluently multiply multi-digit whole numbers using the standard algorithm. Critique the reasoning of others by asking questions, looking for flaws, and using prior knowledge of estimating products. Fluently multiply multi-digit whole numbers using the standard algorithm. Construct viable arguments and critique the reasoning of others. Construct viable arguments and critique the reasoning of others. Multiply multi-digit whole numbers (not to exceed three-digit by three-digit). Construct viable arguments and critique the reasoning of others. Estimate solutions to arithmetic problems in order to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition, subtraction, multiplication and division of multi-digit whole numbers. Use various strategies, including the inverse relationships between operations, the use of technology, and the context of the problem to assess the reasonableness of results. 3-9: Convince Me! Curriculum Standards: Fluently multiply multi-digit whole numbers using the standard algorithm. Construct viable arguments and critique the reasoning of others. Fluently multiply multi-digit whole numbers using the standard algorithm. Fluently multiply multi-digit whole numbers using the standard algorithm. Critique the reasoning of others by asking questions, looking for flaws, and using prior knowledge of estimating products. Fluently multiply multi-digit whole numbers using the standard algorithm. Construct viable arguments and critique the reasoning of others. Construct viable arguments and critique the reasoning of others. Multiply multi-digit whole numbers (not to exceed three-digit by three-digit). Construct viable arguments and critique the reasoning of others. Estimate solutions to arithmetic problems in order to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition, subtraction, multiplication and division of multi-digit whole numbers. Use various strategies, including the inverse relationships between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Practice and Problem Solving 3-9: Student Edition Practice Curriculum Standards: Fluently multiply multi-digit whole numbers using the standard algorithm. Construct viable arguments and critique the reasoning of others. Fluently multiply multi-digit whole numbers using the standard algorithm. Fluently multiply multi-digit whole numbers using the standard algorithm. Critique the reasoning of others by asking questions, looking for flaws, and using prior knowledge of estimating products. Fluently multiply multi-digit whole numbers using the standard algorithm. Construct viable arguments and critique the reasoning of others. Construct viable arguments and critique the reasoning of others. Multiply multi-digit whole numbers (not to exceed three-digit by three-digit). Construct viable arguments and critique the reasoning of others. Estimate solutions to arithmetic problems in order to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition, subtraction, multiplication and division of multi-digit whole numbers. Use various strategies, including the inverse relationships between operations, the use of technology, and the context of the problem to assess the reasonableness of results. 3-9: Practice Buddy: Independent Practice; Problem Solving Curriculum Standards: Fluently multiply multi-digit whole numbers using the standard algorithm. Construct viable arguments and critique the reasoning of others. Fluently multiply multi-digit whole numbers using the standard algorithm. Fluently multiply multi-digit whole numbers using the standard algorithm. Critique the reasoning of others by asking questions, looking for flaws, and using prior knowledge of estimating products. Fluently multiply multi-digit whole numbers using the standard algorithm. Construct viable arguments and critique the reasoning of others. Construct viable arguments and critique the reasoning of others. Multiply multi-digit whole numbers (not to exceed three-digit by three-digit). Construct viable arguments and critique the reasoning of others. Estimate solutions to arithmetic problems in order to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition, subtraction, multiplication and division of multi-digit whole numbers. Use various strategies, including the inverse relationships between operations, the use of technology, and the context of the problem to assess the reasonableness of results. 3-9: Practice Buddy: Additional Practice Curriculum Standards: Fluently multiply multi-digit whole numbers using the standard algorithm. Construct viable arguments and critique the reasoning of others. Fluently multiply multi-digit whole numbers using the standard algorithm. Fluently multiply multi-digit whole numbers using the standard algorithm. Critique the reasoning of others by asking questions, looking for flaws, and using prior knowledge of estimating products. Fluently multiply multi-digit whole numbers using the standard algorithm. Construct viable arguments and critique the reasoning of others. Construct viable arguments and critique the reasoning of others. Multiply multi-digit whole numbers (not to exceed three-digit by three-digit). Construct viable arguments and critique the reasoning of others. Estimate solutions to arithmetic problems in order to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition, subtraction, multiplication and division of multi-digit whole numbers. Use various strategies, including the inverse relationships between operations, the use of technology, and the context of the problem to assess the reasonableness of results. 3-9: Interactive Additional Practice Step 3: Assess & Differentiate 3-9: Practice Buddy: Additional Practice Curriculum Standards: Fluently multiply multi-digit whole numbers using the standard algorithm. Construct viable arguments and critique the reasoning of others. Fluently multiply multi-digit whole numbers using the standard algorithm. Fluently multiply multi-digit whole numbers using the standard algorithm. Critique the reasoning of others by asking questions, looking for flaws, and using prior knowledge of estimating products. Fluently multiply multi-digit whole numbers using the standard algorithm. Construct viable arguments and critique the reasoning of others. Construct viable arguments and critique the reasoning of others. Multiply multi-digit whole numbers (not to exceed three-digit by three-digit). Construct viable arguments and critique the reasoning of others. Estimate solutions to arithmetic problems in order to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition, subtraction, multiplication and division of multi-digit whole numbers. Use various strategies, including the inverse relationships between operations, the use of technology, and the context of the problem to assess the reasonableness of results. 3-9: Enrichment Curriculum Standards: Fluently multiply multi-digit whole numbers using the standard algorithm. Construct viable arguments and critique the reasoning of others. Fluently multiply multi-digit whole numbers using the standard algorithm. Fluently multiply multi-digit whole numbers using the standard algorithm. Critique the reasoning of others by asking questions, looking for flaws, and using prior knowledge of estimating products. Fluently multiply multi-digit whole numbers using the standard algorithm. Construct viable arguments and critique the reasoning of others. Construct viable arguments and critique the reasoning of others. Multiply multi-digit whole numbers (not to exceed three-digit by three-digit). Construct viable arguments and critique the reasoning of others. Estimate solutions to arithmetic problems in order to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition, subtraction, multiplication and division of multi-digit whole numbers. Use various strategies, including the inverse relationships between operations, the use of technology, and the context of the problem to assess the reasonableness of results. 3-9: Quick Check Curriculum Standards: Fluently multiply multi-digit whole numbers using the standard algorithm. Construct viable arguments and critique the reasoning of others. Fluently multiply multi-digit whole numbers using the standard algorithm. Fluently multiply multi-digit whole numbers using the standard algorithm. Critique the reasoning of others by asking questions, looking for flaws, and using prior knowledge of estimating products. Fluently multiply multi-digit whole numbers using the standard algorithm. Construct viable arguments and critique the reasoning of others. Construct viable arguments and critique the reasoning of others. Multiply multi-digit whole numbers (not to exceed three-digit by three-digit). Construct viable arguments and critique the reasoning of others. Estimate solutions to arithmetic problems in order to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition, subtraction, multiplication and division of multi-digit whole numbers. Use various strategies, including the inverse relationships between operations, the use of technology, and the context of the problem to assess the reasonableness of results. 3-9: Lesson Self-Assessment 3-9: Reteach to Build Understanding Curriculum Standards: Fluently multiply multi-digit whole numbers using the standard algorithm. Construct viable arguments and critique the reasoning of others. Fluently multiply multi-digit whole numbers using the standard algorithm. Fluently multiply multi-digit whole numbers using the standard algorithm. Critique the reasoning of others by asking questions, looking for flaws, and using prior knowledge of estimating products. Fluently multiply multi-digit whole numbers using the standard algorithm. Construct viable arguments and critique the reasoning of others. Construct viable arguments and critique the reasoning of others. Multiply multi-digit whole numbers (not to exceed three-digit by three-digit). Construct viable arguments and critique the reasoning of others. Estimate solutions to arithmetic problems in order to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition, subtraction, multiplication and division of multi-digit whole numbers. Use various strategies, including the inverse relationships between operations, the use of technology, and the context of the problem to assess the reasonableness of results. 3-9: Build Mathematical Literacy Curriculum Standards: Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 5 topics and texts, building on others’ ideas and expressing their own clearly. (a) Come to discussions prepared, having read or studied required material; explicitly draw on that preparation and other information known about the topic to explore ideas under discussion. (b) Follow agreed-upon rules for discussions and carry out assigned roles. (c) Pose and respond to specific questions by making comments that contribute to the discussion and elaborate on the remarks of others. (d) Review the key ideas expressed and draw conclusions in light of information and knowledge gained from the discussions. English language learners communicate for social and instructional purposes within the school setting. Summarize a written text read aloud or information presented in diverse media and formats, including visually, quantitatively, and orally. Summarize the points a speaker makes and explain how each claim is supported by reasons and evidence. Write informative/explanatory texts to examine a topic and convey ideas and information clearly. (a) Introduce a topic clearly, provide a general observation and focus, and group related information logically; include formatting (e.g., headings), illustrations, and multimedia when useful to aiding comprehension. (b) Develop the topic with facts, definitions, concrete details, quotations, or other information and examples related to the topic. (c) Link ideas within and across categories of information using words, phrases, and clauses (e.g., in contrast, especially). (d) Use precise language and domain-specific vocabulary to inform about or explain the topic. (e) Provide a concluding statement or section related to the information or explanation presented. English language learners communicate information, ideas and concepts necessary for academic success in the content area of Mathematics. 3-9: Enrichment Game: Fluency - Multiply Multi-Digit Whole Numbers 3-9: enVision STEM Activity Curriculum Standards: Fluently multiply multi-digit whole numbers using the standard algorithm. Construct viable arguments and critique the reasoning of others. Fluently multiply multi-digit whole numbers using the standard algorithm. Fluently multiply multi-digit whole numbers using the standard algorithm. Critique the reasoning of others by asking questions, looking for flaws, and using prior knowledge of estimating products. Fluently multiply multi-digit whole numbers using the standard algorithm. Construct viable arguments and critique the reasoning of others. Construct viable arguments and critique the reasoning of others. Multiply multi-digit whole numbers (not to exceed three-digit by three-digit). Construct viable arguments and critique the reasoning of others. Estimate solutions to arithmetic problems in order to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition, subtraction, multiplication and division of multi-digit whole numbers. Use various strategies, including the inverse relationships between operations, the use of technology, and the context of the problem to assess the reasonableness of results. 3-9: Another Look Curriculum Standards: Fluently multiply multi-digit whole numbers using the standard algorithm. Construct viable arguments and critique the reasoning of others. Fluently multiply multi-digit whole numbers using the standard algorithm. Fluently multiply multi-digit whole numbers using the standard algorithm. Critique the reasoning of others by asking questions, looking for flaws, and using prior knowledge of estimating products. Fluently multiply multi-digit whole numbers using the standard algorithm. Construct viable arguments and critique the reasoning of others. Construct viable arguments and critique the reasoning of others. Multiply multi-digit whole numbers (not to exceed three-digit by three-digit). Construct viable arguments and critique the reasoning of others. Estimate solutions to arithmetic problems in order to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition, subtraction, multiplication and division of multi-digit whole numbers. Use various strategies, including the inverse relationships between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Spanish Resources 3-9: eText del Libro del estudiante 3-9: Repaso diario 3-9: Aprendizaje visual 3-9: Amigo de práctica: Práctica adicional 3-9: Práctica adicional interactiva 3-9: Refuerzo para mejorar la comprensión 3-9: Desarrollar la competencia matemática 3-9: Ampliación Topic 3: End of Topic Interactive Student Edition: End of Topic 3 Topic 3: Fluency Practice Activity Interactive Student Edition: Topic 3 Assessment Practice Interactive Student Edition: Topic 3 Performance Task Topic 3 Performance Task Topic 3 Assessment 5-1: Center Games 3-1: Visual Learning Curriculum Standards: 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. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. 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. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. 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. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. Use place-value understandings and patterns to mentally multiply whole numbers and powers of 10. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10 and 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. 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. 3-2: Visual Learning Curriculum Standards: Fluently multiply multi-digit whole numbers using the standard algorithm. Fluently multiply multi-digit whole numbers using the standard algorithm. Fluently multiply multi-digit whole numbers using the standard algorithm. Use rounding and compatible numbers to estimate products. Fluently multiply multi-digit whole numbers using the standard algorithm. Multiply multi-digit whole numbers (not to exceed three-digit by three-digit). Estimate solutions to arithmetic problems in order to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition, subtraction, multiplication and division of multi-digit whole numbers. Use various strategies, including the inverse relationships between operations, the use of technology, and the context of the problem to assess the reasonableness of results. 3-3: Visual Learning Curriculum Standards: Fluently multiply multi-digit whole numbers using the standard algorithm. Fluently multiply multi-digit whole numbers using the standard algorithm. Fluently multiply multi-digit whole numbers using the standard algorithm. Use place-value strategies and the standard algorithm to multiply multi-digit numbers by 1-digit numbers. Fluently multiply multi-digit whole numbers using the standard algorithm. Multiply multi-digit whole numbers (not to exceed three-digit by three-digit). Estimate solutions to arithmetic problems in order to assess the reasonableness of results. Solve real- world and mathematical problems requiring addition, subtraction, multiplication and division of multi- digit whole numbers. Use various strategies, including the inverse relationships between operations, the use of technology, and the context of the problem to assess the reasonableness of results. 3-4: Visual Learning Curriculum Standards: Fluently multiply multi-digit whole numbers using the standard algorithm. Fluently multiply multi-digit whole numbers using the standard algorithm. Fluently multiply multi-digit whole numbers using the standard algorithm. Use the expanded and the standard algorithm to multiply 2-digit by 2-digit numbers. Estimate to check if products are reasonable. Fluently multiply multi-digit whole numbers using the standard algorithm. Multiply multi-digit whole numbers (not to exceed three- digit by three-digit). Estimate solutions to arithmetic problems in order to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition, subtraction, multiplication and division of multi-digit whole numbers. Use various strategies, including the inverse relationships between operations, the use of technology, and the context of the problem to assess the reasonableness of results. 3-5: Visual Learning Curriculum Standards: Fluently multiply multi-digit whole numbers using the standard algorithm. Fluently multiply multi-digit whole numbers using the standard algorithm. Fluently multiply multi-digit whole numbers using the standard algorithm. Multiply 3-digit by 2-digit numbers by adding partial products or by using the standard algorithm. Fluently multiply multi-digit whole numbers using the standard algorithm. Multiply multi-digit whole numbers (not to exceed three-digit by three-digit). Estimate solutions to arithmetic problems in order to assess the reasonableness of results. Solve real- world and mathematical problems requiring addition, subtraction, multiplication and division of multi- digit whole numbers. Use various strategies, including the inverse relationships between operations, the use of technology, and the context of the problem to assess the reasonableness of results. 3-6: Visual Learning Curriculum Standards: Fluently multiply multi-digit whole numbers using the standard algorithm. Fluently multiply multi-digit whole numbers using the standard algorithm. Fluently multiply multi-digit whole numbers using the standard algorithm. Use knowledge about place value and multiplying with 2- digit and 3-digit numbers to multiply with zeros. Fluently multiply multi-digit whole numbers using the standard algorithm. Multiply multi-digit whole numbers (not to exceed three-digit by three-digit). Estimate solutions to arithmetic problems in order to assess the reasonableness of results. Solve real- world and mathematical problems requiring addition, subtraction, multiplication and division of multi- digit whole numbers. Use various strategies, including the inverse relationships between operations, the use of technology, and the context of the problem to assess the reasonableness of results. 3-7: Visual Learning Curriculum Standards: Fluently multiply multi-digit whole numbers using the standard algorithm. Fluently multiply multi-digit whole numbers using the standard algorithm. Fluently multiply multi-digit whole numbers using the standard algorithm. Use properties and the standard algorithm for multiplication to find the product of multi-digit numbers. Fluently multiply multi-digit whole numbers using the standard algorithm. Multiply multi-digit whole numbers (not to exceed three-digit by three- digit). Estimate solutions to arithmetic problems in order to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition, subtraction, multiplication and division of multi-digit whole numbers. Use various strategies, including the inverse relationships between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Apply the commutative, associative and distributive properties and order of operations to generate equivalent numerical expressions and to solve problems involving whole numbers. 3-8: Visual Learning Curriculum Standards: Fluently multiply multi-digit whole numbers using the standard algorithm. Fluently multiply multi-digit whole numbers using the standard algorithm. Fluently multiply multi-digit whole numbers using the standard algorithm. Use models and strategies to solve word problems. Fluently multiply multi-digit whole numbers using the standard algorithm. Multiply multi-digit whole numbers (not to exceed three-digit by three-digit). Estimate solutions to arithmetic problems in order to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition, subtraction, multiplication and division of multi-digit whole numbers. Use various strategies, including the inverse relationships between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Topic 3 Online Assessment Curriculum Standards: Fluently multiply multi-digit whole numbers using the standard algorithm. Construct viable arguments and critique the reasoning of others. 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. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. Fluently multiply multi-digit whole numbers using the standard algorithm. Fluently multiply multi- digit whole numbers using the standard algorithm. Use models and strategies to solve word problems. Fluently multiply multi-digit whole numbers using the standard algorithm. Multiply multi-digit whole numbers (not to exceed three-digit by three-digit). Estimate solutions to arithmetic problems in order to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition, subtraction, multiplication and division of multi-digit whole numbers. Use various strategies, including the inverse relationships between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Use properties and the standard algorithm for multiplication to find the product of multi-digit numbers. Apply the commutative, associative and distributive properties and order of operations to generate equivalent numerical expressions and to solve problems involving whole numbers. Use knowledge about place value and multiplying with 2-digit and 3-digit numbers to multiply with zeros. Multiply 3-digit by 2-digit numbers by adding partial products or by using the standard algorithm. Critique the reasoning of others by asking questions, looking for flaws, and using prior knowledge of estimating products. Construct viable arguments and critique the reasoning of others. Construct viable arguments and critique the reasoning of others. Construct viable arguments and critique the reasoning of others. Use the expanded and the standard algorithm to multiply 2-digit by 2- digit numbers. Estimate to check if products are reasonable. Use place-value strategies and the standard algorithm to multiply multi-digit numbers by 1-digit numbers. Use rounding and compatible numbers to estimate products. 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. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. 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. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. Use place-value understandings and patterns to mentally multiply whole numbers and powers of 10. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10 and 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. Topic 3 Spanish Assessments Tema 3: Tarea de rendimento Tema 3: Evaluación Topic 4: Use Models and Strategies to Multiply Decimals Topic 4: Today's Challenge Topic 4: Beginning of Topic Interactive Student Edition: Beginning of Topic 4 Topic 4: enVision STEM Activity Grade 5 Topic 4: Review What You Know 4-1: Multiply Decimals by Powers of 10 Interactive Student Edition: Grade 5 Lesson 4-1 Math Anytime 4-1: Daily Review Topic 4: Today's Challenge Step 1: Problem-Based Learning 4-1: Solve & Share Curriculum Standards: Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. English language learners communicate for social and instructional purposes within the school setting. Write informative/explanatory texts to examine a topic and convey ideas and information clearly. (a) Introduce a topic clearly, provide a general observation and focus, and group related information logically; include formatting (e.g., headings), illustrations, and multimedia when useful to aiding comprehension. (b) Develop the topic with facts, definitions, concrete details, quotations, or other information and examples related to the topic. (c) Link ideas within and across categories of information using words, phrases, and clauses (e.g., in contrast, especially). (d) Use precise language and domain-specific vocabulary to inform about or explain the topic. (e) Provide a concluding statement or section related to the information or explanation presented. English language learners communicate information, ideas and concepts necessary for academic success in the content area of Mathematics. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Use knowledge about place value and patterns to find the product of a decimal number and a power of 10. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10 and 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. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 5 topics and texts, building on others’ ideas and expressing their own clearly. (a) Come to discussions prepared, having read or studied required material; explicitly draw on that preparation and other information known about the topic to explore ideas under discussion. (b) Follow agreed-upon rules for discussions and carry out assigned roles. (c) Pose and respond to specific questions by making comments that contribute to the discussion and elaborate on the remarks of others. (d) Review the key ideas expressed and draw conclusions in light of information and knowledge gained from the discussions. Summarize a written text read aloud or information presented in diverse media and formats, including visually, quantitatively, and orally. Summarize the points a speaker makes and explain how each claim is supported by reasons and evidence. Step 2: Visual Learning 4-1: Visual Learning Curriculum Standards: Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Use knowledge about place value and patterns to find the product of a decimal number and a power of 10. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10 and 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. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). Identify the direction the decimal point will move when multiplying or dividing by a multiple of 10. 4-1: Convince Me! Curriculum Standards: Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Use knowledge about place value and patterns to find the product of a decimal number and a power of 10. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10 and 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. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). Practice and Problem Solving 4-1: Student Edition Practice Curriculum Standards: Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Use knowledge about place value and patterns to find the product of a decimal number and a power of 10. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10 and 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. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). 4-1: Practice Buddy: Independent Practice; Problem Solving Curriculum Standards: Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Use knowledge about place value and patterns to find the product of a decimal number and a power of 10. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10 and 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. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). 4-1: Practice Buddy: Additional Practice Curriculum Standards: Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Use knowledge about place value and patterns to find the product of a decimal number and a power of 10. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10 and 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. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). 4-1: Interactive Additional Practice Step 3: Assess & Differentiate 4-1: Practice Buddy: Additional Practice Curriculum Standards: Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Use knowledge about place value and patterns to find the product of a decimal number and a power of 10. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10 and 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. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). 4-1: Enrichment Curriculum Standards: Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Use knowledge about place value and patterns to find the product of a decimal number and a power of 10. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10 and 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. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). 4-1: Quick Check Curriculum Standards: Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Use knowledge about place value and patterns to find the product of a decimal number and a power of 10. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10 and 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. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). 4-1: Lesson Self-Assessment 4-1: Reteach to Build Understanding Curriculum Standards: Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Use knowledge about place value and patterns to find the product of a decimal number and a power of 10. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10 and 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. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). Identify the direction the decimal point will move when multiplying or dividing by a multiple of 10. 4-1: Build Mathematical Literacy Curriculum Standards: Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 5 topics and texts, building on others’ ideas and expressing their own clearly. (a) Come to discussions prepared, having read or studied required material; explicitly draw on that preparation and other information known about the topic to explore ideas under discussion. (b) Follow agreed-upon rules for discussions and carry out assigned roles. (c) Pose and respond to specific questions by making comments that contribute to the discussion and elaborate on the remarks of others. (d) Review the key ideas expressed and draw conclusions in light of information and knowledge gained from the discussions. English language learners communicate for social and instructional purposes within the school setting. Summarize a written text read aloud or information presented in diverse media and formats, including visually, quantitatively, and orally. Summarize the points a speaker makes and explain how each claim is supported by reasons and evidence. Write informative/explanatory texts to examine a topic and convey ideas and information clearly. (a) Introduce a topic clearly, provide a general observation and focus, and group related information logically; include formatting (e.g., headings), illustrations, and multimedia when useful to aiding comprehension. (b) Develop the topic with facts, definitions, concrete details, quotations, or other information and examples related to the topic. (c) Link ideas within and across categories of information using words, phrases, and clauses (e.g., in contrast, especially). (d) Use precise language and domain-specific vocabulary to inform about or explain the topic. (e) Provide a concluding statement or section related to the information or explanation presented. English language learners communicate information, ideas and concepts necessary for academic success in the content area of Mathematics. 4-1: Enrichment 4-1: Digital Math Tool Activity 4-1: enVision STEM Activity Curriculum Standards: Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Use knowledge about place value and patterns to find the product of a decimal number and a power of 10. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10 and 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. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). 4-1: Another Look Curriculum Standards: Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Use knowledge about place value and patterns to find the product of a decimal number and a power of 10. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10 and 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. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). Identify the direction the decimal point will move when multiplying or dividing by a multiple of 10. Spanish Resources 4-1: eText del Libro del estudiante 4-1: Repaso diario 4-1: Aprendizaje visual 4-1: Amigo de práctica: Práctica adicional 4-1: Práctica adicional interactiva 4-1: Refuerzo para mejorar la comprensión 4-1: Desarrollar la competencia matemática 4-1: Ampliación 4-2: Estimate the Product of a Decimal and a Whole Number Interactive Student Edition: Grade 5 Lesson 4-2 Math Anytime 4-2: Daily Review Topic 4: Today's Challenge Step 1: Problem-Based Learning 4-2: Solve & Share Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. English language learners communicate for social and instructional purposes within the school setting. Write informative/explanatory texts to examine a topic and convey ideas and information clearly. (a) Introduce a topic clearly, provide a general observation and focus, and group related information logically; include formatting (e.g., headings), illustrations, and multimedia when useful to aiding comprehension. (b) Develop the topic with facts, definitions, concrete details, quotations, or other information and examples related to the topic. (c) Link ideas within and across categories of information using words, phrases, and clauses (e.g., in contrast, especially). (d) Use precise language and domain- specific vocabulary to inform about or explain the topic. (e) Provide a concluding statement or section related to the information or explanation presented. English language learners communicate information, ideas and concepts necessary for academic success in the content area of Mathematics. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Use rounding and compatible numbers to estimate the product of a decimal and a whole number. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). Estimate solutions to arithmetic problems in order to assess the reasonableness of results. Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher- led) with diverse partners on grade 5 topics and texts, building on others’ ideas and expressing their own clearly. (a) Come to discussions prepared, having read or studied required material; explicitly draw on that preparation and other information known about the topic to explore ideas under discussion. (b) Follow agreed-upon rules for discussions and carry out assigned roles. (c) Pose and respond to specific questions by making comments that contribute to the discussion and elaborate on the remarks of others. (d) Review the key ideas expressed and draw conclusions in light of information and knowledge gained from the discussions. Summarize a written text read aloud or information presented in diverse media and formats, including visually, quantitatively, and orally. Summarize the points a speaker makes and explain how each claim is supported by reasons and evidence. Step 2: Visual Learning 4-2: Visual Learning Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Use rounding and compatible numbers to estimate the product of a decimal and a whole number. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). Estimate solutions to arithmetic problems in order to assess the reasonableness of results. 4-2: Convince Me! Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Use rounding and compatible numbers to estimate the product of a decimal and a whole number. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). Estimate solutions to arithmetic problems in order to assess the reasonableness of results. Practice and Problem Solving 4-2: Student Edition Practice Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Use rounding and compatible numbers to estimate the product of a decimal and a whole number. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). Estimate solutions to arithmetic problems in order to assess the reasonableness of results. 4-2: Practice Buddy: Independent Practice; Problem Solving Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Use rounding and compatible numbers to estimate the product of a decimal and a whole number. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). Estimate solutions to arithmetic problems in order to assess the reasonableness of results. 4-2: Practice Buddy: Additional Practice Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Use rounding and compatible numbers to estimate the product of a decimal and a whole number. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). Estimate solutions to arithmetic problems in order to assess the reasonableness of results. 4-2: Interactive Additional Practice Step 3: Assess & Differentiate 4-2: Practice Buddy: Additional Practice Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Use rounding and compatible numbers to estimate the product of a decimal and a whole number. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). Estimate solutions to arithmetic problems in order to assess the reasonableness of results. 4-2: Enrichment Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Use rounding and compatible numbers to estimate the product of a decimal and a whole number. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). Estimate solutions to arithmetic problems in order to assess the reasonableness of results. 4-2: Quick Check Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Use rounding and compatible numbers to estimate the product of a decimal and a whole number. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). Estimate solutions to arithmetic problems in order to assess the reasonableness of results. 4-2: Lesson Self-Assessment 4-2: Reteach to Build Understanding Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Use rounding and compatible numbers to estimate the product of a decimal and a whole number. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). Estimate solutions to arithmetic problems in order to assess the reasonableness of results. 4-2: Build Mathematical Literacy Curriculum Standards: Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 5 topics and texts, building on others’ ideas and expressing their own clearly. (a) Come to discussions prepared, having read or studied required material; explicitly draw on that preparation and other information known about the topic to explore ideas under discussion. (b) Follow agreed-upon rules for discussions and carry out assigned roles. (c) Pose and respond to specific questions by making comments that contribute to the discussion and elaborate on the remarks of others. (d) Review the key ideas expressed and draw conclusions in light of information and knowledge gained from the discussions. English language learners communicate for social and instructional purposes within the school setting. Summarize a written text read aloud or information presented in diverse media and formats, including visually, quantitatively, and orally. Summarize the points a speaker makes and explain how each claim is supported by reasons and evidence. Write informative/explanatory texts to examine a topic and convey ideas and information clearly. (a) Introduce a topic clearly, provide a general observation and focus, and group related information logically; include formatting (e.g., headings), illustrations, and multimedia when useful to aiding comprehension. (b) Develop the topic with facts, definitions, concrete details, quotations, or other information and examples related to the topic. (c) Link ideas within and across categories of information using words, phrases, and clauses (e.g., in contrast, especially). (d) Use precise language and domain-specific vocabulary to inform about or explain the topic. (e) Provide a concluding statement or section related to the information or explanation presented. English language learners communicate information, ideas and concepts necessary for academic success in the content area of Mathematics. 4-2: Enrichment 4-2: Digital Math Tool Activity 4-2: Pick a Project 4-2: Another Look Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Use rounding and compatible numbers to estimate the product of a decimal and a whole number. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). Estimate solutions to arithmetic problems in order to assess the reasonableness of results. Spanish Resources 4-2: eText del Libro del estudiante 4-2: Repaso diario 4-2: Aprendizaje visual 4-2: Amigo de práctica: Práctica adicional 4-2: Práctica adicional interactiva 4-2: Refuerzo para mejorar la comprensión 4-2: Desarrollar la competencia matemática 4-2: Ampliación 4-3: Use Models to Multiply a Decimal and a Whole Number Interactive Student Edition: Grade 5 Lesson 4-3 Math Anytime 4-3: Daily Review Topic 4: Today's Challenge Step 1: Problem-Based Learning 4-3: Solve & Share Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. English language learners communicate for social and instructional purposes within the school setting. Write informative/explanatory texts to examine a topic and convey ideas and information clearly. (a) Introduce a topic clearly, provide a general observation and focus, and group related information logically; include formatting (e.g., headings), illustrations, and multimedia when useful to aiding comprehension. (b) Develop the topic with facts, definitions, concrete details, quotations, or other information and examples related to the topic. (c) Link ideas within and across categories of information using words, phrases, and clauses (e.g., in contrast, especially). (d) Use precise language and domain- specific vocabulary to inform about or explain the topic. (e) Provide a concluding statement or section related to the information or explanation presented. English language learners communicate information, ideas and concepts necessary for academic success in the content area of Mathematics. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Use models to represent multiplying a decimal and a whole number. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 5 topics and texts, building on others’ ideas and expressing their own clearly. (a) Come to discussions prepared, having read or studied required material; explicitly draw on that preparation and other information known about the topic to explore ideas under discussion. (b) Follow agreed-upon rules for discussions and carry out assigned roles. (c) Pose and respond to specific questions by making comments that contribute to the discussion and elaborate on the remarks of others. (d) Review the key ideas expressed and draw conclusions in light of information and knowledge gained from the discussions. Summarize a written text read aloud or information presented in diverse media and formats, including visually, quantitatively, and orally. Summarize the points a speaker makes and explain how each claim is supported by reasons and evidence. Step 2: Visual Learning 4-3: Visual Learning Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Use models to represent multiplying a decimal and a whole number. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). 4-3: Convince Me! Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Use models to represent multiplying a decimal and a whole number. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). Practice and Problem Solving 4-3: Student Edition Practice Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Use models to represent multiplying a decimal and a whole number. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). 4-3: Practice Buddy: Independent Practice; Problem Solving Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Use models to represent multiplying a decimal and a whole number. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). 4-3: Practice Buddy: Additional Practice Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Use models to represent multiplying a decimal and a whole number. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). 4-3: Interactive Additional Practice Step 3: Assess & Differentiate 4-3: Practice Buddy: Additional Practice Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Use models to represent multiplying a decimal and a whole number. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). 4-3: Enrichment Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Use models to represent multiplying a decimal and a whole number. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). 4-3: Quick Check Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Use models to represent multiplying a decimal and a whole number. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). 4-3: Lesson Self-Assessment 4-3: Reteach to Build Understanding Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Use models to represent multiplying a decimal and a whole number. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). 4-3: Build Mathematical Literacy Curriculum Standards: Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 5 topics and texts, building on others’ ideas and expressing their own clearly. (a) Come to discussions prepared, having read or studied required material; explicitly draw on that preparation and other information known about the topic to explore ideas under discussion. (b) Follow agreed-upon rules for discussions and carry out assigned roles. (c) Pose and respond to specific questions by making comments that contribute to the discussion and elaborate on the remarks of others. (d) Review the key ideas expressed and draw conclusions in light of information and knowledge gained from the discussions. English language learners communicate for social and instructional purposes within the school setting. Summarize a written text read aloud or information presented in diverse media and formats, including visually, quantitatively, and orally. Summarize the points a speaker makes and explain how each claim is supported by reasons and evidence. Write informative/explanatory texts to examine a topic and convey ideas and information clearly. (a) Introduce a topic clearly, provide a general observation and focus, and group related information logically; include formatting (e.g., headings), illustrations, and multimedia when useful to aiding comprehension. (b) Develop the topic with facts, definitions, concrete details, quotations, or other information and examples related to the topic. (c) Link ideas within and across categories of information using words, phrases, and clauses (e.g., in contrast, especially). (d) Use precise language and domain-specific vocabulary to inform about or explain the topic. (e) Provide a concluding statement or section related to the information or explanation presented. English language learners communicate information, ideas and concepts necessary for academic success in the content area of Mathematics. 4-3: Enrichment 4-3: Digital Math Tool Activity 4-3: Problem-Solving Reading Activity Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Use models to represent multiplying a decimal and a whole number. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). 4-3: Another Look Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Use models to represent multiplying a decimal and a whole number. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). Spanish Resources 4-3: eText del Libro del estudiante 4-3: Repaso diario 4-3: Aprendizaje visual 4-3: Amigo de práctica: Práctica adicional 4-3: Práctica adicional interactiva 4-3: Refuerzo para mejorar la comprensión 4-3: Desarrollar la competencia matemática 4-3: Ampliación 4-4: Multiply a Decimal by a Whole Number Interactive Student Edition: Grade 5 Lesson 4-4 Math Anytime 4-4: Daily Review Topic 4: Today's Challenge Step 1: Problem-Based Learning 4-4: Solve & Share Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. English language learners communicate for social and instructional purposes within the school setting. Write informative/explanatory texts to examine a topic and convey ideas and information clearly. (a) Introduce a topic clearly, provide a general observation and focus, and group related information logically; include formatting (e.g., headings), illustrations, and multimedia when useful to aiding comprehension. (b) Develop the topic with facts, definitions, concrete details, quotations, or other information and examples related to the topic. (c) Link ideas within and across categories of information using words, phrases, and clauses (e.g., in contrast, especially). (d) Use precise language and domain- specific vocabulary to inform about or explain the topic. (e) Provide a concluding statement or section related to the information or explanation presented. English language learners communicate information, ideas and concepts necessary for academic success in the content area of Mathematics. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Use place-value understanding and an algorithm for multiplying whole numbers to multiply a decimal and a whole number. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 5 topics and texts, building on others’ ideas and expressing their own clearly. (a) Come to discussions prepared, having read or studied required material; explicitly draw on that preparation and other information known about the topic to explore ideas under discussion. (b) Follow agreed-upon rules for discussions and carry out assigned roles. (c) Pose and respond to specific questions by making comments that contribute to the discussion and elaborate on the remarks of others. (d) Review the key ideas expressed and draw conclusions in light of information and knowledge gained from the discussions. Summarize a written text read aloud or information presented in diverse media and formats, including visually, quantitatively, and orally. Summarize the points a speaker makes and explain how each claim is supported by reasons and evidence. Step 2: Visual Learning 4-4: Visual Learning Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Use place-value understanding and an algorithm for multiplying whole numbers to multiply a decimal and a whole number. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). 4-4: Convince Me! Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Use place-value understanding and an algorithm for multiplying whole numbers to multiply a decimal and a whole number. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). Practice and Problem Solving 4-4: Student Edition Practice Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Use place-value understanding and an algorithm for multiplying whole numbers to multiply a decimal and a whole number. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). 4-4: Practice Buddy: Independent Practice; Problem Solving Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Use place-value understanding and an algorithm for multiplying whole numbers to multiply a decimal and a whole number. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). 4-4: Practice Buddy: Additional Practice Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Use place-value understanding and an algorithm for multiplying whole numbers to multiply a decimal and a whole number. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). 4-4: Interactive Additional Practice Step 3: Assess & Differentiate 4-4: Practice Buddy: Additional Practice Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Use place-value understanding and an algorithm for multiplying whole numbers to multiply a decimal and a whole number. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). 4-4: Enrichment Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Use place-value understanding and an algorithm for multiplying whole numbers to multiply a decimal and a whole number. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). 4-4: Quick Check Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Use place-value understanding and an algorithm for multiplying whole numbers to multiply a decimal and a whole number. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). 4-4: Lesson Self-Assessment 4-4: Reteach to Build Understanding Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Use place-value understanding and an algorithm for multiplying whole numbers to multiply a decimal and a whole number. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). 4-4: Build Mathematical Literacy Curriculum Standards: Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 5 topics and texts, building on others’ ideas and expressing their own clearly. (a) Come to discussions prepared, having read or studied required material; explicitly draw on that preparation and other information known about the topic to explore ideas under discussion. (b) Follow agreed-upon rules for discussions and carry out assigned roles. (c) Pose and respond to specific questions by making comments that contribute to the discussion and elaborate on the remarks of others. (d) Review the key ideas expressed and draw conclusions in light of information and knowledge gained from the discussions. English language learners communicate for social and instructional purposes within the school setting. Summarize a written text read aloud or information presented in diverse media and formats, including visually, quantitatively, and orally. Summarize the points a speaker makes and explain how each claim is supported by reasons and evidence. Write informative/explanatory texts to examine a topic and convey ideas and information clearly. (a) Introduce a topic clearly, provide a general observation and focus, and group related information logically; include formatting (e.g., headings), illustrations, and multimedia when useful to aiding comprehension. (b) Develop the topic with facts, definitions, concrete details, quotations, or other information and examples related to the topic. (c) Link ideas within and across categories of information using words, phrases, and clauses (e.g., in contrast, especially). (d) Use precise language and domain-specific vocabulary to inform about or explain the topic. (e) Provide a concluding statement or section related to the information or explanation presented. English language learners communicate information, ideas and concepts necessary for academic success in the content area of Mathematics. 4-4: Enrichment 4-4: Digital Math Tool Activity 4-4: enVision STEM Activity Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Use place-value understanding and an algorithm for multiplying whole numbers to multiply a decimal and a whole number. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). 4-4: Another Look Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Use place-value understanding and an algorithm for multiplying whole numbers to multiply a decimal and a whole number. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). Spanish Resources 4-4: eText del Libro del estudiante 4-4: Repaso diario 4-4: Aprendizaje visual 4-4: Amigo de práctica: Práctica adicional 4-4: Práctica adicional interactiva 4-4: Refuerzo para mejorar la comprensión 4-4: Desarrollar la competencia matemática 4-4: Ampliación 4-5: Use Models to Multiply a Decimal and a Decimal Interactive Student Edition: Grade 5 Lesson 4-5 Math Anytime 4-5: Daily Review Topic 4: Today's Challenge Step 1: Problem-Based Learning 4-5: Solve & Share Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. English language learners communicate for social and instructional purposes within the school setting. Write informative/explanatory texts to examine a topic and convey ideas and information clearly. (a) Introduce a topic clearly, provide a general observation and focus, and group related information logically; include formatting (e.g., headings), illustrations, and multimedia when useful to aiding comprehension. (b) Develop the topic with facts, definitions, concrete details, quotations, or other information and examples related to the topic. (c) Link ideas within and across categories of information using words, phrases, and clauses (e.g., in contrast, especially). (d) Use precise language and domain- specific vocabulary to inform about or explain the topic. (e) Provide a concluding statement or section related to the information or explanation presented. English language learners communicate information, ideas and concepts necessary for academic success in the content area of Mathematics. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Use grids to model decimals and find the product of a decimal and a decimal. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher- led) with diverse partners on grade 5 topics and texts, building on others’ ideas and expressing their own clearly. (a) Come to discussions prepared, having read or studied required material; explicitly draw on that preparation and other information known about the topic to explore ideas under discussion. (b) Follow agreed-upon rules for discussions and carry out assigned roles. (c) Pose and respond to specific questions by making comments that contribute to the discussion and elaborate on the remarks of others. (d) Review the key ideas expressed and draw conclusions in light of information and knowledge gained from the discussions. Summarize a written text read aloud or information presented in diverse media and formats, including visually, quantitatively, and orally. Summarize the points a speaker makes and explain how each claim is supported by reasons and evidence. Step 2: Visual Learning 4-5: Visual Learning Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Use grids to model decimals and find the product of a decimal and a decimal. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). 4-5: Convince Me! Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Use grids to model decimals and find the product of a decimal and a decimal. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). Practice and Problem Solving 4-5: Student Edition Practice Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Use grids to model decimals and find the product of a decimal and a decimal. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). 4-5: Practice Buddy: Independent Practice; Problem Solving Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Use grids to model decimals and find the product of a decimal and a decimal. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). 4-5: Practice Buddy: Additional Practice Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Use grids to model decimals and find the product of a decimal and a decimal. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). 4-5: Interactive Additional Practice Step 3: Assess & Differentiate 4-5: Practice Buddy: Additional Practice Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Use grids to model decimals and find the product of a decimal and a decimal. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). 4-5: Enrichment Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Use grids to model decimals and find the product of a decimal and a decimal. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). 4-5: Quick Check Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Use grids to model decimals and find the product of a decimal and a decimal. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). 4-5: Lesson Self-Assessment 4-5: Reteach to Build Understanding Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Use grids to model decimals and find the product of a decimal and a decimal. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). 4-5: Build Mathematical Literacy Curriculum Standards: Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 5 topics and texts, building on others’ ideas and expressing their own clearly. (a) Come to discussions prepared, having read or studied required material; explicitly draw on that preparation and other information known about the topic to explore ideas under discussion. (b) Follow agreed-upon rules for discussions and carry out assigned roles. (c) Pose and respond to specific questions by making comments that contribute to the discussion and elaborate on the remarks of others. (d) Review the key ideas expressed and draw conclusions in light of information and knowledge gained from the discussions. English language learners communicate for social and instructional purposes within the school setting. Summarize a written text read aloud or information presented in diverse media and formats, including visually, quantitatively, and orally. Summarize the points a speaker makes and explain how each claim is supported by reasons and evidence. Write informative/explanatory texts to examine a topic and convey ideas and information clearly. (a) Introduce a topic clearly, provide a general observation and focus, and group related information logically; include formatting (e.g., headings), illustrations, and multimedia when useful to aiding comprehension. (b) Develop the topic with facts, definitions, concrete details, quotations, or other information and examples related to the topic. (c) Link ideas within and across categories of information using words, phrases, and clauses (e.g., in contrast, especially). (d) Use precise language and domain-specific vocabulary to inform about or explain the topic. (e) Provide a concluding statement or section related to the information or explanation presented. English language learners communicate information, ideas and concepts necessary for academic success in the content area of Mathematics. 4-5: Enrichment 4-5: Digital Math Tool Activity 4-5: Pick a Project 4-5: Another Look Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Use grids to model decimals and find the product of a decimal and a decimal. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). Spanish Resources 4-5: eText del Libro del estudiante 4-5: Repaso diario 4-5: Aprendizaje visual 4-5: Amigo de práctica: Práctica adicional 4-5: Práctica adicional interactiva 4-5: Refuerzo para mejorar la comprensión 4-5: Desarrollar la competencia matemática 4-5: Ampliación 4-6: Multiply Decimals Using Partial Products Interactive Student Edition: Grade 5 Lesson 4-6 Math Anytime 4-6: Daily Review Topic 4: Today's Challenge Step 1: Problem-Based Learning 4-6: Solve & Share Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. English language learners communicate for social and instructional purposes within the school setting. Write informative/explanatory texts to examine a topic and convey ideas and information clearly. (a) Introduce a topic clearly, provide a general observation and focus, and group related information logically; include formatting (e.g., headings), illustrations, and multimedia when useful to aiding comprehension. (b) Develop the topic with facts, definitions, concrete details, quotations, or other information and examples related to the topic. (c) Link ideas within and across categories of information using words, phrases, and clauses (e.g., in contrast, especially). (d) Use precise language and domain- specific vocabulary to inform about or explain the topic. (e) Provide a concluding statement or section related to the information or explanation presented. English language learners communicate information, ideas and concepts necessary for academic success in the content area of Mathematics. Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 5 topics and texts, building on others’ ideas and expressing their own clearly. (a) Come to discussions prepared, having read or studied required material; explicitly draw on that preparation and other information known about the topic to explore ideas under discussion. (b) Follow agreed-upon rules for discussions and carry out assigned roles. (c) Pose and respond to specific questions by making comments that contribute to the discussion and elaborate on the remarks of others. (d) Review the key ideas expressed and draw conclusions in light of information and knowledge gained from the discussions. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Multiply decimals using partial products and models. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). Summarize a written text read aloud or information presented in diverse media and formats, including visually, quantitatively, and orally. Summarize the points a speaker makes and explain how each claim is supported by reasons and evidence. Step 2: Visual Learning 4-6: Visual Learning Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Multiply decimals using partial products and models. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). 4-6: Convince Me! Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Multiply decimals using partial products and models. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). Practice and Problem Solving 4-6: Student Edition Practice Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Multiply decimals using partial products and models. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). 4-6: Practice Buddy: Independent Practice; Problem Solving Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Multiply decimals using partial products and models. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). 4-6: Practice Buddy: Additional Practice Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Multiply decimals using partial products and models. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). 4-6: Interactive Additional Practice Step 3: Assess & Differentiate 4-6: Practice Buddy: Additional Practice Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Multiply decimals using partial products and models. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). 4-6: Enrichment Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Multiply decimals using partial products and models. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). 4-6: Quick Check Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Multiply decimals using partial products and models. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). 4-6: Lesson Self-Assessment 4-6: Reteach to Build Understanding Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Multiply decimals using partial products and models. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). 4-6: Build Mathematical Literacy Curriculum Standards: Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 5 topics and texts, building on others’ ideas and expressing their own clearly. (a) Come to discussions prepared, having read or studied required material; explicitly draw on that preparation and other information known about the topic to explore ideas under discussion. (b) Follow agreed-upon rules for discussions and carry out assigned roles. (c) Pose and respond to specific questions by making comments that contribute to the discussion and elaborate on the remarks of others. (d) Review the key ideas expressed and draw conclusions in light of information and knowledge gained from the discussions. English language learners communicate for social and instructional purposes within the school setting. Summarize a written text read aloud or information presented in diverse media and formats, including visually, quantitatively, and orally. Summarize the points a speaker makes and explain how each claim is supported by reasons and evidence. Write informative/explanatory texts to examine a topic and convey ideas and information clearly. (a) Introduce a topic clearly, provide a general observation and focus, and group related information logically; include formatting (e.g., headings), illustrations, and multimedia when useful to aiding comprehension. (b) Develop the topic with facts, definitions, concrete details, quotations, or other information and examples related to the topic. (c) Link ideas within and across categories of information using words, phrases, and clauses (e.g., in contrast, especially). (d) Use precise language and domain-specific vocabulary to inform about or explain the topic. (e) Provide a concluding statement or section related to the information or explanation presented. English language learners communicate information, ideas and concepts necessary for academic success in the content area of Mathematics. 4-6: Enrichment Game: Factory Frenzy - Decimals 4-6: Pick a Project 4-6: Another Look Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Multiply decimals using partial products and models. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). Spanish Resources 4-6: eText del Libro del estudiante 4-6: Repaso diario 4-6: Aprendizaje visual 4-6: Amigo de práctica: Práctica adicional 4-6: Práctica adicional interactiva 4-6: Refuerzo para mejorar la comprensión 4-6: Desarrollar la competencia matemática 4-6: Ampliación 4-7: Use Properties to Multiply Decimals Interactive Student Edition: Grade 5 Lesson 4-7 Math Anytime 4-7: Daily Review Topic 4: Today's Challenge Step 1: Problem-Based Learning 4-7: Solve & Share Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. English language learners communicate for social and instructional purposes within the school setting. Write informative/explanatory texts to examine a topic and convey ideas and information clearly. (a) Introduce a topic clearly, provide a general observation and focus, and group related information logically; include formatting (e.g., headings), illustrations, and multimedia when useful to aiding comprehension. (b) Develop the topic with facts, definitions, concrete details, quotations, or other information and examples related to the topic. (c) Link ideas within and across categories of information using words, phrases, and clauses (e.g., in contrast, especially). (d) Use precise language and domain- specific vocabulary to inform about or explain the topic. (e) Provide a concluding statement or section related to the information or explanation presented. English language learners communicate information, ideas and concepts necessary for academic success in the content area of Mathematics. Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 5 topics and texts, building on others’ ideas and expressing their own clearly. (a) Come to discussions prepared, having read or studied required material; explicitly draw on that preparation and other information known about the topic to explore ideas under discussion. (b) Follow agreed-upon rules for discussions and carry out assigned roles. (c) Pose and respond to specific questions by making comments that contribute to the discussion and elaborate on the remarks of others. (d) Review the key ideas expressed and draw conclusions in light of information and knowledge gained from the discussions. Summarize a written text read aloud or information presented in diverse media and formats, including visually, quantitatively, and orally. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Use properties to multiply decimals. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). Summarize the points a speaker makes and explain how each claim is supported by reasons and evidence. Step 2: Visual Learning 4-7: Visual Learning Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Use properties to multiply decimals. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). 4-7: Convince Me! Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Use properties to multiply decimals. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). Practice and Problem Solving 4-7: Student Edition Practice Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Use properties to multiply decimals. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). 4-7: Practice Buddy: Independent Practice; Problem Solving Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Use properties to multiply decimals. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). 4-7: Practice Buddy: Additional Practice Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Use properties to multiply decimals. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). 4-7: Interactive Additional Practice Step 3: Assess & Differentiate 4-7: Practice Buddy: Additional Practice Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Use properties to multiply decimals. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). 4-7: Enrichment Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Use properties to multiply decimals. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). 4-7: Quick Check Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Use properties to multiply decimals. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). 4-7: Lesson Self-Assessment 4-7: Reteach to Build Understanding Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Use properties to multiply decimals. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). 4-7: Build Mathematical Literacy Curriculum Standards: Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 5 topics and texts, building on others’ ideas and expressing their own clearly. (a) Come to discussions prepared, having read or studied required material; explicitly draw on that preparation and other information known about the topic to explore ideas under discussion. (b) Follow agreed-upon rules for discussions and carry out assigned roles. (c) Pose and respond to specific questions by making comments that contribute to the discussion and elaborate on the remarks of others. (d) Review the key ideas expressed and draw conclusions in light of information and knowledge gained from the discussions. English language learners communicate for social and instructional purposes within the school setting. Summarize a written text read aloud or information presented in diverse media and formats, including visually, quantitatively, and orally. Summarize the points a speaker makes and explain how each claim is supported by reasons and evidence. Write informative/explanatory texts to examine a topic and convey ideas and information clearly. (a) Introduce a topic clearly, provide a general observation and focus, and group related information logically; include formatting (e.g., headings), illustrations, and multimedia when useful to aiding comprehension. (b) Develop the topic with facts, definitions, concrete details, quotations, or other information and examples related to the topic. (c) Link ideas within and across categories of information using words, phrases, and clauses (e.g., in contrast, especially). (d) Use precise language and domain-specific vocabulary to inform about or explain the topic. (e) Provide a concluding statement or section related to the information or explanation presented. English language learners communicate information, ideas and concepts necessary for academic success in the content area of Mathematics. 4-7: Enrichment 4-7: Digital Math Tool Activity 4-7: Pick a Project 4-7: Another Look Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Use properties to multiply decimals. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). Spanish Resources 4-7: eText del Libro del estudiante 4-7: Repaso diario 4-7: Aprendizaje visual 4-7: Amigo de práctica: Práctica adicional 4-7: Práctica adicional interactiva 4-7: Refuerzo para mejorar la comprensión 4-7: Desarrollar la competencia matemática 4-7: Ampliación 4-8: Use Number Sense to Multiply Decimals Interactive Student Edition: Grade 5 Lesson 4-8 Math Anytime 4-8: Daily Review Topic 4: Today's Challenge Step 1: Problem-Based Learning 4-8: Solve & Share Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. English language learners communicate for social and instructional purposes within the school setting. Write informative/explanatory texts to examine a topic and convey ideas and information clearly. (a) Introduce a topic clearly, provide a general observation and focus, and group related information logically; include formatting (e.g., headings), illustrations, and multimedia when useful to aiding comprehension. (b) Develop the topic with facts, definitions, concrete details, quotations, or other information and examples related to the topic. (c) Link ideas within and across categories of information using words, phrases, and clauses (e.g., in contrast, especially). (d) Use precise language and domain- specific vocabulary to inform about or explain the topic. (e) Provide a concluding statement or section related to the information or explanation presented. English language learners communicate information, ideas and concepts necessary for academic success in the content area of Mathematics. Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 5 topics and texts, building on others’ ideas and expressing their own clearly. (a) Come to discussions prepared, having read or studied required material; explicitly draw on that preparation and other information known about the topic to explore ideas under discussion. (b) Follow agreed-upon rules for discussions and carry out assigned roles. (c) Pose and respond to specific questions by making comments that contribute to the discussion and elaborate on the remarks of others. (d) Review the key ideas expressed and draw conclusions in light of information and knowledge gained from the discussions. Summarize a written text read aloud or information presented in diverse media and formats, including visually, quantitatively, and orally. Summarize the points a speaker makes and explain how each claim is supported by reasons and evidence. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Use number sense and reasoning to place the decimal point in a product. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). Step 2: Visual Learning 4-8: Visual Learning Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Use number sense and reasoning to place the decimal point in a product. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). 4-8: Convince Me! Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Use number sense and reasoning to place the decimal point in a product. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). Practice and Problem Solving 4-8: Student Edition Practice Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Use number sense and reasoning to place the decimal point in a product. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). 4-8: Practice Buddy: Independent Practice; Problem Solving Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Use number sense and reasoning to place the decimal point in a product. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). 4-8: Practice Buddy: Additional Practice Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Use number sense and reasoning to place the decimal point in a product. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). 4-8: Interactive Additional Practice Step 3: Assess & Differentiate 4-8: Practice Buddy: Additional Practice Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Use number sense and reasoning to place the decimal point in a product. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). 4-8: Enrichment Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Use number sense and reasoning to place the decimal point in a product. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). 4-8: Quick Check Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Use number sense and reasoning to place the decimal point in a product. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). 4-8: Lesson Self-Assessment 4-8: Reteach to Build Understanding Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Use number sense and reasoning to place the decimal point in a product. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). 4-8: Build Mathematical Literacy Curriculum Standards: Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 5 topics and texts, building on others’ ideas and expressing their own clearly. (a) Come to discussions prepared, having read or studied required material; explicitly draw on that preparation and other information known about the topic to explore ideas under discussion. (b) Follow agreed-upon rules for discussions and carry out assigned roles. (c) Pose and respond to specific questions by making comments that contribute to the discussion and elaborate on the remarks of others. (d) Review the key ideas expressed and draw conclusions in light of information and knowledge gained from the discussions. English language learners communicate for social and instructional purposes within the school setting. Summarize a written text read aloud or information presented in diverse media and formats, including visually, quantitatively, and orally. Summarize the points a speaker makes and explain how each claim is supported by reasons and evidence. Write informative/explanatory texts to examine a topic and convey ideas and information clearly. (a) Introduce a topic clearly, provide a general observation and focus, and group related information logically; include formatting (e.g., headings), illustrations, and multimedia when useful to aiding comprehension. (b) Develop the topic with facts, definitions, concrete details, quotations, or other information and examples related to the topic. (c) Link ideas within and across categories of information using words, phrases, and clauses (e.g., in contrast, especially). (d) Use precise language and domain-specific vocabulary to inform about or explain the topic. (e) Provide a concluding statement or section related to the information or explanation presented. English language learners communicate information, ideas and concepts necessary for academic success in the content area of Mathematics. 4-8: Enrichment 4-8: Digital Math Tool Activity 4-8: Problem-Solving Reading Activity Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Use number sense and reasoning to place the decimal point in a product. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). 4-8: Another Look Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Use number sense and reasoning to place the decimal point in a product. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). Spanish Resources 4-8: eText del Libro del estudiante 4-8: Repaso diario 4-8: Aprendizaje visual 4-8: Amigo de práctica: Práctica adicional 4-8: Práctica adicional interactiva 4-8: Refuerzo para mejorar la comprensión 4-8: Desarrollar la competencia matemática 4-8: Ampliación 4-9: Problem Solving: Model with Math Interactive Student Edition: Grade 5 Lesson 4-9 Math Anytime 4-9: Daily Review Topic 4: Today's Challenge Step 1: Problem-Based Learning 4-9: Solve & Share Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Model with mathematics. English language learners communicate for social and instructional purposes within the school setting. Write informative/explanatory texts to examine a topic and convey ideas and information clearly. (a) Introduce a topic clearly, provide a general observation and focus, and group related information logically; include formatting (e.g., headings), illustrations, and multimedia when useful to aiding comprehension. (b) Develop the topic with facts, definitions, concrete details, quotations, or other information and examples related to the topic. (c) Link ideas within and across categories of information using words, phrases, and clauses (e.g., in contrast, especially). (d) Use precise language and domain-specific vocabulary to inform about or explain the topic. (e) Provide a concluding statement or section related to the information or explanation presented. English language learners communicate information, ideas and concepts necessary for academic success in the content area of Mathematics. Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 5 topics and texts, building on others’ ideas and expressing their own clearly. (a) Come to discussions prepared, having read or studied required material; explicitly draw on that preparation and other information known about the topic to explore ideas under discussion. (b) Follow agreed-upon rules for discussions and carry out assigned roles. (c) Pose and respond to specific questions by making comments that contribute to the discussion and elaborate on the remarks of others. (d) Review the key ideas expressed and draw conclusions in light of information and knowledge gained from the discussions. Summarize a written text read aloud or information presented in diverse media and formats, including visually, quantitatively, and orally. Summarize the points a speaker makes and explain how each claim is supported by reasons and evidence. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Model with mathematics. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Model with mathematics. Mathematically proficient students can apply the mathematics they know to solve problems arising in everyday life, society, and the workplace. In early grades, this might be as simple as writing an addition equation to describe a situation. In middle grades, a student might apply proportional reasoning to plan a school event or analyze a problem in the community. By high school, a student might use geometry to solve a design problem or use a function to describe how one quantity of interest depends on another. Mathematically proficient students who can apply what they know are comfortable making assumptions and approximations to simplify a complicated situation, realizing that these may need revision later. They are able to identify important quantities in a practical situation and map their relationships using such tools as diagrams, two-way tables, graphs, flowcharts and formulas. They can analyze those relationships mathematically to draw conclusions. They routinely interpret their mathematical results in the context of the situation and reflect on whether the results make sense, possibly improving the model if it has not served its purpose. Use previously learned concepts and skills to represent and solve problems. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Model with mathematics. Model with mathematics. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). Model with mathematics. Step 2: Visual Learning 4-9: Visual Learning Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Model with mathematics. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Model with mathematics. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Model with mathematics. Mathematically proficient students can apply the mathematics they know to solve problems arising in everyday life, society, and the workplace. In early grades, this might be as simple as writing an addition equation to describe a situation. In middle grades, a student might apply proportional reasoning to plan a school event or analyze a problem in the community. By high school, a student might use geometry to solve a design problem or use a function to describe how one quantity of interest depends on another. Mathematically proficient students who can apply what they know are comfortable making assumptions and approximations to simplify a complicated situation, realizing that these may need revision later. They are able to identify important quantities in a practical situation and map their relationships using such tools as diagrams, two-way tables, graphs, flowcharts and formulas. They can analyze those relationships mathematically to draw conclusions. They routinely interpret their mathematical results in the context of the situation and reflect on whether the results make sense, possibly improving the model if it has not served its purpose. Use previously learned concepts and skills to represent and solve problems. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Model with mathematics. Model with mathematics. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). Model with mathematics. Solve one-step problems using decimals. 4-9: Convince Me! Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Model with mathematics. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Model with mathematics. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Model with mathematics. Mathematically proficient students can apply the mathematics they know to solve problems arising in everyday life, society, and the workplace. In early grades, this might be as simple as writing an addition equation to describe a situation. In middle grades, a student might apply proportional reasoning to plan a school event or analyze a problem in the community. By high school, a student might use geometry to solve a design problem or use a function to describe how one quantity of interest depends on another. Mathematically proficient students who can apply what they know are comfortable making assumptions and approximations to simplify a complicated situation, realizing that these may need revision later. They are able to identify important quantities in a practical situation and map their relationships using such tools as diagrams, two-way tables, graphs, flowcharts and formulas. They can analyze those relationships mathematically to draw conclusions. They routinely interpret their mathematical results in the context of the situation and reflect on whether the results make sense, possibly improving the model if it has not served its purpose. Use previously learned concepts and skills to represent and solve problems. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Model with mathematics. Model with mathematics. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). Model with mathematics. Practice and Problem Solving 4-9: Student Edition Practice Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Model with mathematics. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Model with mathematics. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Model with mathematics. Mathematically proficient students can apply the mathematics they know to solve problems arising in everyday life, society, and the workplace. In early grades, this might be as simple as writing an addition equation to describe a situation. In middle grades, a student might apply proportional reasoning to plan a school event or analyze a problem in the community. By high school, a student might use geometry to solve a design problem or use a function to describe how one quantity of interest depends on another. Mathematically proficient students who can apply what they know are comfortable making assumptions and approximations to simplify a complicated situation, realizing that these may need revision later. They are able to identify important quantities in a practical situation and map their relationships using such tools as diagrams, two-way tables, graphs, flowcharts and formulas. They can analyze those relationships mathematically to draw conclusions. They routinely interpret their mathematical results in the context of the situation and reflect on whether the results make sense, possibly improving the model if it has not served its purpose. Use previously learned concepts and skills to represent and solve problems. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Model with mathematics. Model with mathematics. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). Model with mathematics. 4-9: Practice Buddy: Independent Practice; Problem Solving Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Model with mathematics. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Model with mathematics. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Model with mathematics. Mathematically proficient students can apply the mathematics they know to solve problems arising in everyday life, society, and the workplace. In early grades, this might be as simple as writing an addition equation to describe a situation. In middle grades, a student might apply proportional reasoning to plan a school event or analyze a problem in the community. By high school, a student might use geometry to solve a design problem or use a function to describe how one quantity of interest depends on another. Mathematically proficient students who can apply what they know are comfortable making assumptions and approximations to simplify a complicated situation, realizing that these may need revision later. They are able to identify important quantities in a practical situation and map their relationships using such tools as diagrams, two-way tables, graphs, flowcharts and formulas. They can analyze those relationships mathematically to draw conclusions. They routinely interpret their mathematical results in the context of the situation and reflect on whether the results make sense, possibly improving the model if it has not served its purpose. Use previously learned concepts and skills to represent and solve problems. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Model with mathematics. Model with mathematics. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). Model with mathematics. 4-9: Practice Buddy: Additional Practice Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Model with mathematics. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Model with mathematics. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Model with mathematics. Mathematically proficient students can apply the mathematics they know to solve problems arising in everyday life, society, and the workplace. In early grades, this might be as simple as writing an addition equation to describe a situation. In middle grades, a student might apply proportional reasoning to plan a school event or analyze a problem in the community. By high school, a student might use geometry to solve a design problem or use a function to describe how one quantity of interest depends on another. Mathematically proficient students who can apply what they know are comfortable making assumptions and approximations to simplify a complicated situation, realizing that these may need revision later. They are able to identify important quantities in a practical situation and map their relationships using such tools as diagrams, two-way tables, graphs, flowcharts and formulas. They can analyze those relationships mathematically to draw conclusions. They routinely interpret their mathematical results in the context of the situation and reflect on whether the results make sense, possibly improving the model if it has not served its purpose. Use previously learned concepts and skills to represent and solve problems. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Model with mathematics. Model with mathematics. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). Model with mathematics. 4-9: Interactive Additional Practice Step 3: Assess & Differentiate 4-9: Practice Buddy: Additional Practice Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Model with mathematics. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Model with mathematics. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Model with mathematics. Mathematically proficient students can apply the mathematics they know to solve problems arising in everyday life, society, and the workplace. In early grades, this might be as simple as writing an addition equation to describe a situation. In middle grades, a student might apply proportional reasoning to plan a school event or analyze a problem in the community. By high school, a student might use geometry to solve a design problem or use a function to describe how one quantity of interest depends on another. Mathematically proficient students who can apply what they know are comfortable making assumptions and approximations to simplify a complicated situation, realizing that these may need revision later. They are able to identify important quantities in a practical situation and map their relationships using such tools as diagrams, two-way tables, graphs, flowcharts and formulas. They can analyze those relationships mathematically to draw conclusions. They routinely interpret their mathematical results in the context of the situation and reflect on whether the results make sense, possibly improving the model if it has not served its purpose. Use previously learned concepts and skills to represent and solve problems. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Model with mathematics. Model with mathematics. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). Model with mathematics. 4-9: Enrichment Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Model with mathematics. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Model with mathematics. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Model with mathematics. Mathematically proficient students can apply the mathematics they know to solve problems arising in everyday life, society, and the workplace. In early grades, this might be as simple as writing an addition equation to describe a situation. In middle grades, a student might apply proportional reasoning to plan a school event or analyze a problem in the community. By high school, a student might use geometry to solve a design problem or use a function to describe how one quantity of interest depends on another. Mathematically proficient students who can apply what they know are comfortable making assumptions and approximations to simplify a complicated situation, realizing that these may need revision later. They are able to identify important quantities in a practical situation and map their relationships using such tools as diagrams, two-way tables, graphs, flowcharts and formulas. They can analyze those relationships mathematically to draw conclusions. They routinely interpret their mathematical results in the context of the situation and reflect on whether the results make sense, possibly improving the model if it has not served its purpose. Use previously learned concepts and skills to represent and solve problems. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Model with mathematics. Model with mathematics. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). Model with mathematics. 4-9: Quick Check Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Model with mathematics. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Model with mathematics. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Model with mathematics. Mathematically proficient students can apply the mathematics they know to solve problems arising in everyday life, society, and the workplace. In early grades, this might be as simple as writing an addition equation to describe a situation. In middle grades, a student might apply proportional reasoning to plan a school event or analyze a problem in the community. By high school, a student might use geometry to solve a design problem or use a function to describe how one quantity of interest depends on another. Mathematically proficient students who can apply what they know are comfortable making assumptions and approximations to simplify a complicated situation, realizing that these may need revision later. They are able to identify important quantities in a practical situation and map their relationships using such tools as diagrams, two-way tables, graphs, flowcharts and formulas. They can analyze those relationships mathematically to draw conclusions. They routinely interpret their mathematical results in the context of the situation and reflect on whether the results make sense, possibly improving the model if it has not served its purpose. Use previously learned concepts and skills to represent and solve problems. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Model with mathematics. Model with mathematics. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). Model with mathematics. 4-9: Lesson Self-Assessment 4-9: Reteach to Build Understanding Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Model with mathematics. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Model with mathematics. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Model with mathematics. Mathematically proficient students can apply the mathematics they know to solve problems arising in everyday life, society, and the workplace. In early grades, this might be as simple as writing an addition equation to describe a situation. In middle grades, a student might apply proportional reasoning to plan a school event or analyze a problem in the community. By high school, a student might use geometry to solve a design problem or use a function to describe how one quantity of interest depends on another. Mathematically proficient students who can apply what they know are comfortable making assumptions and approximations to simplify a complicated situation, realizing that these may need revision later. They are able to identify important quantities in a practical situation and map their relationships using such tools as diagrams, two-way tables, graphs, flowcharts and formulas. They can analyze those relationships mathematically to draw conclusions. They routinely interpret their mathematical results in the context of the situation and reflect on whether the results make sense, possibly improving the model if it has not served its purpose. Use previously learned concepts and skills to represent and solve problems. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Model with mathematics. Model with mathematics. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). Model with mathematics. Solve one-step problems using decimals. 4-9: Build Mathematical Literacy Curriculum Standards: Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 5 topics and texts, building on others’ ideas and expressing their own clearly. (a) Come to discussions prepared, having read or studied required material; explicitly draw on that preparation and other information known about the topic to explore ideas under discussion. (b) Follow agreed-upon rules for discussions and carry out assigned roles. (c) Pose and respond to specific questions by making comments that contribute to the discussion and elaborate on the remarks of others. (d) Review the key ideas expressed and draw conclusions in light of information and knowledge gained from the discussions. English language learners communicate for social and instructional purposes within the school setting. Summarize a written text read aloud or information presented in diverse media and formats, including visually, quantitatively, and orally. Summarize the points a speaker makes and explain how each claim is supported by reasons and evidence. Write informative/explanatory texts to examine a topic and convey ideas and information clearly. (a) Introduce a topic clearly, provide a general observation and focus, and group related information logically; include formatting (e.g., headings), illustrations, and multimedia when useful to aiding comprehension. (b) Develop the topic with facts, definitions, concrete details, quotations, or other information and examples related to the topic. (c) Link ideas within and across categories of information using words, phrases, and clauses (e.g., in contrast, especially). (d) Use precise language and domain-specific vocabulary to inform about or explain the topic. (e) Provide a concluding statement or section related to the information or explanation presented. English language learners communicate information, ideas and concepts necessary for academic success in the content area of Mathematics. 4-9: Enrichment Game: Save the Word: Grade 5 Topics 1-4 4-9: Pick a Project 4-9: Another Look Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Model with mathematics. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Model with mathematics. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Model with mathematics. Mathematically proficient students can apply the mathematics they know to solve problems arising in everyday life, society, and the workplace. In early grades, this might be as simple as writing an addition equation to describe a situation. In middle grades, a student might apply proportional reasoning to plan a school event or analyze a problem in the community. By high school, a student might use geometry to solve a design problem or use a function to describe how one quantity of interest depends on another. Mathematically proficient students who can apply what they know are comfortable making assumptions and approximations to simplify a complicated situation, realizing that these may need revision later. They are able to identify important quantities in a practical situation and map their relationships using such tools as diagrams, two-way tables, graphs, flowcharts and formulas. They can analyze those relationships mathematically to draw conclusions. They routinely interpret their mathematical results in the context of the situation and reflect on whether the results make sense, possibly improving the model if it has not served its purpose. Use previously learned concepts and skills to represent and solve problems. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Model with mathematics. Model with mathematics. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). Model with mathematics. Solve one-step problems using decimals. Spanish Resources 4-9: eText del Libro del estudiante 4-9: Repaso diario 4-9: Aprendizaje visual 4-9: Amigo de práctica: Práctica adicional 4-9: Práctica adicional interactiva 4-9: Refuerzo para mejorar la comprensión 4-9: Desarrollar la competencia matemática 4-9: Ampliación Topic 4: End of Topic Interactive Student Edition: End of Topic 4 Topic 4: Fluency Practice Activity Interactive Student Edition: Topic 4 Assessment Practice Interactive Student Edition: Topic 4 Performance Task Topic 4 Performance Task Topic 4 Assessment 6-2: Center Games 4-1: Visual Learning Curriculum Standards: Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Use knowledge about place value and patterns to find the product of a decimal number and a power of 10. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10 and 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. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). 4-2: Visual Learning Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Use rounding and compatible numbers to estimate the product of a decimal and a whole number. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). Estimate solutions to arithmetic problems in order to assess the reasonableness of results. 4-3: Visual Learning Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Use models to represent multiplying a decimal and a whole number. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). 4-4: Visual Learning 4-4: Visual LearningThis is the Visual Learning Bridge from the student edition presented with animations. Some use interactivity to illustrate math ideas. It is designed for whole-class instruction. Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Use place-value understanding and an algorithm for multiplying whole numbers to multiply a decimal and a whole number. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). 4-5: Visual Learning Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Use grids to model decimals and find the product of a decimal and a decimal. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). 4-6: Visual Learning Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Multiply decimals using partial products and models. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). 4-7: Visual Learning Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Use properties to multiply decimals. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). 4-8: Visual Learning Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Use number sense and reasoning to place the decimal point in a product. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). 4-9: Visual Learning Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Model with mathematics. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Model with mathematics. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Model with mathematics. Mathematically proficient students can apply the mathematics they know to solve problems arising in everyday life, society, and the workplace. In early grades, this might be as simple as writing an addition equation to describe a situation. In middle grades, a student might apply proportional reasoning to plan a school event or analyze a problem in the community. By high school, a student might use geometry to solve a design problem or use a function to describe how one quantity of interest depends on another. Mathematically proficient students who can apply what they know are comfortable making assumptions and approximations to simplify a complicated situation, realizing that these may need revision later. They are able to identify important quantities in a practical situation and map their relationships using such tools as diagrams, two-way tables, graphs, flowcharts and formulas. They can analyze those relationships mathematically to draw conclusions. They routinely interpret their mathematical results in the context of the situation and reflect on whether the results make sense, possibly improving the model if it has not served its purpose. Use previously learned concepts and skills to represent and solve problems. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Model with mathematics. Model with mathematics. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). Model with mathematics. Topic 4 Online Assessment Curriculum Standards: Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Model with mathematics. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Use knowledge about place value and patterns to find the product of a decimal number and a power of 10. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10 and 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. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). Use rounding and compatible numbers to estimate the product of a decimal and a whole number. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Estimate solutions to arithmetic problems in order to assess the reasonableness of results. Use models to represent multiplying a decimal and a whole number. Use place-value understanding and an algorithm for multiplying whole numbers to multiply a decimal and a whole number. Use grids to model decimals and find the product of a decimal and a decimal. Multiply decimals using partial products and models. Use properties to multiply decimals. Use number sense and reasoning to place the decimal point in a product. Model with mathematics. Model with mathematics. Mathematically proficient students can apply the mathematics they know to solve problems arising in everyday life, society, and the workplace. In early grades, this might be as simple as writing an addition equation to describe a situation. In middle grades, a student might apply proportional reasoning to plan a school event or analyze a problem in the community. By high school, a student might use geometry to solve a design problem or use a function to describe how one quantity of interest depends on another. Mathematically proficient students who can apply what they know are comfortable making assumptions and approximations to simplify a complicated situation, realizing that these may need revision later. They are able to identify important quantities in a practical situation and map their relationships using such tools as diagrams, two-way tables, graphs, flowcharts and formulas. They can analyze those relationships mathematically to draw conclusions. They routinely interpret their mathematical results in the context of the situation and reflect on whether the results make sense, possibly improving the model if it has not served its purpose. Use previously learned concepts and skills to represent and solve problems. Model with mathematics. Model with mathematics. Model with mathematics. Topic 4 Spanish Assessments Tema 4: Tarea de rendimento Tema 4: Evaluación Topics 1–4: Cumulative/Benchmark Assessments Topics 1–4: Cumulative/Benchmark Assessment 4-1: Another Look Curriculum Standards: Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Use knowledge about place value and patterns to find the product of a decimal number and a power of 10. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10 and 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. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). 2-2: Another Look Curriculum Standards: Use place value understanding to round decimals to any place. Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Use place value understanding to round decimals to any place. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Use place value understanding to round decimals to any place. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Use rounding or compatible numbers to estimate sums and differences. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Round decimals to any place (limit rounding to ones, tenths, hundredths, or thousandths place). Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). Add and subtract decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Estimate sums and differences of decimals and fractions to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. 4-9: Another Look Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Model with mathematics. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Model with mathematics. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Model with mathematics. Mathematically proficient students can apply the mathematics they know to solve problems arising in everyday life, society, and the workplace. In early grades, this might be as simple as writing an addition equation to describe a situation. In middle grades, a student might apply proportional reasoning to plan a school event or analyze a problem in the community. By high school, a student might use geometry to solve a design problem or use a function to describe how one quantity of interest depends on another. Mathematically proficient students who can apply what they know are comfortable making assumptions and approximations to simplify a complicated situation, realizing that these may need revision later. They are able to identify important quantities in a practical situation and map their relationships using such tools as diagrams, two-way tables, graphs, flowcharts and formulas. They can analyze those relationships mathematically to draw conclusions. They routinely interpret their mathematical results in the context of the situation and reflect on whether the results make sense, possibly improving the model if it has not served its purpose. Use previously learned concepts and skills to represent and solve problems. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Model with mathematics. Model with mathematics. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). Model with mathematics. 4-8: Another Look Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Use number sense and reasoning to place the decimal point in a product. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). 4-3: Another Look Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Use models to represent multiplying a decimal and a whole number. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). 3-5: Another Look Curriculum Standards: Fluently multiply multi-digit whole numbers using the standard algorithm. Fluently multiply multi-digit whole numbers using the standard algorithm. Fluently multiply multi-digit whole numbers using the standard algorithm. Multiply 3-digit by 2-digit numbers by adding partial products or by using the standard algorithm. Fluently multiply multi-digit whole numbers using the standard algorithm. Multiply multi-digit whole numbers (not to exceed three-digit by three-digit). Estimate solutions to arithmetic problems in order to assess the reasonableness of results. Solve real- world and mathematical problems requiring addition, subtraction, multiplication and division of multi- digit whole numbers. Use various strategies, including the inverse relationships between operations, the use of technology, and the context of the problem to assess the reasonableness of results. 2-5: Another Look Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Subtract decimals to hundredths familiar strategies, such as partial differences. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). Add and subtract decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Model addition and subtraction of fractions and decimals using a variety of representations. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. 2-4: Another Look Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add decimals to hundredths using familiar strategies, such as partial sums. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). Add and subtract decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Model addition and subtraction of fractions and decimals using a variety of representations. Estimate sums and differences of decimals and fractions to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. 3-7: Another Look 3-7: Another LookThis is the Visual Learning Bridge from the student edition presented with animations. Some use interactivity to illustrate math ideas. It is designed for whole-class instruction. Curriculum Standards: Fluently multiply multi-digit whole numbers using the standard algorithm. Fluently multiply multi-digit whole numbers using the standard algorithm. Fluently multiply multi-digit whole numbers using the standard algorithm. Use properties and the standard algorithm for multiplication to find the product of multi-digit numbers. Fluently multiply multi-digit whole numbers using the standard algorithm. Multiply multi-digit whole numbers (not to exceed three-digit by three- digit). Estimate solutions to arithmetic problems in order to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition, subtraction, multiplication and division of multi-digit whole numbers. Use various strategies, including the inverse relationships between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Apply the commutative, associative and distributive properties and order of operations to generate equivalent numerical expressions and to solve problems involving whole numbers. 1-6: Another Look Curriculum Standards: Use place value understanding to round decimals to any place. Use place value understanding to round decimals to any place. Use place value understanding to round decimals to any place. Use place value to round decimals to different places. Use place value understanding to round decimals to any place. Round decimals to any place (limit rounding to ones, tenths, hundredths, or thousandths place). Round numbers to the nearest 0.1, 0.01 and 0.001. 3-8: Another Look Curriculum Standards: Fluently multiply multi-digit whole numbers using the standard algorithm. Fluently multiply multi-digit whole numbers using the standard algorithm. Fluently multiply multi-digit whole numbers using the standard algorithm. Use models and strategies to solve word problems. Fluently multiply multi-digit whole numbers using the standard algorithm. Multiply multi-digit whole numbers (not to exceed three-digit by three-digit). Estimate solutions to arithmetic problems in order to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition, subtraction, multiplication and division of multi-digit whole numbers. Use various strategies, including the inverse relationships between operations, the use of technology, and the context of the problem to assess the reasonableness of results. 5-5: Center Games 4-6: Another Look Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Multiply decimals using partial products and models. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). 2-3: Another Look Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Model sums and differences of decimals. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). Add and subtract decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Model addition and subtraction of fractions and decimals using a variety of representations. Estimate sums and differences of decimals and fractions to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. 4-4: Another Look Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Use place-value understanding and an algorithm for multiplying whole numbers to multiply a decimal and a whole number. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). 1-1: Another Look Curriculum Standards: Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. Use patterns and the properties of multiplication to calculate a product when multiplying by a power of 10; use whole-number exponents to write powers of 10. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10 and 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. Read and write decimals using place value to describe decimals in terms of groups from millionths to millions. 3-2: Another Look Curriculum Standards: Fluently multiply multi-digit whole numbers using the standard algorithm. Fluently multiply multi-digit whole numbers using the standard algorithm. Fluently multiply multi-digit whole numbers using the standard algorithm. Use rounding and compatible numbers to estimate products. Fluently multiply multi-digit whole numbers using the standard algorithm. Multiply multi-digit whole numbers (not to exceed three-digit by three-digit). Estimate solutions to arithmetic problems in order to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition, subtraction, multiplication and division of multi-digit whole numbers. Use various strategies, including the inverse relationships between operations, the use of technology, and the context of the problem to assess the reasonableness of results. 1-5: Another Look Curriculum Standards: Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and <, symbols to record the results of comparisons. Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. Use place value to compare decimals through thousandths. Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and <, symbols to record the results of comparisons. Compare two decimals to thousandths based on meanings of the digits in each place using >, =, and < symbols. Order fractions and decimals, including mixed numbers and improper fractions, and locate on a number line. 1-7: Another Look Curriculum Standards: Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 x 100 + 4 x 10 + 7 x 1 + 3 x (1/10) + 9 x (1/100) + 2 x (1/1000). Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and <, symbols to record the results of comparisons. Look for and make use of structure. 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). Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. Look for and make use of structure. 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). Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. Look for and make use of structure. Mathematically proficient students look closely to discern a pattern or structure. Young students, for example, might notice that three and seven more is the same amount as seven and three more, or they may sort a collection of shapes according to how many sides the shapes have. Later, students will see 7 × 8 equals the well remembered 7 × 5 + 7 × 3, in preparation for learning about the distributive property. In the expression x² + 9x + 14, older students can see the 14 as 2 × 7 and the 9 as 2 + 7. They recognize the significance of an existing line in a geometric figure and can use the strategy of drawing an auxiliary line for solving problems. They also can step back for an overview and shift perspective. They can see complicated things, such as some algebraic expressions, as single objects or as being composed of several objects. For example, they can see 5 – 3(x – y)² as 5 minus a positive number times a square and use that to realize that its value cannot be more than 5 for any real numbers x and y. 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). Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. Use the structure of the decimal place-value system to solve problems involving patterns. Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 x 100 + 4 x 10 + 7 x 1 + 3 x (1/10) + 9 x (1/100) + 2 x (1/1000). Look for and make use of structure. Look for and make Use of structure. Read and write decimals to thousandths using base-ten numerals, word form, and expanded form. Look for and make use of structure. Read and write decimals using place value to describe decimals in terms of groups from millionths to millions. 4-5: Another Look Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Use grids to model decimals and find the product of a decimal and a decimal. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). 4-2: Another Look Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Use rounding and compatible numbers to estimate the product of a decimal and a whole number. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). Estimate solutions to arithmetic problems in order to assess the reasonableness of results. 1-4: Another Look Curriculum Standards: Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 x 100 + 4 x 10 + 7 x 1 + 3 x (1/10) + 9 x (1/100) + 2 x (1/1000). Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 × 100 + 4 × 10 + 7 × 1 + 3 × (1/10) + 9 × (1/100) + 2 × (1/1000). Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 × 100 + 4 × 10 + 7 × 1 + 3 × (1/10) + 9 × (1/100) + 2 × (1/1000). Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 × 100 + 4 × 10 + 7 × 1 + 3 × (1/10) + 9 × (1/100) + 2 × (1/1000). Read and write numbers with decimals through thousandths using standard form, expanded form, and number names; identify equivalent decimals. Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 x 100 + 4 x 10 + 7 x 1 + 3 x (1/10) + 9 x (1/100) + 2 x (1/1000). Read and write decimals to thousandths using base-ten numerals, word form, and expanded form. Read and write decimals using place value to describe decimals in terms of groups from millionths to millions. Topics 1–4: Online Cumulative/Benchmark Assessment Curriculum Standards: Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Model with mathematics. Fluently multiply multi-digit whole numbers using the standard algorithm. Use place value understanding to round decimals to any place. Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left. Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 x 100 + 4 x 10 + 7 x 1 + 3 x (1/10) + 9 x (1/100) + 2 x (1/1000). Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and <, symbols to record the results of comparisons. Look for and make use of structure. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Use knowledge about place value and patterns to find the product of a decimal number and a power of 10. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10 and 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. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). Use rounding and compatible numbers to estimate the product of a decimal and a whole number. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Estimate solutions to arithmetic problems in order to assess the reasonableness of results. Use models to represent multiplying a decimal and a whole number. Use place-value understanding and an algorithm for multiplying whole numbers to multiply a decimal and a whole number. Use grids to model decimals and find the product of a decimal and a decimal. Multiply decimals using partial products and models. Use number sense and reasoning to place the decimal point in a product. Model with mathematics. Model with mathematics. Mathematically proficient students can apply the mathematics they know to solve problems arising in everyday life, society, and the workplace. In early grades, this might be as simple as writing an addition equation to describe a situation. In middle grades, a student might apply proportional reasoning to plan a school event or analyze a problem in the community. By high school, a student might use geometry to solve a design problem or use a function to describe how one quantity of interest depends on another. Mathematically proficient students who can apply what they know are comfortable making assumptions and approximations to simplify a complicated situation, realizing that these may need revision later. They are able to identify important quantities in a practical situation and map their relationships using such tools as diagrams, two-way tables, graphs, flowcharts and formulas. They can analyze those relationships mathematically to draw conclusions. They routinely interpret their mathematical results in the context of the situation and reflect on whether the results make sense, possibly improving the model if it has not served its purpose. Use previously learned concepts and skills to represent and solve problems. Model with mathematics. Model with mathematics. Model with mathematics. Model sums and differences of decimals. Add and subtract decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Model addition and subtraction of fractions and decimals using a variety of representations. Estimate sums and differences of decimals and fractions to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. Fluently multiply multi- digit whole numbers using the standard algorithm. Fluently multiply multi-digit whole numbers using the standard algorithm. Use models and strategies to solve word problems. Fluently multiply multi-digit whole numbers using the standard algorithm. Multiply multi-digit whole numbers (not to exceed three- digit by three-digit). 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. Add decimals to hundredths using familiar strategies, such as partial sums. Use properties and the standard algorithm for multiplication to find the product of multi-digit numbers. Apply the commutative, associative and distributive properties and order of operations to generate equivalent numerical expressions and to solve problems involving whole numbers. Use place value understanding to round decimals to any place. Use place value understanding to round decimals to any place. Use rounding or compatible numbers to estimate sums and differences. Round decimals to any place (limit rounding to ones, tenths, hundredths, or thousandths place). Multiply 3-digit by 2-digit numbers by adding partial products or by using the standard algorithm. 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. Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left. Read and write whole numbers using standard form, expanded form, and number names. Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left. Demonstrate an understanding that in a multi-digit number, a digit in one place represents 1/10 of what it represents in the place to its left. Read and write decimals using place value to describe decimals in terms of groups from millionths to millions. Use patterns and the properties of multiplication to calculate a product when multiplying by a power of 10; use whole-number exponents to write powers of 10. Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 × 100 + 4 × 10 + 7 × 1 + 3 × (1/10) + 9 × (1/100) + 2 × (1/1000). Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 × 100 + 4 × 10 + 7 × 1 + 3 × (1/10) + 9 × (1/100) + 2 × (1/1000). Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 × 100 + 4 × 10 + 7 × 1 + 3 × (1/10) + 9 × (1/100) + 2 × (1/1000). Read and write numbers with decimals through thousandths using standard form, expanded form, and number names; identify equivalent decimals. Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 x 100 + 4 x 10 + 7 x 1 + 3 x (1/10) + 9 x (1/100) + 2 x (1/1000). Read and write decimals to thousandths using base-ten numerals, word form, and expanded form. Use place value to round decimals to different places. Use place value understanding to round decimals to any place. Round numbers to the nearest 0.1, 0.01 and 0.001. Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. Use place value to compare decimals through thousandths. Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and <, symbols to record the results of comparisons. Compare two decimals to thousandths based on meanings of the digits in each place using >, =, and < symbols. Order fractions and decimals, including mixed numbers and improper fractions, and locate on a number line. Look for and make use of structure. Look for and make use of structure. Mathematically proficient students look closely to discern a pattern or structure. Young students, for example, might notice that three and seven more is the same amount as seven and three more, or they may sort a collection of shapes according to how many sides the shapes have. Later, students will see 7 × 8 equals the well remembered 7 × 5 + 7 × 3, in preparation for learning about the distributive property. In the expression x² + 9x + 14, older students can see the 14 as 2 × 7 and the 9 as 2 + 7. They recognize the significance of an existing line in a geometric figure and can use the strategy of drawing an auxiliary line for solving problems. They also can step back for an overview and shift perspective. They can see complicated things, such as some algebraic expressions, as single objects or as being composed of several objects. For example, they can see 5 – 3(x – y)² as 5 minus a positive number times a square and use that to realize that its value cannot be more than 5 for any real numbers x and y. Use the structure of the decimal place-value system to solve problems involving patterns. Look for and make use of structure. Look for and make Use of structure. Look for and make use of structure. Subtract decimals to hundredths familiar strategies, such as partial differences. Use rounding and compatible numbers to estimate products. Topic 5: Use Models and Strategies to Divide Whole Numbers Topic 5: Today's Challenge Topic 5: Beginning of Topic Interactive Student Edition: Beginning of Topic 5 Topic 5: enVision STEM Activity Grade 5 Topic 5: Review What You Know 5-1: Use Patterns and Mental Math to Divide Interactive Student Edition: Grade 5 Lesson 5-1 Math Anytime 5-1: Daily Review Topic 5: Today's Challenge Step 1: Problem-Based Learning 5-1: Solve & Share Curriculum Standards: 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. 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. 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. Use place-value patterns and mental math to find quotients. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors. 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. 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. English language learners communicate for social and instructional purposes within the school setting. Write informative/explanatory texts to examine a topic and convey ideas and information clearly. (a) Introduce a topic clearly, provide a general observation and focus, and group related information logically; include formatting (e.g., headings), illustrations, and multimedia when useful to aiding comprehension. (b) Develop the topic with facts, definitions, concrete details, quotations, or other information and examples related to the topic. (c) Link ideas within and across categories of information using words, phrases, and clauses (e.g., in contrast, especially). (d) Use precise language and domain- specific vocabulary to inform about or explain the topic. (e) Provide a concluding statement or section related to the information or explanation presented. English language learners communicate information, ideas and concepts necessary for academic success in the content area of Mathematics. Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 5 topics and texts, building on others’ ideas and expressing their own clearly. (a) Come to discussions prepared, having read or studied required material; explicitly draw on that preparation and other information known about the topic to explore ideas under discussion. (b) Follow agreed-upon rules for discussions and carry out assigned roles. (c) Pose and respond to specific questions by making comments that contribute to the discussion and elaborate on the remarks of others. (d) Review the key ideas expressed and draw conclusions in light of information and knowledge gained from the discussions. Summarize a written text read aloud or information presented in diverse media and formats, including visually, quantitatively, and orally. Summarize the points a speaker makes and explain how each claim is supported by reasons and evidence. Step 2: Visual Learning 5-1: Visual Learning Curriculum Standards: 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. 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. 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. Use place-value patterns and mental math to find quotients. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors. 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. 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: Convince Me! Curriculum Standards: 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. 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. 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. Use place-value patterns and mental math to find quotients. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors. 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. 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. Practice and Problem Solving 5-1: Student Edition Practice Curriculum Standards: 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. 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. 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. Use place-value patterns and mental math to find quotients. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors. 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. 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: Practice Buddy: Independent Practice; Problem Solving Curriculum Standards: 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. 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. 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. Use place-value patterns and mental math to find quotients. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors. 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. 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: Practice Buddy: Additional Practice Curriculum Standards: 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. 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. 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. Use place-value patterns and mental math to find quotients. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors. 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. 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: Interactive Additional Practice Step 3: Assess & Differentiate 5-1: Practice Buddy: Additional Practice Curriculum Standards: 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. 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. 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. Use place-value patterns and mental math to find quotients. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors. 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. 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: Enrichment Curriculum Standards: 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. 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. 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. Use place-value patterns and mental math to find quotients. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors. 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. 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: Quick Check Curriculum Standards: 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. 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. 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. Use place-value patterns and mental math to find quotients. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors. 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. 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: Lesson Self-Assessment 5-1: Reteach to Build Understanding Curriculum Standards: 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. 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. 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. Use place-value patterns and mental math to find quotients. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors. 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. 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: Build Mathematical Literacy Curriculum Standards: Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 5 topics and texts, building on others’ ideas and expressing their own clearly. (a) Come to discussions prepared, having read or studied required material; explicitly draw on that preparation and other information known about the topic to explore ideas under discussion. (b) Follow agreed-upon rules for discussions and carry out assigned roles. (c) Pose and respond to specific questions by making comments that contribute to the discussion and elaborate on the remarks of others. (d) Review the key ideas expressed and draw conclusions in light of information and knowledge gained from the discussions. English language learners communicate for social and instructional purposes within the school setting. Summarize a written text read aloud or information presented in diverse media and formats, including visually, quantitatively, and orally. Summarize the points a speaker makes and explain how each claim is supported by reasons and evidence. Write informative/explanatory texts to examine a topic and convey ideas and information clearly. (a) Introduce a topic clearly, provide a general observation and focus, and group related information logically; include formatting (e.g., headings), illustrations, and multimedia when useful to aiding comprehension. (b) Develop the topic with facts, definitions, concrete details, quotations, or other information and examples related to the topic. (c) Link ideas within and across categories of information using words, phrases, and clauses (e.g., in contrast, especially). (d) Use precise language and domain-specific vocabulary to inform about or explain the topic. (e) Provide a concluding statement or section related to the information or explanation presented. English language learners communicate information, ideas and concepts necessary for academic success in the content area of Mathematics. 5-1: Enrichment Game: Cosmic Caravan - Arrays and Multiples of 10 5-1: Pick a Project 5-1: Another Look Curriculum Standards: 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. 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. 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. Use place-value patterns and mental math to find quotients. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors. 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. 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. Spanish Resources 5-1: eText del Libro del estudiante 5-1: Repaso diario 5-1: Aprendizaje visual 5-1: Amigo de práctica: Práctica adicional 5-1: Práctica adicional interactiva 5-1: Refuerzo para mejorar la comprensión 5-1: Desarrollar la competencia matemática 5-1: Ampliación 5-2: Estimate Quotients with 2-Digit Divisors Interactive Student Edition: Grade 5 Lesson 5-2 Math Anytime 5-2: Daily Review Topic 5: Today's Challenge Step 1: Problem-Based Learning 5-2: Solve & Share Curriculum Standards: 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. 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. 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. Use compatible numbers and place-value patterns to estimate quotients. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors. Divide multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Recognize that quotients can be represented in a variety of ways, including a whole number with a remainder, a fraction or mixed number, or a decimal. Estimate solutions to arithmetic problems in order to assess the reasonableness of results. 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. English language learners communicate for social and instructional purposes within the school setting. Write informative/explanatory texts to examine a topic and convey ideas and information clearly. (a) Introduce a topic clearly, provide a general observation and focus, and group related information logically; include formatting (e.g., headings), illustrations, and multimedia when useful to aiding comprehension. (b) Develop the topic with facts, definitions, concrete details, quotations, or other information and examples related to the topic. (c) Link ideas within and across categories of information using words, phrases, and clauses (e.g., in contrast, especially). (d) Use precise language and domain- specific vocabulary to inform about or explain the topic. (e) Provide a concluding statement or section related to the information or explanation presented. English language learners communicate information, ideas and concepts necessary for academic success in the content area of Mathematics. Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 5 topics and texts, building on others’ ideas and expressing their own clearly. (a) Come to discussions prepared, having read or studied required material; explicitly draw on that preparation and other information known about the topic to explore ideas under discussion. (b) Follow agreed-upon rules for discussions and carry out assigned roles. (c) Pose and respond to specific questions by making comments that contribute to the discussion and elaborate on the remarks of others. (d) Review the key ideas expressed and draw conclusions in light of information and knowledge gained from the discussions. Summarize a written text read aloud or information presented in diverse media and formats, including visually, quantitatively, and orally. Summarize the points a speaker makes and explain how each claim is supported by reasons and evidence. Step 2: Visual Learning 5-2: Visual Learning Curriculum Standards: 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. 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. 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. Use compatible numbers and place-value patterns to estimate quotients. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors. Divide multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Recognize that quotients can be represented in a variety of ways, including a whole number with a remainder, a fraction or mixed number, or a decimal. Estimate solutions to arithmetic problems in order to assess the reasonableness of results. 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. 5-2: Convince Me! Curriculum Standards: 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. 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. 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. Use compatible numbers and place-value patterns to estimate quotients. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors. Divide multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Recognize that quotients can be represented in a variety of ways, including a whole number with a remainder, a fraction or mixed number, or a decimal. Estimate solutions to arithmetic problems in order to assess the reasonableness of results. 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. Practice and Problem Solving 5-2: Student Edition Practice Curriculum Standards: 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. 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. 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. Use compatible numbers and place-value patterns to estimate quotients. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors. Divide multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Recognize that quotients can be represented in a variety of ways, including a whole number with a remainder, a fraction or mixed number, or a decimal. Estimate solutions to arithmetic problems in order to assess the reasonableness of results. 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. 5-2: Practice Buddy: Independent Practice; Problem Solving Curriculum Standards: 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. 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. 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. Use compatible numbers and place-value patterns to estimate quotients. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors. Divide multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Recognize that quotients can be represented in a variety of ways, including a whole number with a remainder, a fraction or mixed number, or a decimal. Estimate solutions to arithmetic problems in order to assess the reasonableness of results. 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. 5-2: Practice Buddy: Additional Practice Curriculum Standards: 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. 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. 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. Use compatible numbers and place-value patterns to estimate quotients. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors. Divide multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Recognize that quotients can be represented in a variety of ways, including a whole number with a remainder, a fraction or mixed number, or a decimal. Estimate solutions to arithmetic problems in order to assess the reasonableness of results. 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. 5-2: Interactive Additional Practice Step 3: Assess & Differentiate 5-2: Practice Buddy: Additional Practice Curriculum Standards: 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. 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. 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. Use compatible numbers and place-value patterns to estimate quotients. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors. Divide multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Recognize that quotients can be represented in a variety of ways, including a whole number with a remainder, a fraction or mixed number, or a decimal. Estimate solutions to arithmetic problems in order to assess the reasonableness of results. 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. 5-2: Enrichment Curriculum Standards: 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. 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. 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. Use compatible numbers and place-value patterns to estimate quotients. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors. Divide multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Recognize that quotients can be represented in a variety of ways, including a whole number with a remainder, a fraction or mixed number, or a decimal. Estimate solutions to arithmetic problems in order to assess the reasonableness of results. 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. 5-2: Quick Check Curriculum Standards: 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. 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. 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. Use compatible numbers and place-value patterns to estimate quotients. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors. Divide multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Recognize that quotients can be represented in a variety of ways, including a whole number with a remainder, a fraction or mixed number, or a decimal. Estimate solutions to arithmetic problems in order to assess the reasonableness of results. 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. 5-2: Lesson Self-Assessment 5-2: Reteach to Build Understanding Curriculum Standards: 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. 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. 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. Use compatible numbers and place-value patterns to estimate quotients. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors. Divide multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Recognize that quotients can be represented in a variety of ways, including a whole number with a remainder, a fraction or mixed number, or a decimal. Estimate solutions to arithmetic problems in order to assess the reasonableness of results. 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. 5-2: Build Mathematical Literacy Curriculum Standards: Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 5 topics and texts, building on others’ ideas and expressing their own clearly. (a) Come to discussions prepared, having read or studied required material; explicitly draw on that preparation and other information known about the topic to explore ideas under discussion. (b) Follow agreed-upon rules for discussions and carry out assigned roles. (c) Pose and respond to specific questions by making comments that contribute to the discussion and elaborate on the remarks of others. (d) Review the key ideas expressed and draw conclusions in light of information and knowledge gained from the discussions. English language learners communicate for social and instructional purposes within the school setting. Summarize a written text read aloud or information presented in diverse media and formats, including visually, quantitatively, and orally. Summarize the points a speaker makes and explain how each claim is supported by reasons and evidence. Write informative/explanatory texts to examine a topic and convey ideas and information clearly. (a) Introduce a topic clearly, provide a general observation and focus, and group related information logically; include formatting (e.g., headings), illustrations, and multimedia when useful to aiding comprehension. (b) Develop the topic with facts, definitions, concrete details, quotations, or other information and examples related to the topic. (c) Link ideas within and across categories of information using words, phrases, and clauses (e.g., in contrast, especially). (d) Use precise language and domain-specific vocabulary to inform about or explain the topic. (e) Provide a concluding statement or section related to the information or explanation presented. English language learners communicate information, ideas and concepts necessary for academic success in the content area of Mathematics. 5-2: Enrichment Game: Cosmic Caravan - Arrays and Multiples of 10 5-2: Problem-Solving Reading Activity Curriculum Standards: 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. 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. 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. Use compatible numbers and place-value patterns to estimate quotients. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors. Divide multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Recognize that quotients can be represented in a variety of ways, including a whole number with a remainder, a fraction or mixed number, or a decimal. Estimate solutions to arithmetic problems in order to assess the reasonableness of results. 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. 5-2: Another Look Curriculum Standards: 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. 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. 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. Use compatible numbers and place-value patterns to estimate quotients. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors. Divide multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Recognize that quotients can be represented in a variety of ways, including a whole number with a remainder, a fraction or mixed number, or a decimal. Estimate solutions to arithmetic problems in order to assess the reasonableness of results. 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. Spanish Resources 5-2: eText del Libro del estudiante 5-2: Repaso diario 5-2: Aprendizaje visual 5-2: Amigo de práctica: Práctica adicional 5-2: Práctica adicional interactiva 5-2: Refuerzo para mejorar la comprensión 5-2: Desarrollar la competencia matemática 5-2: Ampliación 5-3: Use Models and Properties to Divide with 2-Digit Divisors Interactive Student Edition: Grade 5 Lesson 5-3 Math Anytime 5-3: Daily Review Topic 5: Today's Challenge Step 1: Problem-Based Learning 5-3: Solve & Share Curriculum Standards: 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. English language learners communicate for social and instructional purposes within the school setting. 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. 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. Use models to find quotients. Find whole-number quotients of whole numbers with up to four- digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors. Divide multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Recognize that quotients can be represented in a variety of ways, including a whole number with a remainder, a fraction or mixed number, or a decimal. Estimate solutions to arithmetic problems in order to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition, subtraction, multiplication and division of multi-digit whole numbers. Use various strategies, including the inverse relationships between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Write informative/explanatory texts to examine a topic and convey ideas and information clearly. (a) Introduce a topic clearly, provide a general observation and focus, and group related information logically; include formatting (e.g., headings), illustrations, and multimedia when useful to aiding comprehension. (b) Develop the topic with facts, definitions, concrete details, quotations, or other information and examples related to the topic. (c) Link ideas within and across categories of information using words, phrases, and clauses (e.g., in contrast, especially). (d) Use precise language and domain-specific vocabulary to inform about or explain the topic. (e) Provide a concluding statement or section related to the information or explanation presented. English language learners communicate information, ideas and concepts necessary for academic success in the content area of Mathematics. Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 5 topics and texts, building on others’ ideas and expressing their own clearly. (a) Come to discussions prepared, having read or studied required material; explicitly draw on that preparation and other information known about the topic to explore ideas under discussion. (b) Follow agreed-upon rules for discussions and carry out assigned roles. (c) Pose and respond to specific questions by making comments that contribute to the discussion and elaborate on the remarks of others. (d) Review the key ideas expressed and draw conclusions in light of information and knowledge gained from the discussions. Summarize a written text read aloud or information presented in diverse media and formats, including visually, quantitatively, and orally. Summarize the points a speaker makes and explain how each claim is supported by reasons and evidence. Step 2: Visual Learning 5-3: Visual Learning Curriculum Standards: 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. Find whole number quotients up to two dividends and two divisors. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. 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. Use models to find quotients. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors. Divide multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Recognize that quotients can be represented in a variety of ways, including a whole number with a remainder, a fraction or mixed number, or a decimal. Estimate solutions to arithmetic problems in order to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition, subtraction, multiplication and division of multi-digit whole numbers. Use various strategies, including the inverse relationships between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Find whole number quotients of whole numbers with up to two-digit dividends and two-digit divisors. 5-3: Convince Me! Curriculum Standards: 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. 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. 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. Use models to find quotients. Find whole-number quotients of whole numbers with up to four- digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors. Divide multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Recognize that quotients can be represented in a variety of ways, including a whole number with a remainder, a fraction or mixed number, or a decimal. Estimate solutions to arithmetic problems in order to assess the reasonableness of results. 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. Practice and Problem Solving 5-3: Student Edition Practice Curriculum Standards: 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. 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. 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. Use models to find quotients. Find whole-number quotients of whole numbers with up to four- digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors. Divide multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Recognize that quotients can be represented in a variety of ways, including a whole number with a remainder, a fraction or mixed number, or a decimal. Estimate solutions to arithmetic problems in order to assess the reasonableness of results. 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. 5-3: Practice Buddy: Independent Practice; Problem Solving Curriculum Standards: 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. 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. 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. Use models to find quotients. Find whole-number quotients of whole numbers with up to four- digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors. Divide multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Recognize that quotients can be represented in a variety of ways, including a whole number with a remainder, a fraction or mixed number, or a decimal. Estimate solutions to arithmetic problems in order to assess the reasonableness of results. 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. 5-3: Practice Buddy: Additional Practice Curriculum Standards: 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. 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. 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. Use models to find quotients. Find whole-number quotients of whole numbers with up to four- digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors. Divide multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Recognize that quotients can be represented in a variety of ways, including a whole number with a remainder, a fraction or mixed number, or a decimal. Estimate solutions to arithmetic problems in order to assess the reasonableness of results. 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. 5-3: Interactive Additional Practice Step 3: Assess & Differentiate 5-3: Practice Buddy: Additional Practice Curriculum Standards: 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. 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. 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. Use models to find quotients. Find whole-number quotients of whole numbers with up to four- digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors. Divide multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Recognize that quotients can be represented in a variety of ways, including a whole number with a remainder, a fraction or mixed number, or a decimal. Estimate solutions to arithmetic problems in order to assess the reasonableness of results. 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. 5-3: Enrichment Curriculum Standards: 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. 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. 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. Use models to find quotients. Find whole-number quotients of whole numbers with up to four- digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors. Divide multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Recognize that quotients can be represented in a variety of ways, including a whole number with a remainder, a fraction or mixed number, or a decimal. Estimate solutions to arithmetic problems in order to assess the reasonableness of results. 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. 5-3: Quick Check Curriculum Standards: 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. 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. 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. Use models to find quotients. Find whole-number quotients of whole numbers with up to four- digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors. Divide multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Recognize that quotients can be represented in a variety of ways, including a whole number with a remainder, a fraction or mixed number, or a decimal. Estimate solutions to arithmetic problems in order to assess the reasonableness of results. 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. 5-3: Lesson Self-Assessment 5-3: Reteach to Build Understanding Curriculum Standards: 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. Find whole number quotients up to two dividends and two divisors. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. 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. Use models to find quotients. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors. Divide multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Recognize that quotients can be represented in a variety of ways, including a whole number with a remainder, a fraction or mixed number, or a decimal. Estimate solutions to arithmetic problems in order to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition, subtraction, multiplication and division of multi-digit whole numbers. Use various strategies, including the inverse relationships between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Find whole number quotients of whole numbers with up to two-digit dividends and two-digit divisors. 5-3: Build Mathematical Literacy Curriculum Standards: Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 5 topics and texts, building on others’ ideas and expressing their own clearly. (a) Come to discussions prepared, having read or studied required material; explicitly draw on that preparation and other information known about the topic to explore ideas under discussion. (b) Follow agreed-upon rules for discussions and carry out assigned roles. (c) Pose and respond to specific questions by making comments that contribute to the discussion and elaborate on the remarks of others. (d) Review the key ideas expressed and draw conclusions in light of information and knowledge gained from the discussions. English language learners communicate for social and instructional purposes within the school setting. Summarize a written text read aloud or information presented in diverse media and formats, including visually, quantitatively, and orally. Summarize the points a speaker makes and explain how each claim is supported by reasons and evidence. Write informative/explanatory texts to examine a topic and convey ideas and information clearly. (a) Introduce a topic clearly, provide a general observation and focus, and group related information logically; include formatting (e.g., headings), illustrations, and multimedia when useful to aiding comprehension. (b) Develop the topic with facts, definitions, concrete details, quotations, or other information and examples related to the topic. (c) Link ideas within and across categories of information using words, phrases, and clauses (e.g., in contrast, especially). (d) Use precise language and domain-specific vocabulary to inform about or explain the topic. (e) Provide a concluding statement or section related to the information or explanation presented. English language learners communicate information, ideas and concepts necessary for academic success in the content area of Mathematics. 5-3: Enrichment 5-3: Digital Math Tool Activity 5-3: Problem-Solving Reading Activity Curriculum Standards: 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. 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. 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. Use models to find quotients. Find whole-number quotients of whole numbers with up to four- digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors. Divide multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Recognize that quotients can be represented in a variety of ways, including a whole number with a remainder, a fraction or mixed number, or a decimal. Estimate solutions to arithmetic problems in order to assess the reasonableness of results. 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. 5-3: Another Look Curriculum Standards: 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. Find whole number quotients up to two dividends and two divisors. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. 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. Use models to find quotients. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors. Divide multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Recognize that quotients can be represented in a variety of ways, including a whole number with a remainder, a fraction or mixed number, or a decimal. Estimate solutions to arithmetic problems in order to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition, subtraction, multiplication and division of multi-digit whole numbers. Use various strategies, including the inverse relationships between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Find whole number quotients of whole numbers with up to two-digit dividends and two-digit divisors. Spanish Resources 5-3: eText del Libro del estudiante 5-3: Repaso diario 5-3: Aprendizaje visual 5-3: Amigo de práctica: Práctica adicional 5-3: Práctica adicional interactiva 5-3: Refuerzo para mejorar la comprensión 5-3: Desarrollar la competencia matemática 5-3: Ampliación 5-4: Use Partial Quotients to Divide Interactive Student Edition: Grade 5 Lesson 5-4 Math Anytime 5-4: Daily Review Topic 5: Today's Challenge Step 1: Problem-Based Learning 5-4: Solve & Share Curriculum Standards: 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. English language learners communicate for social and instructional purposes within the school setting. 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. 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. Solve division problems using partial quotients. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors. Divide multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Recognize that quotients can be represented in a variety of ways, including a whole number with a remainder, a fraction or mixed number, or a decimal. Estimate solutions to arithmetic problems in order to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition, subtraction, multiplication and division of multi-digit whole numbers. Use various strategies, including the inverse relationships between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Write informative/explanatory texts to examine a topic and convey ideas and information clearly. (a) Introduce a topic clearly, provide a general observation and focus, and group related information logically; include formatting (e.g., headings), illustrations, and multimedia when useful to aiding comprehension. (b) Develop the topic with facts, definitions, concrete details, quotations, or other information and examples related to the topic. (c) Link ideas within and across categories of information using words, phrases, and clauses (e.g., in contrast, especially). (d) Use precise language and domain-specific vocabulary to inform about or explain the topic. (e) Provide a concluding statement or section related to the information or explanation presented. English language learners communicate information, ideas and concepts necessary for academic success in the content area of Mathematics. Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 5 topics and texts, building on others’ ideas and expressing their own clearly. (a) Come to discussions prepared, having read or studied required material; explicitly draw on that preparation and other information known about the topic to explore ideas under discussion. (b) Follow agreed-upon rules for discussions and carry out assigned roles. (c) Pose and respond to specific questions by making comments that contribute to the discussion and elaborate on the remarks of others. (d) Review the key ideas expressed and draw conclusions in light of information and knowledge gained from the discussions. Summarize a written text read aloud or information presented in diverse media and formats, including visually, quantitatively, and orally. Summarize the points a speaker makes and explain how each claim is supported by reasons and evidence. Step 2: Visual Learning 5-4: Visual Learning Curriculum Standards: 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. 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. 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. Solve division problems using partial quotients. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors. Divide multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Recognize that quotients can be represented in a variety of ways, including a whole number with a remainder, a fraction or mixed number, or a decimal. Estimate solutions to arithmetic problems in order to assess the reasonableness of results. 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. 5-4: Convince Me! Curriculum Standards: 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. 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. 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. Solve division problems using partial quotients. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors. Divide multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Recognize that quotients can be represented in a variety of ways, including a whole number with a remainder, a fraction or mixed number, or a decimal. Estimate solutions to arithmetic problems in order to assess the reasonableness of results. 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. Practice and Problem Solving 5-4: Student Edition Practice Curriculum Standards: 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. 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. 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. Solve division problems using partial quotients. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors. Divide multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Recognize that quotients can be represented in a variety of ways, including a whole number with a remainder, a fraction or mixed number, or a decimal. Estimate solutions to arithmetic problems in order to assess the reasonableness of results. 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. 5-4: Practice Buddy: Independent Practice; Problem Solving Curriculum Standards: 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. 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. 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. Solve division problems using partial quotients. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors. Divide multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Recognize that quotients can be represented in a variety of ways, including a whole number with a remainder, a fraction or mixed number, or a decimal. Estimate solutions to arithmetic problems in order to assess the reasonableness of results. 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. 5-4: Practice Buddy: Additional Practice Curriculum Standards: 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. 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. 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. Solve division problems using partial quotients. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors. Divide multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Recognize that quotients can be represented in a variety of ways, including a whole number with a remainder, a fraction or mixed number, or a decimal. Estimate solutions to arithmetic problems in order to assess the reasonableness of results. 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. 5-4: Interactive Additional Practice Step 3: Assess & Differentiate 5-4: Practice Buddy: Additional Practice Curriculum Standards: 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. 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. 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. Solve division problems using partial quotients. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors. Divide multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Recognize that quotients can be represented in a variety of ways, including a whole number with a remainder, a fraction or mixed number, or a decimal. Estimate solutions to arithmetic problems in order to assess the reasonableness of results. 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. 5-4: Enrichment Curriculum Standards: 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. 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. 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. Solve division problems using partial quotients. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors. Divide multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Recognize that quotients can be represented in a variety of ways, including a whole number with a remainder, a fraction or mixed number, or a decimal. Estimate solutions to arithmetic problems in order to assess the reasonableness of results. 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. 5-4: Quick Check Curriculum Standards: 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. 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. 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. Solve division problems using partial quotients. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors. Divide multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Recognize that quotients can be represented in a variety of ways, including a whole number with a remainder, a fraction or mixed number, or a decimal. Estimate solutions to arithmetic problems in order to assess the reasonableness of results. 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. 5-4: Lesson Self-Assessment 5-4: Reteach to Build Understanding Curriculum Standards: 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. 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. 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. Solve division problems using partial quotients. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors. Divide multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Recognize that quotients can be represented in a variety of ways, including a whole number with a remainder, a fraction or mixed number, or a decimal. Estimate solutions to arithmetic problems in order to assess the reasonableness of results. 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. 5-4: Build Mathematical Literacy Curriculum Standards: Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 5 topics and texts, building on others’ ideas and expressing their own clearly. (a) Come to discussions prepared, having read or studied required material; explicitly draw on that preparation and other information known about the topic to explore ideas under discussion. (b) Follow agreed-upon rules for discussions and carry out assigned roles. (c) Pose and respond to specific questions by making comments that contribute to the discussion and elaborate on the remarks of others. (d) Review the key ideas expressed and draw conclusions in light of information and knowledge gained from the discussions. English language learners communicate for social and instructional purposes within the school setting. Summarize a written text read aloud or information presented in diverse media and formats, including visually, quantitatively, and orally. Summarize the points a speaker makes and explain how each claim is supported by reasons and evidence. Write informative/explanatory texts to examine a topic and convey ideas and information clearly. (a) Introduce a topic clearly, provide a general observation and focus, and group related information logically; include formatting (e.g., headings), illustrations, and multimedia when useful to aiding comprehension. (b) Develop the topic with facts, definitions, concrete details, quotations, or other information and examples related to the topic. (c) Link ideas within and across categories of information using words, phrases, and clauses (e.g., in contrast, especially). (d) Use precise language and domain-specific vocabulary to inform about or explain the topic. (e) Provide a concluding statement or section related to the information or explanation presented. English language learners communicate information, ideas and concepts necessary for academic success in the content area of Mathematics. 5-4: Enrichment Game: Fluency - Multiply Multi-Digit Whole Numbers 5-4: Pick a Project 5-4: Another Look Curriculum Standards: 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. Find whole number quotients up to two dividends and two divisors. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. 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. Solve division problems using partial quotients. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors. Divide multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Recognize that quotients can be represented in a variety of ways, including a whole number with a remainder, a fraction or mixed number, or a decimal. Estimate solutions to arithmetic problems in order to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition, subtraction, multiplication and division of multi-digit whole numbers. Use various strategies, including the inverse relationships between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Find whole number quotients of whole numbers with up to two-digit dividends and two-digit divisors. Spanish Resources 5-4: eText del Libro del estudiante 5-4: Repaso diario 5-4: Aprendizaje visual 5-4: Amigo de práctica: Práctica adicional 5-4: Práctica adicional interactiva 5-4: Refuerzo para mejorar la comprensión 5-4: Desarrollar la competencia matemática 5-4: Ampliación 5-5: Use Sharing to Divide: 2-Digit Divisors Interactive Student Edition: Grade 5 Lesson 5-5 Math Anytime 5-5: Daily Review Topic 5: Today's Challenge Step 1: Problem-Based Learning 5-5: Solve & Share Curriculum Standards: 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. English language learners communicate for social and instructional purposes within the school setting. Write informative/explanatory texts to examine a topic and convey ideas and information clearly. (a) Introduce a topic clearly, provide a general observation and focus, and group related information logically; include formatting (e.g., headings), illustrations, and multimedia when useful to aiding comprehension. (b) Develop the topic with facts, definitions, concrete details, quotations, or other information and examples related to the topic. (c) Link ideas within and across categories of information using words, phrases, and clauses (e.g., in contrast, especially). (d) Use precise language and domain-specific vocabulary to inform about or explain the topic. (e) Provide a concluding statement or section related to the information or explanation presented. English language learners communicate information, ideas and concepts necessary for academic success in the content area of Mathematics. Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 5 topics and texts, building on others’ ideas and expressing their own clearly. (a) Come to discussions prepared, having read or studied required material; explicitly draw on that preparation and other information known about the topic to explore ideas under discussion. (b) Follow agreed-upon rules for discussions and carry out assigned roles. (c) Pose and respond to specific questions by making comments that contribute to the discussion and elaborate on the remarks of others. (d) Review the key ideas expressed and draw conclusions in light of information and knowledge gained from the discussions. Summarize a written text read aloud or information presented in diverse media and formats, including visually, quantitatively, and orally. Summarize the points a speaker makes and explain how each claim is supported by reasons and evidence. 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. 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. Use place value and sharing to divide by 2-digit divisors. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors. Divide multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Recognize that quotients can be represented in a variety of ways, including a whole number with a remainder, a fraction or mixed number, or a decimal. Consider the context in which a problem is situated to select the most useful form of the quotient for the solution and use the context to interpret the quotient appropriately. 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. Step 2: Visual Learning 5-5: Visual Learning Curriculum Standards: 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. Find whole number quotients up to two dividends and two divisors. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. 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. Use place value and sharing to divide by 2-digit divisors. Find whole-number quotients of whole numbers with up to four- digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors. Divide multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Recognize that quotients can be represented in a variety of ways, including a whole number with a remainder, a fraction or mixed number, or a decimal. Consider the context in which a problem is situated to select the most useful form of the quotient for the solution and use the context to interpret the quotient appropriately. Solve real-world and mathematical problems requiring addition, subtraction, multiplication and division of multi-digit whole numbers. Use various strategies, including the inverse relationships between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Find whole number quotients of whole numbers with up to two-digit dividends and two-digit divisors. 5-5: Convince Me! Curriculum Standards: 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. 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. 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. Use place value and sharing to divide by 2-digit divisors. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors. Divide multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Recognize that quotients can be represented in a variety of ways, including a whole number with a remainder, a fraction or mixed number, or a decimal. Consider the context in which a problem is situated to select the most useful form of the quotient for the solution and use the context to interpret the quotient appropriately. 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. Practice and Problem Solving 5-5: Student Edition Practice Curriculum Standards: 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. 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. 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. Use place value and sharing to divide by 2-digit divisors. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors. Divide multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Recognize that quotients can be represented in a variety of ways, including a whole number with a remainder, a fraction or mixed number, or a decimal. Consider the context in which a problem is situated to select the most useful form of the quotient for the solution and use the context to interpret the quotient appropriately. 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. 5-5: Practice Buddy: Independent Practice; Problem Solving Curriculum Standards: 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. 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. 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. Use place value and sharing to divide by 2-digit divisors. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors. Divide multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Recognize that quotients can be represented in a variety of ways, including a whole number with a remainder, a fraction or mixed number, or a decimal. Consider the context in which a problem is situated to select the most useful form of the quotient for the solution and use the context to interpret the quotient appropriately. 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. 5-5: Practice Buddy: Additional Practice Curriculum Standards: 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. 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. 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. Use place value and sharing to divide by 2-digit divisors. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors. Divide multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Recognize that quotients can be represented in a variety of ways, including a whole number with a remainder, a fraction or mixed number, or a decimal. Consider the context in which a problem is situated to select the most useful form of the quotient for the solution and use the context to interpret the quotient appropriately. 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. 5-5: Interactive Additional Practice Step 3: Assess & Differentiate 5-5: Practice Buddy: Additional Practice Curriculum Standards: 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. 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. 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. Use place value and sharing to divide by 2-digit divisors. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors. Divide multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Recognize that quotients can be represented in a variety of ways, including a whole number with a remainder, a fraction or mixed number, or a decimal. Consider the context in which a problem is situated to select the most useful form of the quotient for the solution and use the context to interpret the quotient appropriately. 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. 5-5: Enrichment Curriculum Standards: 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. 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. 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. Use place value and sharing to divide by 2-digit divisors. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors. Divide multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Recognize that quotients can be represented in a variety of ways, including a whole number with a remainder, a fraction or mixed number, or a decimal. Consider the context in which a problem is situated to select the most useful form of the quotient for the solution and use the context to interpret the quotient appropriately. 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. 5-5: Quick Check Curriculum Standards: 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. 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. 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. Use place value and sharing to divide by 2-digit divisors. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors. Divide multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Recognize that quotients can be represented in a variety of ways, including a whole number with a remainder, a fraction or mixed number, or a decimal. Consider the context in which a problem is situated to select the most useful form of the quotient for the solution and use the context to interpret the quotient appropriately. 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. 5-5: Lesson Self-Assessment 5-5: Reteach to Build Understanding Curriculum Standards: 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. Find whole number quotients up to two dividends and two divisors. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. 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. Use place value and sharing to divide by 2-digit divisors. Find whole-number quotients of whole numbers with up to four- digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors. Divide multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Recognize that quotients can be represented in a variety of ways, including a whole number with a remainder, a fraction or mixed number, or a decimal. Consider the context in which a problem is situated to select the most useful form of the quotient for the solution and use the context to interpret the quotient appropriately. Solve real-world and mathematical problems requiring addition, subtraction, multiplication and division of multi-digit whole numbers. Use various strategies, including the inverse relationships between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Find whole number quotients of whole numbers with up to two-digit dividends and two-digit divisors. 5-5: Build Mathematical Literacy Curriculum Standards: Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 5 topics and texts, building on others’ ideas and expressing their own clearly. (a) Come to discussions prepared, having read or studied required material; explicitly draw on that preparation and other information known about the topic to explore ideas under discussion. (b) Follow agreed-upon rules for discussions and carry out assigned roles. (c) Pose and respond to specific questions by making comments that contribute to the discussion and elaborate on the remarks of others. (d) Review the key ideas expressed and draw conclusions in light of information and knowledge gained from the discussions. English language learners communicate for social and instructional purposes within the school setting. Summarize a written text read aloud or information presented in diverse media and formats, including visually, quantitatively, and orally. Summarize the points a speaker makes and explain how each claim is supported by reasons and evidence. Write informative/explanatory texts to examine a topic and convey ideas and information clearly. (a) Introduce a topic clearly, provide a general observation and focus, and group related information logically; include formatting (e.g., headings), illustrations, and multimedia when useful to aiding comprehension. (b) Develop the topic with facts, definitions, concrete details, quotations, or other information and examples related to the topic. (c) Link ideas within and across categories of information using words, phrases, and clauses (e.g., in contrast, especially). (d) Use precise language and domain-specific vocabulary to inform about or explain the topic. (e) Provide a concluding statement or section related to the information or explanation presented. English language learners communicate information, ideas and concepts necessary for academic success in the content area of Mathematics. 5-5: Enrichment Game: Cosmic Caravan - Arrays and Multiples of 10 5-5: Pick a Project 5-5: Another Look Curriculum Standards: 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. 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. 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. Use place value and sharing to divide by 2-digit divisors. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors. Divide multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Recognize that quotients can be represented in a variety of ways, including a whole number with a remainder, a fraction or mixed number, or a decimal. Consider the context in which a problem is situated to select the most useful form of the quotient for the solution and use the context to interpret the quotient appropriately. 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. Spanish Resources 5-5: eText del Libro del estudiante 5-5: Repaso diario 5-5: Aprendizaje visual 5-5: Amigo de práctica: Práctica adicional 5-5: Práctica adicional interactiva 5-5: Refuerzo para mejorar la comprensión 5-5: Desarrollar la competencia matemática 5-5: Ampliación Topic 5: 3-Act Math: Flapjack Stack Interactive Student Edition: Grade 5, Topic 5: 3-Act Math Mathematical Modeling Topic 5: 3-Act Math: Flapjack Stack, Act 1 Topic 5: 3-Act Math: Flapjack Stack, Act 2 Topic 5: 3-Act Math: Flapjack Stack, Act 3 Topic 5: 3-Act Math: Flapjack Stack, Sequel 5-6: Use Sharing to Divide: Greater Dividends Interactive Student Edition: Grade 5 Lesson 5-6 Math Anytime 5-6: Daily Review Topic 5: Today's Challenge Step 1: Problem-Based Learning 5-6: Solve & Share Curriculum Standards: 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. English language learners communicate for social and instructional purposes within the school setting. Write informative/explanatory texts to examine a topic and convey ideas and information clearly. (a) Introduce a topic clearly, provide a general observation and focus, and group related information logically; include formatting (e.g., headings), illustrations, and multimedia when useful to aiding comprehension. (b) Develop the topic with facts, definitions, concrete details, quotations, or other information and examples related to the topic. (c) Link ideas within and across categories of information using words, phrases, and clauses (e.g., in contrast, especially). (d) Use precise language and domain-specific vocabulary to inform about or explain the topic. (e) Provide a concluding statement or section related to the information or explanation presented. English language learners communicate information, ideas and concepts necessary for academic success in the content area of Mathematics. Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 5 topics and texts, building on others’ ideas and expressing their own clearly. (a) Come to discussions prepared, having read or studied required material; explicitly draw on that preparation and other information known about the topic to explore ideas under discussion. (b) Follow agreed-upon rules for discussions and carry out assigned roles. (c) Pose and respond to specific questions by making comments that contribute to the discussion and elaborate on the remarks of others. (d) Review the key ideas expressed and draw conclusions in light of information and knowledge gained from the discussions. Summarize a written text read aloud or information presented in diverse media and formats, including visually, quantitatively, and orally. Summarize the points a speaker makes and explain how each claim is supported by reasons and evidence. 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. 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. Use place value and sharing to divide greater dividends. 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. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors. Divide multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Recognize that quotients can be represented in a variety of ways, including a whole number with a remainder, a fraction or mixed number, or a decimal. Consider the context in which a problem is situated to select the most useful form of the quotient for the solution and use the context to interpret the quotient appropriately. Estimate solutions to arithmetic problems in order to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition, subtraction, multiplication and division of multi-digit whole numbers. Use various strategies, including the inverse relationships between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Step 2: Visual Learning 5-6: Visual Learning Curriculum Standards: 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. 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. 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. Use place value and sharing to divide greater dividends. 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. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors. Divide multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Recognize that quotients can be represented in a variety of ways, including a whole number with a remainder, a fraction or mixed number, or a decimal. Consider the context in which a problem is situated to select the most useful form of the quotient for the solution and use the context to interpret the quotient appropriately. Estimate solutions to arithmetic problems in order to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition, subtraction, multiplication and division of multi-digit whole numbers. Use various strategies, including the inverse relationships between operations, the use of technology, and the context of the problem to assess the reasonableness of results. 5-6: Convince Me! Curriculum Standards: 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. 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. 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. Use place value and sharing to divide greater dividends. 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. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors. Divide multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Recognize that quotients can be represented in a variety of ways, including a whole number with a remainder, a fraction or mixed number, or a decimal. Consider the context in which a problem is situated to select the most useful form of the quotient for the solution and use the context to interpret the quotient appropriately. Estimate solutions to arithmetic problems in order to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition, subtraction, multiplication and division of multi-digit whole numbers. Use various strategies, including the inverse relationships between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Practice and Problem Solving 5-6: Student Edition Practice Curriculum Standards: 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. 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. 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. Use place value and sharing to divide greater dividends. 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. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors. Divide multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Recognize that quotients can be represented in a variety of ways, including a whole number with a remainder, a fraction or mixed number, or a decimal. Consider the context in which a problem is situated to select the most useful form of the quotient for the solution and use the context to interpret the quotient appropriately. Estimate solutions to arithmetic problems in order to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition, subtraction, multiplication and division of multi-digit whole numbers. Use various strategies, including the inverse relationships between operations, the use of technology, and the context of the problem to assess the reasonableness of results. 5-6: Practice Buddy: Independent Practice; Problem Solving Curriculum Standards: 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. 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. 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. Use place value and sharing to divide greater dividends. 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. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors. Divide multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Recognize that quotients can be represented in a variety of ways, including a whole number with a remainder, a fraction or mixed number, or a decimal. Consider the context in which a problem is situated to select the most useful form of the quotient for the solution and use the context to interpret the quotient appropriately. Estimate solutions to arithmetic problems in order to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition, subtraction, multiplication and division of multi-digit whole numbers. Use various strategies, including the inverse relationships between operations, the use of technology, and the context of the problem to assess the reasonableness of results. 5-6: Practice Buddy: Additional Practice Curriculum Standards: 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. 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. 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. Use place value and sharing to divide greater dividends. 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. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors. Divide multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Recognize that quotients can be represented in a variety of ways, including a whole number with a remainder, a fraction or mixed number, or a decimal. Consider the context in which a problem is situated to select the most useful form of the quotient for the solution and use the context to interpret the quotient appropriately. Estimate solutions to arithmetic problems in order to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition, subtraction, multiplication and division of multi-digit whole numbers. Use various strategies, including the inverse relationships between operations, the use of technology, and the context of the problem to assess the reasonableness of results. 5-6: Interactive Additional Practice Step 3: Assess & Differentiate 5-6: Practice Buddy: Additional Practice Curriculum Standards: 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. 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. 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. Use place value and sharing to divide greater dividends. 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. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors. Divide multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Recognize that quotients can be represented in a variety of ways, including a whole number with a remainder, a fraction or mixed number, or a decimal. Consider the context in which a problem is situated to select the most useful form of the quotient for the solution and use the context to interpret the quotient appropriately. Estimate solutions to arithmetic problems in order to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition, subtraction, multiplication and division of multi-digit whole numbers. Use various strategies, including the inverse relationships between operations, the use of technology, and the context of the problem to assess the reasonableness of results. 5-6: Enrichment Curriculum Standards: 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. 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. 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. Use place value and sharing to divide greater dividends. 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. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors. Divide multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Recognize that quotients can be represented in a variety of ways, including a whole number with a remainder, a fraction or mixed number, or a decimal. Consider the context in which a problem is situated to select the most useful form of the quotient for the solution and use the context to interpret the quotient appropriately. Estimate solutions to arithmetic problems in order to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition, subtraction, multiplication and division of multi-digit whole numbers. Use various strategies, including the inverse relationships between operations, the use of technology, and the context of the problem to assess the reasonableness of results. 5-6: Quick Check Curriculum Standards: 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. 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. 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. Use place value and sharing to divide greater dividends. 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. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors. Divide multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Recognize that quotients can be represented in a variety of ways, including a whole number with a remainder, a fraction or mixed number, or a decimal. Consider the context in which a problem is situated to select the most useful form of the quotient for the solution and use the context to interpret the quotient appropriately. Estimate solutions to arithmetic problems in order to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition, subtraction, multiplication and division of multi-digit whole numbers. Use various strategies, including the inverse relationships between operations, the use of technology, and the context of the problem to assess the reasonableness of results. 5-6: Lesson Self-Assessment 5-6: Reteach to Build Understanding Curriculum Standards: 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. Find whole number quotients up to two dividends and two divisors. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. 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. Use place value and sharing to divide greater dividends. 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. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors. Divide multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Recognize that quotients can be represented in a variety of ways, including a whole number with a remainder, a fraction or mixed number, or a decimal. Consider the context in which a problem is situated to select the most useful form of the quotient for the solution and use the context to interpret the quotient appropriately. Estimate solutions to arithmetic problems in order to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition, subtraction, multiplication and division of multi-digit whole numbers. Use various strategies, including the inverse relationships between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Find whole number quotients of whole numbers with up to two-digit dividends and two-digit divisors. 5-6: Build Mathematical Literacy Curriculum Standards: Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 5 topics and texts, building on others’ ideas and expressing their own clearly. (a) Come to discussions prepared, having read or studied required material; explicitly draw on that preparation and other information known about the topic to explore ideas under discussion. (b) Follow agreed-upon rules for discussions and carry out assigned roles. (c) Pose and respond to specific questions by making comments that contribute to the discussion and elaborate on the remarks of others. (d) Review the key ideas expressed and draw conclusions in light of information and knowledge gained from the discussions. English language learners communicate for social and instructional purposes within the school setting. Summarize a written text read aloud or information presented in diverse media and formats, including visually, quantitatively, and orally. Summarize the points a speaker makes and explain how each claim is supported by reasons and evidence. Write informative/explanatory texts to examine a topic and convey ideas and information clearly. (a) Introduce a topic clearly, provide a general observation and focus, and group related information logically; include formatting (e.g., headings), illustrations, and multimedia when useful to aiding comprehension. (b) Develop the topic with facts, definitions, concrete details, quotations, or other information and examples related to the topic. (c) Link ideas within and across categories of information using words, phrases, and clauses (e.g., in contrast, especially). (d) Use precise language and domain-specific vocabulary to inform about or explain the topic. (e) Provide a concluding statement or section related to the information or explanation presented. English language learners communicate information, ideas and concepts necessary for academic success in the content area of Mathematics. 5-6: Enrichment Game: Fluency - Multiply Multi-Digit Whole Numbers 5-6: enVision STEM Activity Curriculum Standards: 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. 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. 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. Use place value and sharing to divide greater dividends. 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. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors. Divide multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Recognize that quotients can be represented in a variety of ways, including a whole number with a remainder, a fraction or mixed number, or a decimal. Consider the context in which a problem is situated to select the most useful form of the quotient for the solution and use the context to interpret the quotient appropriately. Estimate solutions to arithmetic problems in order to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition, subtraction, multiplication and division of multi-digit whole numbers. Use various strategies, including the inverse relationships between operations, the use of technology, and the context of the problem to assess the reasonableness of results. 5-6: Another Look Curriculum Standards: 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. 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. 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. Use place value and sharing to divide greater dividends. 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. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors. Divide multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Recognize that quotients can be represented in a variety of ways, including a whole number with a remainder, a fraction or mixed number, or a decimal. Consider the context in which a problem is situated to select the most useful form of the quotient for the solution and use the context to interpret the quotient appropriately. Estimate solutions to arithmetic problems in order to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition, subtraction, multiplication and division of multi-digit whole numbers. Use various strategies, including the inverse relationships between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Spanish Resources 5-6: eText del Libro del estudiante 5-6: Repaso diario 5-6: Aprendizaje visual 5-6: Amigo de práctica: Práctica adicional 5-6: Práctica adicional interactiva 5-6: Refuerzo para mejorar la comprensión 5-6: Desarrollar la competencia matemática 5-6: Ampliación 5-7: Choose a Strategy to Divide Interactive Student Edition: Grade 5 Lesson 5-7 Math Anytime 5-7: Daily Review Topic 5: Today's Challenge Step 1: Problem-Based Learning 5-7: Solve & Share Curriculum Standards: 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. English language learners communicate for social and instructional purposes within the school setting. Write informative/explanatory texts to examine a topic and convey ideas and information clearly. (a) Introduce a topic clearly, provide a general observation and focus, and group related information logically; include formatting (e.g., headings), illustrations, and multimedia when useful to aiding comprehension. (b) Develop the topic with facts, definitions, concrete details, quotations, or other information and examples related to the topic. (c) Link ideas within and across categories of information using words, phrases, and clauses (e.g., in contrast, especially). (d) Use precise language and domain-specific vocabulary to inform about or explain the topic. (e) Provide a concluding statement or section related to the information or explanation presented. English language learners communicate information, ideas and concepts necessary for academic success in the content area of Mathematics. Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 5 topics and texts, building on others’ ideas and expressing their own clearly. (a) Come to discussions prepared, having read or studied required material; explicitly draw on that preparation and other information known about the topic to explore ideas under discussion. (b) Follow agreed-upon rules for discussions and carry out assigned roles. (c) Pose and respond to specific questions by making comments that contribute to the discussion and elaborate on the remarks of others. (d) Review the key ideas expressed and draw conclusions in light of information and knowledge gained from the discussions. Summarize a written text read aloud or information presented in diverse media and formats, including visually, quantitatively, and orally. Summarize the points a speaker makes and explain how each claim is supported by reasons and evidence. 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. 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. Select from different strategies to divide 3-and 4-digit numbers by 2-digit numbers. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors. Divide multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Recognize that quotients can be represented in a variety of ways, including a whole number with a remainder, a fraction or mixed number, or a decimal. Consider the context in which a problem is situated to select the most useful form of the quotient for the solution and use the context to interpret the quotient appropriately. Estimate solutions to arithmetic problems in order to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition, subtraction, multiplication and division of multi-digit whole numbers. Use various strategies, including the inverse relationships between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Step 2: Visual Learning 5-7: Visual Learning Curriculum Standards: 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. 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. 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. Select from different strategies to divide 3-and 4-digit numbers by 2-digit numbers. Find whole- number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors. Divide multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Recognize that quotients can be represented in a variety of ways, including a whole number with a remainder, a fraction or mixed number, or a decimal. Consider the context in which a problem is situated to select the most useful form of the quotient for the solution and use the context to interpret the quotient appropriately. Estimate solutions to arithmetic problems in order to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition, subtraction, multiplication and division of multi-digit whole numbers. Use various strategies, including the inverse relationships between operations, the use of technology, and the context of the problem to assess the reasonableness of results. 5-7: Convince Me! Curriculum Standards: 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. 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. 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. Select from different strategies to divide 3-and 4-digit numbers by 2-digit numbers. Find whole- number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors. Divide multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Recognize that quotients can be represented in a variety of ways, including a whole number with a remainder, a fraction or mixed number, or a decimal. Consider the context in which a problem is situated to select the most useful form of the quotient for the solution and use the context to interpret the quotient appropriately. Estimate solutions to arithmetic problems in order to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition, subtraction, multiplication and division of multi-digit whole numbers. Use various strategies, including the inverse relationships between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Practice and Problem Solving 5-7: Student Edition Practice Curriculum Standards: 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. 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. 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. Select from different strategies to divide 3-and 4-digit numbers by 2-digit numbers. Find whole- number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors. Divide multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Recognize that quotients can be represented in a variety of ways, including a whole number with a remainder, a fraction or mixed number, or a decimal. Consider the context in which a problem is situated to select the most useful form of the quotient for the solution and use the context to interpret the quotient appropriately. Estimate solutions to arithmetic problems in order to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition, subtraction, multiplication and division of multi-digit whole numbers. Use various strategies, including the inverse relationships between operations, the use of technology, and the context of the problem to assess the reasonableness of results. 5-7: Practice Buddy: Independent Practice; Problem Solving Curriculum Standards: 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. 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. 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. Select from different strategies to divide 3-and 4-digit numbers by 2-digit numbers. Find whole- number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors. Divide multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Recognize that quotients can be represented in a variety of ways, including a whole number with a remainder, a fraction or mixed number, or a decimal. Consider the context in which a problem is situated to select the most useful form of the quotient for the solution and use the context to interpret the quotient appropriately. Estimate solutions to arithmetic problems in order to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition, subtraction, multiplication and division of multi-digit whole numbers. Use various strategies, including the inverse relationships between operations, the use of technology, and the context of the problem to assess the reasonableness of results. 5-7: Practice Buddy: Additional Practice Curriculum Standards: 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. 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. 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. Select from different strategies to divide 3-and 4-digit numbers by 2-digit numbers. Find whole- number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors. Divide multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Recognize that quotients can be represented in a variety of ways, including a whole number with a remainder, a fraction or mixed number, or a decimal. Consider the context in which a problem is situated to select the most useful form of the quotient for the solution and use the context to interpret the quotient appropriately. Estimate solutions to arithmetic problems in order to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition, subtraction, multiplication and division of multi-digit whole numbers. Use various strategies, including the inverse relationships between operations, the use of technology, and the context of the problem to assess the reasonableness of results. 5-7: Interactive Additional Practice Step 3: Assess & Differentiate 5-7: Practice Buddy: Additional Practice Curriculum Standards: 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. 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. 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. Select from different strategies to divide 3-and 4-digit numbers by 2-digit numbers. Find whole- number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors. Divide multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Recognize that quotients can be represented in a variety of ways, including a whole number with a remainder, a fraction or mixed number, or a decimal. Consider the context in which a problem is situated to select the most useful form of the quotient for the solution and use the context to interpret the quotient appropriately. Estimate solutions to arithmetic problems in order to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition, subtraction, multiplication and division of multi-digit whole numbers. Use various strategies, including the inverse relationships between operations, the use of technology, and the context of the problem to assess the reasonableness of results. 5-7: Enrichment Curriculum Standards: 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. 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. 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. Select from different strategies to divide 3-and 4-digit numbers by 2-digit numbers. Find whole- number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors. Divide multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Recognize that quotients can be represented in a variety of ways, including a whole number with a remainder, a fraction or mixed number, or a decimal. Consider the context in which a problem is situated to select the most useful form of the quotient for the solution and use the context to interpret the quotient appropriately. Estimate solutions to arithmetic problems in order to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition, subtraction, multiplication and division of multi-digit whole numbers. Use various strategies, including the inverse relationships between operations, the use of technology, and the context of the problem to assess the reasonableness of results. 5-7: Quick Check Curriculum Standards: 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. 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. 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. Select from different strategies to divide 3-and 4-digit numbers by 2-digit numbers. Find whole- number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors. Divide multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Recognize that quotients can be represented in a variety of ways, including a whole number with a remainder, a fraction or mixed number, or a decimal. Consider the context in which a problem is situated to select the most useful form of the quotient for the solution and use the context to interpret the quotient appropriately. Estimate solutions to arithmetic problems in order to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition, subtraction, multiplication and division of multi-digit whole numbers. Use various strategies, including the inverse relationships between operations, the use of technology, and the context of the problem to assess the reasonableness of results. 5-7: Lesson Self-Assessment 5-7: Reteach to Build Understanding Curriculum Standards: 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. 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. 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. Select from different strategies to divide 3-and 4-digit numbers by 2-digit numbers. Find whole- number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors. Divide multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Recognize that quotients can be represented in a variety of ways, including a whole number with a remainder, a fraction or mixed number, or a decimal. Consider the context in which a problem is situated to select the most useful form of the quotient for the solution and use the context to interpret the quotient appropriately. Estimate solutions to arithmetic problems in order to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition, subtraction, multiplication and division of multi-digit whole numbers. Use various strategies, including the inverse relationships between operations, the use of technology, and the context of the problem to assess the reasonableness of results. 5-7: Build Mathematical Literacy Curriculum Standards: Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 5 topics and texts, building on others’ ideas and expressing their own clearly. (a) Come to discussions prepared, having read or studied required material; explicitly draw on that preparation and other information known about the topic to explore ideas under discussion. (b) Follow agreed-upon rules for discussions and carry out assigned roles. (c) Pose and respond to specific questions by making comments that contribute to the discussion and elaborate on the remarks of others. (d) Review the key ideas expressed and draw conclusions in light of information and knowledge gained from the discussions. English language learners communicate for social and instructional purposes within the school setting. Summarize a written text read aloud or information presented in diverse media and formats, including visually, quantitatively, and orally. Summarize the points a speaker makes and explain how each claim is supported by reasons and evidence. Write informative/explanatory texts to examine a topic and convey ideas and information clearly. (a) Introduce a topic clearly, provide a general observation and focus, and group related information logically; include formatting (e.g., headings), illustrations, and multimedia when useful to aiding comprehension. (b) Develop the topic with facts, definitions, concrete details, quotations, or other information and examples related to the topic. (c) Link ideas within and across categories of information using words, phrases, and clauses (e.g., in contrast, especially). (d) Use precise language and domain-specific vocabulary to inform about or explain the topic. (e) Provide a concluding statement or section related to the information or explanation presented. English language learners communicate information, ideas and concepts necessary for academic success in the content area of Mathematics. 5-7: Enrichment 5-7: Digital Math Tool Activity 5-7: Pick a Project 5-7: Another Look Curriculum Standards: 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. 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. 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. Select from different strategies to divide 3-and 4-digit numbers by 2-digit numbers. Find whole- number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors. Divide multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Recognize that quotients can be represented in a variety of ways, including a whole number with a remainder, a fraction or mixed number, or a decimal. Consider the context in which a problem is situated to select the most useful form of the quotient for the solution and use the context to interpret the quotient appropriately. Estimate solutions to arithmetic problems in order to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition, subtraction, multiplication and division of multi-digit whole numbers. Use various strategies, including the inverse relationships between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Spanish Resources 5-7: eText del Libro del estudiante 5-7: Repaso diario 5-7: Aprendizaje visual 5-7: Amigo de práctica: Práctica adicional 5-7: Práctica adicional interactiva 5-7: Refuerzo para mejorar la comprensión 5-7: Desarrollar la competencia matemática 5-7: Ampliación 5-8: Problem Solving: Make Sense and Persevere Interactive Student Edition: Grade 5 Lesson 5-8 Math Anytime 5-8: Daily Review Topic 5: Today's Challenge Step 1: Problem-Based Learning 5-8: Solve & Share Curriculum Standards: 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. Make sense of problems and persevere in solving them. English language learners communicate for social and instructional purposes within the school setting. Write informative/explanatory texts to examine a topic and convey ideas and information clearly. (a) Introduce a topic clearly, provide a general observation and focus, and group related information logically; include formatting (e.g., headings), illustrations, and multimedia when useful to aiding comprehension. (b) Develop the topic with facts, definitions, concrete details, quotations, or other information and examples related to the topic. (c) Link ideas within and across categories of information using words, phrases, and clauses (e.g., in contrast, especially). (d) Use precise language and domain-specific vocabulary to inform about or explain the topic. (e) Provide a concluding statement or section related to the information or explanation presented. English language learners communicate information, ideas and concepts necessary for academic success in the content area of Mathematics. Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 5 topics and texts, building on others’ ideas and expressing their own clearly. (a) Come to discussions prepared, having read or studied required material; explicitly draw on that preparation and other information known about the topic to explore ideas under discussion. (b) Follow agreed-upon rules for discussions and carry out assigned roles. (c) Pose and respond to specific questions by making comments that contribute to the discussion and elaborate on the remarks of others. (d) Review the key ideas expressed and draw conclusions in light of information and knowledge gained from the discussions. Summarize a written text read aloud or information presented in diverse media and formats, including visually, quantitatively, and orally. Summarize the points a speaker makes and explain how each claim is supported by reasons and evidence. 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. Make sense of problems and persevere in solving them. 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. Make sense of problems and persevere in solving them. Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution. They analyze givens, constraints, relationships, and goals. They make conjectures about the form and meaning of the solution and plan a solution pathway rather than simply jumping into a solution attempt. They consider analogous problems, and try special cases and simpler forms of the original problem in order to gain insight into its solution. They monitor and evaluate their progress and change course if necessary. Older students might, depending on the context of the problem, transform algebraic expressions or change the viewing window on their graphing calculator to get the information they need. Mathematically proficient students can explain correspondences between equations, verbal descriptions, tables, and graphs or draw diagrams of important features and relationships, graph data, and search for regularity or trends. Younger students might rely on using concrete objects or pictures to help conceptualize and solve a problem. Mathematically proficient students check their answers to problems using a different method, and they continually ask themselves, “Does this make sense?” They can understand the approaches of others to solving complex problems and identify correspondences between different approaches. Make sense of problems and keep working. 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. Construct viable arguments and critique the reasoning of others. Make sense of problems and persevere in solving them. Make sense of problems and persevere in solving them. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors. Make sense of problems and persevere in solving them. Divide multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Recognize that quotients can be represented in a variety of ways, including a whole number with a remainder, a fraction or mixed number, or a decimal. Consider the context in which a problem is situated to select the most useful form of the quotient for the solution and use the context to interpret the quotient appropriately. Estimate solutions to arithmetic problems in order to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition, subtraction, multiplication and division of multi-digit whole numbers. Use various strategies, including the inverse relationships between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Step 2: Visual Learning 5-8: Visual Learning Curriculum Standards: 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. Make sense of problems and persevere in solving them. 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. Make sense of problems and persevere in solving them. 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. Make sense of problems and persevere in solving them. Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution. They analyze givens, constraints, relationships, and goals. They make conjectures about the form and meaning of the solution and plan a solution pathway rather than simply jumping into a solution attempt. They consider analogous problems, and try special cases and simpler forms of the original problem in order to gain insight into its solution. They monitor and evaluate their progress and change course if necessary. Older students might, depending on the context of the problem, transform algebraic expressions or change the viewing window on their graphing calculator to get the information they need. Mathematically proficient students can explain correspondences between equations, verbal descriptions, tables, and graphs or draw diagrams of important features and relationships, graph data, and search for regularity or trends. Younger students might rely on using concrete objects or pictures to help conceptualize and solve a problem. Mathematically proficient students check their answers to problems using a different method, and they continually ask themselves, “Does this make sense?” They can understand the approaches of others to solving complex problems and identify correspondences between different approaches. Make sense of problems and keep working. 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. Construct viable arguments and critique the reasoning of others. Make sense of problems and persevere in solving them. Make sense of problems and persevere in solving them. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors. Make sense of problems and persevere in solving them. Divide multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Recognize that quotients can be represented in a variety of ways, including a whole number with a remainder, a fraction or mixed number, or a decimal. Consider the context in which a problem is situated to select the most useful form of the quotient for the solution and use the context to interpret the quotient appropriately. Estimate solutions to arithmetic problems in order to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition, subtraction, multiplication and division of multi-digit whole numbers. Use various strategies, including the inverse relationships between operations, the use of technology, and the context of the problem to assess the reasonableness of results. 5-8: Convince Me! Curriculum Standards: 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. Make sense of problems and persevere in solving them. 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. Make sense of problems and persevere in solving them. 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. Make sense of problems and persevere in solving them. Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution. They analyze givens, constraints, relationships, and goals. They make conjectures about the form and meaning of the solution and plan a solution pathway rather than simply jumping into a solution attempt. They consider analogous problems, and try special cases and simpler forms of the original problem in order to gain insight into its solution. They monitor and evaluate their progress and change course if necessary. Older students might, depending on the context of the problem, transform algebraic expressions or change the viewing window on their graphing calculator to get the information they need. Mathematically proficient students can explain correspondences between equations, verbal descriptions, tables, and graphs or draw diagrams of important features and relationships, graph data, and search for regularity or trends. Younger students might rely on using concrete objects or pictures to help conceptualize and solve a problem. Mathematically proficient students check their answers to problems using a different method, and they continually ask themselves, “Does this make sense?” They can understand the approaches of others to solving complex problems and identify correspondences between different approaches. Make sense of problems and keep working. 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. Construct viable arguments and critique the reasoning of others. Make sense of problems and persevere in solving them. Make sense of problems and persevere in solving them. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors. Make sense of problems and persevere in solving them. Divide multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Recognize that quotients can be represented in a variety of ways, including a whole number with a remainder, a fraction or mixed number, or a decimal. Consider the context in which a problem is situated to select the most useful form of the quotient for the solution and use the context to interpret the quotient appropriately. Estimate solutions to arithmetic problems in order to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition, subtraction, multiplication and division of multi-digit whole numbers. Use various strategies, including the inverse relationships between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Practice and Problem Solving 5-8: Student Edition Practice Curriculum Standards: 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. Make sense of problems and persevere in solving them. 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. Make sense of problems and persevere in solving them. 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. Make sense of problems and persevere in solving them. Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution. They analyze givens, constraints, relationships, and goals. They make conjectures about the form and meaning of the solution and plan a solution pathway rather than simply jumping into a solution attempt. They consider analogous problems, and try special cases and simpler forms of the original problem in order to gain insight into its solution. They monitor and evaluate their progress and change course if necessary. Older students might, depending on the context of the problem, transform algebraic expressions or change the viewing window on their graphing calculator to get the information they need. Mathematically proficient students can explain correspondences between equations, verbal descriptions, tables, and graphs or draw diagrams of important features and relationships, graph data, and search for regularity or trends. Younger students might rely on using concrete objects or pictures to help conceptualize and solve a problem. Mathematically proficient students check their answers to problems using a different method, and they continually ask themselves, “Does this make sense?” They can understand the approaches of others to solving complex problems and identify correspondences between different approaches. Make sense of problems and keep working. 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. Construct viable arguments and critique the reasoning of others. Make sense of problems and persevere in solving them. Make sense of problems and persevere in solving them. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors. Make sense of problems and persevere in solving them. Divide multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Recognize that quotients can be represented in a variety of ways, including a whole number with a remainder, a fraction or mixed number, or a decimal. Consider the context in which a problem is situated to select the most useful form of the quotient for the solution and use the context to interpret the quotient appropriately. Estimate solutions to arithmetic problems in order to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition, subtraction, multiplication and division of multi-digit whole numbers. Use various strategies, including the inverse relationships between operations, the use of technology, and the context of the problem to assess the reasonableness of results. 5-8: Practice Buddy: Independent Practice; Problem Solving Curriculum Standards: 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. Make sense of problems and persevere in solving them. 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. Make sense of problems and persevere in solving them. 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. Make sense of problems and persevere in solving them. Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution. They analyze givens, constraints, relationships, and goals. They make conjectures about the form and meaning of the solution and plan a solution pathway rather than simply jumping into a solution attempt. They consider analogous problems, and try special cases and simpler forms of the original problem in order to gain insight into its solution. They monitor and evaluate their progress and change course if necessary. Older students might, depending on the context of the problem, transform algebraic expressions or change the viewing window on their graphing calculator to get the information they need. Mathematically proficient students can explain correspondences between equations, verbal descriptions, tables, and graphs or draw diagrams of important features and relationships, graph data, and search for regularity or trends. Younger students might rely on using concrete objects or pictures to help conceptualize and solve a problem. Mathematically proficient students check their answers to problems using a different method, and they continually ask themselves, “Does this make sense?” They can understand the approaches of others to solving complex problems and identify correspondences between different approaches. Make sense of problems and keep working. 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. Construct viable arguments and critique the reasoning of others. Make sense of problems and persevere in solving them. Make sense of problems and persevere in solving them. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors. Make sense of problems and persevere in solving them. Divide multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Recognize that quotients can be represented in a variety of ways, including a whole number with a remainder, a fraction or mixed number, or a decimal. Consider the context in which a problem is situated to select the most useful form of the quotient for the solution and use the context to interpret the quotient appropriately. Estimate solutions to arithmetic problems in order to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition, subtraction, multiplication and division of multi-digit whole numbers. Use various strategies, including the inverse relationships between operations, the use of technology, and the context of the problem to assess the reasonableness of results. 5-8: Practice Buddy: Additional Practice Curriculum Standards: 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. Make sense of problems and persevere in solving them. 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. Make sense of problems and persevere in solving them. 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. Make sense of problems and persevere in solving them. Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution. They analyze givens, constraints, relationships, and goals. They make conjectures about the form and meaning of the solution and plan a solution pathway rather than simply jumping into a solution attempt. They consider analogous problems, and try special cases and simpler forms of the original problem in order to gain insight into its solution. They monitor and evaluate their progress and change course if necessary. Older students might, depending on the context of the problem, transform algebraic expressions or change the viewing window on their graphing calculator to get the information they need. Mathematically proficient students can explain correspondences between equations, verbal descriptions, tables, and graphs or draw diagrams of important features and relationships, graph data, and search for regularity or trends. Younger students might rely on using concrete objects or pictures to help conceptualize and solve a problem. Mathematically proficient students check their answers to problems using a different method, and they continually ask themselves, “Does this make sense?” They can understand the approaches of others to solving complex problems and identify correspondences between different approaches. Make sense of problems and keep working. 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. Construct viable arguments and critique the reasoning of others. Make sense of problems and persevere in solving them. Make sense of problems and persevere in solving them. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors. Make sense of problems and persevere in solving them. Divide multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Recognize that quotients can be represented in a variety of ways, including a whole number with a remainder, a fraction or mixed number, or a decimal. Consider the context in which a problem is situated to select the most useful form of the quotient for the solution and use the context to interpret the quotient appropriately. Estimate solutions to arithmetic problems in order to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition, subtraction, multiplication and division of multi-digit whole numbers. Use various strategies, including the inverse relationships between operations, the use of technology, and the context of the problem to assess the reasonableness of results. 5-8: Interactive Additional Practice Step 3: Assess & Differentiate 5-8: Practice Buddy: Additional Practice Curriculum Standards: 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. Make sense of problems and persevere in solving them. 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. Make sense of problems and persevere in solving them. 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. Make sense of problems and persevere in solving them. Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution. They analyze givens, constraints, relationships, and goals. They make conjectures about the form and meaning of the solution and plan a solution pathway rather than simply jumping into a solution attempt. They consider analogous problems, and try special cases and simpler forms of the original problem in order to gain insight into its solution. They monitor and evaluate their progress and change course if necessary. Older students might, depending on the context of the problem, transform algebraic expressions or change the viewing window on their graphing calculator to get the information they need. Mathematically proficient students can explain correspondences between equations, verbal descriptions, tables, and graphs or draw diagrams of important features and relationships, graph data, and search for regularity or trends. Younger students might rely on using concrete objects or pictures to help conceptualize and solve a problem. Mathematically proficient students check their answers to problems using a different method, and they continually ask themselves, “Does this make sense?” They can understand the approaches of others to solving complex problems and identify correspondences between different approaches. Make sense of problems and keep working. 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. Construct viable arguments and critique the reasoning of others. Make sense of problems and persevere in solving them. Make sense of problems and persevere in solving them. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors. Make sense of problems and persevere in solving them. Divide multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Recognize that quotients can be represented in a variety of ways, including a whole number with a remainder, a fraction or mixed number, or a decimal. Consider the context in which a problem is situated to select the most useful form of the quotient for the solution and use the context to interpret the quotient appropriately. Estimate solutions to arithmetic problems in order to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition, subtraction, multiplication and division of multi-digit whole numbers. Use various strategies, including the inverse relationships between operations, the use of technology, and the context of the problem to assess the reasonableness of results. 5-8: Enrichment Curriculum Standards: 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. Make sense of problems and persevere in solving them. 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. Make sense of problems and persevere in solving them. 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. Make sense of problems and persevere in solving them. Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution. They analyze givens, constraints, relationships, and goals. They make conjectures about the form and meaning of the solution and plan a solution pathway rather than simply jumping into a solution attempt. They consider analogous problems, and try special cases and simpler forms of the original problem in order to gain insight into its solution. They monitor and evaluate their progress and change course if necessary. Older students might, depending on the context of the problem, transform algebraic expressions or change the viewing window on their graphing calculator to get the information they need. Mathematically proficient students can explain correspondences between equations, verbal descriptions, tables, and graphs or draw diagrams of important features and relationships, graph data, and search for regularity or trends. Younger students might rely on using concrete objects or pictures to help conceptualize and solve a problem. Mathematically proficient students check their answers to problems using a different method, and they continually ask themselves, “Does this make sense?” They can understand the approaches of others to solving complex problems and identify correspondences between different approaches. Make sense of problems and keep working. 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. Construct viable arguments and critique the reasoning of others. Make sense of problems and persevere in solving them. Make sense of problems and persevere in solving them. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors. Make sense of problems and persevere in solving them. Divide multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Recognize that quotients can be represented in a variety of ways, including a whole number with a remainder, a fraction or mixed number, or a decimal. Consider the context in which a problem is situated to select the most useful form of the quotient for the solution and use the context to interpret the quotient appropriately. Estimate solutions to arithmetic problems in order to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition, subtraction, multiplication and division of multi-digit whole numbers. Use various strategies, including the inverse relationships between operations, the use of technology, and the context of the problem to assess the reasonableness of results. 5-8: Quick Check Curriculum Standards: 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. Make sense of problems and persevere in solving them. 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. Make sense of problems and persevere in solving them. 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. Make sense of problems and persevere in solving them. Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution. They analyze givens, constraints, relationships, and goals. They make conjectures about the form and meaning of the solution and plan a solution pathway rather than simply jumping into a solution attempt. They consider analogous problems, and try special cases and simpler forms of the original problem in order to gain insight into its solution. They monitor and evaluate their progress and change course if necessary. Older students might, depending on the context of the problem, transform algebraic expressions or change the viewing window on their graphing calculator to get the information they need. Mathematically proficient students can explain correspondences between equations, verbal descriptions, tables, and graphs or draw diagrams of important features and relationships, graph data, and search for regularity or trends. Younger students might rely on using concrete objects or pictures to help conceptualize and solve a problem. Mathematically proficient students check their answers to problems using a different method, and they continually ask themselves, “Does this make sense?” They can understand the approaches of others to solving complex problems and identify correspondences between different approaches. Make sense of problems and keep working. 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. Construct viable arguments and critique the reasoning of others. Make sense of problems and persevere in solving them. Make sense of problems and persevere in solving them. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors. Make sense of problems and persevere in solving them. Divide multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Recognize that quotients can be represented in a variety of ways, including a whole number with a remainder, a fraction or mixed number, or a decimal. Consider the context in which a problem is situated to select the most useful form of the quotient for the solution and use the context to interpret the quotient appropriately. Estimate solutions to arithmetic problems in order to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition, subtraction, multiplication and division of multi-digit whole numbers. Use various strategies, including the inverse relationships between operations, the use of technology, and the context of the problem to assess the reasonableness of results. 5-8: Lesson Self-Assessment 5-8: Reteach to Build Understanding Curriculum Standards: 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. Make sense of problems and persevere in solving them. 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. Make sense of problems and persevere in solving them. 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. Make sense of problems and persevere in solving them. Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution. They analyze givens, constraints, relationships, and goals. They make conjectures about the form and meaning of the solution and plan a solution pathway rather than simply jumping into a solution attempt. They consider analogous problems, and try special cases and simpler forms of the original problem in order to gain insight into its solution. They monitor and evaluate their progress and change course if necessary. Older students might, depending on the context of the problem, transform algebraic expressions or change the viewing window on their graphing calculator to get the information they need. Mathematically proficient students can explain correspondences between equations, verbal descriptions, tables, and graphs or draw diagrams of important features and relationships, graph data, and search for regularity or trends. Younger students might rely on using concrete objects or pictures to help conceptualize and solve a problem. Mathematically proficient students check their answers to problems using a different method, and they continually ask themselves, “Does this make sense?” They can understand the approaches of others to solving complex problems and identify correspondences between different approaches. Make sense of problems and keep working. 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. Construct viable arguments and critique the reasoning of others. Make sense of problems and persevere in solving them. Make sense of problems and persevere in solving them. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors. Make sense of problems and persevere in solving them. Divide multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Recognize that quotients can be represented in a variety of ways, including a whole number with a remainder, a fraction or mixed number, or a decimal. Consider the context in which a problem is situated to select the most useful form of the quotient for the solution and use the context to interpret the quotient appropriately. Estimate solutions to arithmetic problems in order to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition, subtraction, multiplication and division of multi-digit whole numbers. Use various strategies, including the inverse relationships between operations, the use of technology, and the context of the problem to assess the reasonableness of results. 5-8: Build Mathematical Literacy Curriculum Standards: Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 5 topics and texts, building on others’ ideas and expressing their own clearly. (a) Come to discussions prepared, having read or studied required material; explicitly draw on that preparation and other information known about the topic to explore ideas under discussion. (b) Follow agreed-upon rules for discussions and carry out assigned roles. (c) Pose and respond to specific questions by making comments that contribute to the discussion and elaborate on the remarks of others. (d) Review the key ideas expressed and draw conclusions in light of information and knowledge gained from the discussions. English language learners communicate for social and instructional purposes within the school setting. Summarize a written text read aloud or information presented in diverse media and formats, including visually, quantitatively, and orally. Summarize the points a speaker makes and explain how each claim is supported by reasons and evidence. Write informative/explanatory texts to examine a topic and convey ideas and information clearly. (a) Introduce a topic clearly, provide a general observation and focus, and group related information logically; include formatting (e.g., headings), illustrations, and multimedia when useful to aiding comprehension. (b) Develop the topic with facts, definitions, concrete details, quotations, or other information and examples related to the topic. (c) Link ideas within and across categories of information using words, phrases, and clauses (e.g., in contrast, especially). (d) Use precise language and domain-specific vocabulary to inform about or explain the topic. (e) Provide a concluding statement or section related to the information or explanation presented. English language learners communicate information, ideas and concepts necessary for academic success in the content area of Mathematics. 5-8: Enrichment 5-8: Digital Math Tool Activity 5-8: enVision STEM Activity Curriculum Standards: 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. Make sense of problems and persevere in solving them. 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. Make sense of problems and persevere in solving them. 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. Make sense of problems and persevere in solving them. Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution. They analyze givens, constraints, relationships, and goals. They make conjectures about the form and meaning of the solution and plan a solution pathway rather than simply jumping into a solution attempt. They consider analogous problems, and try special cases and simpler forms of the original problem in order to gain insight into its solution. They monitor and evaluate their progress and change course if necessary. Older students might, depending on the context of the problem, transform algebraic expressions or change the viewing window on their graphing calculator to get the information they need. Mathematically proficient students can explain correspondences between equations, verbal descriptions, tables, and graphs or draw diagrams of important features and relationships, graph data, and search for regularity or trends. Younger students might rely on using concrete objects or pictures to help conceptualize and solve a problem. Mathematically proficient students check their answers to problems using a different method, and they continually ask themselves, “Does this make sense?” They can understand the approaches of others to solving complex problems and identify correspondences between different approaches. Make sense of problems and keep working. 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. Construct viable arguments and critique the reasoning of others. Make sense of problems and persevere in solving them. Make sense of problems and persevere in solving them. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors. Make sense of problems and persevere in solving them. Divide multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Recognize that quotients can be represented in a variety of ways, including a whole number with a remainder, a fraction or mixed number, or a decimal. Consider the context in which a problem is situated to select the most useful form of the quotient for the solution and use the context to interpret the quotient appropriately. Estimate solutions to arithmetic problems in order to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition, subtraction, multiplication and division of multi-digit whole numbers. Use various strategies, including the inverse relationships between operations, the use of technology, and the context of the problem to assess the reasonableness of results. 5-8: Another Look Curriculum Standards: 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. Make sense of problems and persevere in solving them. 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. Make sense of problems and persevere in solving them. 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. Make sense of problems and persevere in solving them. Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution. They analyze givens, constraints, relationships, and goals. They make conjectures about the form and meaning of the solution and plan a solution pathway rather than simply jumping into a solution attempt. They consider analogous problems, and try special cases and simpler forms of the original problem in order to gain insight into its solution. They monitor and evaluate their progress and change course if necessary. Older students might, depending on the context of the problem, transform algebraic expressions or change the viewing window on their graphing calculator to get the information they need. Mathematically proficient students can explain correspondences between equations, verbal descriptions, tables, and graphs or draw diagrams of important features and relationships, graph data, and search for regularity or trends. Younger students might rely on using concrete objects or pictures to help conceptualize and solve a problem. Mathematically proficient students check their answers to problems using a different method, and they continually ask themselves, “Does this make sense?” They can understand the approaches of others to solving complex problems and identify correspondences between different approaches. Make sense of problems and keep working. 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. Construct viable arguments and critique the reasoning of others. Make sense of problems and persevere in solving them. Make sense of problems and persevere in solving them. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors. Make sense of problems and persevere in solving them. Divide multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Recognize that quotients can be represented in a variety of ways, including a whole number with a remainder, a fraction or mixed number, or a decimal. Consider the context in which a problem is situated to select the most useful form of the quotient for the solution and use the context to interpret the quotient appropriately. Estimate solutions to arithmetic problems in order to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition, subtraction, multiplication and division of multi-digit whole numbers. Use various strategies, including the inverse relationships between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Spanish Resources 5-8: eText del Libro del estudiante 5-8: Repaso diario 5-8: Aprendizaje visual 5-8: Amigo de práctica: Práctica adicional 5-8: Práctica adicional interactiva 5-8: Refuerzo para mejorar la comprensión 5-8: Desarrollar la competencia matemática 5-8: Ampliación Topic 5: End of Topic Interactive Student Edition: End of Topic 5 Topic 5: Fluency Practice Activity Interactive Student Edition: Topic 5 Assessment Practice Interactive Student Edition: Topic 5 Performance Task Topic 5 Performance Task Topic 5 Assessment 5-6: Visual Learning Curriculum Standards: 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. 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. 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. Use place value and sharing to divide greater dividends. 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. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors. Divide multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Recognize that quotients can be represented in a variety of ways, including a whole number with a remainder, a fraction or mixed number, or a decimal. Consider the context in which a problem is situated to select the most useful form of the quotient for the solution and use the context to interpret the quotient appropriately. Estimate solutions to arithmetic problems in order to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition, subtraction, multiplication and division of multi-digit whole numbers. Use various strategies, including the inverse relationships between operations, the use of technology, and the context of the problem to assess the reasonableness of results. 5-7: Visual Learning Curriculum Standards: 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. 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. 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. Select from different strategies to divide 3-and 4-digit numbers by 2-digit numbers. Find whole- number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors. Divide multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Recognize that quotients can be represented in a variety of ways, including a whole number with a remainder, a fraction or mixed number, or a decimal. Consider the context in which a problem is situated to select the most useful form of the quotient for the solution and use the context to interpret the quotient appropriately. Estimate solutions to arithmetic problems in order to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition, subtraction, multiplication and division of multi-digit whole numbers. Use various strategies, including the inverse relationships between operations, the use of technology, and the context of the problem to assess the reasonableness of results. 5-8: Visual Learning Curriculum Standards: 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. Make sense of problems and persevere in solving them. 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. Make sense of problems and persevere in solving them. 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. Make sense of problems and persevere in solving them. Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution. They analyze givens, constraints, relationships, and goals. They make conjectures about the form and meaning of the solution and plan a solution pathway rather than simply jumping into a solution attempt. They consider analogous problems, and try special cases and simpler forms of the original problem in order to gain insight into its solution. They monitor and evaluate their progress and change course if necessary. Older students might, depending on the context of the problem, transform algebraic expressions or change the viewing window on their graphing calculator to get the information they need. Mathematically proficient students can explain correspondences between equations, verbal descriptions, tables, and graphs or draw diagrams of important features and relationships, graph data, and search for regularity or trends. Younger students might rely on using concrete objects or pictures to help conceptualize and solve a problem. Mathematically proficient students check their answers to problems using a different method, and they continually ask themselves, “Does this make sense?” They can understand the approaches of others to solving complex problems and identify correspondences between different approaches. Make sense of problems and keep working. 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. Construct viable arguments and critique the reasoning of others. Make sense of problems and persevere in solving them. Make sense of problems and persevere in solving them. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors. Make sense of problems and persevere in solving them. Divide multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Recognize that quotients can be represented in a variety of ways, including a whole number with a remainder, a fraction or mixed number, or a decimal. Consider the context in which a problem is situated to select the most useful form of the quotient for the solution and use the context to interpret the quotient appropriately. Estimate solutions to arithmetic problems in order to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition, subtraction, multiplication and division of multi-digit whole numbers. Use various strategies, including the inverse relationships between operations, the use of technology, and the context of the problem to assess the reasonableness of results. 6-6: Center Games 5-1: Visual Learning Curriculum Standards: 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. 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. 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. Use place-value patterns and mental math to find quotients. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors. 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. 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. 5-2: Visual Learning Curriculum Standards: 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. 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. 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. Use compatible numbers and place-value patterns to estimate quotients. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors. Divide multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Recognize that quotients can be represented in a variety of ways, including a whole number with a remainder, a fraction or mixed number, or a decimal. Estimate solutions to arithmetic problems in order to assess the reasonableness of results. 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. 5-3: Visual Learning Curriculum Standards: 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. 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. 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. Use models to find quotients. Find whole-number quotients of whole numbers with up to four- digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors. Divide multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Recognize that quotients can be represented in a variety of ways, including a whole number with a remainder, a fraction or mixed number, or a decimal. Estimate solutions to arithmetic problems in order to assess the reasonableness of results. 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. 5-4: Visual Learning Curriculum Standards: 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. 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. 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. Solve division problems using partial quotients. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors. Divide multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Recognize that quotients can be represented in a variety of ways, including a whole number with a remainder, a fraction or mixed number, or a decimal. Estimate solutions to arithmetic problems in order to assess the reasonableness of results. 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. 5-5: Visual Learning Curriculum Standards: 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. 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. 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. Use place value and sharing to divide by 2-digit divisors. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors. Divide multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Recognize that quotients can be represented in a variety of ways, including a whole number with a remainder, a fraction or mixed number, or a decimal. Consider the context in which a problem is situated to select the most useful form of the quotient for the solution and use the context to interpret the quotient appropriately. 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. Topic 5 Online Assessment Curriculum Standards: 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. Make sense of problems and persevere in solving them. 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. 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. Use compatible numbers and place-value patterns to estimate quotients. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors. Divide multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Recognize that quotients can be represented in a variety of ways, including a whole number with a remainder, a fraction or mixed number, or a decimal. Estimate solutions to arithmetic problems in order to assess the reasonableness of results. 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. Use place-value patterns and mental math to find quotients. Solve division problems using partial quotients. Use models to find quotients. Use place value and sharing to divide greater dividends. 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. Use place value and sharing to divide by 2-digit divisors. Make sense of problems and persevere in solving them. Make sense of problems and persevere in solving them. Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution. They analyze givens, constraints, relationships, and goals. They make conjectures about the form and meaning of the solution and plan a solution pathway rather than simply jumping into a solution attempt. They consider analogous problems, and try special cases and simpler forms of the original problem in order to gain insight into its solution. They monitor and evaluate their progress and change course if necessary. Older students might, depending on the context of the problem, transform algebraic expressions or change the viewing window on their graphing calculator to get the information they need. Mathematically proficient students can explain correspondences between equations, verbal descriptions, tables, and graphs or draw diagrams of important features and relationships, graph data, and search for regularity or trends. Younger students might rely on using concrete objects or pictures to help conceptualize and solve a problem. Mathematically proficient students check their answers to problems using a different method, and they continually ask themselves, “Does this make sense?” They can understand the approaches of others to solving complex problems and identify correspondences between different approaches. Make sense of problems and keep working. Construct viable arguments and critique the reasoning of others. Make sense of problems and persevere in solving them. Make sense of problems and persevere in solving them. Make sense of problems and persevere in solving them. Select from different strategies to divide 3-and 4-digit numbers by 2-digit numbers. Topic 5 Spanish Assessments Tema 5: Tarea de rendimento Tema 5: Evaluación Topic 6: Use Models and Strategies to Divide Decimals Topic 6: Today's Challenge Topic 6: Beginning of Topic Interactive Student Edition: Beginning of Topic 6 Topic 6: enVision STEM Activity Grade 5 Topic 6: Review What You Know 6-1: Patterns for Dividing with Decimals Interactive Student Edition: Grade 5 Lesson 6-1 Math Anytime 6-1: Daily Review Topic 6: Today's Challenge Step 1: Problem-Based Learning 6-1: Solve & Share Curriculum Standards: Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. English language learners communicate for social and instructional purposes within the school setting. Write informative/explanatory texts to examine a topic and convey ideas and information clearly. (a) Introduce a topic clearly, provide a general observation and focus, and group related information logically; include formatting (e.g., headings), illustrations, and multimedia when useful to aiding comprehension. (b) Develop the topic with facts, definitions, concrete details, quotations, or other information and examples related to the topic. (c) Link ideas within and across categories of information using words, phrases, and clauses (e.g., in contrast, especially). (d) Use precise language and domain-specific vocabulary to inform about or explain the topic. (e) Provide a concluding statement or section related to the information or explanation presented. English language learners communicate information, ideas and concepts necessary for academic success in the content area of Mathematics. Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 5 topics and texts, building on others’ ideas and expressing their own clearly. (a) Come to discussions prepared, having read or studied required material; explicitly draw on that preparation and other information known about the topic to explore ideas under discussion. (b) Follow agreed-upon rules for discussions and carry out assigned roles. (c) Pose and respond to specific questions by making comments that contribute to the discussion and elaborate on the remarks of others. (d) Review the key ideas expressed and draw conclusions in light of information and knowledge gained from the discussions. Summarize a written text read aloud or information presented in diverse media and formats, including visually, quantitatively, and orally. Summarize the points a speaker makes and explain how each claim is supported by reasons and evidence. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Use mental math and place-value patterns to divide a decimal by a power of 10. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). Step 2: Visual Learning 6-1: Visual Learning Curriculum Standards: Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Use mental math and place-value patterns to divide a decimal by a power of 10. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. Find whole-number quotients of whole numbers with up to four-digit dividends and two- digit divisors. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). Identify the direction the decimal point will move when multiplying or dividing by a multiple of 10. 6-1: Convince Me! Curriculum Standards: Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Use mental math and place-value patterns to divide a decimal by a power of 10. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. Find whole-number quotients of whole numbers with up to four-digit dividends and two- digit divisors. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). Practice and Problem Solving 6-1: Student Edition Practice Curriculum Standards: Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Use mental math and place-value patterns to divide a decimal by a power of 10. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. Find whole-number quotients of whole numbers with up to four-digit dividends and two- digit divisors. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). 6-1: Practice Buddy: Independent Practice; Problem Solving Curriculum Standards: Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Use mental math and place-value patterns to divide a decimal by a power of 10. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. Find whole-number quotients of whole numbers with up to four-digit dividends and two- digit divisors. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). 6-1: Practice Buddy: Additional Practice Curriculum Standards: Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Use mental math and place-value patterns to divide a decimal by a power of 10. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. Find whole-number quotients of whole numbers with up to four-digit dividends and two- digit divisors. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). 6-1: Interactive Additional Practice Step 3: Assess & Differentiate 6-1: Practice Buddy: Additional Practice Curriculum Standards: Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Use mental math and place-value patterns to divide a decimal by a power of 10. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. Find whole-number quotients of whole numbers with up to four-digit dividends and two- digit divisors. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). 6-1: Enrichment Curriculum Standards: Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Use mental math and place-value patterns to divide a decimal by a power of 10. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. Find whole-number quotients of whole numbers with up to four-digit dividends and two- digit divisors. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). 6-1: Quick Check Curriculum Standards: Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Use mental math and place-value patterns to divide a decimal by a power of 10. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. Find whole-number quotients of whole numbers with up to four-digit dividends and two- digit divisors. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). 6-1: Lesson Self-Assessment 6-1: Reteach to Build Understanding Curriculum Standards: Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Use mental math and place-value patterns to divide a decimal by a power of 10. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. Find whole-number quotients of whole numbers with up to four-digit dividends and two- digit divisors. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). Identify the direction the decimal point will move when multiplying or dividing by a multiple of 10. 6-1: Build Mathematical Literacy Curriculum Standards: Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 5 topics and texts, building on others’ ideas and expressing their own clearly. (a) Come to discussions prepared, having read or studied required material; explicitly draw on that preparation and other information known about the topic to explore ideas under discussion. (b) Follow agreed-upon rules for discussions and carry out assigned roles. (c) Pose and respond to specific questions by making comments that contribute to the discussion and elaborate on the remarks of others. (d) Review the key ideas expressed and draw conclusions in light of information and knowledge gained from the discussions. English language learners communicate for social and instructional purposes within the school setting. Summarize a written text read aloud or information presented in diverse media and formats, including visually, quantitatively, and orally. Summarize the points a speaker makes and explain how each claim is supported by reasons and evidence. Write informative/explanatory texts to examine a topic and convey ideas and information clearly. (a) Introduce a topic clearly, provide a general observation and focus, and group related information logically; include formatting (e.g., headings), illustrations, and multimedia when useful to aiding comprehension. (b) Develop the topic with facts, definitions, concrete details, quotations, or other information and examples related to the topic. (c) Link ideas within and across categories of information using words, phrases, and clauses (e.g., in contrast, especially). (d) Use precise language and domain-specific vocabulary to inform about or explain the topic. (e) Provide a concluding statement or section related to the information or explanation presented. English language learners communicate information, ideas and concepts necessary for academic success in the content area of Mathematics. 6-1: Enrichment 6-1: Digital Math Tool Activity 6-1: Problem-Solving Reading Activity Curriculum Standards: Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Use mental math and place-value patterns to divide a decimal by a power of 10. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. Find whole-number quotients of whole numbers with up to four-digit dividends and two- digit divisors. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). 6-1: Another Look Curriculum Standards: Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Use mental math and place-value patterns to divide a decimal by a power of 10. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. Find whole-number quotients of whole numbers with up to four-digit dividends and two- digit divisors. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). Identify the direction the decimal point will move when multiplying or dividing by a multiple of 10. Spanish Resources 6-1: eText del Libro del estudiante 6-1: Repaso diario 6-1: Aprendizaje visual 6-1: Amigo de práctica: Práctica adicional 6-1: Práctica adicional interactiva 6-1: Refuerzo para mejorar la comprensión 6-1: Desarrollar la competencia matemática 6-1: Ampliación 6-2: Estimate Decimal Quotients Interactive Student Edition: Grade 5 Lesson 6-2 Math Anytime 6-2: Daily Review Topic 6: Today's Challenge Step 1: Problem-Based Learning 6-2: Solve & Share Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. English language learners communicate for social and instructional purposes within the school setting. Write informative/explanatory texts to examine a topic and convey ideas and information clearly. (a) Introduce a topic clearly, provide a general observation and focus, and group related information logically; include formatting (e.g., headings), illustrations, and multimedia when useful to aiding comprehension. (b) Develop the topic with facts, definitions, concrete details, quotations, or other information and examples related to the topic. (c) Link ideas within and across categories of information using words, phrases, and clauses (e.g., in contrast, especially). (d) Use precise language and domain- specific vocabulary to inform about or explain the topic. (e) Provide a concluding statement or section related to the information or explanation presented. English language learners communicate information, ideas and concepts necessary for academic success in the content area of Mathematics. Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 5 topics and texts, building on others’ ideas and expressing their own clearly. (a) Come to discussions prepared, having read or studied required material; explicitly draw on that preparation and other information known about the topic to explore ideas under discussion. (b) Follow agreed-upon rules for discussions and carry out assigned roles. (c) Pose and respond to specific questions by making comments that contribute to the discussion and elaborate on the remarks of others. (d) Review the key ideas expressed and draw conclusions in light of information and knowledge gained from the discussions. Summarize a written text read aloud or information presented in diverse media and formats, including visually, quantitatively, and orally. Summarize the points a speaker makes and explain how each claim is supported by reasons and evidence. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Use reasoning and strategies such as rounding and compatible numbers to estimate quotients in problems with decimals. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). Step 2: Visual Learning 6-2: Visual Learning Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Use reasoning and strategies such as rounding and compatible numbers to estimate quotients in problems with decimals. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). 6-2: Convince Me! Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Use reasoning and strategies such as rounding and compatible numbers to estimate quotients in problems with decimals. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). Practice and Problem Solving 6-2: Student Edition Practice Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Use reasoning and strategies such as rounding and compatible numbers to estimate quotients in problems with decimals. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). 6-2: Practice Buddy: Independent Practice; Problem Solving Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Use reasoning and strategies such as rounding and compatible numbers to estimate quotients in problems with decimals. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). 6-2: Practice Buddy: Additional Practice Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Use reasoning and strategies such as rounding and compatible numbers to estimate quotients in problems with decimals. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). 6-2: Interactive Additional Practice Step 3: Assess & Differentiate 6-2: Practice Buddy: Additional Practice Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Use reasoning and strategies such as rounding and compatible numbers to estimate quotients in problems with decimals. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). 6-2: Enrichment Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Use reasoning and strategies such as rounding and compatible numbers to estimate quotients in problems with decimals. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). 6-2: Quick Check Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Use reasoning and strategies such as rounding and compatible numbers to estimate quotients in problems with decimals. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). 6-2: Lesson Self-Assessment 6-2: Reteach to Build Understanding Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Use reasoning and strategies such as rounding and compatible numbers to estimate quotients in problems with decimals. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). 6-2: Build Mathematical Literacy Curriculum Standards: Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 5 topics and texts, building on others’ ideas and expressing their own clearly. (a) Come to discussions prepared, having read or studied required material; explicitly draw on that preparation and other information known about the topic to explore ideas under discussion. (b) Follow agreed-upon rules for discussions and carry out assigned roles. (c) Pose and respond to specific questions by making comments that contribute to the discussion and elaborate on the remarks of others. (d) Review the key ideas expressed and draw conclusions in light of information and knowledge gained from the discussions. English language learners communicate for social and instructional purposes within the school setting. Summarize a written text read aloud or information presented in diverse media and formats, including visually, quantitatively, and orally. Summarize the points a speaker makes and explain how each claim is supported by reasons and evidence. Write informative/explanatory texts to examine a topic and convey ideas and information clearly. (a) Introduce a topic clearly, provide a general observation and focus, and group related information logically; include formatting (e.g., headings), illustrations, and multimedia when useful to aiding comprehension. (b) Develop the topic with facts, definitions, concrete details, quotations, or other information and examples related to the topic. (c) Link ideas within and across categories of information using words, phrases, and clauses (e.g., in contrast, especially). (d) Use precise language and domain-specific vocabulary to inform about or explain the topic. (e) Provide a concluding statement or section related to the information or explanation presented. English language learners communicate information, ideas and concepts necessary for academic success in the content area of Mathematics. 6-2: Enrichment 6-2: Digital Math Tool Activity 6-2: Pick a Project 6-2: Another Look Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Use reasoning and strategies such as rounding and compatible numbers to estimate quotients in problems with decimals. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). Spanish Resources 6-2: eText del Libro del estudiante 6-2: Repaso diario 6-2: Aprendizaje visual 6-2: Amigo de práctica: Práctica adicional 6-2: Práctica adicional interactiva 6-2: Refuerzo para mejorar la comprensión 6-2: Desarrollar la competencia matemática 6-2: Ampliación 6-3: Use Models to Divide by a 1-Digit Whole Number Interactive Student Edition: Grade 5 Lesson 6-3 Math Anytime 6-3: Daily Review Topic 6: Today's Challenge Step 1: Problem-Based Learning 6-3: Solve & Share Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. English language learners communicate for social and instructional purposes within the school setting. Write informative/explanatory texts to examine a topic and convey ideas and information clearly. (a) Introduce a topic clearly, provide a general observation and focus, and group related information logically; include formatting (e.g., headings), illustrations, and multimedia when useful to aiding comprehension. (b) Develop the topic with facts, definitions, concrete details, quotations, or other information and examples related to the topic. (c) Link ideas within and across categories of information using words, phrases, and clauses (e.g., in contrast, especially). (d) Use precise language and domain- specific vocabulary to inform about or explain the topic. (e) Provide a concluding statement or section related to the information or explanation presented. English language learners communicate information, ideas and concepts necessary for academic success in the content area of Mathematics. Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 5 topics and texts, building on others’ ideas and expressing their own clearly. (a) Come to discussions prepared, having read or studied required material; explicitly draw on that preparation and other information known about the topic to explore ideas under discussion. (b) Follow agreed-upon rules for discussions and carry out assigned roles. (c) Pose and respond to specific questions by making comments that contribute to the discussion and elaborate on the remarks of others. (d) Review the key ideas expressed and draw conclusions in light of information and knowledge gained from the discussions. Summarize a written text read aloud or information presented in diverse media and formats, including visually, quantitatively, and orally. Summarize the points a speaker makes and explain how each claim is supported by reasons and evidence. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Use models to help find quotients in problems involving decimals. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). Step 2: Visual Learning 6-3: Visual Learning Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Use models to help find quotients in problems involving decimals. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). 6-3: Convince Me! Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Use models to help find quotients in problems involving decimals. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). Practice and Problem Solving 6-3: Student Edition Practice Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Use models to help find quotients in problems involving decimals. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). 6-3: Practice Buddy: Independent Practice; Problem Solving Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Use models to help find quotients in problems involving decimals. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). 6-3: Practice Buddy: Additional Practice Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Use models to help find quotients in problems involving decimals. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). 6-3: Interactive Additional Practice Step 3: Assess & Differentiate 6-3: Practice Buddy: Additional Practice Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Use models to help find quotients in problems involving decimals. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). 6-3: Enrichment Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Use models to help find quotients in problems involving decimals. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). 6-3: Quick Check Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Use models to help find quotients in problems involving decimals. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). 6-3: Lesson Self-Assessment 6-3: Reteach to Build Understanding Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Use models to help find quotients in problems involving decimals. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). 6-3: Build Mathematical Literacy Curriculum Standards: Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 5 topics and texts, building on others’ ideas and expressing their own clearly. (a) Come to discussions prepared, having read or studied required material; explicitly draw on that preparation and other information known about the topic to explore ideas under discussion. (b) Follow agreed-upon rules for discussions and carry out assigned roles. (c) Pose and respond to specific questions by making comments that contribute to the discussion and elaborate on the remarks of others. (d) Review the key ideas expressed and draw conclusions in light of information and knowledge gained from the discussions. English language learners communicate for social and instructional purposes within the school setting. Summarize a written text read aloud or information presented in diverse media and formats, including visually, quantitatively, and orally. Summarize the points a speaker makes and explain how each claim is supported by reasons and evidence. Write informative/explanatory texts to examine a topic and convey ideas and information clearly. (a) Introduce a topic clearly, provide a general observation and focus, and group related information logically; include formatting (e.g., headings), illustrations, and multimedia when useful to aiding comprehension. (b) Develop the topic with facts, definitions, concrete details, quotations, or other information and examples related to the topic. (c) Link ideas within and across categories of information using words, phrases, and clauses (e.g., in contrast, especially). (d) Use precise language and domain-specific vocabulary to inform about or explain the topic. (e) Provide a concluding statement or section related to the information or explanation presented. English language learners communicate information, ideas and concepts necessary for academic success in the content area of Mathematics. 6-3: Enrichment 6-3: Digital Math Tool Activity 6-3: Pick a Project 6-3: Another Look Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Use models to help find quotients in problems involving decimals. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). Spanish Resources 6-3: eText del Libro del estudiante 6-3: Repaso diario 6-3: Aprendizaje visual 6-3: Amigo de práctica: Práctica adicional 6-3: Práctica adicional interactiva 6-3: Refuerzo para mejorar la comprensión 6-3: Desarrollar la competencia matemática 6-3: Ampliación 6-4: Divide by a 2-Digit Whole Number Interactive Student Edition: Grade 5 Lesson 6-4 Math Anytime 6-4: Daily Review Topic 6: Today's Challenge Step 1: Problem-Based Learning 6-4: Solve & Share Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. English language learners communicate for social and instructional purposes within the school setting. Write informative/explanatory texts to examine a topic and convey ideas and information clearly. (a) Introduce a topic clearly, provide a general observation and focus, and group related information logically; include formatting (e.g., headings), illustrations, and multimedia when useful to aiding comprehension. (b) Develop the topic with facts, definitions, concrete details, quotations, or other information and examples related to the topic. (c) Link ideas within and across categories of information using words, phrases, and clauses (e.g., in contrast, especially). (d) Use precise language and domain- specific vocabulary to inform about or explain the topic. (e) Provide a concluding statement or section related to the information or explanation presented. English language learners communicate information, ideas and concepts necessary for academic success in the content area of Mathematics. Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 5 topics and texts, building on others’ ideas and expressing their own clearly. (a) Come to discussions prepared, having read or studied required material; explicitly draw on that preparation and other information known about the topic to explore ideas under discussion. (b) Follow agreed-upon rules for discussions and carry out assigned roles. (c) Pose and respond to specific questions by making comments that contribute to the discussion and elaborate on the remarks of others. (d) Review the key ideas expressed and draw conclusions in light of information and knowledge gained from the discussions. Summarize a written text read aloud or information presented in diverse media and formats, including visually, quantitatively, and orally. Summarize the points a speaker makes and explain how each claim is supported by reasons and evidence. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Use models to visualize the relationship between division and multiplication to divide decimals by 2-digit whole numbers. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). Step 2: Visual Learning 6-4: Visual Learning Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Use models to visualize the relationship between division and multiplication to divide decimals by 2-digit whole numbers. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). 6-4: Convince Me! Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Use models to visualize the relationship between division and multiplication to divide decimals by 2-digit whole numbers. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). Practice and Problem Solving 6-4: Student Edition Practice Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Use models to visualize the relationship between division and multiplication to divide decimals by 2-digit whole numbers. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). 6-4: Practice Buddy: Independent Practice; Problem Solving Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Use models to visualize the relationship between division and multiplication to divide decimals by 2-digit whole numbers. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). 6-4: Practice Buddy: Additional Practice Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Use models to visualize the relationship between division and multiplication to divide decimals by 2-digit whole numbers. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). 6-4: Interactive Additional Practice Step 3: Assess & Differentiate 6-4: Practice Buddy: Additional Practice Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Use models to visualize the relationship between division and multiplication to divide decimals by 2-digit whole numbers. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). 6-4: Enrichment Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Use models to visualize the relationship between division and multiplication to divide decimals by 2-digit whole numbers. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). 6-4: Quick Check Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Use models to visualize the relationship between division and multiplication to divide decimals by 2-digit whole numbers. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). 6-4: Lesson Self-Assessment 6-4: Reteach to Build Understanding Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Use models to visualize the relationship between division and multiplication to divide decimals by 2-digit whole numbers. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). 6-4: Build Mathematical Literacy Curriculum Standards: Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 5 topics and texts, building on others’ ideas and expressing their own clearly. (a) Come to discussions prepared, having read or studied required material; explicitly draw on that preparation and other information known about the topic to explore ideas under discussion. (b) Follow agreed-upon rules for discussions and carry out assigned roles. (c) Pose and respond to specific questions by making comments that contribute to the discussion and elaborate on the remarks of others. (d) Review the key ideas expressed and draw conclusions in light of information and knowledge gained from the discussions. English language learners communicate for social and instructional purposes within the school setting. Summarize a written text read aloud or information presented in diverse media and formats, including visually, quantitatively, and orally. Summarize the points a speaker makes and explain how each claim is supported by reasons and evidence. Write informative/explanatory texts to examine a topic and convey ideas and information clearly. (a) Introduce a topic clearly, provide a general observation and focus, and group related information logically; include formatting (e.g., headings), illustrations, and multimedia when useful to aiding comprehension. (b) Develop the topic with facts, definitions, concrete details, quotations, or other information and examples related to the topic. (c) Link ideas within and across categories of information using words, phrases, and clauses (e.g., in contrast, especially). (d) Use precise language and domain-specific vocabulary to inform about or explain the topic. (e) Provide a concluding statement or section related to the information or explanation presented. English language learners communicate information, ideas and concepts necessary for academic success in the content area of Mathematics. 6-4: Enrichment 6-4: Digital Math Tool Activity 6-4: enVision STEM Activity Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Use models to visualize the relationship between division and multiplication to divide decimals by 2-digit whole numbers. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). 6-4: Another Look Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Use models to visualize the relationship between division and multiplication to divide decimals by 2-digit whole numbers. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). Spanish Resources 6-4: eText del Libro del estudiante 6-4: Repaso diario 6-4: Aprendizaje visual 6-4: Amigo de práctica: Práctica adicional 6-4: Práctica adicional interactiva 6-4: Refuerzo para mejorar la comprensión 6-4: Desarrollar la competencia matemática 6-4: Ampliación 6-5: Divide by a Decimal Interactive Student Edition: Grade 5 Lesson 6-5 Math Anytime 6-5: Daily Review Topic 6: Today's Challenge Step 1: Problem-Based Learning 6-5: Solve & Share Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Use models to divide a decimal by a decimal. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). English language learners communicate for social and instructional purposes within the school setting. Write informative/explanatory texts to examine a topic and convey ideas and information clearly. (a) Introduce a topic clearly, provide a general observation and focus, and group related information logically; include formatting (e.g., headings), illustrations, and multimedia when useful to aiding comprehension. (b) Develop the topic with facts, definitions, concrete details, quotations, or other information and examples related to the topic. (c) Link ideas within and across categories of information using words, phrases, and clauses (e.g., in contrast, especially). (d) Use precise language and domain- specific vocabulary to inform about or explain the topic. (e) Provide a concluding statement or section related to the information or explanation presented. English language learners communicate information, ideas and concepts necessary for academic success in the content area of Mathematics. Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 5 topics and texts, building on others’ ideas and expressing their own clearly. (a) Come to discussions prepared, having read or studied required material; explicitly draw on that preparation and other information known about the topic to explore ideas under discussion. (b) Follow agreed-upon rules for discussions and carry out assigned roles. (c) Pose and respond to specific questions by making comments that contribute to the discussion and elaborate on the remarks of others. (d) Review the key ideas expressed and draw conclusions in light of information and knowledge gained from the discussions. Summarize a written text read aloud or information presented in diverse media and formats, including visually, quantitatively, and orally. Summarize the points a speaker makes and explain how each claim is supported by reasons and evidence. Step 2: Visual Learning 6-5: Visual Learning Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Use models to divide a decimal by a decimal. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). 6-5: Convince Me! Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Use models to divide a decimal by a decimal. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). Practice and Problem Solving 6-5: Student Edition Practice Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Use models to divide a decimal by a decimal. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). 6-5: Practice Buddy: Independent Practice; Problem Solving Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Use models to divide a decimal by a decimal. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). 6-5: Practice Buddy: Additional Practice Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Use models to divide a decimal by a decimal. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). 6-5: Interactive Additional Practice Step 3: Assess & Differentiate 6-5: Practice Buddy: Additional Practice Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Use models to divide a decimal by a decimal. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). 6-5: Enrichment Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Use models to divide a decimal by a decimal. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). 6-5: Quick Check Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Use models to divide a decimal by a decimal. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). 6-5: Lesson Self-Assessment 6-5: Reteach to Build Understanding Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Use models to divide a decimal by a decimal. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). 6-5: Build Mathematical Literacy Curriculum Standards: Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 5 topics and texts, building on others’ ideas and expressing their own clearly. (a) Come to discussions prepared, having read or studied required material; explicitly draw on that preparation and other information known about the topic to explore ideas under discussion. (b) Follow agreed-upon rules for discussions and carry out assigned roles. (c) Pose and respond to specific questions by making comments that contribute to the discussion and elaborate on the remarks of others. (d) Review the key ideas expressed and draw conclusions in light of information and knowledge gained from the discussions. English language learners communicate for social and instructional purposes within the school setting. Summarize a written text read aloud or information presented in diverse media and formats, including visually, quantitatively, and orally. Summarize the points a speaker makes and explain how each claim is supported by reasons and evidence. Write informative/explanatory texts to examine a topic and convey ideas and information clearly. (a) Introduce a topic clearly, provide a general observation and focus, and group related information logically; include formatting (e.g., headings), illustrations, and multimedia when useful to aiding comprehension. (b) Develop the topic with facts, definitions, concrete details, quotations, or other information and examples related to the topic. (c) Link ideas within and across categories of information using words, phrases, and clauses (e.g., in contrast, especially). (d) Use precise language and domain-specific vocabulary to inform about or explain the topic. (e) Provide a concluding statement or section related to the information or explanation presented. English language learners communicate information, ideas and concepts necessary for academic success in the content area of Mathematics. 6-5: Enrichment 6-5: Digital Math Tool Activity 6-5: Problem-Solving Reading Activity Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Use models to divide a decimal by a decimal. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). 6-5: Another Look Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Use models to divide a decimal by a decimal. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). Spanish Resources 6-5: eText del Libro del estudiante 6-5: Repaso diario 6-5: Aprendizaje visual 6-5: Amigo de práctica: Práctica adicional 6-5: Práctica adicional interactiva 6-5: Refuerzo para mejorar la comprensión 6-5: Desarrollar la competencia matemática 6-5: Ampliación 6-6: Problem Solving: Reasoning Interactive Student Edition: Grade 5 Lesson 6-6 Math Anytime 6-6: Daily Review Topic 6: Today's Challenge Step 1: Problem-Based Learning 6-6: Solve & Share Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Reason abstractly and quantitatively. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Reason abstractly and quantitatively. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Reason abstractly and quantitatively. Mathematically proficient students make sense of quantities and their relationships in problem situations. They bring two complementary abilities to bear on problems involving quantitative relationships: the ability to decontextualize—to abstract a given situation and represent it symbolically and manipulate the representing symbols as if they have a life of their own, without necessarily attending to their referents—and the ability to contextualize, to pause as needed during the manipulation process in order to probe into the referents for the symbols involved. Quantitative reasoning entails habits of creating a coherent representation of the problem at hand; considering the units involved; attending to the meaning of quantities, not just how to compute them; and knowing and flexibly using different properties of operations and objects. Use reasoning to solve problems by making sense of quantities and relationships in problem situations. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Reason abstractly and quantitatively. Reason abstractly and quantitatively. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). Reason abstractly and quantitatively. English language learners communicate for social and instructional purposes within the school setting. Write informative/explanatory texts to examine a topic and convey ideas and information clearly. (a) Introduce a topic clearly, provide a general observation and focus, and group related information logically; include formatting (e.g., headings), illustrations, and multimedia when useful to aiding comprehension. (b) Develop the topic with facts, definitions, concrete details, quotations, or other information and examples related to the topic. (c) Link ideas within and across categories of information using words, phrases, and clauses (e.g., in contrast, especially). (d) Use precise language and domain-specific vocabulary to inform about or explain the topic. (e) Provide a concluding statement or section related to the information or explanation presented. English language learners communicate information, ideas and concepts necessary for academic success in the content area of Mathematics. Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 5 topics and texts, building on others’ ideas and expressing their own clearly. (a) Come to discussions prepared, having read or studied required material; explicitly draw on that preparation and other information known about the topic to explore ideas under discussion. (b) Follow agreed-upon rules for discussions and carry out assigned roles. (c) Pose and respond to specific questions by making comments that contribute to the discussion and elaborate on the remarks of others. (d) Review the key ideas expressed and draw conclusions in light of information and knowledge gained from the discussions. Summarize a written text read aloud or information presented in diverse media and formats, including visually, quantitatively, and orally. Summarize the points a speaker makes and explain how each claim is supported by reasons and evidence. Step 2: Visual Learning 6-6: Visual Learning Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Reason abstractly and quantitatively. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Reason abstractly and quantitatively. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Reason abstractly and quantitatively. Mathematically proficient students make sense of quantities and their relationships in problem situations. They bring two complementary abilities to bear on problems involving quantitative relationships: the ability to decontextualize—to abstract a given situation and represent it symbolically and manipulate the representing symbols as if they have a life of their own, without necessarily attending to their referents—and the ability to contextualize, to pause as needed during the manipulation process in order to probe into the referents for the symbols involved. Quantitative reasoning entails habits of creating a coherent representation of the problem at hand; considering the units involved; attending to the meaning of quantities, not just how to compute them; and knowing and flexibly using different properties of operations and objects. Use reasoning to solve problems by making sense of quantities and relationships in problem situations. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Reason abstractly and quantitatively. Reason abstractly and quantitatively. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). Reason abstractly and quantitatively. Solve one-step problems using decimals. 6-6: Convince Me! Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Reason abstractly and quantitatively. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Reason abstractly and quantitatively. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Reason abstractly and quantitatively. Mathematically proficient students make sense of quantities and their relationships in problem situations. They bring two complementary abilities to bear on problems involving quantitative relationships: the ability to decontextualize—to abstract a given situation and represent it symbolically and manipulate the representing symbols as if they have a life of their own, without necessarily attending to their referents—and the ability to contextualize, to pause as needed during the manipulation process in order to probe into the referents for the symbols involved. Quantitative reasoning entails habits of creating a coherent representation of the problem at hand; considering the units involved; attending to the meaning of quantities, not just how to compute them; and knowing and flexibly using different properties of operations and objects. Use reasoning to solve problems by making sense of quantities and relationships in problem situations. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Reason abstractly and quantitatively. Reason abstractly and quantitatively. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). Reason abstractly and quantitatively. Practice and Problem Solving 6-6: Student Edition Practice Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Reason abstractly and quantitatively. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Reason abstractly and quantitatively. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Reason abstractly and quantitatively. Mathematically proficient students make sense of quantities and their relationships in problem situations. They bring two complementary abilities to bear on problems involving quantitative relationships: the ability to decontextualize—to abstract a given situation and represent it symbolically and manipulate the representing symbols as if they have a life of their own, without necessarily attending to their referents—and the ability to contextualize, to pause as needed during the manipulation process in order to probe into the referents for the symbols involved. Quantitative reasoning entails habits of creating a coherent representation of the problem at hand; considering the units involved; attending to the meaning of quantities, not just how to compute them; and knowing and flexibly using different properties of operations and objects. Use reasoning to solve problems by making sense of quantities and relationships in problem situations. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Reason abstractly and quantitatively. Reason abstractly and quantitatively. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). Reason abstractly and quantitatively. 6-6: Practice Buddy: Independent Practice; Problem Solving Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Reason abstractly and quantitatively. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Reason abstractly and quantitatively. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Reason abstractly and quantitatively. Mathematically proficient students make sense of quantities and their relationships in problem situations. They bring two complementary abilities to bear on problems involving quantitative relationships: the ability to decontextualize—to abstract a given situation and represent it symbolically and manipulate the representing symbols as if they have a life of their own, without necessarily attending to their referents—and the ability to contextualize, to pause as needed during the manipulation process in order to probe into the referents for the symbols involved. Quantitative reasoning entails habits of creating a coherent representation of the problem at hand; considering the units involved; attending to the meaning of quantities, not just how to compute them; and knowing and flexibly using different properties of operations and objects. Use reasoning to solve problems by making sense of quantities and relationships in problem situations. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Reason abstractly and quantitatively. Reason abstractly and quantitatively. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). Reason abstractly and quantitatively. 6-6: Practice Buddy: Additional Practice Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Reason abstractly and quantitatively. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Reason abstractly and quantitatively. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Reason abstractly and quantitatively. Mathematically proficient students make sense of quantities and their relationships in problem situations. They bring two complementary abilities to bear on problems involving quantitative relationships: the ability to decontextualize—to abstract a given situation and represent it symbolically and manipulate the representing symbols as if they have a life of their own, without necessarily attending to their referents—and the ability to contextualize, to pause as needed during the manipulation process in order to probe into the referents for the symbols involved. Quantitative reasoning entails habits of creating a coherent representation of the problem at hand; considering the units involved; attending to the meaning of quantities, not just how to compute them; and knowing and flexibly using different properties of operations and objects. Use reasoning to solve problems by making sense of quantities and relationships in problem situations. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Reason abstractly and quantitatively. Reason abstractly and quantitatively. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). Reason abstractly and quantitatively. 6-6: Interactive Additional Practice Step 3: Assess & Differentiate 6-6: Practice Buddy: Additional Practice Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Reason abstractly and quantitatively. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Reason abstractly and quantitatively. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Reason abstractly and quantitatively. Mathematically proficient students make sense of quantities and their relationships in problem situations. They bring two complementary abilities to bear on problems involving quantitative relationships: the ability to decontextualize—to abstract a given situation and represent it symbolically and manipulate the representing symbols as if they have a life of their own, without necessarily attending to their referents—and the ability to contextualize, to pause as needed during the manipulation process in order to probe into the referents for the symbols involved. Quantitative reasoning entails habits of creating a coherent representation of the problem at hand; considering the units involved; attending to the meaning of quantities, not just how to compute them; and knowing and flexibly using different properties of operations and objects. Use reasoning to solve problems by making sense of quantities and relationships in problem situations. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Reason abstractly and quantitatively. Reason abstractly and quantitatively. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). Reason abstractly and quantitatively. 6-6: Enrichment Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Reason abstractly and quantitatively. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Reason abstractly and quantitatively. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Reason abstractly and quantitatively. Mathematically proficient students make sense of quantities and their relationships in problem situations. They bring two complementary abilities to bear on problems involving quantitative relationships: the ability to decontextualize—to abstract a given situation and represent it symbolically and manipulate the representing symbols as if they have a life of their own, without necessarily attending to their referents—and the ability to contextualize, to pause as needed during the manipulation process in order to probe into the referents for the symbols involved. Quantitative reasoning entails habits of creating a coherent representation of the problem at hand; considering the units involved; attending to the meaning of quantities, not just how to compute them; and knowing and flexibly using different properties of operations and objects. Use reasoning to solve problems by making sense of quantities and relationships in problem situations. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Reason abstractly and quantitatively. Reason abstractly and quantitatively. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). Reason abstractly and quantitatively. 6-6: Quick Check Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Reason abstractly and quantitatively. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Reason abstractly and quantitatively. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Reason abstractly and quantitatively. Mathematically proficient students make sense of quantities and their relationships in problem situations. They bring two complementary abilities to bear on problems involving quantitative relationships: the ability to decontextualize—to abstract a given situation and represent it symbolically and manipulate the representing symbols as if they have a life of their own, without necessarily attending to their referents—and the ability to contextualize, to pause as needed during the manipulation process in order to probe into the referents for the symbols involved. Quantitative reasoning entails habits of creating a coherent representation of the problem at hand; considering the units involved; attending to the meaning of quantities, not just how to compute them; and knowing and flexibly using different properties of operations and objects. Use reasoning to solve problems by making sense of quantities and relationships in problem situations. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Reason abstractly and quantitatively. Reason abstractly and quantitatively. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). Reason abstractly and quantitatively. 6-6: Lesson Self-Assessment 6-6: Reteach to Build Understanding Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Reason abstractly and quantitatively. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Reason abstractly and quantitatively. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Reason abstractly and quantitatively. Mathematically proficient students make sense of quantities and their relationships in problem situations. They bring two complementary abilities to bear on problems involving quantitative relationships: the ability to decontextualize—to abstract a given situation and represent it symbolically and manipulate the representing symbols as if they have a life of their own, without necessarily attending to their referents—and the ability to contextualize, to pause as needed during the manipulation process in order to probe into the referents for the symbols involved. Quantitative reasoning entails habits of creating a coherent representation of the problem at hand; considering the units involved; attending to the meaning of quantities, not just how to compute them; and knowing and flexibly using different properties of operations and objects. Use reasoning to solve problems by making sense of quantities and relationships in problem situations. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Reason abstractly and quantitatively. Reason abstractly and quantitatively. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). Reason abstractly and quantitatively. Solve one-step problems using decimals. 6-6: Build Mathematical Literacy Curriculum Standards: Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 5 topics and texts, building on others’ ideas and expressing their own clearly. (a) Come to discussions prepared, having read or studied required material; explicitly draw on that preparation and other information known about the topic to explore ideas under discussion. (b) Follow agreed-upon rules for discussions and carry out assigned roles. (c) Pose and respond to specific questions by making comments that contribute to the discussion and elaborate on the remarks of others. (d) Review the key ideas expressed and draw conclusions in light of information and knowledge gained from the discussions. English language learners communicate for social and instructional purposes within the school setting. Summarize a written text read aloud or information presented in diverse media and formats, including visually, quantitatively, and orally. Summarize the points a speaker makes and explain how each claim is supported by reasons and evidence. Write informative/explanatory texts to examine a topic and convey ideas and information clearly. (a) Introduce a topic clearly, provide a general observation and focus, and group related information logically; include formatting (e.g., headings), illustrations, and multimedia when useful to aiding comprehension. (b) Develop the topic with facts, definitions, concrete details, quotations, or other information and examples related to the topic. (c) Link ideas within and across categories of information using words, phrases, and clauses (e.g., in contrast, especially). (d) Use precise language and domain-specific vocabulary to inform about or explain the topic. (e) Provide a concluding statement or section related to the information or explanation presented. English language learners communicate information, ideas and concepts necessary for academic success in the content area of Mathematics. 6-6: Enrichment Game: Fluency - Multiply Multi-Digit Whole Numbers 6-6: enVision STEM Activity Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Reason abstractly and quantitatively. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Reason abstractly and quantitatively. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Reason abstractly and quantitatively. Mathematically proficient students make sense of quantities and their relationships in problem situations. They bring two complementary abilities to bear on problems involving quantitative relationships: the ability to decontextualize—to abstract a given situation and represent it symbolically and manipulate the representing symbols as if they have a life of their own, without necessarily attending to their referents—and the ability to contextualize, to pause as needed during the manipulation process in order to probe into the referents for the symbols involved. Quantitative reasoning entails habits of creating a coherent representation of the problem at hand; considering the units involved; attending to the meaning of quantities, not just how to compute them; and knowing and flexibly using different properties of operations and objects. Use reasoning to solve problems by making sense of quantities and relationships in problem situations. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Reason abstractly and quantitatively. Reason abstractly and quantitatively. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). Reason abstractly and quantitatively. 6-6: Another Look Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Reason abstractly and quantitatively. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Reason abstractly and quantitatively. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Reason abstractly and quantitatively. Mathematically proficient students make sense of quantities and their relationships in problem situations. They bring two complementary abilities to bear on problems involving quantitative relationships: the ability to decontextualize—to abstract a given situation and represent it symbolically and manipulate the representing symbols as if they have a life of their own, without necessarily attending to their referents—and the ability to contextualize, to pause as needed during the manipulation process in order to probe into the referents for the symbols involved. Quantitative reasoning entails habits of creating a coherent representation of the problem at hand; considering the units involved; attending to the meaning of quantities, not just how to compute them; and knowing and flexibly using different properties of operations and objects. Use reasoning to solve problems by making sense of quantities and relationships in problem situations. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Reason abstractly and quantitatively. Reason abstractly and quantitatively. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). Reason abstractly and quantitatively. Solve one-step problems using decimals. Spanish Resources 6-6: eText del Libro del estudiante 6-6: Repaso diario 6-6: Aprendizaje visual 6-6: Amigo de práctica: Práctica adicional 6-6: Práctica adicional interactiva 6-6: Refuerzo para mejorar la comprensión 6-6: Desarrollar la competencia matemática 6-6: Ampliación Topic 6: End of Topic Interactive Student Edition: End of Topic 6 Topic 6: Fluency Practice Activity Interactive Student Edition: Topic 6 Assessment Practice Interactive Student Edition: Topic 6 Performance Task Topic 6 Performance Task Topic 6 Assessment 9-2: Center Games 6-3: Visual Learning Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Use models to help find quotients in problems involving decimals. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). 6-5: Visual Learning Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Use models to divide a decimal by a decimal. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). 6-1: Visual Learning Curriculum Standards: Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Use mental math and place-value patterns to divide a decimal by a power of 10. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). 6-2: Visual Learning Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Use reasoning and strategies such as rounding and compatible numbers to estimate quotients in problems with decimals. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). 6-4: Visual Learning Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Use models to visualize the relationship between division and multiplication to divide decimals by 2-digit whole numbers. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). 6-6: Visual Learning Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Reason abstractly and quantitatively. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Reason abstractly and quantitatively. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Reason abstractly and quantitatively. Mathematically proficient students make sense of quantities and their relationships in problem situations. They bring two complementary abilities to bear on problems involving quantitative relationships: the ability to decontextualize—to abstract a given situation and represent it symbolically and manipulate the representing symbols as if they have a life of their own, without necessarily attending to their referents—and the ability to contextualize, to pause as needed during the manipulation process in order to probe into the referents for the symbols involved. Quantitative reasoning entails habits of creating a coherent representation of the problem at hand; considering the units involved; attending to the meaning of quantities, not just how to compute them; and knowing and flexibly using different properties of operations and objects. Use reasoning to solve problems by making sense of quantities and relationships in problem situations. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Reason abstractly and quantitatively. Reason abstractly and quantitatively. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). Reason abstractly and quantitatively. Topic 6 Online Assessment Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Reason abstractly and quantitatively. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Reason abstractly and quantitatively. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Reason abstractly and quantitatively. Mathematically proficient students make sense of quantities and their relationships in problem situations. They bring two complementary abilities to bear on problems involving quantitative relationships: the ability to decontextualize—to abstract a given situation and represent it symbolically and manipulate the representing symbols as if they have a life of their own, without necessarily attending to their referents—and the ability to contextualize, to pause as needed during the manipulation process in order to probe into the referents for the symbols involved. Quantitative reasoning entails habits of creating a coherent representation of the problem at hand; considering the units involved; attending to the meaning of quantities, not just how to compute them; and knowing and flexibly using different properties of operations and objects. Use reasoning to solve problems by making sense of quantities and relationships in problem situations. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Reason abstractly and quantitatively. Reason abstractly and quantitatively. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). Reason abstractly and quantitatively. Use models to divide a decimal by a decimal. Use reasoning and strategies such as rounding and compatible numbers to estimate quotients in problems with decimals. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. Use mental math and place-value patterns to divide a decimal by a power of 10. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors. Use models to visualize the relationship between division and multiplication to divide decimals by 2-digit whole numbers. Use models to help find quotients in problems involving decimals. Topic 6 Spanish Assessments Tema 6: Tarea de rendimento Tema 6: Evaluación Topic 7: Use Equivalent Fractions to Add and Subtract Fractions Topic 7: Today's Challenge Topic 7: Beginning of Topic Interactive Student Edition: Beginning of Topic 7 Topic 7: enVision STEM Activity Grade 5 Topic 7: Review What You Know Topic 7: Vocabulary Cards 7-1: Estimate Sums and Differences of Fractions Interactive Student Edition: Grade 5 Lesson 7-1 Math Anytime 7-1: Daily Review Topic 7: Today's Challenge Step 1: Problem-Based Learning 7-1: Solve & Share Curriculum Standards: Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. English language learners communicate for social and instructional purposes within the school setting. Write informative/explanatory texts to examine a topic and convey ideas and information clearly. (a) Introduce a topic clearly, provide a general observation and focus, and group related information logically; include formatting (e.g., headings), illustrations, and multimedia when useful to aiding comprehension. (b) Develop the topic with facts, definitions, concrete details, quotations, or other information and examples related to the topic. (c) Link ideas within and across categories of information using words, phrases, and clauses (e.g., in contrast, especially). (d) Use precise language and domain-specific vocabulary to inform about or explain the topic. (e) Provide a concluding statement or section related to the information or explanation presented. English language learners communicate information, ideas and concepts necessary for academic success in the content area of Mathematics. Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 5 topics and texts, building on others’ ideas and expressing their own clearly. (a) Come to discussions prepared, having read or studied required material; explicitly draw on that preparation and other information known about the topic to explore ideas under discussion. (b) Follow agreed-upon rules for discussions and carry out assigned roles. (c) Pose and respond to specific questions by making comments that contribute to the discussion and elaborate on the remarks of others. (d) Review the key ideas expressed and draw conclusions in light of information and knowledge gained from the discussions. Summarize a written text read aloud or information presented in diverse media and formats, including visually, quantitatively, and orally. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Estimate sums and differences of fractions by using the nearest half or whole number. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Add and subtract fractions (including mixed numbers) with unlike denominators. (May include multiple methods and representations.) Estimate sums and differences of decimals and fractions to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. Summarize the points a speaker makes and explain how each claim is supported by reasons and evidence. Step 2: Visual Learning 7-1: Visual Learning Curriculum Standards: Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Estimate sums and differences of fractions by using the nearest half or whole number. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Add and subtract fractions (including mixed numbers) with unlike denominators. (May include multiple methods and representations.) Estimate sums and differences of decimals and fractions to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. 7-1: Convince Me! Curriculum Standards: Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Estimate sums and differences of fractions by using the nearest half or whole number. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Add and subtract fractions (including mixed numbers) with unlike denominators. (May include multiple methods and representations.) Estimate sums and differences of decimals and fractions to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. Practice and Problem Solving 7-1: Student Edition Practice Curriculum Standards: Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Estimate sums and differences of fractions by using the nearest half or whole number. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Add and subtract fractions (including mixed numbers) with unlike denominators. (May include multiple methods and representations.) Estimate sums and differences of decimals and fractions to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. 7-1: Practice Buddy: Independent Practice; Problem Solving Curriculum Standards: Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Estimate sums and differences of fractions by using the nearest half or whole number. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Add and subtract fractions (including mixed numbers) with unlike denominators. (May include multiple methods and representations.) Estimate sums and differences of decimals and fractions to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. 7-1: Practice Buddy: Additional Practice Curriculum Standards: Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Estimate sums and differences of fractions by using the nearest half or whole number. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Add and subtract fractions (including mixed numbers) with unlike denominators. (May include multiple methods and representations.) Estimate sums and differences of decimals and fractions to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. 7-1: Interactive Additional Practice Step 3: Assess & Differentiate 7-1: Practice Buddy: Additional Practice Curriculum Standards: Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Estimate sums and differences of fractions by using the nearest half or whole number. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Add and subtract fractions (including mixed numbers) with unlike denominators. (May include multiple methods and representations.) Estimate sums and differences of decimals and fractions to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. 7-1: Enrichment Curriculum Standards: Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Estimate sums and differences of fractions by using the nearest half or whole number. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Add and subtract fractions (including mixed numbers) with unlike denominators. (May include multiple methods and representations.) Estimate sums and differences of decimals and fractions to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. 7-1: Quick Check Curriculum Standards: Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Estimate sums and differences of fractions by using the nearest half or whole number. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Add and subtract fractions (including mixed numbers) with unlike denominators. (May include multiple methods and representations.) Estimate sums and differences of decimals and fractions to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. 7-1: Lesson Self-Assessment 7-1: Reteach to Build Understanding Curriculum Standards: Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Estimate sums and differences of fractions by using the nearest half or whole number. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Add and subtract fractions (including mixed numbers) with unlike denominators. (May include multiple methods and representations.) Estimate sums and differences of decimals and fractions to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. 7-1: Build Mathematical Literacy Curriculum Standards: Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 5 topics and texts, building on others’ ideas and expressing their own clearly. (a) Come to discussions prepared, having read or studied required material; explicitly draw on that preparation and other information known about the topic to explore ideas under discussion. (b) Follow agreed-upon rules for discussions and carry out assigned roles. (c) Pose and respond to specific questions by making comments that contribute to the discussion and elaborate on the remarks of others. (d) Review the key ideas expressed and draw conclusions in light of information and knowledge gained from the discussions. English language learners communicate for social and instructional purposes within the school setting. Summarize a written text read aloud or information presented in diverse media and formats, including visually, quantitatively, and orally. Summarize the points a speaker makes and explain how each claim is supported by reasons and evidence. Write informative/explanatory texts to examine a topic and convey ideas and information clearly. (a) Introduce a topic clearly, provide a general observation and focus, and group related information logically; include formatting (e.g., headings), illustrations, and multimedia when useful to aiding comprehension. (b) Develop the topic with facts, definitions, concrete details, quotations, or other information and examples related to the topic. (c) Link ideas within and across categories of information using words, phrases, and clauses (e.g., in contrast, especially). (d) Use precise language and domain-specific vocabulary to inform about or explain the topic. (e) Provide a concluding statement or section related to the information or explanation presented. English language learners communicate information, ideas and concepts necessary for academic success in the content area of Mathematics. 7-1: Enrichment Game: Factory Frenzy Fractions 7-1: Pick a Project 7-1: Another Look Curriculum Standards: Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Estimate sums and differences of fractions by using the nearest half or whole number. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Add and subtract fractions (including mixed numbers) with unlike denominators. (May include multiple methods and representations.) Estimate sums and differences of decimals and fractions to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. Spanish Resources 7-1: eText del Libro del estudiante 7-1: Repaso diario 7-1: Aprendizaje visual 7-1: Amigo de práctica: Práctica adicional 7-1: Práctica adicional interactiva 7-1: Refuerzo para mejorar la comprensión 7-1: Desarrollar la competencia matemática 7-1: Ampliación 7-2: Find Common Denominators Interactive Student Edition: Grade 5 Lesson 7-2 Math Anytime 7-2: Daily Review Topic 7: Today's Challenge Step 1: Problem-Based Learning 7-2: Solve & Share Curriculum Standards: Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. English language learners communicate for social and instructional purposes within the school setting. Write informative/explanatory texts to examine a topic and convey ideas and information clearly. (a) Introduce a topic clearly, provide a general observation and focus, and group related information logically; include formatting (e.g., headings), illustrations, and multimedia when useful to aiding comprehension. (b) Develop the topic with facts, definitions, concrete details, quotations, or other information and examples related to the topic. (c) Link ideas within and across categories of information using words, phrases, and clauses (e.g., in contrast, especially). (d) Use precise language and domain-specific vocabulary to inform about or explain the topic. (e) Provide a concluding statement or section related to the information or explanation presented. English language learners communicate information, ideas and concepts necessary for academic success in the content area of Mathematics. Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 5 topics and texts, building on others’ ideas and expressing their own clearly. (a) Come to discussions prepared, having read or studied required material; explicitly draw on that preparation and other information known about the topic to explore ideas under discussion. (b) Follow agreed-upon rules for discussions and carry out assigned roles. (c) Pose and respond to specific questions by making comments that contribute to the discussion and elaborate on the remarks of others. (d) Review the key ideas expressed and draw conclusions in light of information and knowledge gained from the discussions. Summarize a written text read aloud or information presented in diverse media and formats, including visually, quantitatively, and orally. Summarize the points a speaker makes and explain how each claim is supported by reasons and evidence. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Find common denominators for fractions with unlike denominators. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Add and subtract fractions (including mixed numbers) with unlike denominators. (May include multiple methods and representations.) Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. Step 2: Visual Learning 7-2: Visual Learning Curriculum Standards: Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Find common denominators for fractions with unlike denominators. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Add and subtract fractions (including mixed numbers) with unlike denominators. (May include multiple methods and representations.) Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. 7-2: Convince Me! Curriculum Standards: Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Find common denominators for fractions with unlike denominators. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Add and subtract fractions (including mixed numbers) with unlike denominators. (May include multiple methods and representations.) Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. Practice and Problem Solving 7-2: Student Edition Practice Curriculum Standards: Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Find common denominators for fractions with unlike denominators. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Add and subtract fractions (including mixed numbers) with unlike denominators. (May include multiple methods and representations.) Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. 7-2: Practice Buddy: Independent Practice; Problem Solving Curriculum Standards: Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Find common denominators for fractions with unlike denominators. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Add and subtract fractions (including mixed numbers) with unlike denominators. (May include multiple methods and representations.) Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. 7-2: Practice Buddy: Additional Practice Curriculum Standards: Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Find common denominators for fractions with unlike denominators. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Add and subtract fractions (including mixed numbers) with unlike denominators. (May include multiple methods and representations.) Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. 7-2: Interactive Additional Practice Step 3: Assess & Differentiate 7-2: Practice Buddy: Additional Practice Curriculum Standards: Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Find common denominators for fractions with unlike denominators. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Add and subtract fractions (including mixed numbers) with unlike denominators. (May include multiple methods and representations.) Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. 7-2: Enrichment Curriculum Standards: Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Find common denominators for fractions with unlike denominators. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Add and subtract fractions (including mixed numbers) with unlike denominators. (May include multiple methods and representations.) Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. 7-2: Quick Check Curriculum Standards: Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Find common denominators for fractions with unlike denominators. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Add and subtract fractions (including mixed numbers) with unlike denominators. (May include multiple methods and representations.) Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. 7-2: Lesson Self-Assessment 7-2: Reteach to Build Understanding Curriculum Standards: Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Find common denominators for fractions with unlike denominators. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Add and subtract fractions (including mixed numbers) with unlike denominators. (May include multiple methods and representations.) Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. 7-2: Build Mathematical Literacy Curriculum Standards: Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 5 topics and texts, building on others’ ideas and expressing their own clearly. (a) Come to discussions prepared, having read or studied required material; explicitly draw on that preparation and other information known about the topic to explore ideas under discussion. (b) Follow agreed-upon rules for discussions and carry out assigned roles. (c) Pose and respond to specific questions by making comments that contribute to the discussion and elaborate on the remarks of others. (d) Review the key ideas expressed and draw conclusions in light of information and knowledge gained from the discussions. English language learners communicate for social and instructional purposes within the school setting. Summarize a written text read aloud or information presented in diverse media and formats, including visually, quantitatively, and orally. Summarize the points a speaker makes and explain how each claim is supported by reasons and evidence. Write informative/explanatory texts to examine a topic and convey ideas and information clearly. (a) Introduce a topic clearly, provide a general observation and focus, and group related information logically; include formatting (e.g., headings), illustrations, and multimedia when useful to aiding comprehension. (b) Develop the topic with facts, definitions, concrete details, quotations, or other information and examples related to the topic. (c) Link ideas within and across categories of information using words, phrases, and clauses (e.g., in contrast, especially). (d) Use precise language and domain-specific vocabulary to inform about or explain the topic. (e) Provide a concluding statement or section related to the information or explanation presented. English language learners communicate information, ideas and concepts necessary for academic success in the content area of Mathematics. 7-2: Enrichment 7-2: Digital Math Tool Activity 7-2: Pick a Project 7-2: Another Look Curriculum Standards: Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Find common denominators for fractions with unlike denominators. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Add and subtract fractions (including mixed numbers) with unlike denominators. (May include multiple methods and representations.) Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. Spanish Resources 7-2: eText del Libro del estudiante 7-2: Repaso diario 7-2: Aprendizaje visual 7-2: Amigo de práctica: Práctica adicional 7-2: Práctica adicional interactiva 7-2: Refuerzo para mejorar la comprensión 7-2: Desarrollar la competencia matemática 7-2: Ampliación 7-3: Add Fractions with Unlike Denominators Interactive Student Edition: Grade 5 Lesson 7-3 Math Anytime 7-3: Daily Review Topic 7: Today's Challenge Step 1: Problem-Based Learning 7-3: Solve & Share Curriculum Standards: Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. English language learners communicate for social and instructional purposes within the school setting. Write informative/explanatory texts to examine a topic and convey ideas and information clearly. (a) Introduce a topic clearly, provide a general observation and focus, and group related information logically; include formatting (e.g., headings), illustrations, and multimedia when useful to aiding comprehension. (b) Develop the topic with facts, definitions, concrete details, quotations, or other information and examples related to the topic. (c) Link ideas within and across categories of information using words, phrases, and clauses (e.g., in contrast, especially). (d) Use precise language and domain-specific vocabulary to inform about or explain the topic. (e) Provide a concluding statement or section related to the information or explanation presented. English language learners communicate information, ideas and concepts necessary for academic success in the content area of Mathematics. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Add fractions with unlike denominators using equivalent fractions with a common denominator. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Add and subtract fractions (including mixed numbers) with unlike denominators. (May include multiple methods and representations.) Add and subtract decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Model addition and subtraction of fractions and decimals using a variety of representations. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 5 topics and texts, building on others’ ideas and expressing their own clearly. (a) Come to discussions prepared, having read or studied required material; explicitly draw on that preparation and other information known about the topic to explore ideas under discussion. (b) Follow agreed-upon rules for discussions and carry out assigned roles. (c) Pose and respond to specific questions by making comments that contribute to the discussion and elaborate on the remarks of others. (d) Review the key ideas expressed and draw conclusions in light of information and knowledge gained from the discussions. Summarize a written text read aloud or information presented in diverse media and formats, including visually, quantitatively, and orally. Summarize the points a speaker makes and explain how each claim is supported by reasons and evidence. Step 2: Visual Learning 7-3: Visual Learning Curriculum Standards: Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Add fractions with unlike denominators using equivalent fractions with a common denominator. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Add and subtract fractions (including mixed numbers) with unlike denominators. (May include multiple methods and representations.) Add and subtract decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Model addition and subtraction of fractions and decimals using a variety of representations. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. Add or subtract fractions with unlike denominators within one whole unit on a number line. 7-3: Convince Me! Curriculum Standards: Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Add fractions with unlike denominators using equivalent fractions with a common denominator. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Add and subtract fractions (including mixed numbers) with unlike denominators. (May include multiple methods and representations.) Add and subtract decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Model addition and subtraction of fractions and decimals using a variety of representations. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. Practice and Problem Solving 7-3: Student Edition Practice Curriculum Standards: Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Add fractions with unlike denominators using equivalent fractions with a common denominator. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Add and subtract fractions (including mixed numbers) with unlike denominators. (May include multiple methods and representations.) Add and subtract decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Model addition and subtraction of fractions and decimals using a variety of representations. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. 7-3: Practice Buddy: Independent Practice; Problem Solving Curriculum Standards: Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Add fractions with unlike denominators using equivalent fractions with a common denominator. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Add and subtract fractions (including mixed numbers) with unlike denominators. (May include multiple methods and representations.) Add and subtract decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Model addition and subtraction of fractions and decimals using a variety of representations. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. 7-3: Practice Buddy: Additional Practice Curriculum Standards: Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Add fractions with unlike denominators using equivalent fractions with a common denominator. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Add and subtract fractions (including mixed numbers) with unlike denominators. (May include multiple methods and representations.) Add and subtract decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Model addition and subtraction of fractions and decimals using a variety of representations. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. 7-3: Interactive Additional Practice Step 3: Assess & Differentiate 7-3: Practice Buddy: Additional Practice Curriculum Standards: Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Add fractions with unlike denominators using equivalent fractions with a common denominator. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Add and subtract fractions (including mixed numbers) with unlike denominators. (May include multiple methods and representations.) Add and subtract decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Model addition and subtraction of fractions and decimals using a variety of representations. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. 7-3: Enrichment Curriculum Standards: Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Add fractions with unlike denominators using equivalent fractions with a common denominator. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Add and subtract fractions (including mixed numbers) with unlike denominators. (May include multiple methods and representations.) Add and subtract decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Model addition and subtraction of fractions and decimals using a variety of representations. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. 7-3: Quick Check Curriculum Standards: Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Add fractions with unlike denominators using equivalent fractions with a common denominator. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Add and subtract fractions (including mixed numbers) with unlike denominators. (May include multiple methods and representations.) Add and subtract decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Model addition and subtraction of fractions and decimals using a variety of representations. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. 7-3: Lesson Self-Assessment 7-3: Reteach to Build Understanding Curriculum Standards: Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Add fractions with unlike denominators using equivalent fractions with a common denominator. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Add and subtract fractions (including mixed numbers) with unlike denominators. (May include multiple methods and representations.) Add and subtract decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Model addition and subtraction of fractions and decimals using a variety of representations. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. Add or subtract fractions with unlike denominators within one whole unit on a number line. 7-3: Build Mathematical Literacy Curriculum Standards: Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 5 topics and texts, building on others’ ideas and expressing their own clearly. (a) Come to discussions prepared, having read or studied required material; explicitly draw on that preparation and other information known about the topic to explore ideas under discussion. (b) Follow agreed-upon rules for discussions and carry out assigned roles. (c) Pose and respond to specific questions by making comments that contribute to the discussion and elaborate on the remarks of others. (d) Review the key ideas expressed and draw conclusions in light of information and knowledge gained from the discussions. English language learners communicate for social and instructional purposes within the school setting. Summarize a written text read aloud or information presented in diverse media and formats, including visually, quantitatively, and orally. Summarize the points a speaker makes and explain how each claim is supported by reasons and evidence. Write informative/explanatory texts to examine a topic and convey ideas and information clearly. (a) Introduce a topic clearly, provide a general observation and focus, and group related information logically; include formatting (e.g., headings), illustrations, and multimedia when useful to aiding comprehension. (b) Develop the topic with facts, definitions, concrete details, quotations, or other information and examples related to the topic. (c) Link ideas within and across categories of information using words, phrases, and clauses (e.g., in contrast, especially). (d) Use precise language and domain-specific vocabulary to inform about or explain the topic. (e) Provide a concluding statement or section related to the information or explanation presented. English language learners communicate information, ideas and concepts necessary for academic success in the content area of Mathematics. 7-3: Enrichment Game: Fancy Flea - Fractions 7-3: Pick a Project 7-3: Another Look Curriculum Standards: Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Add fractions with unlike denominators using equivalent fractions with a common denominator. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Add and subtract fractions (including mixed numbers) with unlike denominators. (May include multiple methods and representations.) Add and subtract decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Model addition and subtraction of fractions and decimals using a variety of representations. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. Add or subtract fractions with unlike denominators within one whole unit on a number line. Spanish Resources 7-3: eText del Libro del estudiante 7-3: Repaso diario 7-3: Aprendizaje visual 7-3: Amigo de práctica: Práctica adicional 7-3: Práctica adicional interactiva 7-3: Refuerzo para mejorar la comprensión 7-3: Desarrollar la competencia matemática 7-3: Ampliación 7-4: Subtract Fractions with Unlike Denominators Interactive Student Edition: Grade 5 Lesson 7-4 Math Anytime 7-4: Daily Review Topic 7: Today's Challenge Step 1: Problem-Based Learning 7-4: Solve & Share Curriculum Standards: Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. English language learners communicate for social and instructional purposes within the school setting. Write informative/explanatory texts to examine a topic and convey ideas and information clearly. (a) Introduce a topic clearly, provide a general observation and focus, and group related information logically; include formatting (e.g., headings), illustrations, and multimedia when useful to aiding comprehension. (b) Develop the topic with facts, definitions, concrete details, quotations, or other information and examples related to the topic. (c) Link ideas within and across categories of information using words, phrases, and clauses (e.g., in contrast, especially). (d) Use precise language and domain-specific vocabulary to inform about or explain the topic. (e) Provide a concluding statement or section related to the information or explanation presented. English language learners communicate information, ideas and concepts necessary for academic success in the content area of Mathematics. Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 5 topics and texts, building on others’ ideas and expressing their own clearly. (a) Come to discussions prepared, having read or studied required material; explicitly draw on that preparation and other information known about the topic to explore ideas under discussion. (b) Follow agreed-upon rules for discussions and carry out assigned roles. (c) Pose and respond to specific questions by making comments that contribute to the discussion and elaborate on the remarks of others. (d) Review the key ideas expressed and draw conclusions in light of information and knowledge gained from the discussions. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Subtract fractions with unlike denominators. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Add and subtract fractions (including mixed numbers) with unlike denominators. (May include multiple methods and representations.) Add and subtract decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Model addition and subtraction of fractions and decimals using a variety of representations. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. Summarize a written text read aloud or information presented in diverse media and formats, including visually, quantitatively, and orally. Summarize the points a speaker makes and explain how each claim is supported by reasons and evidence. Step 2: Visual Learning 7-4: Visual Learning Curriculum Standards: Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Add or subtract fractions with unlike denominators within one whole unit on a number line. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Subtract fractions with unlike denominators. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Add and subtract fractions (including mixed numbers) with unlike denominators. (May include multiple methods and representations.) Add and subtract decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Model addition and subtraction of fractions and decimals using a variety of representations. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. 7-4: Convince Me! Curriculum Standards: Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Subtract fractions with unlike denominators. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Add and subtract fractions (including mixed numbers) with unlike denominators. (May include multiple methods and representations.) Add and subtract decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Model addition and subtraction of fractions and decimals using a variety of representations. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. Practice and Problem Solving 7-4: Student Edition Practice Curriculum Standards: Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Subtract fractions with unlike denominators. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Add and subtract fractions (including mixed numbers) with unlike denominators. (May include multiple methods and representations.) Add and subtract decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Model addition and subtraction of fractions and decimals using a variety of representations. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. 7-4: Practice Buddy: Independent Practice; Problem Solving Curriculum Standards: Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Subtract fractions with unlike denominators. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Add and subtract fractions (including mixed numbers) with unlike denominators. (May include multiple methods and representations.) Add and subtract decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Model addition and subtraction of fractions and decimals using a variety of representations. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. 7-4: Practice Buddy: Additional Practice Curriculum Standards: Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Subtract fractions with unlike denominators. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Add and subtract fractions (including mixed numbers) with unlike denominators. (May include multiple methods and representations.) Add and subtract decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Model addition and subtraction of fractions and decimals using a variety of representations. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. 7-4: Interactive Additional Practice Step 3: Assess & Differentiate 7-4: Practice Buddy: Additional Practice Curriculum Standards: Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Subtract fractions with unlike denominators. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Add and subtract fractions (including mixed numbers) with unlike denominators. (May include multiple methods and representations.) Add and subtract decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Model addition and subtraction of fractions and decimals using a variety of representations. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. 7-4: Enrichment Curriculum Standards: Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Subtract fractions with unlike denominators. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Add and subtract fractions (including mixed numbers) with unlike denominators. (May include multiple methods and representations.) Add and subtract decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Model addition and subtraction of fractions and decimals using a variety of representations. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. 7-4: Quick Check Curriculum Standards: Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Subtract fractions with unlike denominators. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Add and subtract fractions (including mixed numbers) with unlike denominators. (May include multiple methods and representations.) Add and subtract decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Model addition and subtraction of fractions and decimals using a variety of representations. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. 7-4: Lesson Self-Assessment 7-4: Reteach to Build Understanding Curriculum Standards: Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Add or subtract fractions with unlike denominators within one whole unit on a number line. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Subtract fractions with unlike denominators. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Add and subtract fractions (including mixed numbers) with unlike denominators. (May include multiple methods and representations.) Add and subtract decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Model addition and subtraction of fractions and decimals using a variety of representations. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. 7-4: Build Mathematical Literacy Curriculum Standards: Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 5 topics and texts, building on others’ ideas and expressing their own clearly. (a) Come to discussions prepared, having read or studied required material; explicitly draw on that preparation and other information known about the topic to explore ideas under discussion. (b) Follow agreed-upon rules for discussions and carry out assigned roles. (c) Pose and respond to specific questions by making comments that contribute to the discussion and elaborate on the remarks of others. (d) Review the key ideas expressed and draw conclusions in light of information and knowledge gained from the discussions. English language learners communicate for social and instructional purposes within the school setting. Summarize a written text read aloud or information presented in diverse media and formats, including visually, quantitatively, and orally. Summarize the points a speaker makes and explain how each claim is supported by reasons and evidence. Write informative/explanatory texts to examine a topic and convey ideas and information clearly. (a) Introduce a topic clearly, provide a general observation and focus, and group related information logically; include formatting (e.g., headings), illustrations, and multimedia when useful to aiding comprehension. (b) Develop the topic with facts, definitions, concrete details, quotations, or other information and examples related to the topic. (c) Link ideas within and across categories of information using words, phrases, and clauses (e.g., in contrast, especially). (d) Use precise language and domain-specific vocabulary to inform about or explain the topic. (e) Provide a concluding statement or section related to the information or explanation presented. English language learners communicate information, ideas and concepts necessary for academic success in the content area of Mathematics. 7-4: Enrichment Game: Factory Frenzy Fractions 7-4: Pick a Project 7-4: Another Look Curriculum Standards: Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Add or subtract fractions with unlike denominators within one whole unit on a number line. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Subtract fractions with unlike denominators. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Add and subtract fractions (including mixed numbers) with unlike denominators. (May include multiple methods and representations.) Add and subtract decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Model addition and subtraction of fractions and decimals using a variety of representations. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. Spanish Resources 7-4: eText del Libro del estudiante 7-4: Repaso diario 7-4: Aprendizaje visual 7-4: Amigo de práctica: Práctica adicional 7-4: Práctica adicional interactiva 7-4: Refuerzo para mejorar la comprensión 7-4: Desarrollar la competencia matemática 7-4: Ampliación 7-5: Add and Subtract Fractions Interactive Student Edition: Grade 5 Lesson 7-5 Math Anytime 7-5: Daily Review Topic 7: Today's Challenge Step 1: Problem-Based Learning 7-5: Solve & Share Curriculum Standards: Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. English language learners communicate for social and instructional purposes within the school setting. Write informative/explanatory texts to examine a topic and convey ideas and information clearly. (a) Introduce a topic clearly, provide a general observation and focus, and group related information logically; include formatting (e.g., headings), illustrations, and multimedia when useful to aiding comprehension. (b) Develop the topic with facts, definitions, concrete details, quotations, or other information and examples related to the topic. (c) Link ideas within and across categories of information using words, phrases, and clauses (e.g., in contrast, especially). (d) Use precise language and domain-specific vocabulary to inform about or explain the topic. (e) Provide a concluding statement or section related to the information or explanation presented. English language learners communicate information, ideas and concepts necessary for academic success in the content area of Mathematics. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Write equivalent fractions to add and subtract fractions with unlike denominators. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Add and subtract fractions (including mixed numbers) with unlike denominators. (May include multiple methods and representations.) Add and subtract decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Model addition and subtraction of fractions and decimals using a variety of representations. Estimate sums and differences of decimals and fractions to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 5 topics and texts, building on others’ ideas and expressing their own clearly. (a) Come to discussions prepared, having read or studied required material; explicitly draw on that preparation and other information known about the topic to explore ideas under discussion. (b) Follow agreed-upon rules for discussions and carry out assigned roles. (c) Pose and respond to specific questions by making comments that contribute to the discussion and elaborate on the remarks of others. (d) Review the key ideas expressed and draw conclusions in light of information and knowledge gained from the discussions. Summarize a written text read aloud or information presented in diverse media and formats, including visually, quantitatively, and orally. Summarize the points a speaker makes and explain how each claim is supported by reasons and evidence. Step 2: Visual Learning 7-5: Visual Learning Curriculum Standards: Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Write equivalent fractions to add and subtract fractions with unlike denominators. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Add and subtract fractions (including mixed numbers) with unlike denominators. (May include multiple methods and representations.) Add and subtract decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Model addition and subtraction of fractions and decimals using a variety of representations. Estimate sums and differences of decimals and fractions to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. 7-5: Convince Me! Curriculum Standards: Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Write equivalent fractions to add and subtract fractions with unlike denominators. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Add and subtract fractions (including mixed numbers) with unlike denominators. (May include multiple methods and representations.) Add and subtract decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Model addition and subtraction of fractions and decimals using a variety of representations. Estimate sums and differences of decimals and fractions to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. Practice and Problem Solving 7-5: Student Edition Practice Curriculum Standards: Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Write equivalent fractions to add and subtract fractions with unlike denominators. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Add and subtract fractions (including mixed numbers) with unlike denominators. (May include multiple methods and representations.) Add and subtract decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Model addition and subtraction of fractions and decimals using a variety of representations. Estimate sums and differences of decimals and fractions to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. 7-5: Practice Buddy: Independent Practice; Problem Solving Curriculum Standards: Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Write equivalent fractions to add and subtract fractions with unlike denominators. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Add and subtract fractions (including mixed numbers) with unlike denominators. (May include multiple methods and representations.) Add and subtract decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Model addition and subtraction of fractions and decimals using a variety of representations. Estimate sums and differences of decimals and fractions to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. 7-5: Practice Buddy: Additional Practice Curriculum Standards: Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Write equivalent fractions to add and subtract fractions with unlike denominators. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Add and subtract fractions (including mixed numbers) with unlike denominators. (May include multiple methods and representations.) Add and subtract decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Model addition and subtraction of fractions and decimals using a variety of representations. Estimate sums and differences of decimals and fractions to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. 7-5: Interactive Additional Practice Step 3: Assess & Differentiate 7-5: Practice Buddy: Additional Practice Curriculum Standards: Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Write equivalent fractions to add and subtract fractions with unlike denominators. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Add and subtract fractions (including mixed numbers) with unlike denominators. (May include multiple methods and representations.) Add and subtract decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Model addition and subtraction of fractions and decimals using a variety of representations. Estimate sums and differences of decimals and fractions to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. 7-5: Enrichment Curriculum Standards: Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Write equivalent fractions to add and subtract fractions with unlike denominators. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Add and subtract fractions (including mixed numbers) with unlike denominators. (May include multiple methods and representations.) Add and subtract decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Model addition and subtraction of fractions and decimals using a variety of representations. Estimate sums and differences of decimals and fractions to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. 7-5: Quick Check Curriculum Standards: Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Write equivalent fractions to add and subtract fractions with unlike denominators. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Add and subtract fractions (including mixed numbers) with unlike denominators. (May include multiple methods and representations.) Add and subtract decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Model addition and subtraction of fractions and decimals using a variety of representations. Estimate sums and differences of decimals and fractions to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. 7-5: Lesson Self-Assessment 7-5: Reteach to Build Understanding Curriculum Standards: Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Write equivalent fractions to add and subtract fractions with unlike denominators. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Add and subtract fractions (including mixed numbers) with unlike denominators. (May include multiple methods and representations.) Add and subtract decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Model addition and subtraction of fractions and decimals using a variety of representations. Estimate sums and differences of decimals and fractions to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. 7-5: Build Mathematical Literacy Curriculum Standards: Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 5 topics and texts, building on others’ ideas and expressing their own clearly. (a) Come to discussions prepared, having read or studied required material; explicitly draw on that preparation and other information known about the topic to explore ideas under discussion. (b) Follow agreed-upon rules for discussions and carry out assigned roles. (c) Pose and respond to specific questions by making comments that contribute to the discussion and elaborate on the remarks of others. (d) Review the key ideas expressed and draw conclusions in light of information and knowledge gained from the discussions. English language learners communicate for social and instructional purposes within the school setting. Summarize a written text read aloud or information presented in diverse media and formats, including visually, quantitatively, and orally. Summarize the points a speaker makes and explain how each claim is supported by reasons and evidence. Write informative/explanatory texts to examine a topic and convey ideas and information clearly. (a) Introduce a topic clearly, provide a general observation and focus, and group related information logically; include formatting (e.g., headings), illustrations, and multimedia when useful to aiding comprehension. (b) Develop the topic with facts, definitions, concrete details, quotations, or other information and examples related to the topic. (c) Link ideas within and across categories of information using words, phrases, and clauses (e.g., in contrast, especially). (d) Use precise language and domain-specific vocabulary to inform about or explain the topic. (e) Provide a concluding statement or section related to the information or explanation presented. English language learners communicate information, ideas and concepts necessary for academic success in the content area of Mathematics. 7-5: Enrichment Game: Jungle Quest - Equivalent Fractions 7-5: Problem-Solving Reading Activity Curriculum Standards: Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Write equivalent fractions to add and subtract fractions with unlike denominators. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Add and subtract fractions (including mixed numbers) with unlike denominators. (May include multiple methods and representations.) Add and subtract decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Model addition and subtraction of fractions and decimals using a variety of representations. Estimate sums and differences of decimals and fractions to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. 7-5: Another Look Curriculum Standards: Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Add or subtract fractions with unlike denominators within one whole unit on a number line. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Write equivalent fractions to add and subtract fractions with unlike denominators. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Add and subtract fractions (including mixed numbers) with unlike denominators. (May include multiple methods and representations.) Add and subtract decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Model addition and subtraction of fractions and decimals using a variety of representations. Estimate sums and differences of decimals and fractions to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. Add and subtract fractions with like denominators with sums greater than 1 represented by mixed numbers using visual fraction models. Spanish Resources 7-5: eText del Libro del estudiante 7-5: Repaso diario 7-5: Aprendizaje visual 7-5: Amigo de práctica: Práctica adicional 7-5: Práctica adicional interactiva 7-5: Refuerzo para mejorar la comprensión 7-5: Desarrollar la competencia matemática 7-5: Ampliación 7-6: Estimate Sums and Differences of Mixed Numbers Interactive Student Edition: Grade 5 Lesson 7-6 Math Anytime 7-6: Daily Review Topic 7: Today's Challenge Step 1: Problem-Based Learning 7-6: Solve & Share Curriculum Standards: Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. English language learners communicate for social and instructional purposes within the school setting. Write informative/explanatory texts to examine a topic and convey ideas and information clearly. (a) Introduce a topic clearly, provide a general observation and focus, and group related information logically; include formatting (e.g., headings), illustrations, and multimedia when useful to aiding comprehension. (b) Develop the topic with facts, definitions, concrete details, quotations, or other information and examples related to the topic. (c) Link ideas within and across categories of information using words, phrases, and clauses (e.g., in contrast, especially). (d) Use precise language and domain-specific vocabulary to inform about or explain the topic. (e) Provide a concluding statement or section related to the information or explanation presented. English language learners communicate information, ideas and concepts necessary for academic success in the content area of Mathematics. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Estimate sums and differences of fractions and mixed numbers. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Add and subtract fractions (including mixed numbers) with unlike denominators. (May include multiple methods and representations.) Estimate sums and differences of decimals and fractions to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 5 topics and texts, building on others’ ideas and expressing their own clearly. (a) Come to discussions prepared, having read or studied required material; explicitly draw on that preparation and other information known about the topic to explore ideas under discussion. (b) Follow agreed-upon rules for discussions and carry out assigned roles. (c) Pose and respond to specific questions by making comments that contribute to the discussion and elaborate on the remarks of others. (d) Review the key ideas expressed and draw conclusions in light of information and knowledge gained from the discussions. Summarize a written text read aloud or information presented in diverse media and formats, including visually, quantitatively, and orally. Summarize the points a speaker makes and explain how each claim is supported by reasons and evidence. Step 2: Visual Learning 7-6: Visual Learning Curriculum Standards: Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Estimate sums and differences of fractions and mixed numbers. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Add and subtract fractions (including mixed numbers) with unlike denominators. (May include multiple methods and representations.) Estimate sums and differences of decimals and fractions to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. 7-6: Convince Me! Curriculum Standards: Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Estimate sums and differences of fractions and mixed numbers. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Add and subtract fractions (including mixed numbers) with unlike denominators. (May include multiple methods and representations.) Estimate sums and differences of decimals and fractions to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. Practice and Problem Solving 7-6: Student Edition Practice Curriculum Standards: Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Estimate sums and differences of fractions and mixed numbers. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Add and subtract fractions (including mixed numbers) with unlike denominators. (May include multiple methods and representations.) Estimate sums and differences of decimals and fractions to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. 7-6: Practice Buddy: Independent Practice; Problem Solving Curriculum Standards: Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Estimate sums and differences of fractions and mixed numbers. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Add and subtract fractions (including mixed numbers) with unlike denominators. (May include multiple methods and representations.) Estimate sums and differences of decimals and fractions to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. 7-6: Practice Buddy: Additional Practice Curriculum Standards: Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Estimate sums and differences of fractions and mixed numbers. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Add and subtract fractions (including mixed numbers) with unlike denominators. (May include multiple methods and representations.) Estimate sums and differences of decimals and fractions to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. 7-6: Interactive Additional Practice Step 3: Assess & Differentiate 7-6: Practice Buddy: Additional Practice Curriculum Standards: Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Estimate sums and differences of fractions and mixed numbers. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Add and subtract fractions (including mixed numbers) with unlike denominators. (May include multiple methods and representations.) Estimate sums and differences of decimals and fractions to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. 7-6: Enrichment Curriculum Standards: Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Estimate sums and differences of fractions and mixed numbers. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Add and subtract fractions (including mixed numbers) with unlike denominators. (May include multiple methods and representations.) Estimate sums and differences of decimals and fractions to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. 7-6: Quick Check Curriculum Standards: Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Estimate sums and differences of fractions and mixed numbers. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Add and subtract fractions (including mixed numbers) with unlike denominators. (May include multiple methods and representations.) Estimate sums and differences of decimals and fractions to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. 7-6: Lesson Self-Assessment 7-6: Reteach to Build Understanding Curriculum Standards: Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Estimate sums and differences of fractions and mixed numbers. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Add and subtract fractions (including mixed numbers) with unlike denominators. (May include multiple methods and representations.) Estimate sums and differences of decimals and fractions to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. 7-6: Build Mathematical Literacy Curriculum Standards: Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 5 topics and texts, building on others’ ideas and expressing their own clearly. (a) Come to discussions prepared, having read or studied required material; explicitly draw on that preparation and other information known about the topic to explore ideas under discussion. (b) Follow agreed-upon rules for discussions and carry out assigned roles. (c) Pose and respond to specific questions by making comments that contribute to the discussion and elaborate on the remarks of others. (d) Review the key ideas expressed and draw conclusions in light of information and knowledge gained from the discussions. English language learners communicate for social and instructional purposes within the school setting. Summarize a written text read aloud or information presented in diverse media and formats, including visually, quantitatively, and orally. Summarize the points a speaker makes and explain how each claim is supported by reasons and evidence. Write informative/explanatory texts to examine a topic and convey ideas and information clearly. (a) Introduce a topic clearly, provide a general observation and focus, and group related information logically; include formatting (e.g., headings), illustrations, and multimedia when useful to aiding comprehension. (b) Develop the topic with facts, definitions, concrete details, quotations, or other information and examples related to the topic. (c) Link ideas within and across categories of information using words, phrases, and clauses (e.g., in contrast, especially). (d) Use precise language and domain-specific vocabulary to inform about or explain the topic. (e) Provide a concluding statement or section related to the information or explanation presented. English language learners communicate information, ideas and concepts necessary for academic success in the content area of Mathematics. 7-6: Enrichment Game: Factory Frenzy Fractions 7-6: Pick a Project 7-6: Another Look Curriculum Standards: Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Estimate sums and differences of fractions and mixed numbers. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Add and subtract fractions (including mixed numbers) with unlike denominators. (May include multiple methods and representations.) Estimate sums and differences of decimals and fractions to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. Spanish Resources 7-6: eText del Libro del estudiante 7-6: Repaso diario 7-6: Aprendizaje visual 7-6: Amigo de práctica: Práctica adicional 7-6: Práctica adicional interactiva 7-6: Refuerzo para mejorar la comprensión 7-6: Desarrollar la competencia matemática 7-6: Ampliación 7-7: Use Models to Add Mixed Numbers Interactive Student Edition: Grade 5 Lesson 7-7 Math Anytime 7-7: Daily Review Topic 7: Today's Challenge Step 1: Problem-Based Learning 7-7: Solve & Share Curriculum Standards: Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. English language learners communicate for social and instructional purposes within the school setting. Write informative/explanatory texts to examine a topic and convey ideas and information clearly. (a) Introduce a topic clearly, provide a general observation and focus, and group related information logically; include formatting (e.g., headings), illustrations, and multimedia when useful to aiding comprehension. (b) Develop the topic with facts, definitions, concrete details, quotations, or other information and examples related to the topic. (c) Link ideas within and across categories of information using words, phrases, and clauses (e.g., in contrast, especially). (d) Use precise language and domain-specific vocabulary to inform about or explain the topic. (e) Provide a concluding statement or section related to the information or explanation presented. English language learners communicate information, ideas and concepts necessary for academic success in the content area of Mathematics. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Add mixed numbers using models. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Add and subtract fractions (including mixed numbers) with unlike denominators. (May include multiple methods and representations.) Add and subtract decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Model addition and subtraction of fractions and decimals using a variety of representations. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 5 topics and texts, building on others’ ideas and expressing their own clearly. (a) Come to discussions prepared, having read or studied required material; explicitly draw on that preparation and other information known about the topic to explore ideas under discussion. (b) Follow agreed-upon rules for discussions and carry out assigned roles. (c) Pose and respond to specific questions by making comments that contribute to the discussion and elaborate on the remarks of others. (d) Review the key ideas expressed and draw conclusions in light of information and knowledge gained from the discussions. Summarize a written text read aloud or information presented in diverse media and formats, including visually, quantitatively, and orally. Summarize the points a speaker makes and explain how each claim is supported by reasons and evidence. Step 2: Visual Learning 7-7: Visual Learning Curriculum Standards: Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Add mixed numbers using models. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Add and subtract fractions (including mixed numbers) with unlike denominators. (May include multiple methods and representations.) Add and subtract decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Model addition and subtraction of fractions and decimals using a variety of representations. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. Add and subtract fractions with like denominators with sums greater than 1 represented by mixed numbers using visual fraction models. 7-7: Convince Me! Curriculum Standards: Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Add mixed numbers using models. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Add and subtract fractions (including mixed numbers) with unlike denominators. (May include multiple methods and representations.) Add and subtract decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Model addition and subtraction of fractions and decimals using a variety of representations. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. Practice and Problem Solving 7-7: Student Edition Practice Curriculum Standards: Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Add mixed numbers using models. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Add and subtract fractions (including mixed numbers) with unlike denominators. (May include multiple methods and representations.) Add and subtract decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Model addition and subtraction of fractions and decimals using a variety of representations. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. 7-7: Practice Buddy: Independent Practice; Problem Solving Curriculum Standards: Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Add mixed numbers using models. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Add and subtract fractions (including mixed numbers) with unlike denominators. (May include multiple methods and representations.) Add and subtract decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Model addition and subtraction of fractions and decimals using a variety of representations. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. 7-7: Practice Buddy: Additional Practice Curriculum Standards: Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Add mixed numbers using models. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Add and subtract fractions (including mixed numbers) with unlike denominators. (May include multiple methods and representations.) Add and subtract decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Model addition and subtraction of fractions and decimals using a variety of representations. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. 7-7: Interactive Additional Practice Step 3: Assess & Differentiate 7-7: Practice Buddy: Additional Practice Curriculum Standards: Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Add mixed numbers using models. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Add and subtract fractions (including mixed numbers) with unlike denominators. (May include multiple methods and representations.) Add and subtract decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Model addition and subtraction of fractions and decimals using a variety of representations. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. 7-7: Enrichment Curriculum Standards: Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Add mixed numbers using models. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Add and subtract fractions (including mixed numbers) with unlike denominators. (May include multiple methods and representations.) Add and subtract decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Model addition and subtraction of fractions and decimals using a variety of representations. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. 7-7: Quick Check Curriculum Standards: Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Add mixed numbers using models. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Add and subtract fractions (including mixed numbers) with unlike denominators. (May include multiple methods and representations.) Add and subtract decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Model addition and subtraction of fractions and decimals using a variety of representations. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. 7-7: Lesson Self-Assessment 7-7: Reteach to Build Understanding Curriculum Standards: Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Add mixed numbers using models. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Add and subtract fractions (including mixed numbers) with unlike denominators. (May include multiple methods and representations.) Add and subtract decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Model addition and subtraction of fractions and decimals using a variety of representations. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. Add and subtract fractions with like denominators with sums greater than 1 represented by mixed numbers using visual fraction models. 7-7: Build Mathematical Literacy Curriculum Standards: Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 5 topics and texts, building on others’ ideas and expressing their own clearly. (a) Come to discussions prepared, having read or studied required material; explicitly draw on that preparation and other information known about the topic to explore ideas under discussion. (b) Follow agreed-upon rules for discussions and carry out assigned roles. (c) Pose and respond to specific questions by making comments that contribute to the discussion and elaborate on the remarks of others. (d) Review the key ideas expressed and draw conclusions in light of information and knowledge gained from the discussions. English language learners communicate for social and instructional purposes within the school setting. Summarize a written text read aloud or information presented in diverse media and formats, including visually, quantitatively, and orally. Summarize the points a speaker makes and explain how each claim is supported by reasons and evidence. Write informative/explanatory texts to examine a topic and convey ideas and information clearly. (a) Introduce a topic clearly, provide a general observation and focus, and group related information logically; include formatting (e.g., headings), illustrations, and multimedia when useful to aiding comprehension. (b) Develop the topic with facts, definitions, concrete details, quotations, or other information and examples related to the topic. (c) Link ideas within and across categories of information using words, phrases, and clauses (e.g., in contrast, especially). (d) Use precise language and domain-specific vocabulary to inform about or explain the topic. (e) Provide a concluding statement or section related to the information or explanation presented. English language learners communicate information, ideas and concepts necessary for academic success in the content area of Mathematics. 7-7: Enrichment 7-7: Digital Math Tool Activity 7-7: Pick a Project 7-7: Another Look Curriculum Standards: Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Add mixed numbers using models. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Add and subtract fractions (including mixed numbers) with unlike denominators. (May include multiple methods and representations.) Add and subtract decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Model addition and subtraction of fractions and decimals using a variety of representations. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. Add and subtract fractions with like denominators with sums greater than 1 represented by mixed numbers using visual fraction models. Spanish Resources 7-7: eText del Libro del estudiante 7-7: Repaso diario 7-7: Aprendizaje visual 7-7: Amigo de práctica: Práctica adicional 7-7: Práctica adicional interactiva 7-7: Refuerzo para mejorar la comprensión 7-7: Desarrollar la competencia matemática 7-7: Ampliación 7-8: Add Mixed Numbers Interactive Student Edition: Grade 5 Lesson 7-8 Math Anytime 7-8: Daily Review Topic 7: Today's Challenge Step 1: Problem-Based Learning 7-8: Solve & Share Curriculum Standards: Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. English language learners communicate for social and instructional purposes within the school setting. Write informative/explanatory texts to examine a topic and convey ideas and information clearly. (a) Introduce a topic clearly, provide a general observation and focus, and group related information logically; include formatting (e.g., headings), illustrations, and multimedia when useful to aiding comprehension. (b) Develop the topic with facts, definitions, concrete details, quotations, or other information and examples related to the topic. (c) Link ideas within and across categories of information using words, phrases, and clauses (e.g., in contrast, especially). (d) Use precise language and domain-specific vocabulary to inform about or explain the topic. (e) Provide a concluding statement or section related to the information or explanation presented. English language learners communicate information, ideas and concepts necessary for academic success in the content area of Mathematics. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Add mixed numbers using equivalent fractions and a common denominator. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Add and subtract fractions (including mixed numbers) with unlike denominators. (May include multiple methods and representations.) Add and subtract decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Model addition and subtraction of fractions and decimals using a variety of representations. Estimate sums and differences of decimals and fractions to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. Engage effectively in a range of collaborative discussions (one-on- one, in groups, and teacher-led) with diverse partners on grade 5 topics and texts, building on others’ ideas and expressing their own clearly. (a) Come to discussions prepared, having read or studied required material; explicitly draw on that preparation and other information known about the topic to explore ideas under discussion. (b) Follow agreed-upon rules for discussions and carry out assigned roles. (c) Pose and respond to specific questions by making comments that contribute to the discussion and elaborate on the remarks of others. (d) Review the key ideas expressed and draw conclusions in light of information and knowledge gained from the discussions. Summarize a written text read aloud or information presented in diverse media and formats, including visually, quantitatively, and orally. Summarize the points a speaker makes and explain how each claim is supported by reasons and evidence. Step 2: Visual Learning 7-8: Visual Learning Curriculum Standards: Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Add mixed numbers using equivalent fractions and a common denominator. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Add and subtract fractions (including mixed numbers) with unlike denominators. (May include multiple methods and representations.) Add and subtract decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Model addition and subtraction of fractions and decimals using a variety of representations. Estimate sums and differences of decimals and fractions to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. 7-8: Convince Me! Curriculum Standards: Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Add mixed numbers using equivalent fractions and a common denominator. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Add and subtract fractions (including mixed numbers) with unlike denominators. (May include multiple methods and representations.) Add and subtract decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Model addition and subtraction of fractions and decimals using a variety of representations. Estimate sums and differences of decimals and fractions to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. Practice and Problem Solving 7-8: Student Edition Practice Curriculum Standards: Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Add mixed numbers using equivalent fractions and a common denominator. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Add and subtract fractions (including mixed numbers) with unlike denominators. (May include multiple methods and representations.) Add and subtract decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Model addition and subtraction of fractions and decimals using a variety of representations. Estimate sums and differences of decimals and fractions to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. 7-8: Practice Buddy: Independent Practice; Problem Solving Curriculum Standards: Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Add mixed numbers using equivalent fractions and a common denominator. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Add and subtract fractions (including mixed numbers) with unlike denominators. (May include multiple methods and representations.) Add and subtract decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Model addition and subtraction of fractions and decimals using a variety of representations. Estimate sums and differences of decimals and fractions to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. 7-8: Practice Buddy: Additional Practice Curriculum Standards: Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Add mixed numbers using equivalent fractions and a common denominator. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Add and subtract fractions (including mixed numbers) with unlike denominators. (May include multiple methods and representations.) Add and subtract decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Model addition and subtraction of fractions and decimals using a variety of representations. Estimate sums and differences of decimals and fractions to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. 7-8: Interactive Additional Practice Step 3: Assess & Differentiate 7-8: Practice Buddy: Additional Practice Curriculum Standards: Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Add mixed numbers using equivalent fractions and a common denominator. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Add and subtract fractions (including mixed numbers) with unlike denominators. (May include multiple methods and representations.) Add and subtract decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Model addition and subtraction of fractions and decimals using a variety of representations. Estimate sums and differences of decimals and fractions to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. 7-8: Enrichment Curriculum Standards: Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Add mixed numbers using equivalent fractions and a common denominator. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Add and subtract fractions (including mixed numbers) with unlike denominators. (May include multiple methods and representations.) Add and subtract decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Model addition and subtraction of fractions and decimals using a variety of representations. Estimate sums and differences of decimals and fractions to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. 7-8: Quick Check Curriculum Standards: Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Add mixed numbers using equivalent fractions and a common denominator. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Add and subtract fractions (including mixed numbers) with unlike denominators. (May include multiple methods and representations.) Add and subtract decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Model addition and subtraction of fractions and decimals using a variety of representations. Estimate sums and differences of decimals and fractions to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. 7-8: Lesson Self-Assessment 7-8: Reteach to Build Understanding Curriculum Standards: Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Add mixed numbers using equivalent fractions and a common denominator. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Add and subtract fractions (including mixed numbers) with unlike denominators. (May include multiple methods and representations.) Add and subtract decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Model addition and subtraction of fractions and decimals using a variety of representations. Estimate sums and differences of decimals and fractions to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. 7-8: Build Mathematical Literacy Curriculum Standards: Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 5 topics and texts, building on others’ ideas and expressing their own clearly. (a) Come to discussions prepared, having read or studied required material; explicitly draw on that preparation and other information known about the topic to explore ideas under discussion. (b) Follow agreed-upon rules for discussions and carry out assigned roles. (c) Pose and respond to specific questions by making comments that contribute to the discussion and elaborate on the remarks of others. (d) Review the key ideas expressed and draw conclusions in light of information and knowledge gained from the discussions. English language learners communicate for social and instructional purposes within the school setting. Summarize a written text read aloud or information presented in diverse media and formats, including visually, quantitatively, and orally. Summarize the points a speaker makes and explain how each claim is supported by reasons and evidence. Write informative/explanatory texts to examine a topic and convey ideas and information clearly. (a) Introduce a topic clearly, provide a general observation and focus, and group related information logically; include formatting (e.g., headings), illustrations, and multimedia when useful to aiding comprehension. (b) Develop the topic with facts, definitions, concrete details, quotations, or other information and examples related to the topic. (c) Link ideas within and across categories of information using words, phrases, and clauses (e.g., in contrast, especially). (d) Use precise language and domain-specific vocabulary to inform about or explain the topic. (e) Provide a concluding statement or section related to the information or explanation presented. English language learners communicate information, ideas and concepts necessary for academic success in the content area of Mathematics. 7-8: Enrichment 7-8: Digital Math Tool Activity 7-8: Pick a Project 7-8: Another Look Curriculum Standards: Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Add mixed numbers using equivalent fractions and a common denominator. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Add and subtract fractions (including mixed numbers) with unlike denominators. (May include multiple methods and representations.) Add and subtract decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Model addition and subtraction of fractions and decimals using a variety of representations. Estimate sums and differences of decimals and fractions to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. Spanish Resources 7-8: eText del Libro del estudiante 7-8: Repaso diario 7-8: Aprendizaje visual 7-8: Amigo de práctica: Práctica adicional 7-8: Práctica adicional interactiva 7-8: Refuerzo para mejorar la comprensión 7-8: Desarrollar la competencia matemática 7-8: Ampliación 7-9: Use Models to Subtract Mixed Numbers Interactive Student Edition: Grade 5 Lesson 7-9 Math Anytime 7-9: Daily Review Topic 7: Today's Challenge Step 1: Problem-Based Learning 7-9: Solve & Share Curriculum Standards: Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. English language learners communicate for social and instructional purposes within the school setting. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Use models to subtract mixed numbers. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Add and subtract fractions (including mixed numbers) with unlike denominators. (May include multiple methods and representations.) Add and subtract decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Model addition and subtraction of fractions and decimals using a variety of representations. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. Write informative/explanatory texts to examine a topic and convey ideas and information clearly. (a) Introduce a topic clearly, provide a general observation and focus, and group related information logically; include formatting (e.g., headings), illustrations, and multimedia when useful to aiding comprehension. (b) Develop the topic with facts, definitions, concrete details, quotations, or other information and examples related to the topic. (c) Link ideas within and across categories of information using words, phrases, and clauses (e.g., in contrast, especially). (d) Use precise language and domain- specific vocabulary to inform about or explain the topic. (e) Provide a concluding statement or section related to the information or explanation presented. English language learners communicate information, ideas and concepts necessary for academic success in the content area of Mathematics. Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 5 topics and texts, building on others’ ideas and expressing their own clearly. (a) Come to discussions prepared, having read or studied required material; explicitly draw on that preparation and other information known about the topic to explore ideas under discussion. (b) Follow agreed-upon rules for discussions and carry out assigned roles. (c) Pose and respond to specific questions by making comments that contribute to the discussion and elaborate on the remarks of others. (d) Review the key ideas expressed and draw conclusions in light of information and knowledge gained from the discussions. Summarize a written text read aloud or information presented in diverse media and formats, including visually, quantitatively, and orally. Summarize the points a speaker makes and explain how each claim is supported by reasons and evidence. Step 2: Visual Learning 7-9: Visual Learning Curriculum Standards: Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Use models to subtract mixed numbers. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Add and subtract fractions (including mixed numbers) with unlike denominators. (May include multiple methods and representations.) Add and subtract decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Model addition and subtraction of fractions and decimals using a variety of representations. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. Add and subtract fractions with like denominators with sums greater than 1 represented by mixed numbers using visual fraction models. 7-9: Convince Me! Curriculum Standards: Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Use models to subtract mixed numbers. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Add and subtract fractions (including mixed numbers) with unlike denominators. (May include multiple methods and representations.) Add and subtract decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Model addition and subtraction of fractions and decimals using a variety of representations. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. Practice and Problem Solving 7-9: Student Edition Practice Curriculum Standards: Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Use models to subtract mixed numbers. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Add and subtract fractions (including mixed numbers) with unlike denominators. (May include multiple methods and representations.) Add and subtract decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Model addition and subtraction of fractions and decimals using a variety of representations. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. 7-9: Practice Buddy: Independent Practice; Problem Solving Curriculum Standards: Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Use models to subtract mixed numbers. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Add and subtract fractions (including mixed numbers) with unlike denominators. (May include multiple methods and representations.) Add and subtract decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Model addition and subtraction of fractions and decimals using a variety of representations. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. 7-9: Practice Buddy: Additional Practice Curriculum Standards: Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Use models to subtract mixed numbers. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Add and subtract fractions (including mixed numbers) with unlike denominators. (May include multiple methods and representations.) Add and subtract decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Model addition and subtraction of fractions and decimals using a variety of representations. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. 7-9: Interactive Additional Practice Step 3: Assess & Differentiate 7-9: Practice Buddy: Additional Practice Curriculum Standards: Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Use models to subtract mixed numbers. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Add and subtract fractions (including mixed numbers) with unlike denominators. (May include multiple methods and representations.) Add and subtract decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Model addition and subtraction of fractions and decimals using a variety of representations. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. 7-9: Enrichment Curriculum Standards: Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Use models to subtract mixed numbers. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Add and subtract fractions (including mixed numbers) with unlike denominators. (May include multiple methods and representations.) Add and subtract decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Model addition and subtraction of fractions and decimals using a variety of representations. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. 7-9: Quick Check Curriculum Standards: Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Use models to subtract mixed numbers. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Add and subtract fractions (including mixed numbers) with unlike denominators. (May include multiple methods and representations.) Add and subtract decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Model addition and subtraction of fractions and decimals using a variety of representations. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. 7-9: Lesson Self-Assessment 7-9: Reteach to Build Understanding Curriculum Standards: Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Use models to subtract mixed numbers. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Add and subtract fractions (including mixed numbers) with unlike denominators. (May include multiple methods and representations.) Add and subtract decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Model addition and subtraction of fractions and decimals using a variety of representations. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. Add and subtract fractions with like denominators with sums greater than 1 represented by mixed numbers using visual fraction models. 7-9: Build Mathematical Literacy Curriculum Standards: Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 5 topics and texts, building on others’ ideas and expressing their own clearly. (a) Come to discussions prepared, having read or studied required material; explicitly draw on that preparation and other information known about the topic to explore ideas under discussion. (b) Follow agreed-upon rules for discussions and carry out assigned roles. (c) Pose and respond to specific questions by making comments that contribute to the discussion and elaborate on the remarks of others. (d) Review the key ideas expressed and draw conclusions in light of information and knowledge gained from the discussions. English language learners communicate for social and instructional purposes within the school setting. Summarize a written text read aloud or information presented in diverse media and formats, including visually, quantitatively, and orally. Summarize the points a speaker makes and explain how each claim is supported by reasons and evidence. Write informative/explanatory texts to examine a topic and convey ideas and information clearly. (a) Introduce a topic clearly, provide a general observation and focus, and group related information logically; include formatting (e.g., headings), illustrations, and multimedia when useful to aiding comprehension. (b) Develop the topic with facts, definitions, concrete details, quotations, or other information and examples related to the topic. (c) Link ideas within and across categories of information using words, phrases, and clauses (e.g., in contrast, especially). (d) Use precise language and domain-specific vocabulary to inform about or explain the topic. (e) Provide a concluding statement or section related to the information or explanation presented. English language learners communicate information, ideas and concepts necessary for academic success in the content area of Mathematics. 7-9: Enrichment 7-9: Digital Math Tool Activity 7-9: enVision STEM Activity Curriculum Standards: Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Use models to subtract mixed numbers. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Add and subtract fractions (including mixed numbers) with unlike denominators. (May include multiple methods and representations.) Add and subtract decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Model addition and subtraction of fractions and decimals using a variety of representations. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. 7-9: Another Look Curriculum Standards: Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Use models to subtract mixed numbers. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Add and subtract fractions (including mixed numbers) with unlike denominators. (May include multiple methods and representations.) Add and subtract decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Model addition and subtraction of fractions and decimals using a variety of representations. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. Add and subtract fractions with like denominators with sums greater than 1 represented by mixed numbers using visual fraction models. Spanish Resources 7-9: eText del Libro del estudiante 7-9: Repaso diario 7-9: Aprendizaje visual 7-9: Amigo de práctica: Práctica adicional 7-9: Práctica adicional interactiva 7-9: Refuerzo para mejorar la comprensión 7-9: Desarrollar la competencia matemática 7-9: Ampliación 7-10: Subtract Mixed Numbers Interactive Student Edition: Grade 5 Lesson 7-10 Math Anytime 7-10: Daily Review Topic 7: Today's Challenge Step 1: Problem-Based Learning 7-10: Solve & Share Curriculum Standards: Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. English language learners communicate for social and instructional purposes within the school setting. Write informative/explanatory texts to examine a topic and convey ideas and information clearly. (a) Introduce a topic clearly, provide a general observation and focus, and group related information logically; include formatting (e.g., headings), illustrations, and multimedia when useful to aiding comprehension. (b) Develop the topic with facts, definitions, concrete details, quotations, or other information and examples related to the topic. (c) Link ideas within and across categories of information using words, phrases, and clauses (e.g., in contrast, especially). (d) Use precise language and domain-specific vocabulary to inform about or explain the topic. (e) Provide a concluding statement or section related to the information or explanation presented. English language learners communicate information, ideas and concepts necessary for academic success in the content area of Mathematics. Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 5 topics and texts, building on others’ ideas and expressing their own clearly. (a) Come to discussions prepared, having read or studied required material; explicitly draw on that preparation and other information known about the topic to explore ideas under discussion. (b) Follow agreed-upon rules for discussions and carry out assigned roles. (c) Pose and respond to specific questions by making comments that contribute to the discussion and elaborate on the remarks of others. (d) Review the key ideas expressed and draw conclusions in light of information and knowledge gained from the discussions. Summarize a written text read aloud or information presented in diverse media and formats, including visually, quantitatively, and orally. Summarize the points a speaker makes and explain how each claim is supported by reasons and evidence. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Subtract mixed numbers using equivalent fractions and a common denominator. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Add and subtract fractions (including mixed numbers) with unlike denominators. (May include multiple methods and representations.) Add and subtract decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Model addition and subtraction of fractions and decimals using a variety of representations. Estimate sums and differences of decimals and fractions to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. Step 2: Visual Learning 7-10: Visual Learning Curriculum Standards: Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Subtract mixed numbers using equivalent fractions and a common denominator. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Add and subtract fractions (including mixed numbers) with unlike denominators. (May include multiple methods and representations.) Add and subtract decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Model addition and subtraction of fractions and decimals using a variety of representations. Estimate sums and differences of decimals and fractions to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. 7-10: Convince Me! Curriculum Standards: Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Subtract mixed numbers using equivalent fractions and a common denominator. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Add and subtract fractions (including mixed numbers) with unlike denominators. (May include multiple methods and representations.) Add and subtract decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Model addition and subtraction of fractions and decimals using a variety of representations. Estimate sums and differences of decimals and fractions to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. Practice and Problem Solving 7-10: Student Edition Practice Curriculum Standards: Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Subtract mixed numbers using equivalent fractions and a common denominator. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Add and subtract fractions (including mixed numbers) with unlike denominators. (May include multiple methods and representations.) Add and subtract decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Model addition and subtraction of fractions and decimals using a variety of representations. Estimate sums and differences of decimals and fractions to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. 7-10: Practice Buddy: Independent Practice; Problem Solving Curriculum Standards: Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Subtract mixed numbers using equivalent fractions and a common denominator. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Add and subtract fractions (including mixed numbers) with unlike denominators. (May include multiple methods and representations.) Add and subtract decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Model addition and subtraction of fractions and decimals using a variety of representations. Estimate sums and differences of decimals and fractions to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. 7-10: Practice Buddy: Additional Practice Curriculum Standards: Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Subtract mixed numbers using equivalent fractions and a common denominator. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Add and subtract fractions (including mixed numbers) with unlike denominators. (May include multiple methods and representations.) Add and subtract decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Model addition and subtraction of fractions and decimals using a variety of representations. Estimate sums and differences of decimals and fractions to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. 7-10: Interactive Additional Practice Step 3: Assess & Differentiate 7-10: Practice Buddy: Additional Practice Curriculum Standards: Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Subtract mixed numbers using equivalent fractions and a common denominator. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Add and subtract fractions (including mixed numbers) with unlike denominators. (May include multiple methods and representations.) Add and subtract decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Model addition and subtraction of fractions and decimals using a variety of representations. Estimate sums and differences of decimals and fractions to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. 7-10: Enrichment Curriculum Standards: Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Subtract mixed numbers using equivalent fractions and a common denominator. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Add and subtract fractions (including mixed numbers) with unlike denominators. (May include multiple methods and representations.) Add and subtract decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Model addition and subtraction of fractions and decimals using a variety of representations. Estimate sums and differences of decimals and fractions to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. 7-10: Quick Check Curriculum Standards: Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Subtract mixed numbers using equivalent fractions and a common denominator. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Add and subtract fractions (including mixed numbers) with unlike denominators. (May include multiple methods and representations.) Add and subtract decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Model addition and subtraction of fractions and decimals using a variety of representations. Estimate sums and differences of decimals and fractions to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. 7-10: Lesson Self-Assessment 7-10: Reteach to Build Understanding Curriculum Standards: Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Subtract mixed numbers using equivalent fractions and a common denominator. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Add and subtract fractions (including mixed numbers) with unlike denominators. (May include multiple methods and representations.) Add and subtract decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Model addition and subtraction of fractions and decimals using a variety of representations. Estimate sums and differences of decimals and fractions to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. 7-10: Build Mathematical Literacy Curriculum Standards: Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 5 topics and texts, building on others’ ideas and expressing their own clearly. (a) Come to discussions prepared, having read or studied required material; explicitly draw on that preparation and other information known about the topic to explore ideas under discussion. (b) Follow agreed-upon rules for discussions and carry out assigned roles. (c) Pose and respond to specific questions by making comments that contribute to the discussion and elaborate on the remarks of others. (d) Review the key ideas expressed and draw conclusions in light of information and knowledge gained from the discussions. English language learners communicate for social and instructional purposes within the school setting. Summarize a written text read aloud or information presented in diverse media and formats, including visually, quantitatively, and orally. Summarize the points a speaker makes and explain how each claim is supported by reasons and evidence. Write informative/explanatory texts to examine a topic and convey ideas and information clearly. (a) Introduce a topic clearly, provide a general observation and focus, and group related information logically; include formatting (e.g., headings), illustrations, and multimedia when useful to aiding comprehension. (b) Develop the topic with facts, definitions, concrete details, quotations, or other information and examples related to the topic. (c) Link ideas within and across categories of information using words, phrases, and clauses (e.g., in contrast, especially). (d) Use precise language and domain-specific vocabulary to inform about or explain the topic. (e) Provide a concluding statement or section related to the information or explanation presented. English language learners communicate information, ideas and concepts necessary for academic success in the content area of Mathematics. 7-10: Enrichment 7-10: Digital Math Tool Activity 7-10: Pick a Project 7-10: Another Look Curriculum Standards: Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Subtract mixed numbers using equivalent fractions and a common denominator. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Add and subtract fractions (including mixed numbers) with unlike denominators. (May include multiple methods and representations.) Add and subtract decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Model addition and subtraction of fractions and decimals using a variety of representations. Estimate sums and differences of decimals and fractions to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. Spanish Resources 7-10: eText del Libro del estudiante 7-10: Repaso diario 7-10: Aprendizaje visual 7-10: Amigo de práctica: Práctica adicional 7-10: Práctica adicional interactiva 7-10: Refuerzo para mejorar la comprensión 7-10: Desarrollar la competencia matemática 7-10: Ampliación 7-11: Add and Subtract Mixed Numbers Interactive Student Edition: Grade 5 Lesson 7-11 Math Anytime 7-11: Daily Review Topic 7: Today's Challenge Step 1: Problem-Based Learning 7-11: Solve & Share Curriculum Standards: Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. English language learners communicate for social and instructional purposes within the school setting. Write informative/explanatory texts to examine a topic and convey ideas and information clearly. (a) Introduce a topic clearly, provide a general observation and focus, and group related information logically; include formatting (e.g., headings), illustrations, and multimedia when useful to aiding comprehension. (b) Develop the topic with facts, definitions, concrete details, quotations, or other information and examples related to the topic. (c) Link ideas within and across categories of information using words, phrases, and clauses (e.g., in contrast, especially). (d) Use precise language and domain-specific vocabulary to inform about or explain the topic. (e) Provide a concluding statement or section related to the information or explanation presented. English language learners communicate information, ideas and concepts necessary for academic success in the content area of Mathematics. Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 5 topics and texts, building on others’ ideas and expressing their own clearly. (a) Come to discussions prepared, having read or studied required material; explicitly draw on that preparation and other information known about the topic to explore ideas under discussion. (b) Follow agreed-upon rules for discussions and carry out assigned roles. (c) Pose and respond to specific questions by making comments that contribute to the discussion and elaborate on the remarks of others. (d) Review the key ideas expressed and draw conclusions in light of information and knowledge gained from the discussions. Summarize a written text read aloud or information presented in diverse media and formats, including visually, quantitatively, and orally. Summarize the points a speaker makes and explain how each claim is supported by reasons and evidence. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Add and subtract mixed numbers using equivalent fractions and a common denominator. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Add and subtract fractions (including mixed numbers) with unlike denominators. (May include multiple methods and representations.) Add and subtract decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Estimate sums and differences of decimals and fractions to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. Step 2: Visual Learning 7-11: Visual Learning Curriculum Standards: Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Add and subtract mixed numbers using equivalent fractions and a common denominator. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Add and subtract fractions (including mixed numbers) with unlike denominators. (May include multiple methods and representations.) Add and subtract decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Estimate sums and differences of decimals and fractions to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. 7-11: Convince Me! Curriculum Standards: Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Add and subtract mixed numbers using equivalent fractions and a common denominator. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Add and subtract fractions (including mixed numbers) with unlike denominators. (May include multiple methods and representations.) Add and subtract decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Estimate sums and differences of decimals and fractions to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. Practice and Problem Solving 7-11: Student Edition Practice Curriculum Standards: Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Add and subtract mixed numbers using equivalent fractions and a common denominator. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Add and subtract fractions (including mixed numbers) with unlike denominators. (May include multiple methods and representations.) Add and subtract decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Estimate sums and differences of decimals and fractions to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. 7-11: Practice Buddy: Independent Practice; Problem Solving Curriculum Standards: Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Add and subtract mixed numbers using equivalent fractions and a common denominator. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Add and subtract fractions (including mixed numbers) with unlike denominators. (May include multiple methods and representations.) Add and subtract decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Estimate sums and differences of decimals and fractions to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. 7-11: Practice Buddy: Additional Practice Curriculum Standards: Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Add and subtract mixed numbers using equivalent fractions and a common denominator. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Add and subtract fractions (including mixed numbers) with unlike denominators. (May include multiple methods and representations.) Add and subtract decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Estimate sums and differences of decimals and fractions to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. 7-11: Interactive Additional Practice Step 3: Assess & Differentiate 7-11: Practice Buddy: Additional Practice Curriculum Standards: Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Add and subtract mixed numbers using equivalent fractions and a common denominator. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Add and subtract fractions (including mixed numbers) with unlike denominators. (May include multiple methods and representations.) Add and subtract decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Estimate sums and differences of decimals and fractions to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. 7-11: Enrichment Curriculum Standards: Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Add and subtract mixed numbers using equivalent fractions and a common denominator. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Add and subtract fractions (including mixed numbers) with unlike denominators. (May include multiple methods and representations.) Add and subtract decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Estimate sums and differences of decimals and fractions to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. 7-11: Quick Check Curriculum Standards: Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Add and subtract mixed numbers using equivalent fractions and a common denominator. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Add and subtract fractions (including mixed numbers) with unlike denominators. (May include multiple methods and representations.) Add and subtract decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Estimate sums and differences of decimals and fractions to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. 7-11: Lesson Self-Assessment 7-11: Reteach to Build Understanding Curriculum Standards: Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Add and subtract mixed numbers using equivalent fractions and a common denominator. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Add and subtract fractions (including mixed numbers) with unlike denominators. (May include multiple methods and representations.) Add and subtract decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Estimate sums and differences of decimals and fractions to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. 7-11: Build Mathematical Literacy Curriculum Standards: Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 5 topics and texts, building on others’ ideas and expressing their own clearly. (a) Come to discussions prepared, having read or studied required material; explicitly draw on that preparation and other information known about the topic to explore ideas under discussion. (b) Follow agreed-upon rules for discussions and carry out assigned roles. (c) Pose and respond to specific questions by making comments that contribute to the discussion and elaborate on the remarks of others. (d) Review the key ideas expressed and draw conclusions in light of information and knowledge gained from the discussions. English language learners communicate for social and instructional purposes within the school setting. Summarize a written text read aloud or information presented in diverse media and formats, including visually, quantitatively, and orally. Summarize the points a speaker makes and explain how each claim is supported by reasons and evidence. Write informative/explanatory texts to examine a topic and convey ideas and information clearly. (a) Introduce a topic clearly, provide a general observation and focus, and group related information logically; include formatting (e.g., headings), illustrations, and multimedia when useful to aiding comprehension. (b) Develop the topic with facts, definitions, concrete details, quotations, or other information and examples related to the topic. (c) Link ideas within and across categories of information using words, phrases, and clauses (e.g., in contrast, especially). (d) Use precise language and domain-specific vocabulary to inform about or explain the topic. (e) Provide a concluding statement or section related to the information or explanation presented. English language learners communicate information, ideas and concepts necessary for academic success in the content area of Mathematics. 7-11: Enrichment Game: Fluency - Multiply Multi-Digit Whole Numbers 7-11: Problem-Solving Reading Activity Curriculum Standards: Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Add and subtract mixed numbers using equivalent fractions and a common denominator. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Add and subtract fractions (including mixed numbers) with unlike denominators. (May include multiple methods and representations.) Add and subtract decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Estimate sums and differences of decimals and fractions to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. 7-11: Another Look Curriculum Standards: Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Add and subtract mixed numbers using equivalent fractions and a common denominator. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Add and subtract fractions (including mixed numbers) with unlike denominators. (May include multiple methods and representations.) Add and subtract decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Estimate sums and differences of decimals and fractions to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. Spanish Resources 7-11: eText del Libro del estudiante 7-11: Repaso diario 7-11: Aprendizaje visual 7-11: Amigo de práctica: Práctica adicional 7-11: Práctica adicional interactiva 7-11: Refuerzo para mejorar la comprensión 7-11: Desarrollar la competencia matemática 7-11: Ampliación Topic 7: 3-Act Math: The Gif Recipe Interactive Student Edition: Grade 5, Topic 7: 3-Act Math Mathematical Modeling Topic 7: 3-Act Math: The Gif Recipe, Act 1 Topic 7: 3-Act Math: The Gif Recipe, Act 2 Topic 7: 3-Act Math: The Gif Recipe, Act 3 Topic 7: 3-Act Math: The Gif Recipe, Sequel 7-12: Problem Solving: Model with Math Interactive Student Edition: Grade 5 Lesson 7-12 Math Anytime 7-12: Daily Review Topic 7: Today's Challenge Step 1: Problem-Based Learning 7-12: Solve & Share Curriculum Standards: Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Model with mathematics. English language learners communicate for social and instructional purposes within the school setting. Write informative/explanatory texts to examine a topic and convey ideas and information clearly. (a) Introduce a topic clearly, provide a general observation and focus, and group related information logically; include formatting (e.g., headings), illustrations, and multimedia when useful to aiding comprehension. (b) Develop the topic with facts, definitions, concrete details, quotations, or other information and examples related to the topic. (c) Link ideas within and across categories of information using words, phrases, and clauses (e.g., in contrast, especially). (d) Use precise language and domain- specific vocabulary to inform about or explain the topic. (e) Provide a concluding statement or section related to the information or explanation presented. English language learners communicate information, ideas and concepts necessary for academic success in the content area of Mathematics. Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 5 topics and texts, building on others’ ideas and expressing their own clearly. (a) Come to discussions prepared, having read or studied required material; explicitly draw on that preparation and other information known about the topic to explore ideas under discussion. (b) Follow agreed-upon rules for discussions and carry out assigned roles. (c) Pose and respond to specific questions by making comments that contribute to the discussion and elaborate on the remarks of others. (d) Review the key ideas expressed and draw conclusions in light of information and knowledge gained from the discussions. Summarize a written text read aloud or information presented in diverse media and formats, including visually, quantitatively, and orally. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. Model with mathematics. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Model with mathematics. Mathematically proficient students can apply the mathematics they know to solve problems arising in everyday life, society, and the workplace. In early grades, this might be as simple as writing an addition equation to describe a situation. In middle grades, a student might apply proportional reasoning to plan a school event or analyze a problem in the community. By high school, a student might use geometry to solve a design problem or use a function to describe how one quantity of interest depends on another. Mathematically proficient students who can apply what they know are comfortable making assumptions and approximations to simplify a complicated situation, realizing that these may need revision later. They are able to identify important quantities in a practical situation and map their relationships using such tools as diagrams, two-way tables, graphs, flowcharts and formulas. They can analyze those relationships mathematically to draw conclusions. They routinely interpret their mathematical results in the context of the situation and reflect on whether the results make sense, possibly improving the model if it has not served its purpose. Represent a problem situation with a mathematical model. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Model with mathematics. Model with mathematics. Add and subtract fractions (including mixed numbers) with unlike denominators. (May include multiple methods and representations.) Model with mathematics. Add and subtract decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Model addition and subtraction of fractions and decimals using a variety of representations. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. Summarize the points a speaker makes and explain how each claim is supported by reasons and evidence. Step 2: Visual Learning 7-12: Visual Learning Curriculum Standards: Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Model with mathematics. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. Model with mathematics. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Model with mathematics. Mathematically proficient students can apply the mathematics they know to solve problems arising in everyday life, society, and the workplace. In early grades, this might be as simple as writing an addition equation to describe a situation. In middle grades, a student might apply proportional reasoning to plan a school event or analyze a problem in the community. By high school, a student might use geometry to solve a design problem or use a function to describe how one quantity of interest depends on another. Mathematically proficient students who can apply what they know are comfortable making assumptions and approximations to simplify a complicated situation, realizing that these may need revision later. They are able to identify important quantities in a practical situation and map their relationships using such tools as diagrams, two-way tables, graphs, flowcharts and formulas. They can analyze those relationships mathematically to draw conclusions. They routinely interpret their mathematical results in the context of the situation and reflect on whether the results make sense, possibly improving the model if it has not served its purpose. Represent a problem situation with a mathematical model. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Model with mathematics. Model with mathematics. Add and subtract fractions (including mixed numbers) with unlike denominators. (May include multiple methods and representations.) Model with mathematics. Add and subtract decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Model addition and subtraction of fractions and decimals using a variety of representations. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. Solve word problems involving the addition and subtraction of fractions using visual fraction models. 7-12: Convince Me! Curriculum Standards: Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Model with mathematics. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. Model with mathematics. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Model with mathematics. Mathematically proficient students can apply the mathematics they know to solve problems arising in everyday life, society, and the workplace. In early grades, this might be as simple as writing an addition equation to describe a situation. In middle grades, a student might apply proportional reasoning to plan a school event or analyze a problem in the community. By high school, a student might use geometry to solve a design problem or use a function to describe how one quantity of interest depends on another. Mathematically proficient students who can apply what they know are comfortable making assumptions and approximations to simplify a complicated situation, realizing that these may need revision later. They are able to identify important quantities in a practical situation and map their relationships using such tools as diagrams, two-way tables, graphs, flowcharts and formulas. They can analyze those relationships mathematically to draw conclusions. They routinely interpret their mathematical results in the context of the situation and reflect on whether the results make sense, possibly improving the model if it has not served its purpose. Represent a problem situation with a mathematical model. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Model with mathematics. Model with mathematics. Add and subtract fractions (including mixed numbers) with unlike denominators. (May include multiple methods and representations.) Model with mathematics. Add and subtract decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Model addition and subtraction of fractions and decimals using a variety of representations. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. Practice and Problem Solving 7-12: Student Edition Practice Curriculum Standards: Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Model with mathematics. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. Model with mathematics. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Model with mathematics. Mathematically proficient students can apply the mathematics they know to solve problems arising in everyday life, society, and the workplace. In early grades, this might be as simple as writing an addition equation to describe a situation. In middle grades, a student might apply proportional reasoning to plan a school event or analyze a problem in the community. By high school, a student might use geometry to solve a design problem or use a function to describe how one quantity of interest depends on another. Mathematically proficient students who can apply what they know are comfortable making assumptions and approximations to simplify a complicated situation, realizing that these may need revision later. They are able to identify important quantities in a practical situation and map their relationships using such tools as diagrams, two-way tables, graphs, flowcharts and formulas. They can analyze those relationships mathematically to draw conclusions. They routinely interpret their mathematical results in the context of the situation and reflect on whether the results make sense, possibly improving the model if it has not served its purpose. Represent a problem situation with a mathematical model. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Model with mathematics. Model with mathematics. Add and subtract fractions (including mixed numbers) with unlike denominators. (May include multiple methods and representations.) Model with mathematics. Add and subtract decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Model addition and subtraction of fractions and decimals using a variety of representations. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. 7-12: Practice Buddy: Independent Practice; Problem Solving Curriculum Standards: Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Model with mathematics. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. Model with mathematics. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Model with mathematics. Mathematically proficient students can apply the mathematics they know to solve problems arising in everyday life, society, and the workplace. In early grades, this might be as simple as writing an addition equation to describe a situation. In middle grades, a student might apply proportional reasoning to plan a school event or analyze a problem in the community. By high school, a student might use geometry to solve a design problem or use a function to describe how one quantity of interest depends on another. Mathematically proficient students who can apply what they know are comfortable making assumptions and approximations to simplify a complicated situation, realizing that these may need revision later. They are able to identify important quantities in a practical situation and map their relationships using such tools as diagrams, two-way tables, graphs, flowcharts and formulas. They can analyze those relationships mathematically to draw conclusions. They routinely interpret their mathematical results in the context of the situation and reflect on whether the results make sense, possibly improving the model if it has not served its purpose. Represent a problem situation with a mathematical model. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Model with mathematics. Model with mathematics. Add and subtract fractions (including mixed numbers) with unlike denominators. (May include multiple methods and representations.) Model with mathematics. Add and subtract decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Model addition and subtraction of fractions and decimals using a variety of representations. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. 7-12: Practice Buddy: Additional Practice Curriculum Standards: Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Model with mathematics. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. Model with mathematics. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Model with mathematics. Mathematically proficient students can apply the mathematics they know to solve problems arising in everyday life, society, and the workplace. In early grades, this might be as simple as writing an addition equation to describe a situation. In middle grades, a student might apply proportional reasoning to plan a school event or analyze a problem in the community. By high school, a student might use geometry to solve a design problem or use a function to describe how one quantity of interest depends on another. Mathematically proficient students who can apply what they know are comfortable making assumptions and approximations to simplify a complicated situation, realizing that these may need revision later. They are able to identify important quantities in a practical situation and map their relationships using such tools as diagrams, two-way tables, graphs, flowcharts and formulas. They can analyze those relationships mathematically to draw conclusions. They routinely interpret their mathematical results in the context of the situation and reflect on whether the results make sense, possibly improving the model if it has not served its purpose. Represent a problem situation with a mathematical model. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Model with mathematics. Model with mathematics. Add and subtract fractions (including mixed numbers) with unlike denominators. (May include multiple methods and representations.) Model with mathematics. Add and subtract decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Model addition and subtraction of fractions and decimals using a variety of representations. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. 7-12: Interactive Additional Practice Step 3: Assess & Differentiate 7-12: Practice Buddy: Additional Practice Curriculum Standards: Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Model with mathematics. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. Model with mathematics. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Model with mathematics. Mathematically proficient students can apply the mathematics they know to solve problems arising in everyday life, society, and the workplace. In early grades, this might be as simple as writing an addition equation to describe a situation. In middle grades, a student might apply proportional reasoning to plan a school event or analyze a problem in the community. By high school, a student might use geometry to solve a design problem or use a function to describe how one quantity of interest depends on another. Mathematically proficient students who can apply what they know are comfortable making assumptions and approximations to simplify a complicated situation, realizing that these may need revision later. They are able to identify important quantities in a practical situation and map their relationships using such tools as diagrams, two-way tables, graphs, flowcharts and formulas. They can analyze those relationships mathematically to draw conclusions. They routinely interpret their mathematical results in the context of the situation and reflect on whether the results make sense, possibly improving the model if it has not served its purpose. Represent a problem situation with a mathematical model. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Model with mathematics. Model with mathematics. Add and subtract fractions (including mixed numbers) with unlike denominators. (May include multiple methods and representations.) Model with mathematics. Add and subtract decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Model addition and subtraction of fractions and decimals using a variety of representations. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. 7-12: Enrichment Curriculum Standards: Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Model with mathematics. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. Model with mathematics. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Model with mathematics. Mathematically proficient students can apply the mathematics they know to solve problems arising in everyday life, society, and the workplace. In early grades, this might be as simple as writing an addition equation to describe a situation. In middle grades, a student might apply proportional reasoning to plan a school event or analyze a problem in the community. By high school, a student might use geometry to solve a design problem or use a function to describe how one quantity of interest depends on another. Mathematically proficient students who can apply what they know are comfortable making assumptions and approximations to simplify a complicated situation, realizing that these may need revision later. They are able to identify important quantities in a practical situation and map their relationships using such tools as diagrams, two-way tables, graphs, flowcharts and formulas. They can analyze those relationships mathematically to draw conclusions. They routinely interpret their mathematical results in the context of the situation and reflect on whether the results make sense, possibly improving the model if it has not served its purpose. Represent a problem situation with a mathematical model. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Model with mathematics. Model with mathematics. Add and subtract fractions (including mixed numbers) with unlike denominators. (May include multiple methods and representations.) Model with mathematics. Add and subtract decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Model addition and subtraction of fractions and decimals using a variety of representations. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. 7-12: Quick Check Curriculum Standards: Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Model with mathematics. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. Model with mathematics. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Model with mathematics. Mathematically proficient students can apply the mathematics they know to solve problems arising in everyday life, society, and the workplace. In early grades, this might be as simple as writing an addition equation to describe a situation. In middle grades, a student might apply proportional reasoning to plan a school event or analyze a problem in the community. By high school, a student might use geometry to solve a design problem or use a function to describe how one quantity of interest depends on another. Mathematically proficient students who can apply what they know are comfortable making assumptions and approximations to simplify a complicated situation, realizing that these may need revision later. They are able to identify important quantities in a practical situation and map their relationships using such tools as diagrams, two-way tables, graphs, flowcharts and formulas. They can analyze those relationships mathematically to draw conclusions. They routinely interpret their mathematical results in the context of the situation and reflect on whether the results make sense, possibly improving the model if it has not served its purpose. Represent a problem situation with a mathematical model. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Model with mathematics. Model with mathematics. Add and subtract fractions (including mixed numbers) with unlike denominators. (May include multiple methods and representations.) Model with mathematics. Add and subtract decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Model addition and subtraction of fractions and decimals using a variety of representations. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. 7-12: Lesson Self-Assessment 7-12: Reteach to Build Understanding Curriculum Standards: Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Model with mathematics. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. Model with mathematics. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Model with mathematics. Mathematically proficient students can apply the mathematics they know to solve problems arising in everyday life, society, and the workplace. In early grades, this might be as simple as writing an addition equation to describe a situation. In middle grades, a student might apply proportional reasoning to plan a school event or analyze a problem in the community. By high school, a student might use geometry to solve a design problem or use a function to describe how one quantity of interest depends on another. Mathematically proficient students who can apply what they know are comfortable making assumptions and approximations to simplify a complicated situation, realizing that these may need revision later. They are able to identify important quantities in a practical situation and map their relationships using such tools as diagrams, two-way tables, graphs, flowcharts and formulas. They can analyze those relationships mathematically to draw conclusions. They routinely interpret their mathematical results in the context of the situation and reflect on whether the results make sense, possibly improving the model if it has not served its purpose. Represent a problem situation with a mathematical model. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Model with mathematics. Model with mathematics. Add and subtract fractions (including mixed numbers) with unlike denominators. (May include multiple methods and representations.) Model with mathematics. Add and subtract decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Model addition and subtraction of fractions and decimals using a variety of representations. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. Solve word problems involving the addition and subtraction of fractions using visual fraction models. 7-12: Build Mathematical Literacy Curriculum Standards: Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 5 topics and texts, building on others’ ideas and expressing their own clearly. (a) Come to discussions prepared, having read or studied required material; explicitly draw on that preparation and other information known about the topic to explore ideas under discussion. (b) Follow agreed-upon rules for discussions and carry out assigned roles. (c) Pose and respond to specific questions by making comments that contribute to the discussion and elaborate on the remarks of others. (d) Review the key ideas expressed and draw conclusions in light of information and knowledge gained from the discussions. English language learners communicate for social and instructional purposes within the school setting. Summarize a written text read aloud or information presented in diverse media and formats, including visually, quantitatively, and orally. Summarize the points a speaker makes and explain how each claim is supported by reasons and evidence. Write informative/explanatory texts to examine a topic and convey ideas and information clearly. (a) Introduce a topic clearly, provide a general observation and focus, and group related information logically; include formatting (e.g., headings), illustrations, and multimedia when useful to aiding comprehension. (b) Develop the topic with facts, definitions, concrete details, quotations, or other information and examples related to the topic. (c) Link ideas within and across categories of information using words, phrases, and clauses (e.g., in contrast, especially). (d) Use precise language and domain-specific vocabulary to inform about or explain the topic. (e) Provide a concluding statement or section related to the information or explanation presented. English language learners communicate information, ideas and concepts necessary for academic success in the content area of Mathematics. 7-12: Enrichment 7-12: Digital Math Tool Activity 7-12: enVision STEM Activity Curriculum Standards: Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Model with mathematics. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. Model with mathematics. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Model with mathematics. Mathematically proficient students can apply the mathematics they know to solve problems arising in everyday life, society, and the workplace. In early grades, this might be as simple as writing an addition equation to describe a situation. In middle grades, a student might apply proportional reasoning to plan a school event or analyze a problem in the community. By high school, a student might use geometry to solve a design problem or use a function to describe how one quantity of interest depends on another. Mathematically proficient students who can apply what they know are comfortable making assumptions and approximations to simplify a complicated situation, realizing that these may need revision later. They are able to identify important quantities in a practical situation and map their relationships using such tools as diagrams, two-way tables, graphs, flowcharts and formulas. They can analyze those relationships mathematically to draw conclusions. They routinely interpret their mathematical results in the context of the situation and reflect on whether the results make sense, possibly improving the model if it has not served its purpose. Represent a problem situation with a mathematical model. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Model with mathematics. Model with mathematics. Add and subtract fractions (including mixed numbers) with unlike denominators. (May include multiple methods and representations.) Model with mathematics. Add and subtract decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Model addition and subtraction of fractions and decimals using a variety of representations. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. 7-12: Another Look Curriculum Standards: Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Model with mathematics. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. Model with mathematics. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Model with mathematics. Mathematically proficient students can apply the mathematics they know to solve problems arising in everyday life, society, and the workplace. In early grades, this might be as simple as writing an addition equation to describe a situation. In middle grades, a student might apply proportional reasoning to plan a school event or analyze a problem in the community. By high school, a student might use geometry to solve a design problem or use a function to describe how one quantity of interest depends on another. Mathematically proficient students who can apply what they know are comfortable making assumptions and approximations to simplify a complicated situation, realizing that these may need revision later. They are able to identify important quantities in a practical situation and map their relationships using such tools as diagrams, two-way tables, graphs, flowcharts and formulas. They can analyze those relationships mathematically to draw conclusions. They routinely interpret their mathematical results in the context of the situation and reflect on whether the results make sense, possibly improving the model if it has not served its purpose. Represent a problem situation with a mathematical model. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Model with mathematics. Model with mathematics. Add and subtract fractions (including mixed numbers) with unlike denominators. (May include multiple methods and representations.) Model with mathematics. Add and subtract decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Model addition and subtraction of fractions and decimals using a variety of representations. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. Solve word problems involving the addition and subtraction of fractions using visual fraction models. Spanish Resources 7-12: eText del Libro del estudiante 7-12: Repaso diario 7-12: Aprendizaje visual 7-12: Amigo de práctica: Práctica adicional 7-12: Práctica adicional interactiva 7-12: Refuerzo para mejorar la comprensión 7-12: Desarrollar la competencia matemática 7-12: Ampliación Topic 7: End of Topic Interactive Student Edition: End of Topic 6 Topic 7: Fluency Practice Activity Interactive Student Edition: Topic 7 Assessment Practice Interactive Student Edition: Topic 7 Performance Task Topic 7 Performance Task Topic 7 Assessment 8-1: Center Games 7-2: Visual Learning Curriculum Standards: Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Find common denominators for fractions with unlike denominators. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Add and subtract fractions (including mixed numbers) with unlike denominators. (May include multiple methods and representations.) Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. 7-3: Visual Learning Curriculum Standards: Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Add fractions with unlike denominators using equivalent fractions with a common denominator. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Add and subtract fractions (including mixed numbers) with unlike denominators. (May include multiple methods and representations.) Add and subtract decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Model addition and subtraction of fractions and decimals using a variety of representations. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. 7-7: Visual Learning Curriculum Standards: Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Add mixed numbers using models. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Add and subtract fractions (including mixed numbers) with unlike denominators. (May include multiple methods and representations.) Add and subtract decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Model addition and subtraction of fractions and decimals using a variety of representations. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. 7-9: Visual Learning Curriculum Standards: Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Use models to subtract mixed numbers. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Add and subtract fractions (including mixed numbers) with unlike denominators. (May include multiple methods and representations.) Add and subtract decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Model addition and subtraction of fractions and decimals using a variety of representations. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. 7-10: Visual Learning Curriculum Standards: Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Subtract mixed numbers using equivalent fractions and a common denominator. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Add and subtract fractions (including mixed numbers) with unlike denominators. (May include multiple methods and representations.) Add and subtract decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Model addition and subtraction of fractions and decimals using a variety of representations. Estimate sums and differences of decimals and fractions to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. 7-1: Visual Learning Curriculum Standards: Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Estimate sums and differences of fractions by using the nearest half or whole number. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Add and subtract fractions (including mixed numbers) with unlike denominators. (May include multiple methods and representations.) Estimate sums and differences of decimals and fractions to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. 7-11: Visual Learning Curriculum Standards: Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Add and subtract mixed numbers using equivalent fractions and a common denominator. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Add and subtract fractions (including mixed numbers) with unlike denominators. (May include multiple methods and representations.) Add and subtract decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Estimate sums and differences of decimals and fractions to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. 7-5: Visual Learning Curriculum Standards: Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Write equivalent fractions to add and subtract fractions with unlike denominators. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Add and subtract fractions (including mixed numbers) with unlike denominators. (May include multiple methods and representations.) Add and subtract decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Model addition and subtraction of fractions and decimals using a variety of representations. Estimate sums and differences of decimals and fractions to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. 7-6: Visual Learning Curriculum Standards: Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Estimate sums and differences of fractions and mixed numbers. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Add and subtract fractions (including mixed numbers) with unlike denominators. (May include multiple methods and representations.) Estimate sums and differences of decimals and fractions to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. 7-12: Visual Learning Curriculum Standards: Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Model with mathematics. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. Model with mathematics. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Model with mathematics. Mathematically proficient students can apply the mathematics they know to solve problems arising in everyday life, society, and the workplace. In early grades, this might be as simple as writing an addition equation to describe a situation. In middle grades, a student might apply proportional reasoning to plan a school event or analyze a problem in the community. By high school, a student might use geometry to solve a design problem or use a function to describe how one quantity of interest depends on another. Mathematically proficient students who can apply what they know are comfortable making assumptions and approximations to simplify a complicated situation, realizing that these may need revision later. They are able to identify important quantities in a practical situation and map their relationships using such tools as diagrams, two-way tables, graphs, flowcharts and formulas. They can analyze those relationships mathematically to draw conclusions. They routinely interpret their mathematical results in the context of the situation and reflect on whether the results make sense, possibly improving the model if it has not served its purpose. Represent a problem situation with a mathematical model. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Model with mathematics. Model with mathematics. Add and subtract fractions (including mixed numbers) with unlike denominators. (May include multiple methods and representations.) Model with mathematics. Add and subtract decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Model addition and subtraction of fractions and decimals using a variety of representations. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. Topic 7 Online Assessment Curriculum Standards: Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Model with mathematics. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Use models to subtract mixed numbers. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Add and subtract fractions (including mixed numbers) with unlike denominators. (May include multiple methods and representations.) Add and subtract decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Model addition and subtraction of fractions and decimals using a variety of representations. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. Add mixed numbers using models. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Write equivalent fractions to add and subtract fractions with unlike denominators. Estimate sums and differences of decimals and fractions to assess the reasonableness of results. Estimate sums and differences of fractions and mixed numbers. Add fractions with unlike denominators using equivalent fractions with a common denominator. Estimate sums and differences of fractions by using the nearest half or whole number. Model with mathematics. Model with mathematics. Mathematically proficient students can apply the mathematics they know to solve problems arising in everyday life, society, and the workplace. In early grades, this might be as simple as writing an addition equation to describe a situation. In middle grades, a student might apply proportional reasoning to plan a school event or analyze a problem in the community. By high school, a student might use geometry to solve a design problem or use a function to describe how one quantity of interest depends on another. Mathematically proficient students who can apply what they know are comfortable making assumptions and approximations to simplify a complicated situation, realizing that these may need revision later. They are able to identify important quantities in a practical situation and map their relationships using such tools as diagrams, two-way tables, graphs, flowcharts and formulas. They can analyze those relationships mathematically to draw conclusions. They routinely interpret their mathematical results in the context of the situation and reflect on whether the results make sense, possibly improving the model if it has not served its purpose. Represent a problem situation with a mathematical model. Model with mathematics. Model with mathematics. Model with mathematics. Find common denominators for fractions with unlike denominators. Subtract mixed numbers using equivalent fractions and a common denominator. Add and subtract mixed numbers using equivalent fractions and a common denominator. Topic 7 Spanish Assessments Tema 7: Tarea de rendimento Tema 7: Evaluación Topic 8: Apply Understanding of Multiplication to Multiply Fractions Topic 8: Today's Challenge Topic 8: Beginning of Topic Interactive Student Edition: Beginning of Topic 8 Topic 8: enVision STEM Activity Grade 5 Topic 8: Review What You Know 8-1: Multiply a Fraction by a Whole Number Interactive Student Edition: Grade 5 Lesson 8-1 Math Anytime 8-1: Daily Review Topic 8: Today's Challenge Step 1: Problem-Based Learning 8-1: Solve & Share Curriculum Standards: Interpret the product a/b x q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = (ac)/(bd). Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. English language learners communicate for social and instructional purposes within the school setting. Write informative/explanatory texts to examine a topic and convey ideas and information clearly. (a) Introduce a topic clearly, provide a general observation and focus, and group related information logically; include formatting (e.g., headings), illustrations, and multimedia when useful to aiding comprehension. (b) Develop the topic with facts, definitions, concrete details, quotations, or other information and examples related to the topic. (c) Link ideas within and across categories of information using words, phrases, and clauses (e.g., in contrast, especially). (d) Use precise language and domain-specific vocabulary to inform about or explain the topic. (e) Provide a concluding statement or section related to the information or explanation presented. English language learners communicate information, ideas and concepts necessary for academic success in the content area of Mathematics. Interpret the product (a/b) × q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction. Interpret the product (a/b) × q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = ac/bd.) Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Multiply a fraction by a whole number. Interpret the product a/b x q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = (ac)/(bd). Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 5 topics and texts, building on others’ ideas and expressing their own clearly. (a) Come to discussions prepared, having read or studied required material; explicitly draw on that preparation and other information known about the topic to explore ideas under discussion. (b) Follow agreed-upon rules for discussions and carry out assigned roles. (c) Pose and respond to specific questions by making comments that contribute to the discussion and elaborate on the remarks of others. (d) Review the key ideas expressed and draw conclusions in light of information and knowledge gained from the discussions. Summarize a written text read aloud or information presented in diverse media and formats, including visually, quantitatively, and orally. Summarize the points a speaker makes and explain how each claim is supported by reasons and evidence. Step 2: Visual Learning 8-1: Visual Learning Curriculum Standards: Interpret the product a/b x q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = (ac)/(bd). Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Multiply a fraction by a whole or mixed number using visual fraction models. Multiply a fraction by a whole or mixed number using visual fraction models. Interpret the product (a/b) × q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction. Interpret the product (a/b) × q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = ac/bd.) Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Multiply a fraction by a whole number. Interpret the product a/b x q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = (ac)/(bd). 8-1: Convince Me! Curriculum Standards: Interpret the product a/b x q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = (ac)/(bd). Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Interpret the product (a/b) × q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction. Interpret the product (a/b) × q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = ac/bd.) Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Multiply a fraction by a whole number. Interpret the product a/b x q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = (ac)/(bd). Practice and Problem Solving 8-1: Student Edition Practice Curriculum Standards: Interpret the product a/b x q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = (ac)/(bd). Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Interpret the product (a/b) × q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction. Interpret the product (a/b) × q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = ac/bd.) Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Multiply a fraction by a whole number. Interpret the product a/b x q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = (ac)/(bd). 8-1: Practice Buddy: Independent Practice; Problem Solving Curriculum Standards: Interpret the product a/b x q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = (ac)/(bd). Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Interpret the product (a/b) × q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction. Interpret the product (a/b) × q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = ac/bd.) Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Multiply a fraction by a whole number. Interpret the product a/b x q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = (ac)/(bd). 8-1: Practice Buddy: Additional Practice Curriculum Standards: Interpret the product a/b x q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = (ac)/(bd). Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Interpret the product (a/b) × q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction. Interpret the product (a/b) × q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = ac/bd.) Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Multiply a fraction by a whole number. Interpret the product a/b x q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = (ac)/(bd). 8-1: Interactive Additional Practice Step 3: Assess & Differentiate 8-1: Practice Buddy: Additional Practice Curriculum Standards: Interpret the product a/b x q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = (ac)/(bd). Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Interpret the product (a/b) × q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction. Interpret the product (a/b) × q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = ac/bd.) Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Multiply a fraction by a whole number. Interpret the product a/b x q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = (ac)/(bd). 8-1: Enrichment Curriculum Standards: Interpret the product a/b x q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = (ac)/(bd). Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Interpret the product (a/b) × q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction. Interpret the product (a/b) × q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = ac/bd.) Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Multiply a fraction by a whole number. Interpret the product a/b x q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = (ac)/(bd). 8-1: Quick Check Curriculum Standards: Interpret the product a/b x q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = (ac)/(bd). Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Interpret the product (a/b) × q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction. Interpret the product (a/b) × q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = ac/bd.) Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Multiply a fraction by a whole number. Interpret the product a/b x q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = (ac)/(bd). 8-1: Lesson Self-Assessment 8-1: Reteach to Build Understanding Curriculum Standards: Interpret the product a/b x q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = (ac)/(bd). Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Multiply a fraction by a whole or mixed number using visual fraction models. Multiply a fraction by a whole or mixed number using visual fraction models. Interpret the product (a/b) × q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction. Interpret the product (a/b) × q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = ac/bd.) Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Multiply a fraction by a whole number. Interpret the product a/b x q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = (ac)/(bd). 8-1: Build Mathematical Literacy Curriculum Standards: Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 5 topics and texts, building on others’ ideas and expressing their own clearly. (a) Come to discussions prepared, having read or studied required material; explicitly draw on that preparation and other information known about the topic to explore ideas under discussion. (b) Follow agreed-upon rules for discussions and carry out assigned roles. (c) Pose and respond to specific questions by making comments that contribute to the discussion and elaborate on the remarks of others. (d) Review the key ideas expressed and draw conclusions in light of information and knowledge gained from the discussions. English language learners communicate for social and instructional purposes within the school setting. Summarize a written text read aloud or information presented in diverse media and formats, including visually, quantitatively, and orally. Summarize the points a speaker makes and explain how each claim is supported by reasons and evidence. Write informative/explanatory texts to examine a topic and convey ideas and information clearly. (a) Introduce a topic clearly, provide a general observation and focus, and group related information logically; include formatting (e.g., headings), illustrations, and multimedia when useful to aiding comprehension. (b) Develop the topic with facts, definitions, concrete details, quotations, or other information and examples related to the topic. (c) Link ideas within and across categories of information using words, phrases, and clauses (e.g., in contrast, especially). (d) Use precise language and domain-specific vocabulary to inform about or explain the topic. (e) Provide a concluding statement or section related to the information or explanation presented. English language learners communicate information, ideas and concepts necessary for academic success in the content area of Mathematics. 8-1: Enrichment Game: Fancy Flea - Fractions 8-1: Pick a Project 8-1: Another Look Curriculum Standards: Interpret the product a/b x q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = (ac)/(bd). Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Multiply a fraction by a whole or mixed number using visual fraction models. Multiply a fraction by a whole or mixed number using visual fraction models. Interpret the product (a/b) × q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction. Interpret the product (a/b) × q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = ac/bd.) Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Multiply a fraction by a whole number. Interpret the product a/b x q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = (ac)/(bd). Spanish Resources 8-1: eText del Libro del estudiante 8-1: Repaso diario 8-1: Aprendizaje visual 8-1: Amigo de práctica: Práctica adicional 8-1: Práctica adicional interactiva 8-1: Refuerzo para mejorar la comprensión 8-1: Desarrollar la competencia matemática 8-1: Ampliación 8-2: Multiply a Whole Number by a Fraction Interactive Student Edition: Grade 5 Lesson 8-2 Math Anytime 8-2: Daily Review Topic 8: Today's Challenge Step 1: Problem-Based Learning 8-2: Solve & Share Curriculum Standards: Interpret the product a/b x q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = (ac)/(bd). Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. English language learners communicate for social and instructional purposes within the school setting. Write informative/explanatory texts to examine a topic and convey ideas and information clearly. (a) Introduce a topic clearly, provide a general observation and focus, and group related information logically; include formatting (e.g., headings), illustrations, and multimedia when useful to aiding comprehension. (b) Develop the topic with facts, definitions, concrete details, quotations, or other information and examples related to the topic. (c) Link ideas within and across categories of information using words, phrases, and clauses (e.g., in contrast, especially). (d) Use precise language and domain-specific vocabulary to inform about or explain the topic. (e) Provide a concluding statement or section related to the information or explanation presented. English language learners communicate information, ideas and concepts necessary for academic success in the content area of Mathematics. Interpret the product (a/b) × q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Interpret the product (a/b) × q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = ac/bd.) Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Multiply a whole number by a fraction. Interpret the product a/b x q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = (ac)/(bd). Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 5 topics and texts, building on others’ ideas and expressing their own clearly. (a) Come to discussions prepared, having read or studied required material; explicitly draw on that preparation and other information known about the topic to explore ideas under discussion. (b) Follow agreed-upon rules for discussions and carry out assigned roles. (c) Pose and respond to specific questions by making comments that contribute to the discussion and elaborate on the remarks of others. (d) Review the key ideas expressed and draw conclusions in light of information and knowledge gained from the discussions. Summarize a written text read aloud or information presented in diverse media and formats, including visually, quantitatively, and orally. Summarize the points a speaker makes and explain how each claim is supported by reasons and evidence. Step 2: Visual Learning 8-2: Visual Learning Curriculum Standards: Interpret the product a/b x q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = (ac)/(bd). Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Multiply a fraction by a whole or mixed number using visual fraction models. Interpret the product (a/b) × q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Interpret the product (a/b) × q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = ac/bd.) Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Multiply a whole number by a fraction. Interpret the product a/b x q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = (ac)/(bd). Multiply a fraction by a whole or mixed number using visual fraction models. 8-2: Convince Me! Curriculum Standards: Interpret the product a/b x q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = (ac)/(bd). Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Interpret the product (a/b) × q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Interpret the product (a/b) × q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = ac/bd.) Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Multiply a whole number by a fraction. Interpret the product a/b x q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = (ac)/(bd). Practice and Problem Solving 8-2: Student Edition Practice Curriculum Standards: Interpret the product a/b x q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = (ac)/(bd). Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Interpret the product (a/b) × q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Interpret the product (a/b) × q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = ac/bd.) Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Multiply a whole number by a fraction. Interpret the product a/b x q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = (ac)/(bd). 8-2: Practice Buddy: Independent Practice; Problem Solving Curriculum Standards: Interpret the product a/b x q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = (ac)/(bd). Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Interpret the product (a/b) × q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Interpret the product (a/b) × q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = ac/bd.) Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Multiply a whole number by a fraction. Interpret the product a/b x q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = (ac)/(bd). 8-2: Practice Buddy: Additional Practice Curriculum Standards: Interpret the product a/b x q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = (ac)/(bd). Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Interpret the product (a/b) × q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Interpret the product (a/b) × q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = ac/bd.) Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Multiply a whole number by a fraction. Interpret the product a/b x q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = (ac)/(bd). 8-2: Interactive Additional Practice Step 3: Assess & Differentiate 8-2: Practice Buddy: Additional Practice Curriculum Standards: Interpret the product a/b x q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = (ac)/(bd). Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Interpret the product (a/b) × q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Interpret the product (a/b) × q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = ac/bd.) Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Multiply a whole number by a fraction. Interpret the product a/b x q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = (ac)/(bd). 8-2: Enrichment Curriculum Standards: Interpret the product a/b x q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = (ac)/(bd). Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Interpret the product (a/b) × q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Interpret the product (a/b) × q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = ac/bd.) Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Multiply a whole number by a fraction. Interpret the product a/b x q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = (ac)/(bd). 8-2: Quick Check Curriculum Standards: Interpret the product a/b x q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = (ac)/(bd). Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Interpret the product (a/b) × q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Interpret the product (a/b) × q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = ac/bd.) Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Multiply a whole number by a fraction. Interpret the product a/b x q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = (ac)/(bd). 8-2: Lesson Self-Assessment 8-2: Reteach to Build Understanding Curriculum Standards: Interpret the product a/b x q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = (ac)/(bd). Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Multiply a fraction by a whole or mixed number using visual fraction models. Interpret the product (a/b) × q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Interpret the product (a/b) × q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = ac/bd.) Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Multiply a whole number by a fraction. Interpret the product a/b x q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = (ac)/(bd). Multiply a fraction by a whole or mixed number using visual fraction models. 8-2: Build Mathematical Literacy Curriculum Standards: Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 5 topics and texts, building on others’ ideas and expressing their own clearly. (a) Come to discussions prepared, having read or studied required material; explicitly draw on that preparation and other information known about the topic to explore ideas under discussion. (b) Follow agreed-upon rules for discussions and carry out assigned roles. (c) Pose and respond to specific questions by making comments that contribute to the discussion and elaborate on the remarks of others. (d) Review the key ideas expressed and draw conclusions in light of information and knowledge gained from the discussions. English language learners communicate for social and instructional purposes within the school setting. Summarize a written text read aloud or information presented in diverse media and formats, including visually, quantitatively, and orally. Summarize the points a speaker makes and explain how each claim is supported by reasons and evidence. Write informative/explanatory texts to examine a topic and convey ideas and information clearly. (a) Introduce a topic clearly, provide a general observation and focus, and group related information logically; include formatting (e.g., headings), illustrations, and multimedia when useful to aiding comprehension. (b) Develop the topic with facts, definitions, concrete details, quotations, or other information and examples related to the topic. (c) Link ideas within and across categories of information using words, phrases, and clauses (e.g., in contrast, especially). (d) Use precise language and domain-specific vocabulary to inform about or explain the topic. (e) Provide a concluding statement or section related to the information or explanation presented. English language learners communicate information, ideas and concepts necessary for academic success in the content area of Mathematics. 8-2: Enrichment 8-2: Digital Math Tool Activity 8-2: Problem-Solving Reading Activity Curriculum Standards: Interpret the product a/b x q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = (ac)/(bd). Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Interpret the product (a/b) × q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Interpret the product (a/b) × q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = ac/bd.) Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Multiply a whole number by a fraction. Interpret the product a/b x q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = (ac)/(bd). 8-2: Another Look Curriculum Standards: Interpret the product a/b x q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = (ac)/(bd). Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Multiply a fraction by a whole or mixed number using visual fraction models. Interpret the product (a/b) × q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Interpret the product (a/b) × q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = ac/bd.) Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Multiply a whole number by a fraction. Interpret the product a/b x q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = (ac)/(bd). Multiply a fraction by a whole or mixed number using visual fraction models. Spanish Resources 8-2: eText del Libro del estudiante 8-2: Repaso diario 8-2: Aprendizaje visual 8-2: Amigo de práctica: Práctica adicional 8-2: Práctica adicional interactiva 8-2: Refuerzo para mejorar la comprensión 8-2: Desarrollar la competencia matemática 8-2: Ampliación 8-3: Multiply Fractions and Whole Numbers Interactive Student Edition: Grade 5 Lesson 8-3 Math Anytime 8-3: Daily Review Topic 8: Today's Challenge Step 1: Problem-Based Learning 8-3: Solve & Share Curriculum Standards: Interpret the product a/b x q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = (ac)/(bd). English language learners communicate for social and instructional purposes within the school setting. Write informative/explanatory texts to examine a topic and convey ideas and information clearly. (a) Introduce a topic clearly, provide a general observation and focus, and group related information logically; include formatting (e.g., headings), illustrations, and multimedia when useful to aiding comprehension. (b) Develop the topic with facts, definitions, concrete details, quotations, or other information and examples related to the topic. (c) Link ideas within and across categories of information using words, phrases, and clauses (e.g., in contrast, especially). (d) Use precise language and domain-specific vocabulary to inform about or explain the topic. (e) Provide a concluding statement or section related to the information or explanation presented. English language learners communicate information, ideas and concepts necessary for academic success in the content area of Mathematics. Interpret the product (a/b) × q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. Interpret the product (a/b) × q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = ac/bd.) Multiply fractions and whole numbers. Interpret the product a/b x q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = (ac)/(bd). Engage effectively in a range of collaborative discussions (one- on-one, in groups, and teacher-led) with diverse partners on grade 5 topics and texts, building on others’ ideas and expressing their own clearly. (a) Come to discussions prepared, having read or studied required material; explicitly draw on that preparation and other information known about the topic to explore ideas under discussion. (b) Follow agreed-upon rules for discussions and carry out assigned roles. (c) Pose and respond to specific questions by making comments that contribute to the discussion and elaborate on the remarks of others. (d) Review the key ideas expressed and draw conclusions in light of information and knowledge gained from the discussions. Summarize a written text read aloud or information presented in diverse media and formats, including visually, quantitatively, and orally. Summarize the points a speaker makes and explain how each claim is supported by reasons and evidence. Step 2: Visual Learning 8-3: Visual Learning Curriculum Standards: Interpret the product a/b x q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = (ac)/(bd). Interpret the product (a/b) × q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. Interpret the product (a/b) × q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = ac/bd.) Multiply fractions and whole numbers. Interpret the product a/b x q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = (ac)/(bd). 8-3: Convince Me! Curriculum Standards: Interpret the product a/b x q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = (ac)/(bd). Interpret the product (a/b) × q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. Interpret the product (a/b) × q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = ac/bd.) Multiply fractions and whole numbers. Interpret the product a/b x q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = (ac)/(bd). Practice and Problem Solving 8-3: Student Edition Practice Curriculum Standards: Interpret the product a/b x q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = (ac)/(bd). Interpret the product (a/b) × q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. Interpret the product (a/b) × q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = ac/bd.) Multiply fractions and whole numbers. Interpret the product a/b x q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = (ac)/(bd). 8-3: Practice Buddy: Independent Practice; Problem Solving Curriculum Standards: Interpret the product a/b x q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = (ac)/(bd). Interpret the product (a/b) × q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. Interpret the product (a/b) × q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = ac/bd.) Multiply fractions and whole numbers. Interpret the product a/b x q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = (ac)/(bd). 8-3: Practice Buddy: Additional Practice Curriculum Standards: Interpret the product a/b x q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = (ac)/(bd). Interpret the product (a/b) × q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. Interpret the product (a/b) × q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = ac/bd.) Multiply fractions and whole numbers. Interpret the product a/b x q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = (ac)/(bd). 8-3: Interactive Additional Practice Step 3: Assess & Differentiate 8-3: Practice Buddy: Additional Practice Curriculum Standards: Interpret the product a/b x q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = (ac)/(bd). Interpret the product (a/b) × q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. Interpret the product (a/b) × q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = ac/bd.) Multiply fractions and whole numbers. Interpret the product a/b x q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = (ac)/(bd). 8-3: Enrichment Curriculum Standards: Interpret the product a/b x q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = (ac)/(bd). Interpret the product (a/b) × q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. Interpret the product (a/b) × q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = ac/bd.) Multiply fractions and whole numbers. Interpret the product a/b x q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = (ac)/(bd). 8-3: Quick Check Curriculum Standards: Interpret the product a/b x q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = (ac)/(bd). Interpret the product (a/b) × q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. Interpret the product (a/b) × q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = ac/bd.) Multiply fractions and whole numbers. Interpret the product a/b x q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = (ac)/(bd). 8-3: Lesson Self-Assessment 8-3: Reteach to Build Understanding Curriculum Standards: Interpret the product a/b x q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = (ac)/(bd). Interpret the product (a/b) × q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. Interpret the product (a/b) × q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = ac/bd.) Multiply fractions and whole numbers. Interpret the product a/b x q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = (ac)/(bd). 8-3: Build Mathematical Literacy Curriculum Standards: Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 5 topics and texts, building on others’ ideas and expressing their own clearly. (a) Come to discussions prepared, having read or studied required material; explicitly draw on that preparation and other information known about the topic to explore ideas under discussion. (b) Follow agreed-upon rules for discussions and carry out assigned roles. (c) Pose and respond to specific questions by making comments that contribute to the discussion and elaborate on the remarks of others. (d) Review the key ideas expressed and draw conclusions in light of information and knowledge gained from the discussions. English language learners communicate for social and instructional purposes within the school setting. Summarize a written text read aloud or information presented in diverse media and formats, including visually, quantitatively, and orally. Summarize the points a speaker makes and explain how each claim is supported by reasons and evidence. Write informative/explanatory texts to examine a topic and convey ideas and information clearly. (a) Introduce a topic clearly, provide a general observation and focus, and group related information logically; include formatting (e.g., headings), illustrations, and multimedia when useful to aiding comprehension. (b) Develop the topic with facts, definitions, concrete details, quotations, or other information and examples related to the topic. (c) Link ideas within and across categories of information using words, phrases, and clauses (e.g., in contrast, especially). (d) Use precise language and domain-specific vocabulary to inform about or explain the topic. (e) Provide a concluding statement or section related to the information or explanation presented. English language learners communicate information, ideas and concepts necessary for academic success in the content area of Mathematics. 8-3: Enrichment 8-3: Digital Math Tool Activity 8-3: enVision STEM Activity Curriculum Standards: Interpret the product a/b x q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = (ac)/(bd). Interpret the product (a/b) × q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. Interpret the product (a/b) × q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = ac/bd.) Multiply fractions and whole numbers. Interpret the product a/b x q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = (ac)/(bd). 8-3: Another Look Curriculum Standards: Interpret the product a/b x q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = (ac)/(bd). Interpret the product (a/b) × q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. Interpret the product (a/b) × q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = ac/bd.) Multiply fractions and whole numbers. Interpret the product a/b x q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = (ac)/(bd). Spanish Resources 8-3: eText del Libro del estudiante 8-3: Repaso diario 8-3: Aprendizaje visual 8-3: Amigo de práctica: Práctica adicional 8-3: Práctica adicional interactiva 8-3: Refuerzo para mejorar la comprensión 8-3: Desarrollar la competencia matemática 8-3: Ampliación 8-4: Use Models to Multiply Two Fractions Interactive Student Edition: Grade 5 Lesson 8-4 Math Anytime 8-4: Daily Review Topic 8: Today's Challenge Step 1: Problem-Based Learning 8-4: Solve & Share Curriculum Standards: Interpret the product a/b x q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = (ac)/(bd). English language learners communicate for social and instructional purposes within the school setting. Write informative/explanatory texts to examine a topic and convey ideas and information clearly. (a) Introduce a topic clearly, provide a general observation and focus, and group related information logically; include formatting (e.g., headings), illustrations, and multimedia when useful to aiding comprehension. (b) Develop the topic with facts, definitions, concrete details, quotations, or other information and examples related to the topic. (c) Link ideas within and across categories of information using words, phrases, and clauses (e.g., in contrast, especially). (d) Use precise language and domain-specific vocabulary to inform about or explain the topic. (e) Provide a concluding statement or section related to the information or explanation presented. English language learners communicate information, ideas and concepts necessary for academic success in the content area of Mathematics. Interpret the product (a/b) × q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. Interpret the product (a/b) × q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = ac/bd.) Use models to multiply two fractions. Interpret the product a/b x q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = (ac)/(bd). Multiply a fraction (including mixed numbers) by a fraction. Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 5 topics and texts, building on others’ ideas and expressing their own clearly. (a) Come to discussions prepared, having read or studied required material; explicitly draw on that preparation and other information known about the topic to explore ideas under discussion. (b) Follow agreed-upon rules for discussions and carry out assigned roles. (c) Pose and respond to specific questions by making comments that contribute to the discussion and elaborate on the remarks of others. (d) Review the key ideas expressed and draw conclusions in light of information and knowledge gained from the discussions. Summarize a written text read aloud or information presented in diverse media and formats, including visually, quantitatively, and orally. Summarize the points a speaker makes and explain how each claim is supported by reasons and evidence. Step 2: Visual Learning 8-4: Visual Learning Curriculum Standards: Interpret the product a/b x q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = (ac)/(bd). Interpret the product (a/b) × q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. Interpret the product (a/b) × q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = ac/bd.) Use models to multiply two fractions. Interpret the product a/b x q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = (ac)/(bd). Multiply a fraction (including mixed numbers) by a fraction. 8-4: Convince Me! Curriculum Standards: Interpret the product a/b x q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = (ac)/(bd). Interpret the product (a/b) × q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. Interpret the product (a/b) × q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = ac/bd.) Use models to multiply two fractions. Interpret the product a/b x q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = (ac)/(bd). Multiply a fraction (including mixed numbers) by a fraction. Practice and Problem Solving 8-4: Student Edition Practice Curriculum Standards: Interpret the product a/b x q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = (ac)/(bd). Interpret the product (a/b) × q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. Interpret the product (a/b) × q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = ac/bd.) Use models to multiply two fractions. Interpret the product a/b x q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = (ac)/(bd). Multiply a fraction (including mixed numbers) by a fraction. 8-4: Practice Buddy: Independent Practice; Problem Solving Curriculum Standards: Interpret the product a/b x q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = (ac)/(bd). Interpret the product (a/b) × q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. Interpret the product (a/b) × q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = ac/bd.) Use models to multiply two fractions. Interpret the product a/b x q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = (ac)/(bd). Multiply a fraction (including mixed numbers) by a fraction. 8-4: Practice Buddy: Additional Practice Curriculum Standards: Interpret the product a/b x q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = (ac)/(bd). Interpret the product (a/b) × q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. Interpret the product (a/b) × q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = ac/bd.) Use models to multiply two fractions. Interpret the product a/b x q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = (ac)/(bd). Multiply a fraction (including mixed numbers) by a fraction. 8-4: Interactive Additional Practice Step 3: Assess & Differentiate 8-4: Practice Buddy: Additional Practice Curriculum Standards: Interpret the product a/b x q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = (ac)/(bd). Interpret the product (a/b) × q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. Interpret the product (a/b) × q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = ac/bd.) Use models to multiply two fractions. Interpret the product a/b x q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = (ac)/(bd). Multiply a fraction (including mixed numbers) by a fraction. 8-4: Enrichment Curriculum Standards: Interpret the product a/b x q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = (ac)/(bd). Interpret the product (a/b) × q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. Interpret the product (a/b) × q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = ac/bd.) Use models to multiply two fractions. Interpret the product a/b x q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = (ac)/(bd). Multiply a fraction (including mixed numbers) by a fraction. 8-4: Quick Check Curriculum Standards: Interpret the product a/b x q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = (ac)/(bd). Interpret the product (a/b) × q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. Interpret the product (a/b) × q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = ac/bd.) Use models to multiply two fractions. Interpret the product a/b x q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = (ac)/(bd). Multiply a fraction (including mixed numbers) by a fraction. 8-4: Lesson Self-Assessment 8-4: Reteach to Build Understanding Curriculum Standards: Interpret the product a/b x q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = (ac)/(bd). Interpret the product (a/b) × q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. Interpret the product (a/b) × q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = ac/bd.) Use models to multiply two fractions. Interpret the product a/b x q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = (ac)/(bd). Multiply a fraction (including mixed numbers) by a fraction. 8-4: Build Mathematical Literacy Curriculum Standards: Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 5 topics and texts, building on others’ ideas and expressing their own clearly. (a) Come to discussions prepared, having read or studied required material; explicitly draw on that preparation and other information known about the topic to explore ideas under discussion. (b) Follow agreed-upon rules for discussions and carry out assigned roles. (c) Pose and respond to specific questions by making comments that contribute to the discussion and elaborate on the remarks of others. (d) Review the key ideas expressed and draw conclusions in light of information and knowledge gained from the discussions. English language learners communicate for social and instructional purposes within the school setting. Summarize a written text read aloud or information presented in diverse media and formats, including visually, quantitatively, and orally. Summarize the points a speaker makes and explain how each claim is supported by reasons and evidence. Write informative/explanatory texts to examine a topic and convey ideas and information clearly. (a) Introduce a topic clearly, provide a general observation and focus, and group related information logically; include formatting (e.g., headings), illustrations, and multimedia when useful to aiding comprehension. (b) Develop the topic with facts, definitions, concrete details, quotations, or other information and examples related to the topic. (c) Link ideas within and across categories of information using words, phrases, and clauses (e.g., in contrast, especially). (d) Use precise language and domain-specific vocabulary to inform about or explain the topic. (e) Provide a concluding statement or section related to the information or explanation presented. English language learners communicate information, ideas and concepts necessary for academic success in the content area of Mathematics. 8-4: Enrichment 8-4: Digital Math Tool Activity 8-4: Pick a Project 8-4: Another Look Curriculum Standards: Interpret the product a/b x q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = (ac)/(bd). Interpret the product (a/b) × q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. Interpret the product (a/b) × q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = ac/bd.) Use models to multiply two fractions. Interpret the product a/b x q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = (ac)/(bd). Multiply a fraction (including mixed numbers) by a fraction. Spanish Resources 8-4: eText del Libro del estudiante 8-4: Repaso diario 8-4: Aprendizaje visual 8-4: Amigo de práctica: Práctica adicional 8-4: Práctica adicional interactiva 8-4: Refuerzo para mejorar la comprensión 8-4: Desarrollar la competencia matemática 8-4: Ampliación 8-5: Multiply Two Fractions Interactive Student Edition: Grade 5 Lesson 8-5 Math Anytime 8-5: Daily Review Topic 8: Today's Challenge Step 1: Problem-Based Learning 8-5: Solve & Share Curriculum Standards: Interpret the product a/b x q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = (ac)/(bd). English language learners communicate for social and instructional purposes within the school setting. Write informative/explanatory texts to examine a topic and convey ideas and information clearly. (a) Introduce a topic clearly, provide a general observation and focus, and group related information logically; include formatting (e.g., headings), illustrations, and multimedia when useful to aiding comprehension. (b) Develop the topic with facts, definitions, concrete details, quotations, or other information and examples related to the topic. (c) Link ideas within and across categories of information using words, phrases, and clauses (e.g., in contrast, especially). (d) Use precise language and domain-specific vocabulary to inform about or explain the topic. (e) Provide a concluding statement or section related to the information or explanation presented. English language learners communicate information, ideas and concepts necessary for academic success in the content area of Mathematics. Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 5 topics and texts, building on others’ ideas and expressing their own clearly. (a) Come to discussions prepared, having read or studied required material; explicitly draw on that preparation and other information known about the topic to explore ideas under discussion. (b) Follow agreed-upon rules for discussions and carry out assigned roles. (c) Pose and respond to specific questions by making comments that contribute to the discussion and elaborate on the remarks of others. (d) Review the key ideas expressed and draw conclusions in light of information and knowledge gained from the discussions. Summarize a written text read aloud or information presented in diverse media and formats, including visually, quantitatively, and orally. Summarize the points a speaker makes and explain how each claim is supported by reasons and evidence. Interpret the product (a/b) × q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. Interpret the product (a/b) × q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = ac/bd.) Multiply two fractions. Interpret the product a/b x q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = (ac)/(bd). Multiply a fraction (including mixed numbers) by a fraction. Step 2: Visual Learning 8-5: Visual Learning Curriculum Standards: Interpret the product a/b x q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = (ac)/(bd). Interpret the product (a/b) × q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. Interpret the product (a/b) × q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = ac/bd.) Multiply two fractions. Interpret the product a/b x q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = (ac)/(bd). Multiply a fraction (including mixed numbers) by a fraction. 8-5: Convince Me! Curriculum Standards: Interpret the product a/b x q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = (ac)/(bd). Interpret the product (a/b) × q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. Interpret the product (a/b) × q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = ac/bd.) Multiply two fractions. Interpret the product a/b x q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = (ac)/(bd). Multiply a fraction (including mixed numbers) by a fraction. Practice and Problem Solving 8-5: Student Edition Practice Curriculum Standards: Interpret the product a/b x q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = (ac)/(bd). Interpret the product (a/b) × q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. Interpret the product (a/b) × q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = ac/bd.) Multiply two fractions. Interpret the product a/b x q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = (ac)/(bd). Multiply a fraction (including mixed numbers) by a fraction. 8-5: Practice Buddy: Independent Practice; Problem Solving Curriculum Standards: Interpret the product a/b x q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = (ac)/(bd). Interpret the product (a/b) × q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. Interpret the product (a/b) × q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = ac/bd.) Multiply two fractions. Interpret the product a/b x q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = (ac)/(bd). Multiply a fraction (including mixed numbers) by a fraction. 8-5: Practice Buddy: Additional Practice Curriculum Standards: Interpret the product a/b x q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = (ac)/(bd). Interpret the product (a/b) × q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. Interpret the product (a/b) × q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = ac/bd.) Multiply two fractions. Interpret the product a/b x q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = (ac)/(bd). Multiply a fraction (including mixed numbers) by a fraction. 8-5: Interactive Additional Practice Step 3: Assess & Differentiate 8-5: Practice Buddy: Additional Practice Curriculum Standards: Interpret the product a/b x q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = (ac)/(bd). Interpret the product (a/b) × q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. Interpret the product (a/b) × q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = ac/bd.) Multiply two fractions. Interpret the product a/b x q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = (ac)/(bd). Multiply a fraction (including mixed numbers) by a fraction. 8-5: Enrichment Curriculum Standards: Interpret the product a/b x q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = (ac)/(bd). Interpret the product (a/b) × q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. Interpret the product (a/b) × q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = ac/bd.) Multiply two fractions. Interpret the product a/b x q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = (ac)/(bd). Multiply a fraction (including mixed numbers) by a fraction. 8-5: Quick Check Curriculum Standards: Interpret the product a/b x q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = (ac)/(bd). Interpret the product (a/b) × q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. Interpret the product (a/b) × q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = ac/bd.) Multiply two fractions. Interpret the product a/b x q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = (ac)/(bd). Multiply a fraction (including mixed numbers) by a fraction. 8-5: Lesson Self-Assessment 8-5: Reteach to Build Understanding Curriculum Standards: Interpret the product a/b x q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = (ac)/(bd). Interpret the product (a/b) × q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. Interpret the product (a/b) × q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = ac/bd.) Multiply two fractions. Interpret the product a/b x q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = (ac)/(bd). Multiply a fraction (including mixed numbers) by a fraction. 8-5: Build Mathematical Literacy Curriculum Standards: Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 5 topics and texts, building on others’ ideas and expressing their own clearly. (a) Come to discussions prepared, having read or studied required material; explicitly draw on that preparation and other information known about the topic to explore ideas under discussion. (b) Follow agreed-upon rules for discussions and carry out assigned roles. (c) Pose and respond to specific questions by making comments that contribute to the discussion and elaborate on the remarks of others. (d) Review the key ideas expressed and draw conclusions in light of information and knowledge gained from the discussions. English language learners communicate for social and instructional purposes within the school setting. Summarize a written text read aloud or information presented in diverse media and formats, including visually, quantitatively, and orally. Summarize the points a speaker makes and explain how each claim is supported by reasons and evidence. Write informative/explanatory texts to examine a topic and convey ideas and information clearly. (a) Introduce a topic clearly, provide a general observation and focus, and group related information logically; include formatting (e.g., headings), illustrations, and multimedia when useful to aiding comprehension. (b) Develop the topic with facts, definitions, concrete details, quotations, or other information and examples related to the topic. (c) Link ideas within and across categories of information using words, phrases, and clauses (e.g., in contrast, especially). (d) Use precise language and domain-specific vocabulary to inform about or explain the topic. (e) Provide a concluding statement or section related to the information or explanation presented. English language learners communicate information, ideas and concepts necessary for academic success in the content area of Mathematics. 8-5: Enrichment Game: Jungle Quest - Equivalent Fractions 8-5: Problem-Solving Reading Activity Curriculum Standards: Interpret the product a/b x q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = (ac)/(bd). Interpret the product (a/b) × q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. Interpret the product (a/b) × q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = ac/bd.) Multiply two fractions. Interpret the product a/b x q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = (ac)/(bd). Multiply a fraction (including mixed numbers) by a fraction. 8-5: Another Look Curriculum Standards: Interpret the product a/b x q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = (ac)/(bd). Interpret the product (a/b) × q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. Interpret the product (a/b) × q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = ac/bd.) Multiply two fractions. Interpret the product a/b x q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = (ac)/(bd). Multiply a fraction (including mixed numbers) by a fraction. Spanish Resources 8-5: eText del Libro del estudiante 8-5: Repaso diario 8-5: Aprendizaje visual 8-5: Amigo de práctica: Práctica adicional 8-5: Práctica adicional interactiva 8-5: Refuerzo para mejorar la comprensión 8-5: Desarrollar la competencia matemática 8-5: Ampliación 8-6: Area of a Rectangle Interactive Student Edition: Grade 5 Lesson 8-6 Math Anytime 8-6: Daily Review Topic 8: Today's Challenge Step 1: Problem-Based Learning 8-6: Solve & Share Curriculum Standards: Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side lengths, and show that the area is the same as would be found by multiplying the side lengths. Multiply fractional side lengths to find areas of rectangles, and represent fraction products as rectangular areas. English language learners communicate for social and instructional purposes within the school setting. Write informative/explanatory texts to examine a topic and convey ideas and information clearly. (a) Introduce a topic clearly, provide a general observation and focus, and group related information logically; include formatting (e.g., headings), illustrations, and multimedia when useful to aiding comprehension. (b) Develop the topic with facts, definitions, concrete details, quotations, or other information and examples related to the topic. (c) Link ideas within and across categories of information using words, phrases, and clauses (e.g., in contrast, especially). (d) Use precise language and domain-specific vocabulary to inform about or explain the topic. (e) Provide a concluding statement or section related to the information or explanation presented. English language learners communicate information, ideas and concepts necessary for academic success in the content area of Mathematics. Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 5 topics and texts, building on others’ ideas and expressing their own clearly. (a) Come to discussions prepared, having read or studied required material; explicitly draw on that preparation and other information known about the topic to explore ideas under discussion. (b) Follow agreed-upon rules for discussions and carry out assigned roles. (c) Pose and respond to specific questions by making comments that contribute to the discussion and elaborate on the remarks of others. (d) Review the key ideas expressed and draw conclusions in light of information and knowledge gained from the discussions. Summarize a written text read aloud or information presented in diverse media and formats, including visually, quantitatively, and orally. Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side lengths, and show that the area is the same as would be found by multiplying the side lengths. Multiply fractional side lengths to find areas of rectangles, and represent fraction products as rectangular areas. Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side lengths, and show that the area is the same as would be found by multiplying the side lengths. Multiply fractional side lengths to find areas of rectangles, and represent fraction products as rectangular areas. Find the area of a rectangle using fractions and diagrams. Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side lengths, and show that the area is the same as would be found by multiplying the side lengths. Multiply fractional side lengths to find areas of rectangles, and represent fraction products as rectangular areas. Multiply a fraction (including mixed numbers) by a fraction. Summarize the points a speaker makes and explain how each claim is supported by reasons and evidence. Step 2: Visual Learning 8-6: Visual Learning Curriculum Standards: Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side lengths, and show that the area is the same as would be found by multiplying the side lengths. Multiply fractional side lengths to find areas of rectangles, and represent fraction products as rectangular areas. Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side lengths, and show that the area is the same as would be found by multiplying the side lengths. Multiply fractional side lengths to find areas of rectangles, and represent fraction products as rectangular areas. Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side lengths, and show that the area is the same as would be found by multiplying the side lengths. Multiply fractional side lengths to find areas of rectangles, and represent fraction products as rectangular areas. Find the area of a rectangle using fractions and diagrams. Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side lengths, and show that the area is the same as would be found by multiplying the side lengths. Multiply fractional side lengths to find areas of rectangles, and represent fraction products as rectangular areas. Multiply a fraction (including mixed numbers) by a fraction. 8-6: Convince Me! Curriculum Standards: Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side lengths, and show that the area is the same as would be found by multiplying the side lengths. Multiply fractional side lengths to find areas of rectangles, and represent fraction products as rectangular areas. Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side lengths, and show that the area is the same as would be found by multiplying the side lengths. Multiply fractional side lengths to find areas of rectangles, and represent fraction products as rectangular areas. Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side lengths, and show that the area is the same as would be found by multiplying the side lengths. Multiply fractional side lengths to find areas of rectangles, and represent fraction products as rectangular areas. Find the area of a rectangle using fractions and diagrams. Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side lengths, and show that the area is the same as would be found by multiplying the side lengths. Multiply fractional side lengths to find areas of rectangles, and represent fraction products as rectangular areas. Multiply a fraction (including mixed numbers) by a fraction. Practice and Problem Solving 8-6: Student Edition Practice Curriculum Standards: Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side lengths, and show that the area is the same as would be found by multiplying the side lengths. Multiply fractional side lengths to find areas of rectangles, and represent fraction products as rectangular areas. Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side lengths, and show that the area is the same as would be found by multiplying the side lengths. Multiply fractional side lengths to find areas of rectangles, and represent fraction products as rectangular areas. Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side lengths, and show that the area is the same as would be found by multiplying the side lengths. Multiply fractional side lengths to find areas of rectangles, and represent fraction products as rectangular areas. Find the area of a rectangle using fractions and diagrams. Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side lengths, and show that the area is the same as would be found by multiplying the side lengths. Multiply fractional side lengths to find areas of rectangles, and represent fraction products as rectangular areas. Multiply a fraction (including mixed numbers) by a fraction. 8-6: Practice Buddy: Independent Practice; Problem Solving Curriculum Standards: Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side lengths, and show that the area is the same as would be found by multiplying the side lengths. Multiply fractional side lengths to find areas of rectangles, and represent fraction products as rectangular areas. Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side lengths, and show that the area is the same as would be found by multiplying the side lengths. Multiply fractional side lengths to find areas of rectangles, and represent fraction products as rectangular areas. Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side lengths, and show that the area is the same as would be found by multiplying the side lengths. Multiply fractional side lengths to find areas of rectangles, and represent fraction products as rectangular areas. Find the area of a rectangle using fractions and diagrams. Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side lengths, and show that the area is the same as would be found by multiplying the side lengths. Multiply fractional side lengths to find areas of rectangles, and represent fraction products as rectangular areas. Multiply a fraction (including mixed numbers) by a fraction. 8-6: Practice Buddy: Additional Practice Curriculum Standards: Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side lengths, and show that the area is the same as would be found by multiplying the side lengths. Multiply fractional side lengths to find areas of rectangles, and represent fraction products as rectangular areas. Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side lengths, and show that the area is the same as would be found by multiplying the side lengths. Multiply fractional side lengths to find areas of rectangles, and represent fraction products as rectangular areas. Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side lengths, and show that the area is the same as would be found by multiplying the side lengths. Multiply fractional side lengths to find areas of rectangles, and represent fraction products as rectangular areas. Find the area of a rectangle using fractions and diagrams. Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side lengths, and show that the area is the same as would be found by multiplying the side lengths. Multiply fractional side lengths to find areas of rectangles, and represent fraction products as rectangular areas. Multiply a fraction (including mixed numbers) by a fraction. 8-6: Interactive Additional Practice Step 3: Assess & Differentiate 8-6: Practice Buddy: Additional Practice Curriculum Standards: Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side lengths, and show that the area is the same as would be found by multiplying the side lengths. Multiply fractional side lengths to find areas of rectangles, and represent fraction products as rectangular areas. Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side lengths, and show that the area is the same as would be found by multiplying the side lengths. Multiply fractional side lengths to find areas of rectangles, and represent fraction products as rectangular areas. Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side lengths, and show that the area is the same as would be found by multiplying the side lengths. Multiply fractional side lengths to find areas of rectangles, and represent fraction products as rectangular areas. Find the area of a rectangle using fractions and diagrams. Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side lengths, and show that the area is the same as would be found by multiplying the side lengths. Multiply fractional side lengths to find areas of rectangles, and represent fraction products as rectangular areas. Multiply a fraction (including mixed numbers) by a fraction. 8-6: Enrichment Curriculum Standards: Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side lengths, and show that the area is the same as would be found by multiplying the side lengths. Multiply fractional side lengths to find areas of rectangles, and represent fraction products as rectangular areas. Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side lengths, and show that the area is the same as would be found by multiplying the side lengths. Multiply fractional side lengths to find areas of rectangles, and represent fraction products as rectangular areas. Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side lengths, and show that the area is the same as would be found by multiplying the side lengths. Multiply fractional side lengths to find areas of rectangles, and represent fraction products as rectangular areas. Find the area of a rectangle using fractions and diagrams. Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side lengths, and show that the area is the same as would be found by multiplying the side lengths. Multiply fractional side lengths to find areas of rectangles, and represent fraction products as rectangular areas. Multiply a fraction (including mixed numbers) by a fraction. 8-6: Quick Check Curriculum Standards: Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side lengths, and show that the area is the same as would be found by multiplying the side lengths. Multiply fractional side lengths to find areas of rectangles, and represent fraction products as rectangular areas. Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side lengths, and show that the area is the same as would be found by multiplying the side lengths. Multiply fractional side lengths to find areas of rectangles, and represent fraction products as rectangular areas. Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side lengths, and show that the area is the same as would be found by multiplying the side lengths. Multiply fractional side lengths to find areas of rectangles, and represent fraction products as rectangular areas. Find the area of a rectangle using fractions and diagrams. Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side lengths, and show that the area is the same as would be found by multiplying the side lengths. Multiply fractional side lengths to find areas of rectangles, and represent fraction products as rectangular areas. Multiply a fraction (including mixed numbers) by a fraction. 8-6: Lesson Self-Assessment 8-6: Reteach to Build Understanding Curriculum Standards: Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side lengths, and show that the area is the same as would be found by multiplying the side lengths. Multiply fractional side lengths to find areas of rectangles, and represent fraction products as rectangular areas. Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side lengths, and show that the area is the same as would be found by multiplying the side lengths. Multiply fractional side lengths to find areas of rectangles, and represent fraction products as rectangular areas. Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side lengths, and show that the area is the same as would be found by multiplying the side lengths. Multiply fractional side lengths to find areas of rectangles, and represent fraction products as rectangular areas. Find the area of a rectangle using fractions and diagrams. Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side lengths, and show that the area is the same as would be found by multiplying the side lengths. Multiply fractional side lengths to find areas of rectangles, and represent fraction products as rectangular areas. Multiply a fraction (including mixed numbers) by a fraction. 8-6: Build Mathematical Literacy Curriculum Standards: Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 5 topics and texts, building on others’ ideas and expressing their own clearly. (a) Come to discussions prepared, having read or studied required material; explicitly draw on that preparation and other information known about the topic to explore ideas under discussion. (b) Follow agreed-upon rules for discussions and carry out assigned roles. (c) Pose and respond to specific questions by making comments that contribute to the discussion and elaborate on the remarks of others. (d) Review the key ideas expressed and draw conclusions in light of information and knowledge gained from the discussions. English language learners communicate for social and instructional purposes within the school setting. Summarize a written text read aloud or information presented in diverse media and formats, including visually, quantitatively, and orally. Summarize the points a speaker makes and explain how each claim is supported by reasons and evidence. Write informative/explanatory texts to examine a topic and convey ideas and information clearly. (a) Introduce a topic clearly, provide a general observation and focus, and group related information logically; include formatting (e.g., headings), illustrations, and multimedia when useful to aiding comprehension. (b) Develop the topic with facts, definitions, concrete details, quotations, or other information and examples related to the topic. (c) Link ideas within and across categories of information using words, phrases, and clauses (e.g., in contrast, especially). (d) Use precise language and domain-specific vocabulary to inform about or explain the topic. (e) Provide a concluding statement or section related to the information or explanation presented. English language learners communicate information, ideas and concepts necessary for academic success in the content area of Mathematics. 8-6: Enrichment 8-6: Digital Math Tool Activity 8-6: Pick a Project 8-6: Another Look Curriculum Standards: Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side lengths, and show that the area is the same as would be found by multiplying the side lengths. Multiply fractional side lengths to find areas of rectangles, and represent fraction products as rectangular areas. Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side lengths, and show that the area is the same as would be found by multiplying the side lengths. Multiply fractional side lengths to find areas of rectangles, and represent fraction products as rectangular areas. Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side lengths, and show that the area is the same as would be found by multiplying the side lengths. Multiply fractional side lengths to find areas of rectangles, and represent fraction products as rectangular areas. Find the area of a rectangle using fractions and diagrams. Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side lengths, and show that the area is the same as would be found by multiplying the side lengths. Multiply fractional side lengths to find areas of rectangles, and represent fraction products as rectangular areas. Multiply a fraction (including mixed numbers) by a fraction. Spanish Resources 8-6: eText del Libro del estudiante 8-6: Repaso diario 8-6: Aprendizaje visual 8-6: Amigo de práctica: Práctica adicional 8-6: Práctica adicional interactiva 8-6: Refuerzo para mejorar la comprensión 8-6: Desarrollar la competencia matemática 8-6: Ampliación 8-7: Multiply Mixed Numbers Interactive Student Edition: Grade 5 Lesson 8-7 Math Anytime 8-7: Daily Review Topic 8: Today's Challenge Step 1: Problem-Based Learning 8-7: Solve & Share Curriculum Standards: Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. English language learners communicate for social and instructional purposes within the school setting. Write informative/explanatory texts to examine a topic and convey ideas and information clearly. (a) Introduce a topic clearly, provide a general observation and focus, and group related information logically; include formatting (e.g., headings), illustrations, and multimedia when useful to aiding comprehension. (b) Develop the topic with facts, definitions, concrete details, quotations, or other information and examples related to the topic. (c) Link ideas within and across categories of information using words, phrases, and clauses (e.g., in contrast, especially). (d) Use precise language and domain- specific vocabulary to inform about or explain the topic. (e) Provide a concluding statement or section related to the information or explanation presented. English language learners communicate information, ideas and concepts necessary for academic success in the content area of Mathematics. Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 5 topics and texts, building on others’ ideas and expressing their own clearly. (a) Come to discussions prepared, having read or studied required material; explicitly draw on that preparation and other information known about the topic to explore ideas under discussion. (b) Follow agreed-upon rules for discussions and carry out assigned roles. (c) Pose and respond to specific questions by making comments that contribute to the discussion and elaborate on the remarks of others. (d) Review the key ideas expressed and draw conclusions in light of information and knowledge gained from the discussions. Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Use models, equations and previously learned strategies to multiply mixed numbers. Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Multiply a fraction (including mixed numbers) by a fraction. Summarize a written text read aloud or information presented in diverse media and formats, including visually, quantitatively, and orally. Summarize the points a speaker makes and explain how each claim is supported by reasons and evidence. Step 2: Visual Learning 8-7: Visual Learning Curriculum Standards: Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Use models, equations and previously learned strategies to multiply mixed numbers. Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Multiply a fraction (including mixed numbers) by a fraction. 8-7: Convince Me! Curriculum Standards: Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Use models, equations and previously learned strategies to multiply mixed numbers. Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Multiply a fraction (including mixed numbers) by a fraction. Practice and Problem Solving 8-7: Student Edition Practice Curriculum Standards: Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Use models, equations and previously learned strategies to multiply mixed numbers. Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Multiply a fraction (including mixed numbers) by a fraction. 8-7: Practice Buddy: Independent Practice; Problem Solving Curriculum Standards: Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Use models, equations and previously learned strategies to multiply mixed numbers. Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Multiply a fraction (including mixed numbers) by a fraction. 8-7: Practice Buddy: Additional Practice Curriculum Standards: Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Use models, equations and previously learned strategies to multiply mixed numbers. Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Multiply a fraction (including mixed numbers) by a fraction. 8-7: Interactive Additional Practice Step 3: Assess & Differentiate 8-7: Practice Buddy: Additional Practice Curriculum Standards: Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Use models, equations and previously learned strategies to multiply mixed numbers. Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Multiply a fraction (including mixed numbers) by a fraction. 8-7: Enrichment Curriculum Standards: Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Use models, equations and previously learned strategies to multiply mixed numbers. Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Multiply a fraction (including mixed numbers) by a fraction. 8-7: Quick Check Curriculum Standards: Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Use models, equations and previously learned strategies to multiply mixed numbers. Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Multiply a fraction (including mixed numbers) by a fraction. 8-7: Lesson Self-Assessment 8-7: Reteach to Build Understanding Curriculum Standards: Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Use models, equations and previously learned strategies to multiply mixed numbers. Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Multiply a fraction (including mixed numbers) by a fraction. 8-7: Build Mathematical Literacy Curriculum Standards: Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 5 topics and texts, building on others’ ideas and expressing their own clearly. (a) Come to discussions prepared, having read or studied required material; explicitly draw on that preparation and other information known about the topic to explore ideas under discussion. (b) Follow agreed-upon rules for discussions and carry out assigned roles. (c) Pose and respond to specific questions by making comments that contribute to the discussion and elaborate on the remarks of others. (d) Review the key ideas expressed and draw conclusions in light of information and knowledge gained from the discussions. English language learners communicate for social and instructional purposes within the school setting. Summarize a written text read aloud or information presented in diverse media and formats, including visually, quantitatively, and orally. Summarize the points a speaker makes and explain how each claim is supported by reasons and evidence. Write informative/explanatory texts to examine a topic and convey ideas and information clearly. (a) Introduce a topic clearly, provide a general observation and focus, and group related information logically; include formatting (e.g., headings), illustrations, and multimedia when useful to aiding comprehension. (b) Develop the topic with facts, definitions, concrete details, quotations, or other information and examples related to the topic. (c) Link ideas within and across categories of information using words, phrases, and clauses (e.g., in contrast, especially). (d) Use precise language and domain-specific vocabulary to inform about or explain the topic. (e) Provide a concluding statement or section related to the information or explanation presented. English language learners communicate information, ideas and concepts necessary for academic success in the content area of Mathematics. 8-7: Enrichment Game: Factory Frenzy Fractions 8-7: Pick a Project 8-7: Another Look Curriculum Standards: Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Use models, equations and previously learned strategies to multiply mixed numbers. Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Multiply a fraction (including mixed numbers) by a fraction. Spanish Resources 8-7: eText del Libro del estudiante 8-7: Repaso diario 8-7: Aprendizaje visual 8-7: Amigo de práctica: Práctica adicional 8-7: Práctica adicional interactiva 8-7: Refuerzo para mejorar la comprensión 8-7: Desarrollar la competencia matemática 8-7: Ampliación 8-8: Multiplication as Scaling Interactive Student Edition: Grade 5 Lesson 8-8 Math Anytime 8-8: Daily Review Topic 8: Today's Challenge Step 1: Problem-Based Learning 8-8: Solve & Share Curriculum Standards: Comparing the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication. Explaining why multiplying a given number by a fraction greater than 1 results in a product greater than the given number (recognizing multiplication by whole numbers greater than 1 as a familiar case); explaining why multiplying a given number by a fraction less than 1 results in a product smaller than the given number; and relating the principle of fraction equivalence a/b = (n × a)/(n × b) to the effect of multiplying a/b by 1. English language learners communicate for social and instructional purposes within the school setting. Write informative/explanatory texts to examine a topic and convey ideas and information clearly. (a) Introduce a topic clearly, provide a general observation and focus, and group related information logically; include formatting (e.g., headings), illustrations, and multimedia when useful to aiding comprehension. (b) Develop the topic with facts, definitions, concrete details, quotations, or other information and examples related to the topic. (c) Link ideas within and across categories of information using words, phrases, and clauses (e.g., in contrast, especially). (d) Use precise language and domain- specific vocabulary to inform about or explain the topic. (e) Provide a concluding statement or section related to the information or explanation presented. English language learners communicate information, ideas and concepts necessary for academic success in the content area of Mathematics. Comparing the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication. Explaining why multiplying a given number by a fraction greater than 1 results in a product greater than the given number (recognizing multiplication by whole numbers greater than 1 as a familiar case); explaining why multiplying a given number by a fraction less than 1 results in a product smaller than the given number; and relating the principle of fraction equivalence a/b = (n × a)/(n × b) to the effect of multiplying a/b by 1. Interpret multiplication as scaling (resizing), by: Comparing the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication. Explaining why multiplying a given number by a fraction greater than 1 results in a product greater than the given number (recognizing multiplication by whole numbers greater than 1 as a familiar case); explaining why multiplying a given number by a fraction less than 1 results in a product smaller than the given number; and relating the principle of fraction equivalence a/b = (n × a)/(n × b) to the effect of multiplying a/b by 1. Compare the size of the product to the size of one factor without multiplying to consider multiplication as scaling. Comparing the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication. Explaining why multiplying a given number by a fraction greater than 1 results in a product greater than the given number (recognizing multiplication by whole numbers greater than 1 as a familiar case); explaining why multiplying a given number by a fraction less than 1 results in a product smaller than the given number; and relating the principle of fraction equivalence a/b = (n × a)/(n × b) to the effect of multiplying a/b by 1. Demonstrate an understanding of multiplication as scaling (resizing). Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 5 topics and texts, building on others’ ideas and expressing their own clearly. (a) Come to discussions prepared, having read or studied required material; explicitly draw on that preparation and other information known about the topic to explore ideas under discussion. (b) Follow agreed-upon rules for discussions and carry out assigned roles. (c) Pose and respond to specific questions by making comments that contribute to the discussion and elaborate on the remarks of others. (d) Review the key ideas expressed and draw conclusions in light of information and knowledge gained from the discussions. Summarize a written text read aloud or information presented in diverse media and formats, including visually, quantitatively, and orally. Summarize the points a speaker makes and explain how each claim is supported by reasons and evidence. Step 2: Visual Learning 8-8: Visual Learning Curriculum Standards: Comparing the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication. Explaining why multiplying a given number by a fraction greater than 1 results in a product greater than the given number (recognizing multiplication by whole numbers greater than 1 as a familiar case); explaining why multiplying a given number by a fraction less than 1 results in a product smaller than the given number; and relating the principle of fraction equivalence a/b = (n × a)/(n × b) to the effect of multiplying a/b by 1. Comparing the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication. Explaining why multiplying a given number by a fraction greater than 1 results in a product greater than the given number (recognizing multiplication by whole numbers greater than 1 as a familiar case); explaining why multiplying a given number by a fraction less than 1 results in a product smaller than the given number; and relating the principle of fraction equivalence a/b = (n × a)/(n × b) to the effect of multiplying a/b by 1. Interpret multiplication as scaling (resizing), by: Comparing the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication. Explaining why multiplying a given number by a fraction greater than 1 results in a product greater than the given number (recognizing multiplication by whole numbers greater than 1 as a familiar case); explaining why multiplying a given number by a fraction less than 1 results in a product smaller than the given number; and relating the principle of fraction equivalence a/b = (n × a)/(n × b) to the effect of multiplying a/b by 1. Compare the size of the product to the size of one factor without multiplying to consider multiplication as scaling. Comparing the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication. Explaining why multiplying a given number by a fraction greater than 1 results in a product greater than the given number (recognizing multiplication by whole numbers greater than 1 as a familiar case); explaining why multiplying a given number by a fraction less than 1 results in a product smaller than the given number; and relating the principle of fraction equivalence a/b = (n × a)/(n × b) to the effect of multiplying a/b by 1. Demonstrate an understanding of multiplication as scaling (resizing). Determine whether the product will increase or decrease based on the multiple using visual fraction models. 8-8: Convince Me! Curriculum Standards: Comparing the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication. Explaining why multiplying a given number by a fraction greater than 1 results in a product greater than the given number (recognizing multiplication by whole numbers greater than 1 as a familiar case); explaining why multiplying a given number by a fraction less than 1 results in a product smaller than the given number; and relating the principle of fraction equivalence a/b = (n × a)/(n × b) to the effect of multiplying a/b by 1. Comparing the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication. Explaining why multiplying a given number by a fraction greater than 1 results in a product greater than the given number (recognizing multiplication by whole numbers greater than 1 as a familiar case); explaining why multiplying a given number by a fraction less than 1 results in a product smaller than the given number; and relating the principle of fraction equivalence a/b = (n × a)/(n × b) to the effect of multiplying a/b by 1. Interpret multiplication as scaling (resizing), by: Comparing the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication. Explaining why multiplying a given number by a fraction greater than 1 results in a product greater than the given number (recognizing multiplication by whole numbers greater than 1 as a familiar case); explaining why multiplying a given number by a fraction less than 1 results in a product smaller than the given number; and relating the principle of fraction equivalence a/b = (n × a)/(n × b) to the effect of multiplying a/b by 1. Compare the size of the product to the size of one factor without multiplying to consider multiplication as scaling. Comparing the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication. Explaining why multiplying a given number by a fraction greater than 1 results in a product greater than the given number (recognizing multiplication by whole numbers greater than 1 as a familiar case); explaining why multiplying a given number by a fraction less than 1 results in a product smaller than the given number; and relating the principle of fraction equivalence a/b = (n × a)/(n × b) to the effect of multiplying a/b by 1. Demonstrate an understanding of multiplication as scaling (resizing). Practice and Problem Solving 8-8: Student Edition Practice Curriculum Standards: Comparing the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication. Explaining why multiplying a given number by a fraction greater than 1 results in a product greater than the given number (recognizing multiplication by whole numbers greater than 1 as a familiar case); explaining why multiplying a given number by a fraction less than 1 results in a product smaller than the given number; and relating the principle of fraction equivalence a/b = (n × a)/(n × b) to the effect of multiplying a/b by 1. Comparing the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication. Explaining why multiplying a given number by a fraction greater than 1 results in a product greater than the given number (recognizing multiplication by whole numbers greater than 1 as a familiar case); explaining why multiplying a given number by a fraction less than 1 results in a product smaller than the given number; and relating the principle of fraction equivalence a/b = (n × a)/(n × b) to the effect of multiplying a/b by 1. Interpret multiplication as scaling (resizing), by: Comparing the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication. Explaining why multiplying a given number by a fraction greater than 1 results in a product greater than the given number (recognizing multiplication by whole numbers greater than 1 as a familiar case); explaining why multiplying a given number by a fraction less than 1 results in a product smaller than the given number; and relating the principle of fraction equivalence a/b = (n × a)/(n × b) to the effect of multiplying a/b by 1. Compare the size of the product to the size of one factor without multiplying to consider multiplication as scaling. Comparing the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication. Explaining why multiplying a given number by a fraction greater than 1 results in a product greater than the given number (recognizing multiplication by whole numbers greater than 1 as a familiar case); explaining why multiplying a given number by a fraction less than 1 results in a product smaller than the given number; and relating the principle of fraction equivalence a/b = (n × a)/(n × b) to the effect of multiplying a/b by 1. Demonstrate an understanding of multiplication as scaling (resizing). 8-8: Practice Buddy: Independent Practice; Problem Solving Curriculum Standards: Comparing the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication. Explaining why multiplying a given number by a fraction greater than 1 results in a product greater than the given number (recognizing multiplication by whole numbers greater than 1 as a familiar case); explaining why multiplying a given number by a fraction less than 1 results in a product smaller than the given number; and relating the principle of fraction equivalence a/b = (n × a)/(n × b) to the effect of multiplying a/b by 1. Comparing the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication. Explaining why multiplying a given number by a fraction greater than 1 results in a product greater than the given number (recognizing multiplication by whole numbers greater than 1 as a familiar case); explaining why multiplying a given number by a fraction less than 1 results in a product smaller than the given number; and relating the principle of fraction equivalence a/b = (n × a)/(n × b) to the effect of multiplying a/b by 1. Interpret multiplication as scaling (resizing), by: Comparing the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication. Explaining why multiplying a given number by a fraction greater than 1 results in a product greater than the given number (recognizing multiplication by whole numbers greater than 1 as a familiar case); explaining why multiplying a given number by a fraction less than 1 results in a product smaller than the given number; and relating the principle of fraction equivalence a/b = (n × a)/(n × b) to the effect of multiplying a/b by 1. Compare the size of the product to the size of one factor without multiplying to consider multiplication as scaling. Comparing the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication. Explaining why multiplying a given number by a fraction greater than 1 results in a product greater than the given number (recognizing multiplication by whole numbers greater than 1 as a familiar case); explaining why multiplying a given number by a fraction less than 1 results in a product smaller than the given number; and relating the principle of fraction equivalence a/b = (n × a)/(n × b) to the effect of multiplying a/b by 1. Demonstrate an understanding of multiplication as scaling (resizing). 8-8: Practice Buddy: Additional Practice Curriculum Standards: Comparing the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication. Explaining why multiplying a given number by a fraction greater than 1 results in a product greater than the given number (recognizing multiplication by whole numbers greater than 1 as a familiar case); explaining why multiplying a given number by a fraction less than 1 results in a product smaller than the given number; and relating the principle of fraction equivalence a/b = (n × a)/(n × b) to the effect of multiplying a/b by 1. Comparing the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication. Explaining why multiplying a given number by a fraction greater than 1 results in a product greater than the given number (recognizing multiplication by whole numbers greater than 1 as a familiar case); explaining why multiplying a given number by a fraction less than 1 results in a product smaller than the given number; and relating the principle of fraction equivalence a/b = (n × a)/(n × b) to the effect of multiplying a/b by 1. Interpret multiplication as scaling (resizing), by: Comparing the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication. Explaining why multiplying a given number by a fraction greater than 1 results in a product greater than the given number (recognizing multiplication by whole numbers greater than 1 as a familiar case); explaining why multiplying a given number by a fraction less than 1 results in a product smaller than the given number; and relating the principle of fraction equivalence a/b = (n × a)/(n × b) to the effect of multiplying a/b by 1. Compare the size of the product to the size of one factor without multiplying to consider multiplication as scaling. Comparing the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication. Explaining why multiplying a given number by a fraction greater than 1 results in a product greater than the given number (recognizing multiplication by whole numbers greater than 1 as a familiar case); explaining why multiplying a given number by a fraction less than 1 results in a product smaller than the given number; and relating the principle of fraction equivalence a/b = (n × a)/(n × b) to the effect of multiplying a/b by 1. Demonstrate an understanding of multiplication as scaling (resizing). 8-8: Interactive Additional Practice Step 3: Assess & Differentiate 8-8: Practice Buddy: Additional Practice Curriculum Standards: Comparing the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication. Explaining why multiplying a given number by a fraction greater than 1 results in a product greater than the given number (recognizing multiplication by whole numbers greater than 1 as a familiar case); explaining why multiplying a given number by a fraction less than 1 results in a product smaller than the given number; and relating the principle of fraction equivalence a/b = (n × a)/(n × b) to the effect of multiplying a/b by 1. Comparing the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication. Explaining why multiplying a given number by a fraction greater than 1 results in a product greater than the given number (recognizing multiplication by whole numbers greater than 1 as a familiar case); explaining why multiplying a given number by a fraction less than 1 results in a product smaller than the given number; and relating the principle of fraction equivalence a/b = (n × a)/(n × b) to the effect of multiplying a/b by 1. Interpret multiplication as scaling (resizing), by: Comparing the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication. Explaining why multiplying a given number by a fraction greater than 1 results in a product greater than the given number (recognizing multiplication by whole numbers greater than 1 as a familiar case); explaining why multiplying a given number by a fraction less than 1 results in a product smaller than the given number; and relating the principle of fraction equivalence a/b = (n × a)/(n × b) to the effect of multiplying a/b by 1. Compare the size of the product to the size of one factor without multiplying to consider multiplication as scaling. Comparing the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication. Explaining why multiplying a given number by a fraction greater than 1 results in a product greater than the given number (recognizing multiplication by whole numbers greater than 1 as a familiar case); explaining why multiplying a given number by a fraction less than 1 results in a product smaller than the given number; and relating the principle of fraction equivalence a/b = (n × a)/(n × b) to the effect of multiplying a/b by 1. Demonstrate an understanding of multiplication as scaling (resizing). 8-8: Enrichment Curriculum Standards: Comparing the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication. Explaining why multiplying a given number by a fraction greater than 1 results in a product greater than the given number (recognizing multiplication by whole numbers greater than 1 as a familiar case); explaining why multiplying a given number by a fraction less than 1 results in a product smaller than the given number; and relating the principle of fraction equivalence a/b = (n × a)/(n × b) to the effect of multiplying a/b by 1. Comparing the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication. Explaining why multiplying a given number by a fraction greater than 1 results in a product greater than the given number (recognizing multiplication by whole numbers greater than 1 as a familiar case); explaining why multiplying a given number by a fraction less than 1 results in a product smaller than the given number; and relating the principle of fraction equivalence a/b = (n × a)/(n × b) to the effect of multiplying a/b by 1. Interpret multiplication as scaling (resizing), by: Comparing the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication. Explaining why multiplying a given number by a fraction greater than 1 results in a product greater than the given number (recognizing multiplication by whole numbers greater than 1 as a familiar case); explaining why multiplying a given number by a fraction less than 1 results in a product smaller than the given number; and relating the principle of fraction equivalence a/b = (n × a)/(n × b) to the effect of multiplying a/b by 1. Compare the size of the product to the size of one factor without multiplying to consider multiplication as scaling. Comparing the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication. Explaining why multiplying a given number by a fraction greater than 1 results in a product greater than the given number (recognizing multiplication by whole numbers greater than 1 as a familiar case); explaining why multiplying a given number by a fraction less than 1 results in a product smaller than the given number; and relating the principle of fraction equivalence a/b = (n × a)/(n × b) to the effect of multiplying a/b by 1. Demonstrate an understanding of multiplication as scaling (resizing). 8-8: Quick Check Curriculum Standards: Comparing the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication. Explaining why multiplying a given number by a fraction greater than 1 results in a product greater than the given number (recognizing multiplication by whole numbers greater than 1 as a familiar case); explaining why multiplying a given number by a fraction less than 1 results in a product smaller than the given number; and relating the principle of fraction equivalence a/b = (n × a)/(n × b) to the effect of multiplying a/b by 1. Comparing the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication. Explaining why multiplying a given number by a fraction greater than 1 results in a product greater than the given number (recognizing multiplication by whole numbers greater than 1 as a familiar case); explaining why multiplying a given number by a fraction less than 1 results in a product smaller than the given number; and relating the principle of fraction equivalence a/b = (n × a)/(n × b) to the effect of multiplying a/b by 1. Interpret multiplication as scaling (resizing), by: Comparing the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication. Explaining why multiplying a given number by a fraction greater than 1 results in a product greater than the given number (recognizing multiplication by whole numbers greater than 1 as a familiar case); explaining why multiplying a given number by a fraction less than 1 results in a product smaller than the given number; and relating the principle of fraction equivalence a/b = (n × a)/(n × b) to the effect of multiplying a/b by 1. Compare the size of the product to the size of one factor without multiplying to consider multiplication as scaling. Comparing the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication. Explaining why multiplying a given number by a fraction greater than 1 results in a product greater than the given number (recognizing multiplication by whole numbers greater than 1 as a familiar case); explaining why multiplying a given number by a fraction less than 1 results in a product smaller than the given number; and relating the principle of fraction equivalence a/b = (n × a)/(n × b) to the effect of multiplying a/b by 1. Demonstrate an understanding of multiplication as scaling (resizing). 8-8: Lesson Self-Assessment 8-8: Reteach to Build Understanding Curriculum Standards: Comparing the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication. Explaining why multiplying a given number by a fraction greater than 1 results in a product greater than the given number (recognizing multiplication by whole numbers greater than 1 as a familiar case); explaining why multiplying a given number by a fraction less than 1 results in a product smaller than the given number; and relating the principle of fraction equivalence a/b = (n × a)/(n × b) to the effect of multiplying a/b by 1. Comparing the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication. Explaining why multiplying a given number by a fraction greater than 1 results in a product greater than the given number (recognizing multiplication by whole numbers greater than 1 as a familiar case); explaining why multiplying a given number by a fraction less than 1 results in a product smaller than the given number; and relating the principle of fraction equivalence a/b = (n × a)/(n × b) to the effect of multiplying a/b by 1. Interpret multiplication as scaling (resizing), by: Comparing the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication. Explaining why multiplying a given number by a fraction greater than 1 results in a product greater than the given number (recognizing multiplication by whole numbers greater than 1 as a familiar case); explaining why multiplying a given number by a fraction less than 1 results in a product smaller than the given number; and relating the principle of fraction equivalence a/b = (n × a)/(n × b) to the effect of multiplying a/b by 1. Compare the size of the product to the size of one factor without multiplying to consider multiplication as scaling. Comparing the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication. Explaining why multiplying a given number by a fraction greater than 1 results in a product greater than the given number (recognizing multiplication by whole numbers greater than 1 as a familiar case); explaining why multiplying a given number by a fraction less than 1 results in a product smaller than the given number; and relating the principle of fraction equivalence a/b = (n × a)/(n × b) to the effect of multiplying a/b by 1. Demonstrate an understanding of multiplication as scaling (resizing). Determine whether the product will increase or decrease based on the multiple using visual fraction models. 8-8: Build Mathematical Literacy Curriculum Standards: Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 5 topics and texts, building on others’ ideas and expressing their own clearly. (a) Come to discussions prepared, having read or studied required material; explicitly draw on that preparation and other information known about the topic to explore ideas under discussion. (b) Follow agreed-upon rules for discussions and carry out assigned roles. (c) Pose and respond to specific questions by making comments that contribute to the discussion and elaborate on the remarks of others. (d) Review the key ideas expressed and draw conclusions in light of information and knowledge gained from the discussions. English language learners communicate for social and instructional purposes within the school setting. Summarize a written text read aloud or information presented in diverse media and formats, including visually, quantitatively, and orally. Summarize the points a speaker makes and explain how each claim is supported by reasons and evidence. Write informative/explanatory texts to examine a topic and convey ideas and information clearly. (a) Introduce a topic clearly, provide a general observation and focus, and group related information logically; include formatting (e.g., headings), illustrations, and multimedia when useful to aiding comprehension. (b) Develop the topic with facts, definitions, concrete details, quotations, or other information and examples related to the topic. (c) Link ideas within and across categories of information using words, phrases, and clauses (e.g., in contrast, especially). (d) Use precise language and domain-specific vocabulary to inform about or explain the topic. (e) Provide a concluding statement or section related to the information or explanation presented. English language learners communicate information, ideas and concepts necessary for academic success in the content area of Mathematics. 8-8: Enrichment Game: Fluency - Multiply Multi-Digit Whole Numbers 8-8: Pick a Project 8-8: Another Look Curriculum Standards: Comparing the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication. Explaining why multiplying a given number by a fraction greater than 1 results in a product greater than the given number (recognizing multiplication by whole numbers greater than 1 as a familiar case); explaining why multiplying a given number by a fraction less than 1 results in a product smaller than the given number; and relating the principle of fraction equivalence a/b = (n × a)/(n × b) to the effect of multiplying a/b by 1. Comparing the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication. Explaining why multiplying a given number by a fraction greater than 1 results in a product greater than the given number (recognizing multiplication by whole numbers greater than 1 as a familiar case); explaining why multiplying a given number by a fraction less than 1 results in a product smaller than the given number; and relating the principle of fraction equivalence a/b = (n × a)/(n × b) to the effect of multiplying a/b by 1. Interpret multiplication as scaling (resizing), by: Comparing the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication. Explaining why multiplying a given number by a fraction greater than 1 results in a product greater than the given number (recognizing multiplication by whole numbers greater than 1 as a familiar case); explaining why multiplying a given number by a fraction less than 1 results in a product smaller than the given number; and relating the principle of fraction equivalence a/b = (n × a)/(n × b) to the effect of multiplying a/b by 1. Compare the size of the product to the size of one factor without multiplying to consider multiplication as scaling. Comparing the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication. Explaining why multiplying a given number by a fraction greater than 1 results in a product greater than the given number (recognizing multiplication by whole numbers greater than 1 as a familiar case); explaining why multiplying a given number by a fraction less than 1 results in a product smaller than the given number; and relating the principle of fraction equivalence a/b = (n × a)/(n × b) to the effect of multiplying a/b by 1. Demonstrate an understanding of multiplication as scaling (resizing). Determine whether the product will increase or decrease based on the multiple using visual fraction models. Spanish Resources 8-8: eText del Libro del estudiante 8-8: Repaso diario 8-8: Aprendizaje visual 8-8: Amigo de práctica: Práctica adicional 8-8: Práctica adicional interactiva 8-8: Refuerzo para mejorar la comprensión 8-8: Desarrollar la competencia matemática 8-8: Ampliación 8-9: Problem Solving: Make Sense and Persevere Interactive Student Edition: Grade 5 Lesson 8-9 Math Anytime 8-9: Daily Review Topic 8: Today's Challenge Step 1: Problem-Based Learning 8-9: Solve & Share Curriculum Standards: Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Make sense of problems and persevere in solving them. English language learners communicate for social and instructional purposes within the school setting. Write informative/explanatory texts to examine a topic and convey ideas and information clearly. (a) Introduce a topic clearly, provide a general observation and focus, and group related information logically; include formatting (e.g., headings), illustrations, and multimedia when useful to aiding comprehension. (b) Develop the topic with facts, definitions, concrete details, quotations, or other information and examples related to the topic. (c) Link ideas within and across categories of information using words, phrases, and clauses (e.g., in contrast, especially). (d) Use precise language and domain-specific vocabulary to inform about or explain the topic. (e) Provide a concluding statement or section related to the information or explanation presented. English language learners communicate information, ideas and concepts necessary for academic success in the content area of Mathematics. Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 5 topics and texts, building on others’ ideas and expressing their own clearly. (a) Come to discussions prepared, having read or studied required material; explicitly draw on that preparation and other information known about the topic to explore ideas under discussion. (b) Follow agreed-upon rules for discussions and carry out assigned roles. (c) Pose and respond to specific questions by making comments that contribute to the discussion and elaborate on the remarks of others. (d) Review the key ideas expressed and draw conclusions in light of information and knowledge gained from the discussions. Summarize a written text read aloud or information presented in diverse media and formats, including visually, quantitatively, and orally. Summarize the points a speaker makes and explain how each claim is supported by reasons and evidence. Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Make sense of problems and persevere in solving them. Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Make sense of problems and persevere in solving them. Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution. They analyze givens, constraints, relationships, and goals. They make conjectures about the form and meaning of the solution and plan a solution pathway rather than simply jumping into a solution attempt. They consider analogous problems, and try special cases and simpler forms of the original problem in order to gain insight into its solution. They monitor and evaluate their progress and change course if necessary. Older students might, depending on the context of the problem, transform algebraic expressions or change the viewing window on their graphing calculator to get the information they need. Mathematically proficient students can explain correspondences between equations, verbal descriptions, tables, and graphs or draw diagrams of important features and relationships, graph data, and search for regularity or trends. Younger students might rely on using concrete objects or pictures to help conceptualize and solve a problem. Mathematically proficient students check their answers to problems using a different method, and they continually ask themselves, “Does this make sense?” They can understand the approaches of others to solving complex problems and identify correspondences between different approaches. Use previously learned knowledge to make sense of problems and persevere in solving them. Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Make sense of problems and persevere in solving them. Make sense of problems and persevere in solving them. Make sense of problems and persevere in solving them. Step 2: Visual Learning 8-9: Visual Learning Curriculum Standards: Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Make sense of problems and persevere in solving them. Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Make sense of problems and persevere in solving them. Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Make sense of problems and persevere in solving them. Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution. They analyze givens, constraints, relationships, and goals. They make conjectures about the form and meaning of the solution and plan a solution pathway rather than simply jumping into a solution attempt. They consider analogous problems, and try special cases and simpler forms of the original problem in order to gain insight into its solution. They monitor and evaluate their progress and change course if necessary. Older students might, depending on the context of the problem, transform algebraic expressions or change the viewing window on their graphing calculator to get the information they need. Mathematically proficient students can explain correspondences between equations, verbal descriptions, tables, and graphs or draw diagrams of important features and relationships, graph data, and search for regularity or trends. Younger students might rely on using concrete objects or pictures to help conceptualize and solve a problem. Mathematically proficient students check their answers to problems using a different method, and they continually ask themselves, “Does this make sense?” They can understand the approaches of others to solving complex problems and identify correspondences between different approaches. Use previously learned knowledge to make sense of problems and persevere in solving them. Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Make sense of problems and persevere in solving them. Make sense of problems and persevere in solving them. Make sense of problems and persevere in solving them. 8-9: Convince Me! Curriculum Standards: Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Make sense of problems and persevere in solving them. Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Make sense of problems and persevere in solving them. Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Make sense of problems and persevere in solving them. Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution. They analyze givens, constraints, relationships, and goals. They make conjectures about the form and meaning of the solution and plan a solution pathway rather than simply jumping into a solution attempt. They consider analogous problems, and try special cases and simpler forms of the original problem in order to gain insight into its solution. They monitor and evaluate their progress and change course if necessary. Older students might, depending on the context of the problem, transform algebraic expressions or change the viewing window on their graphing calculator to get the information they need. Mathematically proficient students can explain correspondences between equations, verbal descriptions, tables, and graphs or draw diagrams of important features and relationships, graph data, and search for regularity or trends. Younger students might rely on using concrete objects or pictures to help conceptualize and solve a problem. Mathematically proficient students check their answers to problems using a different method, and they continually ask themselves, “Does this make sense?” They can understand the approaches of others to solving complex problems and identify correspondences between different approaches. Use previously learned knowledge to make sense of problems and persevere in solving them. Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Make sense of problems and persevere in solving them. Make sense of problems and persevere in solving them. Make sense of problems and persevere in solving them. Practice and Problem Solving 8-9: Student Edition Practice Curriculum Standards: Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Make sense of problems and persevere in solving them. Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Make sense of problems and persevere in solving them. Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Make sense of problems and persevere in solving them. Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution. They analyze givens, constraints, relationships, and goals. They make conjectures about the form and meaning of the solution and plan a solution pathway rather than simply jumping into a solution attempt. They consider analogous problems, and try special cases and simpler forms of the original problem in order to gain insight into its solution. They monitor and evaluate their progress and change course if necessary. Older students might, depending on the context of the problem, transform algebraic expressions or change the viewing window on their graphing calculator to get the information they need. Mathematically proficient students can explain correspondences between equations, verbal descriptions, tables, and graphs or draw diagrams of important features and relationships, graph data, and search for regularity or trends. Younger students might rely on using concrete objects or pictures to help conceptualize and solve a problem. Mathematically proficient students check their answers to problems using a different method, and they continually ask themselves, “Does this make sense?” They can understand the approaches of others to solving complex problems and identify correspondences between different approaches. Use previously learned knowledge to make sense of problems and persevere in solving them. Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Make sense of problems and persevere in solving them. Make sense of problems and persevere in solving them. Make sense of problems and persevere in solving them. 8-9: Practice Buddy: Independent Practice; Problem Solving Curriculum Standards: Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Make sense of problems and persevere in solving them. Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Make sense of problems and persevere in solving them. Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Make sense of problems and persevere in solving them. Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution. They analyze givens, constraints, relationships, and goals. They make conjectures about the form and meaning of the solution and plan a solution pathway rather than simply jumping into a solution attempt. They consider analogous problems, and try special cases and simpler forms of the original problem in order to gain insight into its solution. They monitor and evaluate their progress and change course if necessary. Older students might, depending on the context of the problem, transform algebraic expressions or change the viewing window on their graphing calculator to get the information they need. Mathematically proficient students can explain correspondences between equations, verbal descriptions, tables, and graphs or draw diagrams of important features and relationships, graph data, and search for regularity or trends. Younger students might rely on using concrete objects or pictures to help conceptualize and solve a problem. Mathematically proficient students check their answers to problems using a different method, and they continually ask themselves, “Does this make sense?” They can understand the approaches of others to solving complex problems and identify correspondences between different approaches. Use previously learned knowledge to make sense of problems and persevere in solving them. Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Make sense of problems and persevere in solving them. Make sense of problems and persevere in solving them. Make sense of problems and persevere in solving them. 8-9: Practice Buddy: Additional Practice Curriculum Standards: Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Make sense of problems and persevere in solving them. Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Make sense of problems and persevere in solving them. Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Make sense of problems and persevere in solving them. Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution. They analyze givens, constraints, relationships, and goals. They make conjectures about the form and meaning of the solution and plan a solution pathway rather than simply jumping into a solution attempt. They consider analogous problems, and try special cases and simpler forms of the original problem in order to gain insight into its solution. They monitor and evaluate their progress and change course if necessary. Older students might, depending on the context of the problem, transform algebraic expressions or change the viewing window on their graphing calculator to get the information they need. Mathematically proficient students can explain correspondences between equations, verbal descriptions, tables, and graphs or draw diagrams of important features and relationships, graph data, and search for regularity or trends. Younger students might rely on using concrete objects or pictures to help conceptualize and solve a problem. Mathematically proficient students check their answers to problems using a different method, and they continually ask themselves, “Does this make sense?” They can understand the approaches of others to solving complex problems and identify correspondences between different approaches. Use previously learned knowledge to make sense of problems and persevere in solving them. Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Make sense of problems and persevere in solving them. Make sense of problems and persevere in solving them. Make sense of problems and persevere in solving them. 8-9: Interactive Additional Practice Step 3: Assess & Differentiate 8-9: Practice Buddy: Additional Practice Curriculum Standards: Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Make sense of problems and persevere in solving them. Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Make sense of problems and persevere in solving them. Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Make sense of problems and persevere in solving them. Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution. They analyze givens, constraints, relationships, and goals. They make conjectures about the form and meaning of the solution and plan a solution pathway rather than simply jumping into a solution attempt. They consider analogous problems, and try special cases and simpler forms of the original problem in order to gain insight into its solution. They monitor and evaluate their progress and change course if necessary. Older students might, depending on the context of the problem, transform algebraic expressions or change the viewing window on their graphing calculator to get the information they need. Mathematically proficient students can explain correspondences between equations, verbal descriptions, tables, and graphs or draw diagrams of important features and relationships, graph data, and search for regularity or trends. Younger students might rely on using concrete objects or pictures to help conceptualize and solve a problem. Mathematically proficient students check their answers to problems using a different method, and they continually ask themselves, “Does this make sense?” They can understand the approaches of others to solving complex problems and identify correspondences between different approaches. Use previously learned knowledge to make sense of problems and persevere in solving them. Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Make sense of problems and persevere in solving them. Make sense of problems and persevere in solving them. Make sense of problems and persevere in solving them. 8-9: Enrichment Curriculum Standards: Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Make sense of problems and persevere in solving them. Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Make sense of problems and persevere in solving them. Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Make sense of problems and persevere in solving them. Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution. They analyze givens, constraints, relationships, and goals. They make conjectures about the form and meaning of the solution and plan a solution pathway rather than simply jumping into a solution attempt. They consider analogous problems, and try special cases and simpler forms of the original problem in order to gain insight into its solution. They monitor and evaluate their progress and change course if necessary. Older students might, depending on the context of the problem, transform algebraic expressions or change the viewing window on their graphing calculator to get the information they need. Mathematically proficient students can explain correspondences between equations, verbal descriptions, tables, and graphs or draw diagrams of important features and relationships, graph data, and search for regularity or trends. Younger students might rely on using concrete objects or pictures to help conceptualize and solve a problem. Mathematically proficient students check their answers to problems using a different method, and they continually ask themselves, “Does this make sense?” They can understand the approaches of others to solving complex problems and identify correspondences between different approaches. Use previously learned knowledge to make sense of problems and persevere in solving them. Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Make sense of problems and persevere in solving them. Make sense of problems and persevere in solving them. Make sense of problems and persevere in solving them. 8-9: Quick Check Curriculum Standards: Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Make sense of problems and persevere in solving them. Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Make sense of problems and persevere in solving them. Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Make sense of problems and persevere in solving them. Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution. They analyze givens, constraints, relationships, and goals. They make conjectures about the form and meaning of the solution and plan a solution pathway rather than simply jumping into a solution attempt. They consider analogous problems, and try special cases and simpler forms of the original problem in order to gain insight into its solution. They monitor and evaluate their progress and change course if necessary. Older students might, depending on the context of the problem, transform algebraic expressions or change the viewing window on their graphing calculator to get the information they need. Mathematically proficient students can explain correspondences between equations, verbal descriptions, tables, and graphs or draw diagrams of important features and relationships, graph data, and search for regularity or trends. Younger students might rely on using concrete objects or pictures to help conceptualize and solve a problem. Mathematically proficient students check their answers to problems using a different method, and they continually ask themselves, “Does this make sense?” They can understand the approaches of others to solving complex problems and identify correspondences between different approaches. Use previously learned knowledge to make sense of problems and persevere in solving them. Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Make sense of problems and persevere in solving them. Make sense of problems and persevere in solving them. Make sense of problems and persevere in solving them. 8-9: Lesson Self-Assessment 8-9: Reteach to Build Understanding Curriculum Standards: Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Make sense of problems and persevere in solving them. Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Make sense of problems and persevere in solving them. Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Make sense of problems and persevere in solving them. Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution. They analyze givens, constraints, relationships, and goals. They make conjectures about the form and meaning of the solution and plan a solution pathway rather than simply jumping into a solution attempt. They consider analogous problems, and try special cases and simpler forms of the original problem in order to gain insight into its solution. They monitor and evaluate their progress and change course if necessary. Older students might, depending on the context of the problem, transform algebraic expressions or change the viewing window on their graphing calculator to get the information they need. Mathematically proficient students can explain correspondences between equations, verbal descriptions, tables, and graphs or draw diagrams of important features and relationships, graph data, and search for regularity or trends. Younger students might rely on using concrete objects or pictures to help conceptualize and solve a problem. Mathematically proficient students check their answers to problems using a different method, and they continually ask themselves, “Does this make sense?” They can understand the approaches of others to solving complex problems and identify correspondences between different approaches. Use previously learned knowledge to make sense of problems and persevere in solving them. Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Make sense of problems and persevere in solving them. Make sense of problems and persevere in solving them. Make sense of problems and persevere in solving them. 8-9: Build Mathematical Literacy Curriculum Standards: Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 5 topics and texts, building on others’ ideas and expressing their own clearly. (a) Come to discussions prepared, having read or studied required material; explicitly draw on that preparation and other information known about the topic to explore ideas under discussion. (b) Follow agreed-upon rules for discussions and carry out assigned roles. (c) Pose and respond to specific questions by making comments that contribute to the discussion and elaborate on the remarks of others. (d) Review the key ideas expressed and draw conclusions in light of information and knowledge gained from the discussions. English language learners communicate for social and instructional purposes within the school setting. Summarize a written text read aloud or information presented in diverse media and formats, including visually, quantitatively, and orally. Summarize the points a speaker makes and explain how each claim is supported by reasons and evidence. Write informative/explanatory texts to examine a topic and convey ideas and information clearly. (a) Introduce a topic clearly, provide a general observation and focus, and group related information logically; include formatting (e.g., headings), illustrations, and multimedia when useful to aiding comprehension. (b) Develop the topic with facts, definitions, concrete details, quotations, or other information and examples related to the topic. (c) Link ideas within and across categories of information using words, phrases, and clauses (e.g., in contrast, especially). (d) Use precise language and domain-specific vocabulary to inform about or explain the topic. (e) Provide a concluding statement or section related to the information or explanation presented. English language learners communicate information, ideas and concepts necessary for academic success in the content area of Mathematics. 8-9: Enrichment Game: Save the Word: Grade 5 Topics 1-8 8-9: enVision STEM Activity Curriculum Standards: Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Make sense of problems and persevere in solving them. Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Make sense of problems and persevere in solving them. Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Make sense of problems and persevere in solving them. Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution. They analyze givens, constraints, relationships, and goals. They make conjectures about the form and meaning of the solution and plan a solution pathway rather than simply jumping into a solution attempt. They consider analogous problems, and try special cases and simpler forms of the original problem in order to gain insight into its solution. They monitor and evaluate their progress and change course if necessary. Older students might, depending on the context of the problem, transform algebraic expressions or change the viewing window on their graphing calculator to get the information they need. Mathematically proficient students can explain correspondences between equations, verbal descriptions, tables, and graphs or draw diagrams of important features and relationships, graph data, and search for regularity or trends. Younger students might rely on using concrete objects or pictures to help conceptualize and solve a problem. Mathematically proficient students check their answers to problems using a different method, and they continually ask themselves, “Does this make sense?” They can understand the approaches of others to solving complex problems and identify correspondences between different approaches. Use previously learned knowledge to make sense of problems and persevere in solving them. Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Make sense of problems and persevere in solving them. Make sense of problems and persevere in solving them. Make sense of problems and persevere in solving them. 8-9: Another Look Curriculum Standards: Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Make sense of problems and persevere in solving them. Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Make sense of problems and persevere in solving them. Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Make sense of problems and persevere in solving them. Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution. They analyze givens, constraints, relationships, and goals. They make conjectures about the form and meaning of the solution and plan a solution pathway rather than simply jumping into a solution attempt. They consider analogous problems, and try special cases and simpler forms of the original problem in order to gain insight into its solution. They monitor and evaluate their progress and change course if necessary. Older students might, depending on the context of the problem, transform algebraic expressions or change the viewing window on their graphing calculator to get the information they need. Mathematically proficient students can explain correspondences between equations, verbal descriptions, tables, and graphs or draw diagrams of important features and relationships, graph data, and search for regularity or trends. Younger students might rely on using concrete objects or pictures to help conceptualize and solve a problem. Mathematically proficient students check their answers to problems using a different method, and they continually ask themselves, “Does this make sense?” They can understand the approaches of others to solving complex problems and identify correspondences between different approaches. Use previously learned knowledge to make sense of problems and persevere in solving them. Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Make sense of problems and persevere in solving them. Make sense of problems and persevere in solving them. Make sense of problems and persevere in solving them. Spanish Resources 8-9: eText del Libro del estudiante 8-9: Repaso diario 8-9: Aprendizaje visual 8-9: Amigo de práctica: Práctica adicional 8-9: Práctica adicional interactiva 8-9: Refuerzo para mejorar la comprensión 8-9: Desarrollar la competencia matemática 8-9: Ampliación Topic 8: End of Topic Interactive Student Edition: End of Topic 8 Topic 8: Fluency Practice Activity Interactive Student Edition: Topic 8 Assessment Practice Interactive Student Edition: Topic 8 Performance Task Topic 8 Performance Task Topic 8 Assessment 9-4: Center Games 8-5: Visual Learning Curriculum Standards: Interpret the product a/b x q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = (ac)/(bd). Interpret the product (a/b) × q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. Interpret the product (a/b) × q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = ac/bd.) Multiply two fractions. Interpret the product a/b x q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = (ac)/(bd). Multiply a fraction (including mixed numbers) by a fraction. 8-1: Visual Learning Curriculum Standards: Interpret the product a/b x q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = (ac)/(bd). Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Interpret the product (a/b) × q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction. Interpret the product (a/b) × q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = ac/bd.) Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Multiply a fraction by a whole number. Interpret the product a/b x q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = (ac)/(bd). 8-2: Visual Learning Curriculum Standards: Interpret the product a/b x q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = (ac)/(bd). Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Interpret the product (a/b) × q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Interpret the product (a/b) × q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = ac/bd.) Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Multiply a whole number by a fraction. Interpret the product a/b x q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = (ac)/(bd). 8-3: Visual Learning Curriculum Standards: Interpret the product a/b x q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = (ac)/(bd). Interpret the product (a/b) × q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. Interpret the product (a/b) × q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = ac/bd.) Multiply fractions and whole numbers. Interpret the product a/b x q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = (ac)/(bd). 8-9: Visual Learning Curriculum Standards: Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Make sense of problems and persevere in solving them. Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Make sense of problems and persevere in solving them. Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Make sense of problems and persevere in solving them. Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution. They analyze givens, constraints, relationships, and goals. They make conjectures about the form and meaning of the solution and plan a solution pathway rather than simply jumping into a solution attempt. They consider analogous problems, and try special cases and simpler forms of the original problem in order to gain insight into its solution. They monitor and evaluate their progress and change course if necessary. Older students might, depending on the context of the problem, transform algebraic expressions or change the viewing window on their graphing calculator to get the information they need. Mathematically proficient students can explain correspondences between equations, verbal descriptions, tables, and graphs or draw diagrams of important features and relationships, graph data, and search for regularity or trends. Younger students might rely on using concrete objects or pictures to help conceptualize and solve a problem. Mathematically proficient students check their answers to problems using a different method, and they continually ask themselves, “Does this make sense?” They can understand the approaches of others to solving complex problems and identify correspondences between different approaches. Use previously learned knowledge to make sense of problems and persevere in solving them. Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Make sense of problems and persevere in solving them. Make sense of problems and persevere in solving them. Make sense of problems and persevere in solving them. 8-6: Visual Learning Curriculum Standards: Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side lengths, and show that the area is the same as would be found by multiplying the side lengths. Multiply fractional side lengths to find areas of rectangles, and represent fraction products as rectangular areas. Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side lengths, and show that the area is the same as would be found by multiplying the side lengths. Multiply fractional side lengths to find areas of rectangles, and represent fraction products as rectangular areas. Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side lengths, and show that the area is the same as would be found by multiplying the side lengths. Multiply fractional side lengths to find areas of rectangles, and represent fraction products as rectangular areas. Find the area of a rectangle using fractions and diagrams. Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side lengths, and show that the area is the same as would be found by multiplying the side lengths. Multiply fractional side lengths to find areas of rectangles, and represent fraction products as rectangular areas. Multiply a fraction (including mixed numbers) by a fraction. 8-7: Visual Learning Curriculum Standards: Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Use models, equations and previously learned strategies to multiply mixed numbers. Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Multiply a fraction (including mixed numbers) by a fraction. Topic 8 Online Assessment Curriculum Standards: Interpret the product a/b x q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = (ac)/(bd). Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side lengths, and show that the area is the same as would be found by multiplying the side lengths. Multiply fractional side lengths to find areas of rectangles, and represent fraction products as rectangular areas. Make sense of problems and persevere in solving them. Interpret the product (a/b) × q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. Interpret the product (a/b) × q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = ac/bd.) Multiply fractions and whole numbers. Interpret the product a/b x q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = (ac)/(bd). Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Multiply a whole number by a fraction. Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction. Multiply a fraction by a whole number. Use models, equations and previously learned strategies to multiply mixed numbers. Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Multiply a fraction (including mixed numbers) by a fraction. Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side lengths, and show that the area is the same as would be found by multiplying the side lengths. Multiply fractional side lengths to find areas of rectangles, and represent fraction products as rectangular areas. Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side lengths, and show that the area is the same as would be found by multiplying the side lengths. Multiply fractional side lengths to find areas of rectangles, and represent fraction products as rectangular areas. Find the area of a rectangle using fractions and diagrams. Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side lengths, and show that the area is the same as would be found by multiplying the side lengths. Multiply fractional side lengths to find areas of rectangles, and represent fraction products as rectangular areas. Multiply two fractions. Make sense of problems and persevere in solving them. Make sense of problems and persevere in solving them. Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution. They analyze givens, constraints, relationships, and goals. They make conjectures about the form and meaning of the solution and plan a solution pathway rather than simply jumping into a solution attempt. They consider analogous problems, and try special cases and simpler forms of the original problem in order to gain insight into its solution. They monitor and evaluate their progress and change course if necessary. Older students might, depending on the context of the problem, transform algebraic expressions or change the viewing window on their graphing calculator to get the information they need. Mathematically proficient students can explain correspondences between equations, verbal descriptions, tables, and graphs or draw diagrams of important features and relationships, graph data, and search for regularity or trends. Younger students might rely on using concrete objects or pictures to help conceptualize and solve a problem. Mathematically proficient students check their answers to problems using a different method, and they continually ask themselves, “Does this make sense?” They can understand the approaches of others to solving complex problems and identify correspondences between different approaches. Use previously learned knowledge to make sense of problems and persevere in solving them. Make sense of problems and persevere in solving them. Make sense of problems and persevere in solving them. Make sense of problems and persevere in solving them. Topic 8 Spanish Assessments Tema 8: Tarea de rendimento Tema 8: Evaluación Topics 1–8: Cumulative/Benchmark Assessments Topics 1–8: Cumulative/Benchmark Assessment 2-6: Another Look Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Model with mathematics. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Model with mathematics. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Model with mathematics. Mathematically proficient students can apply the mathematics they know to solve problems arising in everyday life, society, and the workplace. In early grades, this might be as simple as writing an addition equation to describe a situation. In middle grades, a student might apply proportional reasoning to plan a school event or analyze a problem in the community. By high school, a student might use geometry to solve a design problem or use a function to describe how one quantity of interest depends on another. Mathematically proficient students who can apply what they know are comfortable making assumptions and approximations to simplify a complicated situation, realizing that these may need revision later. They are able to identify important quantities in a practical situation and map their relationships using such tools as diagrams, two-way tables, graphs, flowcharts and formulas. They can analyze those relationships mathematically to draw conclusions. They routinely interpret their mathematical results in the context of the situation and reflect on whether the results make sense, possibly improving the model if it has not served its purpose. Use prior math knowledge and equations or bar diagrams to solve problems. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Model with mathematics. Model with mathematics. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). Model with mathematics. Add and subtract decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Model addition and subtraction of fractions and decimals using a variety of representations. Estimate sums and differences of decimals and fractions to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. 4-9: Another Look Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Model with mathematics. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Model with mathematics. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Model with mathematics. Mathematically proficient students can apply the mathematics they know to solve problems arising in everyday life, society, and the workplace. In early grades, this might be as simple as writing an addition equation to describe a situation. In middle grades, a student might apply proportional reasoning to plan a school event or analyze a problem in the community. By high school, a student might use geometry to solve a design problem or use a function to describe how one quantity of interest depends on another. Mathematically proficient students who can apply what they know are comfortable making assumptions and approximations to simplify a complicated situation, realizing that these may need revision later. They are able to identify important quantities in a practical situation and map their relationships using such tools as diagrams, two-way tables, graphs, flowcharts and formulas. They can analyze those relationships mathematically to draw conclusions. They routinely interpret their mathematical results in the context of the situation and reflect on whether the results make sense, possibly improving the model if it has not served its purpose. Use previously learned concepts and skills to represent and solve problems. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Model with mathematics. Model with mathematics. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). Model with mathematics. 4-1: Another Look Curriculum Standards: Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Use knowledge about place value and patterns to find the product of a decimal number and a power of 10. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10 and 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. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). 8-1: Another Look Curriculum Standards: Interpret the product a/b x q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = (ac)/(bd). Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Interpret the product (a/b) × q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction. Interpret the product (a/b) × q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = ac/bd.) Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Multiply a fraction by a whole number. Interpret the product a/b x q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = (ac)/(bd). 1-6: Another Look Curriculum Standards: Use place value understanding to round decimals to any place. Use place value understanding to round decimals to any place. Use place value understanding to round decimals to any place. Use place value to round decimals to different places. Use place value understanding to round decimals to any place. Round decimals to any place (limit rounding to ones, tenths, hundredths, or thousandths place). Round numbers to the nearest 0.1, 0.01 and 0.001. 8-5: Another Look Curriculum Standards: Interpret the product a/b x q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = (ac)/(bd). Interpret the product (a/b) × q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. Interpret the product (a/b) × q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = ac/bd.) Multiply two fractions. Interpret the product a/b x q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = (ac)/(bd). Multiply a fraction (including mixed numbers) by a fraction. 1-4: Another Look Curriculum Standards: Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 x 100 + 4 x 10 + 7 x 1 + 3 x (1/10) + 9 x (1/100) + 2 x (1/1000). Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 × 100 + 4 × 10 + 7 × 1 + 3 × (1/10) + 9 × (1/100) + 2 × (1/1000). Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 × 100 + 4 × 10 + 7 × 1 + 3 × (1/10) + 9 × (1/100) + 2 × (1/1000). Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 × 100 + 4 × 10 + 7 × 1 + 3 × (1/10) + 9 × (1/100) + 2 × (1/1000). Read and write numbers with decimals through thousandths using standard form, expanded form, and number names; identify equivalent decimals. Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 x 100 + 4 x 10 + 7 x 1 + 3 x (1/10) + 9 x (1/100) + 2 x (1/1000). Read and write decimals to thousandths using base-ten numerals, word form, and expanded form. Read and write decimals using place value to describe decimals in terms of groups from millionths to millions. 1-1: Another Look Curriculum Standards: Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. Use patterns and the properties of multiplication to calculate a product when multiplying by a power of 10; use whole-number exponents to write powers of 10. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10 and 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. Read and write decimals using place value to describe decimals in terms of groups from millionths to millions. 2-3: Another Look Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Model sums and differences of decimals. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). Add and subtract decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Model addition and subtraction of fractions and decimals using a variety of representations. Estimate sums and differences of decimals and fractions to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. 2-4: Another Look Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add decimals to hundredths using familiar strategies, such as partial sums. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). Add and subtract decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Model addition and subtraction of fractions and decimals using a variety of representations. Estimate sums and differences of decimals and fractions to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. 6-5: Another Look Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Use models to divide a decimal by a decimal. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). 7-4: Another Look Curriculum Standards: Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Subtract fractions with unlike denominators. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Add and subtract fractions (including mixed numbers) with unlike denominators. (May include multiple methods and representations.) Add and subtract decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Model addition and subtraction of fractions and decimals using a variety of representations. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. 5-8: Another Look Curriculum Standards: 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. Make sense of problems and persevere in solving them. 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. Make sense of problems and persevere in solving them. 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. Make sense of problems and persevere in solving them. Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution. They analyze givens, constraints, relationships, and goals. They make conjectures about the form and meaning of the solution and plan a solution pathway rather than simply jumping into a solution attempt. They consider analogous problems, and try special cases and simpler forms of the original problem in order to gain insight into its solution. They monitor and evaluate their progress and change course if necessary. Older students might, depending on the context of the problem, transform algebraic expressions or change the viewing window on their graphing calculator to get the information they need. Mathematically proficient students can explain correspondences between equations, verbal descriptions, tables, and graphs or draw diagrams of important features and relationships, graph data, and search for regularity or trends. Younger students might rely on using concrete objects or pictures to help conceptualize and solve a problem. Mathematically proficient students check their answers to problems using a different method, and they continually ask themselves, “Does this make sense?” They can understand the approaches of others to solving complex problems and identify correspondences between different approaches. Make sense of problems and keep working. 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. Construct viable arguments and critique the reasoning of others. Make sense of problems and persevere in solving them. Make sense of problems and persevere in solving them. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors. Make sense of problems and persevere in solving them. Divide multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Recognize that quotients can be represented in a variety of ways, including a whole number with a remainder, a fraction or mixed number, or a decimal. Consider the context in which a problem is situated to select the most useful form of the quotient for the solution and use the context to interpret the quotient appropriately. Estimate solutions to arithmetic problems in order to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition, subtraction, multiplication and division of multi-digit whole numbers. Use various strategies, including the inverse relationships between operations, the use of technology, and the context of the problem to assess the reasonableness of results. 7-8: Another Look Curriculum Standards: Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Add mixed numbers using equivalent fractions and a common denominator. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Add and subtract fractions (including mixed numbers) with unlike denominators. (May include multiple methods and representations.) Add and subtract decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Model addition and subtraction of fractions and decimals using a variety of representations. Estimate sums and differences of decimals and fractions to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. 9-1: Center Games 6-6: Another Look Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Reason abstractly and quantitatively. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Reason abstractly and quantitatively. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Reason abstractly and quantitatively. Mathematically proficient students make sense of quantities and their relationships in problem situations. They bring two complementary abilities to bear on problems involving quantitative relationships: the ability to decontextualize—to abstract a given situation and represent it symbolically and manipulate the representing symbols as if they have a life of their own, without necessarily attending to their referents—and the ability to contextualize, to pause as needed during the manipulation process in order to probe into the referents for the symbols involved. Quantitative reasoning entails habits of creating a coherent representation of the problem at hand; considering the units involved; attending to the meaning of quantities, not just how to compute them; and knowing and flexibly using different properties of operations and objects. Use reasoning to solve problems by making sense of quantities and relationships in problem situations. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Reason abstractly and quantitatively. Reason abstractly and quantitatively. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). Reason abstractly and quantitatively. 8-6: Another Look Curriculum Standards: Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side lengths, and show that the area is the same as would be found by multiplying the side lengths. Multiply fractional side lengths to find areas of rectangles, and represent fraction products as rectangular areas. Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side lengths, and show that the area is the same as would be found by multiplying the side lengths. Multiply fractional side lengths to find areas of rectangles, and represent fraction products as rectangular areas. Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side lengths, and show that the area is the same as would be found by multiplying the side lengths. Multiply fractional side lengths to find areas of rectangles, and represent fraction products as rectangular areas. Find the area of a rectangle using fractions and diagrams. Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side lengths, and show that the area is the same as would be found by multiplying the side lengths. Multiply fractional side lengths to find areas of rectangles, and represent fraction products as rectangular areas. Multiply a fraction (including mixed numbers) by a fraction. 8-9: Another Look Curriculum Standards: Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Make sense of problems and persevere in solving them. Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Make sense of problems and persevere in solving them. Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Make sense of problems and persevere in solving them. Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution. They analyze givens, constraints, relationships, and goals. They make conjectures about the form and meaning of the solution and plan a solution pathway rather than simply jumping into a solution attempt. They consider analogous problems, and try special cases and simpler forms of the original problem in order to gain insight into its solution. They monitor and evaluate their progress and change course if necessary. Older students might, depending on the context of the problem, transform algebraic expressions or change the viewing window on their graphing calculator to get the information they need. Mathematically proficient students can explain correspondences between equations, verbal descriptions, tables, and graphs or draw diagrams of important features and relationships, graph data, and search for regularity or trends. Younger students might rely on using concrete objects or pictures to help conceptualize and solve a problem. Mathematically proficient students check their answers to problems using a different method, and they continually ask themselves, “Does this make sense?” They can understand the approaches of others to solving complex problems and identify correspondences between different approaches. Use previously learned knowledge to make sense of problems and persevere in solving them. Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Make sense of problems and persevere in solving them. Make sense of problems and persevere in solving them. Make sense of problems and persevere in solving them. 5-1: Another Look Curriculum Standards: 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. 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. 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. Use place-value patterns and mental math to find quotients. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors. 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. 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. 6-1: Another Look Curriculum Standards: Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Use mental math and place-value patterns to divide a decimal by a power of 10. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). 7-12: Another Look Curriculum Standards: Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Model with mathematics. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. Model with mathematics. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Model with mathematics. Mathematically proficient students can apply the mathematics they know to solve problems arising in everyday life, society, and the workplace. In early grades, this might be as simple as writing an addition equation to describe a situation. In middle grades, a student might apply proportional reasoning to plan a school event or analyze a problem in the community. By high school, a student might use geometry to solve a design problem or use a function to describe how one quantity of interest depends on another. Mathematically proficient students who can apply what they know are comfortable making assumptions and approximations to simplify a complicated situation, realizing that these may need revision later. They are able to identify important quantities in a practical situation and map their relationships using such tools as diagrams, two-way tables, graphs, flowcharts and formulas. They can analyze those relationships mathematically to draw conclusions. They routinely interpret their mathematical results in the context of the situation and reflect on whether the results make sense, possibly improving the model if it has not served its purpose. Represent a problem situation with a mathematical model. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Model with mathematics. Model with mathematics. Add and subtract fractions (including mixed numbers) with unlike denominators. (May include multiple methods and representations.) Model with mathematics. Add and subtract decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Model addition and subtraction of fractions and decimals using a variety of representations. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. 7-3: Another Look Curriculum Standards: Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Add fractions with unlike denominators using equivalent fractions with a common denominator. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Add and subtract fractions (including mixed numbers) with unlike denominators. (May include multiple methods and representations.) Add and subtract decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Model addition and subtraction of fractions and decimals using a variety of representations. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. Topics 1–8: Online Cumulative/Benchmark Assessment Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Reason abstractly and quantitatively. 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. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Model with mathematics. Make sense of problems and persevere in solving them. Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 x 100 + 4 x 10 + 7 x 1 + 3 x (1/10) + 9 x (1/100) + 2 x (1/1000). Interpret the product a/b x q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = (ac)/(bd). Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Use place value understanding to round decimals to any place. Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side lengths, and show that the area is the same as would be found by multiplying the side lengths. Multiply fractional side lengths to find areas of rectangles, and represent fraction products as rectangular areas. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Reason abstractly and quantitatively. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Reason abstractly and quantitatively. Mathematically proficient students make sense of quantities and their relationships in problem situations. They bring two complementary abilities to bear on problems involving quantitative relationships: the ability to decontextualize—to abstract a given situation and represent it symbolically and manipulate the representing symbols as if they have a life of their own, without necessarily attending to their referents—and the ability to contextualize, to pause as needed during the manipulation process in order to probe into the referents for the symbols involved. Quantitative reasoning entails habits of creating a coherent representation of the problem at hand; considering the units involved; attending to the meaning of quantities, not just how to compute them; and knowing and flexibly using different properties of operations and objects. Use reasoning to solve problems by making sense of quantities and relationships in problem situations. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Reason abstractly and quantitatively. Reason abstractly and quantitatively. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). Reason abstractly and quantitatively. 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. 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. Use place-value patterns and mental math to find quotients. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors. 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. 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. Use models to divide a decimal by a decimal. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. Use knowledge about place value and patterns to find the product of a decimal number and a power of 10. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10 and 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. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Add mixed numbers using equivalent fractions and a common denominator. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Add and subtract fractions (including mixed numbers) with unlike denominators. (May include multiple methods and representations.) Add and subtract decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Model addition and subtraction of fractions and decimals using a variety of representations. Estimate sums and differences of decimals and fractions to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. Add fractions with unlike denominators using equivalent fractions with a common denominator. Subtract fractions with unlike denominators. Model with mathematics. Model with mathematics. Mathematically proficient students can apply the mathematics they know to solve problems arising in everyday life, society, and the workplace. In early grades, this might be as simple as writing an addition equation to describe a situation. In middle grades, a student might apply proportional reasoning to plan a school event or analyze a problem in the community. By high school, a student might use geometry to solve a design problem or use a function to describe how one quantity of interest depends on another. Mathematically proficient students who can apply what they know are comfortable making assumptions and approximations to simplify a complicated situation, realizing that these may need revision later. They are able to identify important quantities in a practical situation and map their relationships using such tools as diagrams, two-way tables, graphs, flowcharts and formulas. They can analyze those relationships mathematically to draw conclusions. They routinely interpret their mathematical results in the context of the situation and reflect on whether the results make sense, possibly improving the model if it has not served its purpose. Represent a problem situation with a mathematical model. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Model with mathematics. Model with mathematics. Model with mathematics. Use previously learned concepts and skills to represent and solve problems. Use mental math and place-value patterns to divide a decimal by a power of 10. Make sense of problems and persevere in solving them. Make sense of problems and persevere in solving them. Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution. They analyze givens, constraints, relationships, and goals. They make conjectures about the form and meaning of the solution and plan a solution pathway rather than simply jumping into a solution attempt. They consider analogous problems, and try special cases and simpler forms of the original problem in order to gain insight into its solution. They monitor and evaluate their progress and change course if necessary. Older students might, depending on the context of the problem, transform algebraic expressions or change the viewing window on their graphing calculator to get the information they need. Mathematically proficient students can explain correspondences between equations, verbal descriptions, tables, and graphs or draw diagrams of important features and relationships, graph data, and search for regularity or trends. Younger students might rely on using concrete objects or pictures to help conceptualize and solve a problem. Mathematically proficient students check their answers to problems using a different method, and they continually ask themselves, “Does this make sense?” They can understand the approaches of others to solving complex problems and identify correspondences between different approaches. Make sense of problems and keep working. Construct viable arguments and critique the reasoning of others. Make sense of problems and persevere in solving them. Make sense of problems and persevere in solving them. Make sense of problems and persevere in solving them. Consider the context in which a problem is situated to select the most useful form of the quotient for the solution and use the context to interpret the quotient appropriately. Estimate solutions to arithmetic problems in order to assess the reasonableness of results. Model sums and differences of decimals. Add decimals to hundredths using familiar strategies, such as partial sums. Use patterns and the properties of multiplication to calculate a product when multiplying by a power of 10; use whole- number exponents to write powers of 10. Read and write decimals using place value to describe decimals in terms of groups from millionths to millions. Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 × 100 + 4 × 10 + 7 × 1 + 3 × (1/10) + 9 × (1/100) + 2 × (1/1000). Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 × 100 + 4 × 10 + 7 × 1 + 3 × (1/10) + 9 × (1/100) + 2 × (1/1000). Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 × 100 + 4 × 10 + 7 × 1 + 3 × (1/10) + 9 × (1/100) + 2 × (1/1000). Read and write numbers with decimals through thousandths using standard form, expanded form, and number names; identify equivalent decimals. Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 x 100 + 4 x 10 + 7 x 1 + 3 x (1/10) + 9 x (1/100) + 2 x (1/1000). Read and write decimals to thousandths using base-ten numerals, word form, and expanded form. Interpret the product (a/b) × q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction. Interpret the product (a/b) × q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = ac/bd.) Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Multiply a fraction by a whole number. Interpret the product a/b x q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = (ac)/(bd). Use place value understanding to round decimals to any place. Use place value understanding to round decimals to any place. Use place value to round decimals to different places. Use place value understanding to round decimals to any place. Round decimals to any place (limit rounding to ones, tenths, hundredths, or thousandths place). Round numbers to the nearest 0.1, 0.01 and 0.001. Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side lengths, and show that the area is the same as would be found by multiplying the side lengths. Multiply fractional side lengths to find areas of rectangles, and represent fraction products as rectangular areas. Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side lengths, and show that the area is the same as would be found by multiplying the side lengths. Multiply fractional side lengths to find areas of rectangles, and represent fraction products as rectangular areas. Find the area of a rectangle using fractions and diagrams. Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side lengths, and show that the area is the same as would be found by multiplying the side lengths. Multiply fractional side lengths to find areas of rectangles, and represent fraction products as rectangular areas. Multiply a fraction (including mixed numbers) by a fraction. Multiply two fractions. Use prior math knowledge and equations or bar diagrams to solve problems. Use previously learned knowledge to make sense of problems and persevere in solving them. Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Topic 9: Apply Understanding of Division to Divide Fractions Topic 9: Today's Challenge Topic 9: Beginning of Topic Interactive Student Edition: Beginning of Topic 9 Topic 9: enVision STEM Activity Grade 5 Topic 9: Review What You Know Topic 9: Vocabulary Cards 9-1: Fractions and Division Interactive Student Edition: Grade 5 Lesson 9-1 Math Anytime 9-1: Daily Review Topic 9: Today's Challenge Step 1: Problem-Based Learning 9-1: Solve & Share Curriculum Standards: Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. For example, interpret 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3, and that when 3 wholes are shared equally among 4 people each person has a share of size 3/4. If 9 people want to share a 50-pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie? English language learners communicate for social and instructional purposes within the school setting. Write informative/explanatory texts to examine a topic and convey ideas and information clearly. (a) Introduce a topic clearly, provide a general observation and focus, and group related information logically; include formatting (e.g., headings), illustrations, and multimedia when useful to aiding comprehension. (b) Develop the topic with facts, definitions, concrete details, quotations, or other information and examples related to the topic. (c) Link ideas within and across categories of information using words, phrases, and clauses (e.g., in contrast, especially). (d) Use precise language and domain-specific vocabulary to inform about or explain the topic. (e) Provide a concluding statement or section related to the information or explanation presented. English language learners communicate information, ideas and concepts necessary for academic success in the content area of Mathematics. Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 5 topics and texts, building on others’ ideas and expressing their own clearly. (a) Come to discussions prepared, having read or studied required material; explicitly draw on that preparation and other information known about the topic to explore ideas under discussion. (b) Follow agreed-upon rules for discussions and carry out assigned roles. (c) Pose and respond to specific questions by making comments that contribute to the discussion and elaborate on the remarks of others. (d) Review the key ideas expressed and draw conclusions in light of information and knowledge gained from the discussions. Summarize a written text read aloud or information presented in diverse media and formats, including visually, quantitatively, and orally. Summarize the points a speaker makes and explain how each claim is supported by reasons and evidence. Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. For example, interpret 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3, and that when 3 wholes are shared equally among 4 people each person has a share of size 3/4. If 9 people want to share a 50-pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie? Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. For example, interpret 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3, and that when 3 wholes are shared equally among 4 people each person has a share of size 3/4. If 9 people want to share a 50-pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie? Understand how fractions are related to division. Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. For example, interpret 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3, and that when 3 wholes are shared equally among 4 people each person has a share of size 3/4. If 9 people want to share a 50-pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie? Solve word problems involving division of whole numbers leading to answers in the form of fractions (including mixed numbers). Step 2: Visual Learning 9-1: Visual Learning Curriculum Standards: Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. For example, interpret 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3, and that when 3 wholes are shared equally among 4 people each person has a share of size 3/4. If 9 people want to share a 50-pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie? Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. For example, interpret 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3, and that when 3 wholes are shared equally among 4 people each person has a share of size 3/4. If 9 people want to share a 50-pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie? Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. For example, interpret 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3, and that when 3 wholes are shared equally among 4 people each person has a share of size 3/4. If 9 people want to share a 50-pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie? Understand how fractions are related to division. Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. For example, interpret 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3, and that when 3 wholes are shared equally among 4 people each person has a share of size 3/4. If 9 people want to share a 50-pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie? Solve word problems involving division of whole numbers leading to answers in the form of fractions (including mixed numbers). 9-1: Convince Me! Curriculum Standards: Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. For example, interpret 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3, and that when 3 wholes are shared equally among 4 people each person has a share of size 3/4. If 9 people want to share a 50-pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie? Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. For example, interpret 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3, and that when 3 wholes are shared equally among 4 people each person has a share of size 3/4. If 9 people want to share a 50-pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie? Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. For example, interpret 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3, and that when 3 wholes are shared equally among 4 people each person has a share of size 3/4. If 9 people want to share a 50-pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie? Understand how fractions are related to division. Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. For example, interpret 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3, and that when 3 wholes are shared equally among 4 people each person has a share of size 3/4. If 9 people want to share a 50-pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie? Solve word problems involving division of whole numbers leading to answers in the form of fractions (including mixed numbers). Practice and Problem Solving 9-1: Student Edition Practice Curriculum Standards: Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. For example, interpret 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3, and that when 3 wholes are shared equally among 4 people each person has a share of size 3/4. If 9 people want to share a 50-pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie? Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. For example, interpret 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3, and that when 3 wholes are shared equally among 4 people each person has a share of size 3/4. If 9 people want to share a 50-pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie? Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. For example, interpret 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3, and that when 3 wholes are shared equally among 4 people each person has a share of size 3/4. If 9 people want to share a 50-pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie? Understand how fractions are related to division. Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. For example, interpret 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3, and that when 3 wholes are shared equally among 4 people each person has a share of size 3/4. If 9 people want to share a 50-pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie? Solve word problems involving division of whole numbers leading to answers in the form of fractions (including mixed numbers). 9-1: Practice Buddy: Independent Practice; Problem Solving Curriculum Standards: Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. For example, interpret 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3, and that when 3 wholes are shared equally among 4 people each person has a share of size 3/4. If 9 people want to share a 50-pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie? Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. For example, interpret 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3, and that when 3 wholes are shared equally among 4 people each person has a share of size 3/4. If 9 people want to share a 50-pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie? Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. For example, interpret 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3, and that when 3 wholes are shared equally among 4 people each person has a share of size 3/4. If 9 people want to share a 50-pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie? Understand how fractions are related to division. Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. For example, interpret 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3, and that when 3 wholes are shared equally among 4 people each person has a share of size 3/4. If 9 people want to share a 50-pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie? Solve word problems involving division of whole numbers leading to answers in the form of fractions (including mixed numbers). 9-1: Practice Buddy: Additional Practice Curriculum Standards: Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. For example, interpret 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3, and that when 3 wholes are shared equally among 4 people each person has a share of size 3/4. If 9 people want to share a 50-pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie? Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. For example, interpret 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3, and that when 3 wholes are shared equally among 4 people each person has a share of size 3/4. If 9 people want to share a 50-pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie? Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. For example, interpret 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3, and that when 3 wholes are shared equally among 4 people each person has a share of size 3/4. If 9 people want to share a 50-pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie? Understand how fractions are related to division. Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. For example, interpret 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3, and that when 3 wholes are shared equally among 4 people each person has a share of size 3/4. If 9 people want to share a 50-pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie? Solve word problems involving division of whole numbers leading to answers in the form of fractions (including mixed numbers). 9-1: Interactive Additional Practice Step 3: Assess & Differentiate 9-1: Practice Buddy: Additional Practice Curriculum Standards: Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. For example, interpret 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3, and that when 3 wholes are shared equally among 4 people each person has a share of size 3/4. If 9 people want to share a 50-pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie? Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. For example, interpret 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3, and that when 3 wholes are shared equally among 4 people each person has a share of size 3/4. If 9 people want to share a 50-pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie? Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. For example, interpret 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3, and that when 3 wholes are shared equally among 4 people each person has a share of size 3/4. If 9 people want to share a 50-pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie? Understand how fractions are related to division. Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. For example, interpret 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3, and that when 3 wholes are shared equally among 4 people each person has a share of size 3/4. If 9 people want to share a 50-pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie? Solve word problems involving division of whole numbers leading to answers in the form of fractions (including mixed numbers). 9-1: Enrichment Curriculum Standards: Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. For example, interpret 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3, and that when 3 wholes are shared equally among 4 people each person has a share of size 3/4. If 9 people want to share a 50-pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie? Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. For example, interpret 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3, and that when 3 wholes are shared equally among 4 people each person has a share of size 3/4. If 9 people want to share a 50-pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie? Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. For example, interpret 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3, and that when 3 wholes are shared equally among 4 people each person has a share of size 3/4. If 9 people want to share a 50-pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie? Understand how fractions are related to division. Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. For example, interpret 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3, and that when 3 wholes are shared equally among 4 people each person has a share of size 3/4. If 9 people want to share a 50-pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie? Solve word problems involving division of whole numbers leading to answers in the form of fractions (including mixed numbers). 9-1: Quick Check Curriculum Standards: Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. For example, interpret 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3, and that when 3 wholes are shared equally among 4 people each person has a share of size 3/4. If 9 people want to share a 50-pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie? Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. For example, interpret 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3, and that when 3 wholes are shared equally among 4 people each person has a share of size 3/4. If 9 people want to share a 50-pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie? Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. For example, interpret 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3, and that when 3 wholes are shared equally among 4 people each person has a share of size 3/4. If 9 people want to share a 50-pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie? Understand how fractions are related to division. Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. For example, interpret 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3, and that when 3 wholes are shared equally among 4 people each person has a share of size 3/4. If 9 people want to share a 50-pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie? Solve word problems involving division of whole numbers leading to answers in the form of fractions (including mixed numbers). 9-1: Lesson Self-Assessment 9-1: Reteach to Build Understanding Curriculum Standards: Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. For example, interpret 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3, and that when 3 wholes are shared equally among 4 people each person has a share of size 3/4. If 9 people want to share a 50-pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie? Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. For example, interpret 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3, and that when 3 wholes are shared equally among 4 people each person has a share of size 3/4. If 9 people want to share a 50-pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie? Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. For example, interpret 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3, and that when 3 wholes are shared equally among 4 people each person has a share of size 3/4. If 9 people want to share a 50-pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie? Understand how fractions are related to division. Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. For example, interpret 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3, and that when 3 wholes are shared equally among 4 people each person has a share of size 3/4. If 9 people want to share a 50-pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie? Solve word problems involving division of whole numbers leading to answers in the form of fractions (including mixed numbers). 9-1: Build Mathematical Literacy Curriculum Standards: Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 5 topics and texts, building on others’ ideas and expressing their own clearly. (a) Come to discussions prepared, having read or studied required material; explicitly draw on that preparation and other information known about the topic to explore ideas under discussion. (b) Follow agreed-upon rules for discussions and carry out assigned roles. (c) Pose and respond to specific questions by making comments that contribute to the discussion and elaborate on the remarks of others. (d) Review the key ideas expressed and draw conclusions in light of information and knowledge gained from the discussions. English language learners communicate for social and instructional purposes within the school setting. Summarize a written text read aloud or information presented in diverse media and formats, including visually, quantitatively, and orally. Summarize the points a speaker makes and explain how each claim is supported by reasons and evidence. Write informative/explanatory texts to examine a topic and convey ideas and information clearly. (a) Introduce a topic clearly, provide a general observation and focus, and group related information logically; include formatting (e.g., headings), illustrations, and multimedia when useful to aiding comprehension. (b) Develop the topic with facts, definitions, concrete details, quotations, or other information and examples related to the topic. (c) Link ideas within and across categories of information using words, phrases, and clauses (e.g., in contrast, especially). (d) Use precise language and domain-specific vocabulary to inform about or explain the topic. (e) Provide a concluding statement or section related to the information or explanation presented. English language learners communicate information, ideas and concepts necessary for academic success in the content area of Mathematics. 9-1: Enrichment 9-1: Digital Math Tool Activity 9-1: Pick a Project 9-1: Another Look Curriculum Standards: Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. For example, interpret 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3, and that when 3 wholes are shared equally among 4 people each person has a share of size 3/4. If 9 people want to share a 50-pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie? Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. For example, interpret 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3, and that when 3 wholes are shared equally among 4 people each person has a share of size 3/4. If 9 people want to share a 50-pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie? Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. For example, interpret 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3, and that when 3 wholes are shared equally among 4 people each person has a share of size 3/4. If 9 people want to share a 50-pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie? Understand how fractions are related to division. Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. For example, interpret 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3, and that when 3 wholes are shared equally among 4 people each person has a share of size 3/4. If 9 people want to share a 50-pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie? Solve word problems involving division of whole numbers leading to answers in the form of fractions (including mixed numbers). Spanish Resources 9-1: eText del Libro del estudiante 9-1: Repaso diario 9-1: Aprendizaje visual 9-1: Amigo de práctica: Práctica adicional 9-1: Práctica adicional interactiva 9-1: Refuerzo para mejorar la comprensión 9-1: Desarrollar la competencia matemática 9-1: Ampliación 9-2: Fractions and Mixed Numbers as Quotients Interactive Student Edition: Grade 5 Lesson 9-2 Math Anytime 9-2: Daily Review Topic 9: Today's Challenge Step 1: Problem-Based Learning 9-2: Solve & Share Curriculum Standards: Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. For example, interpret 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3, and that when 3 wholes are shared equally among 4 people each person has a share of size 3/4. If 9 people want to share a 50-pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie? English language learners communicate for social and instructional purposes within the school setting. Write informative/explanatory texts to examine a topic and convey ideas and information clearly. (a) Introduce a topic clearly, provide a general observation and focus, and group related information logically; include formatting (e.g., headings), illustrations, and multimedia when useful to aiding comprehension. (b) Develop the topic with facts, definitions, concrete details, quotations, or other information and examples related to the topic. (c) Link ideas within and across categories of information using words, phrases, and clauses (e.g., in contrast, especially). (d) Use precise language and domain-specific vocabulary to inform about or explain the topic. (e) Provide a concluding statement or section related to the information or explanation presented. English language learners communicate information, ideas and concepts necessary for academic success in the content area of Mathematics. Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 5 topics and texts, building on others’ ideas and expressing their own clearly. (a) Come to discussions prepared, having read or studied required material; explicitly draw on that preparation and other information known about the topic to explore ideas under discussion. (b) Follow agreed-upon rules for discussions and carry out assigned roles. (c) Pose and respond to specific questions by making comments that contribute to the discussion and elaborate on the remarks of others. (d) Review the key ideas expressed and draw conclusions in light of information and knowledge gained from the discussions. Summarize a written text read aloud or information presented in diverse media and formats, including visually, quantitatively, and orally. Summarize the points a speaker makes and explain how each claim is supported by reasons and evidence. Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. For example, interpret 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3, and that when 3 wholes are shared equally among 4 people each person has a share of size 3/4. If 9 people want to share a 50-pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie? Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. For example, interpret 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3, and that when 3 wholes are shared equally among 4 people each person has a share of size 3/4. If 9 people want to share a 50-pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie? Implement division of fractions to show quotients as fractions and mixed numbers. Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. For example, interpret 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3, and that when 3 wholes are shared equally among 4 people each person has a share of size 3/4. If 9 people want to share a 50-pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie? Solve word problems involving division of whole numbers leading to answers in the form of fractions (including mixed numbers). Step 2: Visual Learning 9-2: Visual Learning Curriculum Standards: Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. For example, interpret 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3, and that when 3 wholes are shared equally among 4 people each person has a share of size 3/4. If 9 people want to share a 50-pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie? Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. For example, interpret 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3, and that when 3 wholes are shared equally among 4 people each person has a share of size 3/4. If 9 people want to share a 50-pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie? Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. For example, interpret 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3, and that when 3 wholes are shared equally among 4 people each person has a share of size 3/4. If 9 people want to share a 50-pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie? Implement division of fractions to show quotients as fractions and mixed numbers. Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. For example, interpret 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3, and that when 3 wholes are shared equally among 4 people each person has a share of size 3/4. If 9 people want to share a 50-pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie? Solve word problems involving division of whole numbers leading to answers in the form of fractions (including mixed numbers). 9-2: Convince Me! Curriculum Standards: Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. For example, interpret 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3, and that when 3 wholes are shared equally among 4 people each person has a share of size 3/4. If 9 people want to share a 50-pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie? Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. For example, interpret 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3, and that when 3 wholes are shared equally among 4 people each person has a share of size 3/4. If 9 people want to share a 50-pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie? Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. For example, interpret 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3, and that when 3 wholes are shared equally among 4 people each person has a share of size 3/4. If 9 people want to share a 50-pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie? Implement division of fractions to show quotients as fractions and mixed numbers. Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. For example, interpret 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3, and that when 3 wholes are shared equally among 4 people each person has a share of size 3/4. If 9 people want to share a 50-pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie? Solve word problems involving division of whole numbers leading to answers in the form of fractions (including mixed numbers). Practice and Problem Solving 9-2: Student Edition Practice Curriculum Standards: Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. For example, interpret 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3, and that when 3 wholes are shared equally among 4 people each person has a share of size 3/4. If 9 people want to share a 50-pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie? Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. For example, interpret 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3, and that when 3 wholes are shared equally among 4 people each person has a share of size 3/4. If 9 people want to share a 50-pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie? Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. For example, interpret 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3, and that when 3 wholes are shared equally among 4 people each person has a share of size 3/4. If 9 people want to share a 50-pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie? Implement division of fractions to show quotients as fractions and mixed numbers. Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. For example, interpret 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3, and that when 3 wholes are shared equally among 4 people each person has a share of size 3/4. If 9 people want to share a 50-pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie? Solve word problems involving division of whole numbers leading to answers in the form of fractions (including mixed numbers). 9-2: Practice Buddy: Independent Practice; Problem Solving Curriculum Standards: Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. For example, interpret 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3, and that when 3 wholes are shared equally among 4 people each person has a share of size 3/4. If 9 people want to share a 50-pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie? Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. For example, interpret 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3, and that when 3 wholes are shared equally among 4 people each person has a share of size 3/4. If 9 people want to share a 50-pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie? Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. For example, interpret 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3, and that when 3 wholes are shared equally among 4 people each person has a share of size 3/4. If 9 people want to share a 50-pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie? Implement division of fractions to show quotients as fractions and mixed numbers. Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. For example, interpret 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3, and that when 3 wholes are shared equally among 4 people each person has a share of size 3/4. If 9 people want to share a 50-pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie? Solve word problems involving division of whole numbers leading to answers in the form of fractions (including mixed numbers). 9-2: Practice Buddy: Additional Practice Curriculum Standards: Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. For example, interpret 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3, and that when 3 wholes are shared equally among 4 people each person has a share of size 3/4. If 9 people want to share a 50-pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie? Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. For example, interpret 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3, and that when 3 wholes are shared equally among 4 people each person has a share of size 3/4. If 9 people want to share a 50-pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie? Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. For example, interpret 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3, and that when 3 wholes are shared equally among 4 people each person has a share of size 3/4. If 9 people want to share a 50-pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie? Implement division of fractions to show quotients as fractions and mixed numbers. Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. For example, interpret 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3, and that when 3 wholes are shared equally among 4 people each person has a share of size 3/4. If 9 people want to share a 50-pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie? Solve word problems involving division of whole numbers leading to answers in the form of fractions (including mixed numbers). 9-2: Interactive Additional Practice Step 3: Assess & Differentiate 9-2: Practice Buddy: Additional Practice Curriculum Standards: Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. For example, interpret 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3, and that when 3 wholes are shared equally among 4 people each person has a share of size 3/4. If 9 people want to share a 50-pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie? Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. For example, interpret 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3, and that when 3 wholes are shared equally among 4 people each person has a share of size 3/4. If 9 people want to share a 50-pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie? Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. For example, interpret 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3, and that when 3 wholes are shared equally among 4 people each person has a share of size 3/4. If 9 people want to share a 50-pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie? Implement division of fractions to show quotients as fractions and mixed numbers. Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. For example, interpret 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3, and that when 3 wholes are shared equally among 4 people each person has a share of size 3/4. If 9 people want to share a 50-pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie? Solve word problems involving division of whole numbers leading to answers in the form of fractions (including mixed numbers). 9-2: Enrichment Curriculum Standards: Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. For example, interpret 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3, and that when 3 wholes are shared equally among 4 people each person has a share of size 3/4. If 9 people want to share a 50-pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie? Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. For example, interpret 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3, and that when 3 wholes are shared equally among 4 people each person has a share of size 3/4. If 9 people want to share a 50-pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie? Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. For example, interpret 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3, and that when 3 wholes are shared equally among 4 people each person has a share of size 3/4. If 9 people want to share a 50-pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie? Implement division of fractions to show quotients as fractions and mixed numbers. Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. For example, interpret 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3, and that when 3 wholes are shared equally among 4 people each person has a share of size 3/4. If 9 people want to share a 50-pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie? Solve word problems involving division of whole numbers leading to answers in the form of fractions (including mixed numbers). 9-2: Quick Check Curriculum Standards: Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. For example, interpret 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3, and that when 3 wholes are shared equally among 4 people each person has a share of size 3/4. If 9 people want to share a 50-pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie? Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. For example, interpret 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3, and that when 3 wholes are shared equally among 4 people each person has a share of size 3/4. If 9 people want to share a 50-pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie? Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. For example, interpret 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3, and that when 3 wholes are shared equally among 4 people each person has a share of size 3/4. If 9 people want to share a 50-pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie? Implement division of fractions to show quotients as fractions and mixed numbers. Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. For example, interpret 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3, and that when 3 wholes are shared equally among 4 people each person has a share of size 3/4. If 9 people want to share a 50-pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie? Solve word problems involving division of whole numbers leading to answers in the form of fractions (including mixed numbers). 9-2: Lesson Self-Assessment 9-2: Reteach to Build Understanding Curriculum Standards: Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. For example, interpret 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3, and that when 3 wholes are shared equally among 4 people each person has a share of size 3/4. If 9 people want to share a 50-pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie? Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. For example, interpret 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3, and that when 3 wholes are shared equally among 4 people each person has a share of size 3/4. If 9 people want to share a 50-pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie? Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. For example, interpret 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3, and that when 3 wholes are shared equally among 4 people each person has a share of size 3/4. If 9 people want to share a 50-pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie? Implement division of fractions to show quotients as fractions and mixed numbers. Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. For example, interpret 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3, and that when 3 wholes are shared equally among 4 people each person has a share of size 3/4. If 9 people want to share a 50-pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie? Solve word problems involving division of whole numbers leading to answers in the form of fractions (including mixed numbers). 9-2: Build Mathematical Literacy Curriculum Standards: Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 5 topics and texts, building on others’ ideas and expressing their own clearly. (a) Come to discussions prepared, having read or studied required material; explicitly draw on that preparation and other information known about the topic to explore ideas under discussion. (b) Follow agreed-upon rules for discussions and carry out assigned roles. (c) Pose and respond to specific questions by making comments that contribute to the discussion and elaborate on the remarks of others. (d) Review the key ideas expressed and draw conclusions in light of information and knowledge gained from the discussions. English language learners communicate for social and instructional purposes within the school setting. Summarize a written text read aloud or information presented in diverse media and formats, including visually, quantitatively, and orally. Summarize the points a speaker makes and explain how each claim is supported by reasons and evidence. Write informative/explanatory texts to examine a topic and convey ideas and information clearly. (a) Introduce a topic clearly, provide a general observation and focus, and group related information logically; include formatting (e.g., headings), illustrations, and multimedia when useful to aiding comprehension. (b) Develop the topic with facts, definitions, concrete details, quotations, or other information and examples related to the topic. (c) Link ideas within and across categories of information using words, phrases, and clauses (e.g., in contrast, especially). (d) Use precise language and domain-specific vocabulary to inform about or explain the topic. (e) Provide a concluding statement or section related to the information or explanation presented. English language learners communicate information, ideas and concepts necessary for academic success in the content area of Mathematics. 9-2: Enrichment Game: Gem Quest - Fractions 9-2: Pick a Project 9-2: Another Look Curriculum Standards: Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. For example, interpret 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3, and that when 3 wholes are shared equally among 4 people each person has a share of size 3/4. If 9 people want to share a 50-pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie? Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. For example, interpret 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3, and that when 3 wholes are shared equally among 4 people each person has a share of size 3/4. If 9 people want to share a 50-pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie? Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. For example, interpret 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3, and that when 3 wholes are shared equally among 4 people each person has a share of size 3/4. If 9 people want to share a 50-pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie? Implement division of fractions to show quotients as fractions and mixed numbers. Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. For example, interpret 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3, and that when 3 wholes are shared equally among 4 people each person has a share of size 3/4. If 9 people want to share a 50-pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie? Solve word problems involving division of whole numbers leading to answers in the form of fractions (including mixed numbers). Spanish Resources 9-2: eText del Libro del estudiante 9-2: Repaso diario 9-2: Aprendizaje visual 9-2: Amigo de práctica: Práctica adicional 9-2: Práctica adicional interactiva 9-2: Refuerzo para mejorar la comprensión 9-2: Desarrollar la competencia matemática 9-2: Ampliación 9-3: Use Multiplication to Divide Interactive Student Edition: Grade 5 Lesson 9-3 Math Anytime 9-3: Daily Review Topic 9: Today's Challenge Step 1: Problem-Based Learning 9-3: Solve & Share Curriculum Standards: Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for 4 ÷ (1/5), and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 × (1/5) = 4. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins? English language learners communicate for social and instructional purposes within the school setting. Write informative/explanatory texts to examine a topic and convey ideas and information clearly. (a) Introduce a topic clearly, provide a general observation and focus, and group related information logically; include formatting (e.g., headings), illustrations, and multimedia when useful to aiding comprehension. (b) Develop the topic with facts, definitions, concrete details, quotations, or other information and examples related to the topic. (c) Link ideas within and across categories of information using words, phrases, and clauses (e.g., in contrast, especially). (d) Use precise language and domain- specific vocabulary to inform about or explain the topic. (e) Provide a concluding statement or section related to the information or explanation presented. English language learners communicate information, ideas and concepts necessary for academic success in the content area of Mathematics. Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 5 topics and texts, building on others’ ideas and expressing their own clearly. (a) Come to discussions prepared, having read or studied required material; explicitly draw on that preparation and other information known about the topic to explore ideas under discussion. (b) Follow agreed-upon rules for discussions and carry out assigned roles. (c) Pose and respond to specific questions by making comments that contribute to the discussion and elaborate on the remarks of others. (d) Review the key ideas expressed and draw conclusions in light of information and knowledge gained from the discussions. Summarize a written text read aloud or information presented in diverse media and formats, including visually, quantitatively, and orally. Summarize the points a speaker makes and explain how each claim is supported by reasons and evidence. Interpret division of a whole number by a unit fraction, and compute such quotients. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for 4 ÷ (1/5), and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 × (1/5) = 4. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins? Use multiplication to divide a whole number by a unit fraction. Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for 4 ÷ (1/5), and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 × (1/5) = 4. Divide unit fractions by whole numbers and whole numbers by unit fractions. Step 2: Visual Learning 9-3: Visual Learning Curriculum Standards: Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for 4 ÷ (1/5), and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 × (1/5) = 4. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins? Interpret division of a whole number by a unit fraction, and compute such quotients. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for 4 ÷ (1/5), and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 × (1/5) = 4. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins? Use multiplication to divide a whole number by a unit fraction. Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for 4 ÷ (1/5), and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 × (1/5) = 4. Divide unit fractions by whole numbers and whole numbers by unit fractions. 9-3: Convince Me! Curriculum Standards: Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for 4 ÷ (1/5), and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 × (1/5) = 4. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins? Interpret division of a whole number by a unit fraction, and compute such quotients. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for 4 ÷ (1/5), and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 × (1/5) = 4. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins? Use multiplication to divide a whole number by a unit fraction. Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for 4 ÷ (1/5), and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 × (1/5) = 4. Divide unit fractions by whole numbers and whole numbers by unit fractions. Practice and Problem Solving 9-3: Student Edition Practice Curriculum Standards: Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for 4 ÷ (1/5), and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 × (1/5) = 4. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins? Interpret division of a whole number by a unit fraction, and compute such quotients. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for 4 ÷ (1/5), and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 × (1/5) = 4. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins? Use multiplication to divide a whole number by a unit fraction. Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for 4 ÷ (1/5), and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 × (1/5) = 4. Divide unit fractions by whole numbers and whole numbers by unit fractions. 9-3: Practice Buddy: Independent Practice; Problem Solving Curriculum Standards: Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for 4 ÷ (1/5), and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 × (1/5) = 4. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins? Interpret division of a whole number by a unit fraction, and compute such quotients. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for 4 ÷ (1/5), and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 × (1/5) = 4. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins? Use multiplication to divide a whole number by a unit fraction. Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for 4 ÷ (1/5), and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 × (1/5) = 4. Divide unit fractions by whole numbers and whole numbers by unit fractions. 9-3: Practice Buddy: Additional Practice Curriculum Standards: Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for 4 ÷ (1/5), and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 × (1/5) = 4. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins? Interpret division of a whole number by a unit fraction, and compute such quotients. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for 4 ÷ (1/5), and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 × (1/5) = 4. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins? Use multiplication to divide a whole number by a unit fraction. Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for 4 ÷ (1/5), and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 × (1/5) = 4. Divide unit fractions by whole numbers and whole numbers by unit fractions. 9-3: Interactive Additional Practice Step 3: Assess & Differentiate 9-3: Practice Buddy: Additional Practice Curriculum Standards: Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for 4 ÷ (1/5), and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 × (1/5) = 4. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins? Interpret division of a whole number by a unit fraction, and compute such quotients. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for 4 ÷ (1/5), and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 × (1/5) = 4. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins? Use multiplication to divide a whole number by a unit fraction. Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for 4 ÷ (1/5), and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 × (1/5) = 4. Divide unit fractions by whole numbers and whole numbers by unit fractions. 9-3: Enrichment Curriculum Standards: Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for 4 ÷ (1/5), and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 × (1/5) = 4. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins? Interpret division of a whole number by a unit fraction, and compute such quotients. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for 4 ÷ (1/5), and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 × (1/5) = 4. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins? Use multiplication to divide a whole number by a unit fraction. Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for 4 ÷ (1/5), and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 × (1/5) = 4. Divide unit fractions by whole numbers and whole numbers by unit fractions. 9-3: Quick Check Curriculum Standards: Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for 4 ÷ (1/5), and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 × (1/5) = 4. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins? Interpret division of a whole number by a unit fraction, and compute such quotients. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for 4 ÷ (1/5), and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 × (1/5) = 4. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins? Use multiplication to divide a whole number by a unit fraction. Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for 4 ÷ (1/5), and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 × (1/5) = 4. Divide unit fractions by whole numbers and whole numbers by unit fractions. 9-3: Lesson Self-Assessment 9-3: Reteach to Build Understanding Curriculum Standards: Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for 4 ÷ (1/5), and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 × (1/5) = 4. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins? Interpret division of a whole number by a unit fraction, and compute such quotients. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for 4 ÷ (1/5), and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 × (1/5) = 4. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins? Use multiplication to divide a whole number by a unit fraction. Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for 4 ÷ (1/5), and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 × (1/5) = 4. Divide unit fractions by whole numbers and whole numbers by unit fractions. 9-3: Build Mathematical Literacy Curriculum Standards: Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 5 topics and texts, building on others’ ideas and expressing their own clearly. (a) Come to discussions prepared, having read or studied required material; explicitly draw on that preparation and other information known about the topic to explore ideas under discussion. (b) Follow agreed-upon rules for discussions and carry out assigned roles. (c) Pose and respond to specific questions by making comments that contribute to the discussion and elaborate on the remarks of others. (d) Review the key ideas expressed and draw conclusions in light of information and knowledge gained from the discussions. English language learners communicate for social and instructional purposes within the school setting. Summarize a written text read aloud or information presented in diverse media and formats, including visually, quantitatively, and orally. Summarize the points a speaker makes and explain how each claim is supported by reasons and evidence. Write informative/explanatory texts to examine a topic and convey ideas and information clearly. (a) Introduce a topic clearly, provide a general observation and focus, and group related information logically; include formatting (e.g., headings), illustrations, and multimedia when useful to aiding comprehension. (b) Develop the topic with facts, definitions, concrete details, quotations, or other information and examples related to the topic. (c) Link ideas within and across categories of information using words, phrases, and clauses (e.g., in contrast, especially). (d) Use precise language and domain-specific vocabulary to inform about or explain the topic. (e) Provide a concluding statement or section related to the information or explanation presented. English language learners communicate information, ideas and concepts necessary for academic success in the content area of Mathematics. 9-3: Enrichment Game: Factory Frenzy Fractions 9-3: enVision STEM Activity Curriculum Standards: Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for 4 ÷ (1/5), and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 × (1/5) = 4. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins? Interpret division of a whole number by a unit fraction, and compute such quotients. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for 4 ÷ (1/5), and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 × (1/5) = 4. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins? Use multiplication to divide a whole number by a unit fraction. Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for 4 ÷ (1/5), and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 × (1/5) = 4. Divide unit fractions by whole numbers and whole numbers by unit fractions. 9-3: Another Look Curriculum Standards: Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for 4 ÷ (1/5), and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 × (1/5) = 4. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins? Interpret division of a whole number by a unit fraction, and compute such quotients. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for 4 ÷ (1/5), and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 × (1/5) = 4. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins? Use multiplication to divide a whole number by a unit fraction. Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for 4 ÷ (1/5), and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 × (1/5) = 4. Divide unit fractions by whole numbers and whole numbers by unit fractions. Spanish Resources 9-3: eText del Libro del estudiante 9-3: Repaso diario 9-3: Aprendizaje visual 9-3: Amigo de práctica: Práctica adicional 9-3: Práctica adicional interactiva 9-3: Refuerzo para mejorar la comprensión 9-3: Desarrollar la competencia matemática 9-3: Ampliación 9-4: Divide Whole Numbers by Unit Fractions Interactive Student Edition: Grade 5 Lesson 9-4 Math Anytime 9-4: Daily Review Topic 9: Today's Challenge Step 1: Problem-Based Learning 9-4: Solve & Share Curriculum Standards: Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for 4 ÷ (1/5), and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 × (1/5) = 4. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins? English language learners communicate for social and instructional purposes within the school setting. Write informative/explanatory texts to examine a topic and convey ideas and information clearly. (a) Introduce a topic clearly, provide a general observation and focus, and group related information logically; include formatting (e.g., headings), illustrations, and multimedia when useful to aiding comprehension. (b) Develop the topic with facts, definitions, concrete details, quotations, or other information and examples related to the topic. (c) Link ideas within and across categories of information using words, phrases, and clauses (e.g., in contrast, especially). (d) Use precise language and domain- specific vocabulary to inform about or explain the topic. (e) Provide a concluding statement or section related to the information or explanation presented. English language learners communicate information, ideas and concepts necessary for academic success in the content area of Mathematics. Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 5 topics and texts, building on others’ ideas and expressing their own clearly. (a) Come to discussions prepared, having read or studied required material; explicitly draw on that preparation and other information known about the topic to explore ideas under discussion. (b) Follow agreed-upon rules for discussions and carry out assigned roles. (c) Pose and respond to specific questions by making comments that contribute to the discussion and elaborate on the remarks of others. (d) Review the key ideas expressed and draw conclusions in light of information and knowledge gained from the discussions. Summarize a written text read aloud or information presented in diverse media and formats, including visually, quantitatively, and orally. Summarize the points a speaker makes and explain how each claim is supported by reasons and evidence. Interpret division of a whole number by a unit fraction, and compute such quotients. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for 4 ÷ (1/5), and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 × (1/5) = 4. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins? Use models, such as pictorial models or a number line, to show dividing a whole number by a unit fraction. Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for 4 ÷ (1/5), and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 × (1/5) = 4. Divide unit fractions by whole numbers and whole numbers by unit fractions. Step 2: Visual Learning 9-4: Visual Learning Curriculum Standards: Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for 4 ÷ (1/5), and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 × (1/5) = 4. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins? Divide unit fractions by whole numbers and whole numbers by unit fractions using visual fraction models. Divide unit fractions by whole numbers and whole numbers by unit fractions using visual fraction models. Interpret division of a whole number by a unit fraction, and compute such quotients. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for 4 ÷ (1/5), and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 × (1/5) = 4. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins? Use models, such as pictorial models or a number line, to show dividing a whole number by a unit fraction. Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for 4 ÷ (1/5), and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 × (1/5) = 4. Divide unit fractions by whole numbers and whole numbers by unit fractions. 9-4: Convince Me! Curriculum Standards: Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for 4 ÷ (1/5), and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 × (1/5) = 4. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins? Interpret division of a whole number by a unit fraction, and compute such quotients. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for 4 ÷ (1/5), and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 × (1/5) = 4. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins? Use models, such as pictorial models or a number line, to show dividing a whole number by a unit fraction. Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for 4 ÷ (1/5), and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 × (1/5) = 4. Divide unit fractions by whole numbers and whole numbers by unit fractions. Practice and Problem Solving 9-4: Student Edition Practice Curriculum Standards: Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for 4 ÷ (1/5), and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 × (1/5) = 4. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins? Interpret division of a whole number by a unit fraction, and compute such quotients. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for 4 ÷ (1/5), and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 × (1/5) = 4. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins? Use models, such as pictorial models or a number line, to show dividing a whole number by a unit fraction. Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for 4 ÷ (1/5), and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 × (1/5) = 4. Divide unit fractions by whole numbers and whole numbers by unit fractions. 9-4: Practice Buddy: Independent Practice; Problem Solving Curriculum Standards: Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for 4 ÷ (1/5), and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 × (1/5) = 4. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins? Interpret division of a whole number by a unit fraction, and compute such quotients. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for 4 ÷ (1/5), and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 × (1/5) = 4. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins? Use models, such as pictorial models or a number line, to show dividing a whole number by a unit fraction. Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for 4 ÷ (1/5), and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 × (1/5) = 4. Divide unit fractions by whole numbers and whole numbers by unit fractions. 9-4: Practice Buddy: Additional Practice Curriculum Standards: Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for 4 ÷ (1/5), and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 × (1/5) = 4. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins? Interpret division of a whole number by a unit fraction, and compute such quotients. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for 4 ÷ (1/5), and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 × (1/5) = 4. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins? Use models, such as pictorial models or a number line, to show dividing a whole number by a unit fraction. Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for 4 ÷ (1/5), and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 × (1/5) = 4. Divide unit fractions by whole numbers and whole numbers by unit fractions. 9-4: Interactive Additional Practice Step 3: Assess & Differentiate 9-4: Practice Buddy: Additional Practice Curriculum Standards: Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for 4 ÷ (1/5), and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 × (1/5) = 4. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins? Interpret division of a whole number by a unit fraction, and compute such quotients. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for 4 ÷ (1/5), and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 × (1/5) = 4. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins? Use models, such as pictorial models or a number line, to show dividing a whole number by a unit fraction. Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for 4 ÷ (1/5), and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 × (1/5) = 4. Divide unit fractions by whole numbers and whole numbers by unit fractions. 9-4: Enrichment Curriculum Standards: Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for 4 ÷ (1/5), and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 × (1/5) = 4. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins? Interpret division of a whole number by a unit fraction, and compute such quotients. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for 4 ÷ (1/5), and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 × (1/5) = 4. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins? Use models, such as pictorial models or a number line, to show dividing a whole number by a unit fraction. Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for 4 ÷ (1/5), and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 × (1/5) = 4. Divide unit fractions by whole numbers and whole numbers by unit fractions. 9-4: Quick Check Curriculum Standards: Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for 4 ÷ (1/5), and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 × (1/5) = 4. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins? Interpret division of a whole number by a unit fraction, and compute such quotients. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for 4 ÷ (1/5), and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 × (1/5) = 4. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins? Use models, such as pictorial models or a number line, to show dividing a whole number by a unit fraction. Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for 4 ÷ (1/5), and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 × (1/5) = 4. Divide unit fractions by whole numbers and whole numbers by unit fractions. 9-4: Lesson Self-Assessment 9-4: Reteach to Build Understanding Curriculum Standards: Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for 4 ÷ (1/5), and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 × (1/5) = 4. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins? Divide unit fractions by whole numbers and whole numbers by unit fractions using visual fraction models. Divide unit fractions by whole numbers and whole numbers by unit fractions using visual fraction models. Interpret division of a whole number by a unit fraction, and compute such quotients. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for 4 ÷ (1/5), and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 × (1/5) = 4. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins? Use models, such as pictorial models or a number line, to show dividing a whole number by a unit fraction. Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for 4 ÷ (1/5), and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 × (1/5) = 4. Divide unit fractions by whole numbers and whole numbers by unit fractions. 9-4: Build Mathematical Literacy Curriculum Standards: Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 5 topics and texts, building on others’ ideas and expressing their own clearly. (a) Come to discussions prepared, having read or studied required material; explicitly draw on that preparation and other information known about the topic to explore ideas under discussion. (b) Follow agreed-upon rules for discussions and carry out assigned roles. (c) Pose and respond to specific questions by making comments that contribute to the discussion and elaborate on the remarks of others. (d) Review the key ideas expressed and draw conclusions in light of information and knowledge gained from the discussions. English language learners communicate for social and instructional purposes within the school setting. Summarize a written text read aloud or information presented in diverse media and formats, including visually, quantitatively, and orally. Summarize the points a speaker makes and explain how each claim is supported by reasons and evidence. Write informative/explanatory texts to examine a topic and convey ideas and information clearly. (a) Introduce a topic clearly, provide a general observation and focus, and group related information logically; include formatting (e.g., headings), illustrations, and multimedia when useful to aiding comprehension. (b) Develop the topic with facts, definitions, concrete details, quotations, or other information and examples related to the topic. (c) Link ideas within and across categories of information using words, phrases, and clauses (e.g., in contrast, especially). (d) Use precise language and domain-specific vocabulary to inform about or explain the topic. (e) Provide a concluding statement or section related to the information or explanation presented. English language learners communicate information, ideas and concepts necessary for academic success in the content area of Mathematics. 9-4: Enrichment 9-4: Digital Math Tool Activity 9-4: Pick a Project 9-4: Another Look Curriculum Standards: Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for 4 ÷ (1/5), and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 × (1/5) = 4. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins? Divide unit fractions by whole numbers and whole numbers by unit fractions using visual fraction models. Divide unit fractions by whole numbers and whole numbers by unit fractions using visual fraction models. Interpret division of a whole number by a unit fraction, and compute such quotients. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for 4 ÷ (1/5), and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 × (1/5) = 4. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins? Use models, such as pictorial models or a number line, to show dividing a whole number by a unit fraction. Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for 4 ÷ (1/5), and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 × (1/5) = 4. Divide unit fractions by whole numbers and whole numbers by unit fractions. Spanish Resources 9-4: eText del Libro del estudiante 9-4: Repaso diario 9-4: Aprendizaje visual 9-4: Amigo de práctica: Práctica adicional 9-4: Práctica adicional interactiva 9-4: Refuerzo para mejorar la comprensión 9-4: Desarrollar la competencia matemática 9-4: Ampliación 9-5: Divide Unit Fractions by Non-Zero Whole Numbers Interactive Student Edition: Grade 5 Lesson 9-5 Math Anytime 9-5: Daily Review Topic 9: Today's Challenge Step 1: Problem-Based Learning 9-5: Solve & Share Curriculum Standards: Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. For example, create a story context for (1/3) ÷ 4, and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that (1/3) ÷ 4 = 1/12 because (1/12) × 4 = 1/3. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins? Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. For example, create a story context for (1/3) ÷ 4, and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that (1/3) ÷ 4 = 1/12 because (1/12) × 4 = 1/3. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins? Use models to divide unit fractions by non-zero whole numbers. Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. For example, create a story context for (1/3) ÷ 4, and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that (1/3) ÷ 4 = 1/12 because (1/12) × 4 = 1/3. Divide unit fractions by whole numbers and whole numbers by unit fractions. English language learners communicate for social and instructional purposes within the school setting. Write informative/explanatory texts to examine a topic and convey ideas and information clearly. (a) Introduce a topic clearly, provide a general observation and focus, and group related information logically; include formatting (e.g., headings), illustrations, and multimedia when useful to aiding comprehension. (b) Develop the topic with facts, definitions, concrete details, quotations, or other information and examples related to the topic. (c) Link ideas within and across categories of information using words, phrases, and clauses (e.g., in contrast, especially). (d) Use precise language and domain-specific vocabulary to inform about or explain the topic. (e) Provide a concluding statement or section related to the information or explanation presented. English language learners communicate information, ideas and concepts necessary for academic success in the content area of Mathematics. Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 5 topics and texts, building on others’ ideas and expressing their own clearly. (a) Come to discussions prepared, having read or studied required material; explicitly draw on that preparation and other information known about the topic to explore ideas under discussion. (b) Follow agreed-upon rules for discussions and carry out assigned roles. (c) Pose and respond to specific questions by making comments that contribute to the discussion and elaborate on the remarks of others. (d) Review the key ideas expressed and draw conclusions in light of information and knowledge gained from the discussions. Summarize a written text read aloud or information presented in diverse media and formats, including visually, quantitatively, and orally. Summarize the points a speaker makes and explain how each claim is supported by reasons and evidence. Step 2: Visual Learning 9-5: Visual Learning Curriculum Standards: Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. For example, create a story context for (1/3) ÷ 4, and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that (1/3) ÷ 4 = 1/12 because (1/12) × 4 = 1/3. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins? Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. For example, create a story context for (1/3) ÷ 4, and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that (1/3) ÷ 4 = 1/12 because (1/12) × 4 = 1/3. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins? Use models to divide unit fractions by non-zero whole numbers. Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. For example, create a story context for (1/3) ÷ 4, and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that (1/3) ÷ 4 = 1/12 because (1/12) × 4 = 1/3. Divide unit fractions by whole numbers and whole numbers by unit fractions. Divide unit fractions by whole numbers and whole numbers by unit fractions using visual fraction models. Divide unit fractions by whole numbers and whole numbers by unit fractions using visual fraction models. 9-5: Convince Me! Curriculum Standards: Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. For example, create a story context for (1/3) ÷ 4, and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that (1/3) ÷ 4 = 1/12 because (1/12) × 4 = 1/3. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins? Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. For example, create a story context for (1/3) ÷ 4, and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that (1/3) ÷ 4 = 1/12 because (1/12) × 4 = 1/3. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins? Use models to divide unit fractions by non-zero whole numbers. Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. For example, create a story context for (1/3) ÷ 4, and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that (1/3) ÷ 4 = 1/12 because (1/12) × 4 = 1/3. Divide unit fractions by whole numbers and whole numbers by unit fractions. Practice and Problem Solving 9-5: Student Edition Practice Curriculum Standards: Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. For example, create a story context for (1/3) ÷ 4, and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that (1/3) ÷ 4 = 1/12 because (1/12) × 4 = 1/3. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins? Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. For example, create a story context for (1/3) ÷ 4, and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that (1/3) ÷ 4 = 1/12 because (1/12) × 4 = 1/3. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins? Use models to divide unit fractions by non-zero whole numbers. Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. For example, create a story context for (1/3) ÷ 4, and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that (1/3) ÷ 4 = 1/12 because (1/12) × 4 = 1/3. Divide unit fractions by whole numbers and whole numbers by unit fractions. 9-5: Practice Buddy: Independent Practice; Problem Solving Curriculum Standards: Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. For example, create a story context for (1/3) ÷ 4, and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that (1/3) ÷ 4 = 1/12 because (1/12) × 4 = 1/3. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins? Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. For example, create a story context for (1/3) ÷ 4, and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that (1/3) ÷ 4 = 1/12 because (1/12) × 4 = 1/3. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins? Use models to divide unit fractions by non-zero whole numbers. Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. For example, create a story context for (1/3) ÷ 4, and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that (1/3) ÷ 4 = 1/12 because (1/12) × 4 = 1/3. Divide unit fractions by whole numbers and whole numbers by unit fractions. 9-5: Practice Buddy: Additional Practice Curriculum Standards: Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. For example, create a story context for (1/3) ÷ 4, and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that (1/3) ÷ 4 = 1/12 because (1/12) × 4 = 1/3. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins? Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. For example, create a story context for (1/3) ÷ 4, and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that (1/3) ÷ 4 = 1/12 because (1/12) × 4 = 1/3. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins? Use models to divide unit fractions by non-zero whole numbers. Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. For example, create a story context for (1/3) ÷ 4, and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that (1/3) ÷ 4 = 1/12 because (1/12) × 4 = 1/3. Divide unit fractions by whole numbers and whole numbers by unit fractions. 9-5: Interactive Additional Practice Step 3: Assess & Differentiate 9-5: Practice Buddy: Additional Practice Curriculum Standards: Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. For example, create a story context for (1/3) ÷ 4, and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that (1/3) ÷ 4 = 1/12 because (1/12) × 4 = 1/3. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins? Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. For example, create a story context for (1/3) ÷ 4, and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that (1/3) ÷ 4 = 1/12 because (1/12) × 4 = 1/3. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins? Use models to divide unit fractions by non-zero whole numbers. Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. For example, create a story context for (1/3) ÷ 4, and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that (1/3) ÷ 4 = 1/12 because (1/12) × 4 = 1/3. Divide unit fractions by whole numbers and whole numbers by unit fractions. 9-5: Enrichment Curriculum Standards: Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. For example, create a story context for (1/3) ÷ 4, and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that (1/3) ÷ 4 = 1/12 because (1/12) × 4 = 1/3. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins? Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. For example, create a story context for (1/3) ÷ 4, and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that (1/3) ÷ 4 = 1/12 because (1/12) × 4 = 1/3. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins? Use models to divide unit fractions by non-zero whole numbers. Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. For example, create a story context for (1/3) ÷ 4, and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that (1/3) ÷ 4 = 1/12 because (1/12) × 4 = 1/3. Divide unit fractions by whole numbers and whole numbers by unit fractions. 9-5: Quick Check Curriculum Standards: Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. For example, create a story context for (1/3) ÷ 4, and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that (1/3) ÷ 4 = 1/12 because (1/12) × 4 = 1/3. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins? Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. For example, create a story context for (1/3) ÷ 4, and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that (1/3) ÷ 4 = 1/12 because (1/12) × 4 = 1/3. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins? Use models to divide unit fractions by non-zero whole numbers. Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. For example, create a story context for (1/3) ÷ 4, and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that (1/3) ÷ 4 = 1/12 because (1/12) × 4 = 1/3. Divide unit fractions by whole numbers and whole numbers by unit fractions. 9-5: Lesson Self-Assessment 9-5: Reteach to Build Understanding Curriculum Standards: Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. For example, create a story context for (1/3) ÷ 4, and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that (1/3) ÷ 4 = 1/12 because (1/12) × 4 = 1/3. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins? Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. For example, create a story context for (1/3) ÷ 4, and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that (1/3) ÷ 4 = 1/12 because (1/12) × 4 = 1/3. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins? Use models to divide unit fractions by non-zero whole numbers. Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. For example, create a story context for (1/3) ÷ 4, and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that (1/3) ÷ 4 = 1/12 because (1/12) × 4 = 1/3. Divide unit fractions by whole numbers and whole numbers by unit fractions. Divide unit fractions by whole numbers and whole numbers by unit fractions using visual fraction models. Divide unit fractions by whole numbers and whole numbers by unit fractions using visual fraction models. 9-5: Build Mathematical Literacy Curriculum Standards: Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 5 topics and texts, building on others’ ideas and expressing their own clearly. (a) Come to discussions prepared, having read or studied required material; explicitly draw on that preparation and other information known about the topic to explore ideas under discussion. (b) Follow agreed-upon rules for discussions and carry out assigned roles. (c) Pose and respond to specific questions by making comments that contribute to the discussion and elaborate on the remarks of others. (d) Review the key ideas expressed and draw conclusions in light of information and knowledge gained from the discussions. English language learners communicate for social and instructional purposes within the school setting. Summarize a written text read aloud or information presented in diverse media and formats, including visually, quantitatively, and orally. Summarize the points a speaker makes and explain how each claim is supported by reasons and evidence. Write informative/explanatory texts to examine a topic and convey ideas and information clearly. (a) Introduce a topic clearly, provide a general observation and focus, and group related information logically; include formatting (e.g., headings), illustrations, and multimedia when useful to aiding comprehension. (b) Develop the topic with facts, definitions, concrete details, quotations, or other information and examples related to the topic. (c) Link ideas within and across categories of information using words, phrases, and clauses (e.g., in contrast, especially). (d) Use precise language and domain-specific vocabulary to inform about or explain the topic. (e) Provide a concluding statement or section related to the information or explanation presented. English language learners communicate information, ideas and concepts necessary for academic success in the content area of Mathematics. 9-5: Enrichment 9-5: Digital Math Tool Activity 9-5: enVision STEM Activity Curriculum Standards: Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. For example, create a story context for (1/3) ÷ 4, and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that (1/3) ÷ 4 = 1/12 because (1/12) × 4 = 1/3. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins? Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. For example, create a story context for (1/3) ÷ 4, and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that (1/3) ÷ 4 = 1/12 because (1/12) × 4 = 1/3. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins? Use models to divide unit fractions by non-zero whole numbers. Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. For example, create a story context for (1/3) ÷ 4, and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that (1/3) ÷ 4 = 1/12 because (1/12) × 4 = 1/3. Divide unit fractions by whole numbers and whole numbers by unit fractions. 9-5: Another Look Curriculum Standards: Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. For example, create a story context for (1/3) ÷ 4, and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that (1/3) ÷ 4 = 1/12 because (1/12) × 4 = 1/3. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins? Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. For example, create a story context for (1/3) ÷ 4, and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that (1/3) ÷ 4 = 1/12 because (1/12) × 4 = 1/3. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins? Use models to divide unit fractions by non-zero whole numbers. Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. For example, create a story context for (1/3) ÷ 4, and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that (1/3) ÷ 4 = 1/12 because (1/12) × 4 = 1/3. Divide unit fractions by whole numbers and whole numbers by unit fractions. Divide unit fractions by whole numbers and whole numbers by unit fractions using visual fraction models. Divide unit fractions by whole numbers and whole numbers by unit fractions using visual fraction models. Spanish Resources 9-5: eText del Libro del estudiante 9-5: Repaso diario 9-5: Aprendizaje visual 9-5: Amigo de práctica: Práctica adicional 9-5: Práctica adicional interactiva 9-5: Refuerzo para mejorar la comprensión 9-5: Desarrollar la competencia matemática 9-5: Ampliación 9-6: Divide Whole Numbers and Unit Fractions Interactive Student Edition: Grade 5 Lesson 9-6 Math Anytime 9-6: Daily Review Topic 9: Today's Challenge Step 1: Problem-Based Learning 9-6: Solve & Share Curriculum Standards: Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. For example, create a story context for (1/3) ÷ 4, and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that (1/3) ÷ 4 = 1/12 because (1/12) × 4 = 1/3. Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for 4 ÷ (1/5), and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 × (1/5) = 4. Solve real world problems involving division of unit fractions by non- zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins? Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. Interpret division of a whole number by a unit fraction, and compute such quotients. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. For example, create a story context for (1/3) ÷ 4, and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that (1/3) ÷ 4 = 1/12 because (1/12) × 4 = 1/3. Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for 4 ÷ (1/5), and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 × (1/5) = 4. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins? Use models to divide whole numbers and unit fractions. Check your answer using multiplication. Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. For example, create a story context for (1/3) ÷ 4, and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that (1/3) ÷ 4 = 1/12 because (1/12) × 4 = 1/3. Divide unit fractions by whole numbers and whole numbers by unit fractions. English language learners communicate for social and instructional purposes within the school setting. Write informative/explanatory texts to examine a topic and convey ideas and information clearly. (a) Introduce a topic clearly, provide a general observation and focus, and group related information logically; include formatting (e.g., headings), illustrations, and multimedia when useful to aiding comprehension. (b) Develop the topic with facts, definitions, concrete details, quotations, or other information and examples related to the topic. (c) Link ideas within and across categories of information using words, phrases, and clauses (e.g., in contrast, especially). (d) Use precise language and domain-specific vocabulary to inform about or explain the topic. (e) Provide a concluding statement or section related to the information or explanation presented. English language learners communicate information, ideas and concepts necessary for academic success in the content area of Mathematics. Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 5 topics and texts, building on others’ ideas and expressing their own clearly. (a) Come to discussions prepared, having read or studied required material; explicitly draw on that preparation and other information known about the topic to explore ideas under discussion. (b) Follow agreed-upon rules for discussions and carry out assigned roles. (c) Pose and respond to specific questions by making comments that contribute to the discussion and elaborate on the remarks of others. (d) Review the key ideas expressed and draw conclusions in light of information and knowledge gained from the discussions. Summarize a written text read aloud or information presented in diverse media and formats, including visually, quantitatively, and orally. Summarize the points a speaker makes and explain how each claim is supported by reasons and evidence. Step 2: Visual Learning 9-6: Visual Learning Curriculum Standards: Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. For example, create a story context for (1/3) ÷ 4, and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that (1/3) ÷ 4 = 1/12 because (1/12) × 4 = 1/3. Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for 4 ÷ (1/5), and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 × (1/5) = 4. Solve real world problems involving division of unit fractions by non- zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins? Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. Interpret division of a whole number by a unit fraction, and compute such quotients. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. For example, create a story context for (1/3) ÷ 4, and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that (1/3) ÷ 4 = 1/12 because (1/12) × 4 = 1/3. Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for 4 ÷ (1/5), and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 × (1/5) = 4. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins? Use models to divide whole numbers and unit fractions. Check your answer using multiplication. Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. For example, create a story context for (1/3) ÷ 4, and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that (1/3) ÷ 4 = 1/12 because (1/12) × 4 = 1/3. Divide unit fractions by whole numbers and whole numbers by unit fractions. 9-6: Convince Me! Curriculum Standards: Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. For example, create a story context for (1/3) ÷ 4, and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that (1/3) ÷ 4 = 1/12 because (1/12) × 4 = 1/3. Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for 4 ÷ (1/5), and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 × (1/5) = 4. Solve real world problems involving division of unit fractions by non- zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins? Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. Interpret division of a whole number by a unit fraction, and compute such quotients. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. For example, create a story context for (1/3) ÷ 4, and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that (1/3) ÷ 4 = 1/12 because (1/12) × 4 = 1/3. Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for 4 ÷ (1/5), and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 × (1/5) = 4. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins? Use models to divide whole numbers and unit fractions. Check your answer using multiplication. Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. For example, create a story context for (1/3) ÷ 4, and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that (1/3) ÷ 4 = 1/12 because (1/12) × 4 = 1/3. Divide unit fractions by whole numbers and whole numbers by unit fractions. Practice and Problem Solving 9-6: Student Edition Practice Curriculum Standards: Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. For example, create a story context for (1/3) ÷ 4, and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that (1/3) ÷ 4 = 1/12 because (1/12) × 4 = 1/3. Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for 4 ÷ (1/5), and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 × (1/5) = 4. Solve real world problems involving division of unit fractions by non- zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins? Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. Interpret division of a whole number by a unit fraction, and compute such quotients. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. For example, create a story context for (1/3) ÷ 4, and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that (1/3) ÷ 4 = 1/12 because (1/12) × 4 = 1/3. Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for 4 ÷ (1/5), and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 × (1/5) = 4. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins? Use models to divide whole numbers and unit fractions. Check your answer using multiplication. Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. For example, create a story context for (1/3) ÷ 4, and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that (1/3) ÷ 4 = 1/12 because (1/12) × 4 = 1/3. Divide unit fractions by whole numbers and whole numbers by unit fractions. 9-6: Practice Buddy: Independent Practice; Problem Solving Curriculum Standards: Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. For example, create a story context for (1/3) ÷ 4, and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that (1/3) ÷ 4 = 1/12 because (1/12) × 4 = 1/3. Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for 4 ÷ (1/5), and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 × (1/5) = 4. Solve real world problems involving division of unit fractions by non- zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins? Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. Interpret division of a whole number by a unit fraction, and compute such quotients. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. For example, create a story context for (1/3) ÷ 4, and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that (1/3) ÷ 4 = 1/12 because (1/12) × 4 = 1/3. Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for 4 ÷ (1/5), and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 × (1/5) = 4. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins? Use models to divide whole numbers and unit fractions. Check your answer using multiplication. Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. For example, create a story context for (1/3) ÷ 4, and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that (1/3) ÷ 4 = 1/12 because (1/12) × 4 = 1/3. Divide unit fractions by whole numbers and whole numbers by unit fractions. 9-6: Practice Buddy: Additional Practice Curriculum Standards: Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. For example, create a story context for (1/3) ÷ 4, and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that (1/3) ÷ 4 = 1/12 because (1/12) × 4 = 1/3. Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for 4 ÷ (1/5), and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 × (1/5) = 4. Solve real world problems involving division of unit fractions by non- zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins? Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. Interpret division of a whole number by a unit fraction, and compute such quotients. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. For example, create a story context for (1/3) ÷ 4, and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that (1/3) ÷ 4 = 1/12 because (1/12) × 4 = 1/3. Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for 4 ÷ (1/5), and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 × (1/5) = 4. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins? Use models to divide whole numbers and unit fractions. Check your answer using multiplication. Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. For example, create a story context for (1/3) ÷ 4, and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that (1/3) ÷ 4 = 1/12 because (1/12) × 4 = 1/3. Divide unit fractions by whole numbers and whole numbers by unit fractions. 9-6: Interactive Additional Practice Step 3: Assess & Differentiate 9-6: Practice Buddy: Additional Practice Curriculum Standards: Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. For example, create a story context for (1/3) ÷ 4, and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that (1/3) ÷ 4 = 1/12 because (1/12) × 4 = 1/3. Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for 4 ÷ (1/5), and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 × (1/5) = 4. Solve real world problems involving division of unit fractions by non- zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins? Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. Interpret division of a whole number by a unit fraction, and compute such quotients. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. For example, create a story context for (1/3) ÷ 4, and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that (1/3) ÷ 4 = 1/12 because (1/12) × 4 = 1/3. Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for 4 ÷ (1/5), and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 × (1/5) = 4. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins? Use models to divide whole numbers and unit fractions. Check your answer using multiplication. Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. For example, create a story context for (1/3) ÷ 4, and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that (1/3) ÷ 4 = 1/12 because (1/12) × 4 = 1/3. Divide unit fractions by whole numbers and whole numbers by unit fractions. 9-6: Enrichment Curriculum Standards: Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. For example, create a story context for (1/3) ÷ 4, and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that (1/3) ÷ 4 = 1/12 because (1/12) × 4 = 1/3. Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for 4 ÷ (1/5), and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 × (1/5) = 4. Solve real world problems involving division of unit fractions by non- zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins? Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. Interpret division of a whole number by a unit fraction, and compute such quotients. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. For example, create a story context for (1/3) ÷ 4, and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that (1/3) ÷ 4 = 1/12 because (1/12) × 4 = 1/3. Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for 4 ÷ (1/5), and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 × (1/5) = 4. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins? Use models to divide whole numbers and unit fractions. Check your answer using multiplication. Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. For example, create a story context for (1/3) ÷ 4, and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that (1/3) ÷ 4 = 1/12 because (1/12) × 4 = 1/3. Divide unit fractions by whole numbers and whole numbers by unit fractions. 9-6: Quick Check Curriculum Standards: Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. For example, create a story context for (1/3) ÷ 4, and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that (1/3) ÷ 4 = 1/12 because (1/12) × 4 = 1/3. Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for 4 ÷ (1/5), and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 × (1/5) = 4. Solve real world problems involving division of unit fractions by non- zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins? Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. Interpret division of a whole number by a unit fraction, and compute such quotients. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. For example, create a story context for (1/3) ÷ 4, and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that (1/3) ÷ 4 = 1/12 because (1/12) × 4 = 1/3. Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for 4 ÷ (1/5), and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 × (1/5) = 4. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins? Use models to divide whole numbers and unit fractions. Check your answer using multiplication. Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. For example, create a story context for (1/3) ÷ 4, and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that (1/3) ÷ 4 = 1/12 because (1/12) × 4 = 1/3. Divide unit fractions by whole numbers and whole numbers by unit fractions. 9-6: Lesson Self-Assessment 9-6: Reteach to Build Understanding Curriculum Standards: Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. For example, create a story context for (1/3) ÷ 4, and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that (1/3) ÷ 4 = 1/12 because (1/12) × 4 = 1/3. Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for 4 ÷ (1/5), and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 × (1/5) = 4. Solve real world problems involving division of unit fractions by non- zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins? Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. Interpret division of a whole number by a unit fraction, and compute such quotients. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. For example, create a story context for (1/3) ÷ 4, and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that (1/3) ÷ 4 = 1/12 because (1/12) × 4 = 1/3. Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for 4 ÷ (1/5), and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 × (1/5) = 4. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins? Use models to divide whole numbers and unit fractions. Check your answer using multiplication. Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. For example, create a story context for (1/3) ÷ 4, and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that (1/3) ÷ 4 = 1/12 because (1/12) × 4 = 1/3. Divide unit fractions by whole numbers and whole numbers by unit fractions. 9-6: Build Mathematical Literacy Curriculum Standards: Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 5 topics and texts, building on others’ ideas and expressing their own clearly. (a) Come to discussions prepared, having read or studied required material; explicitly draw on that preparation and other information known about the topic to explore ideas under discussion. (b) Follow agreed-upon rules for discussions and carry out assigned roles. (c) Pose and respond to specific questions by making comments that contribute to the discussion and elaborate on the remarks of others. (d) Review the key ideas expressed and draw conclusions in light of information and knowledge gained from the discussions. English language learners communicate for social and instructional purposes within the school setting. Summarize a written text read aloud or information presented in diverse media and formats, including visually, quantitatively, and orally. Summarize the points a speaker makes and explain how each claim is supported by reasons and evidence. Write informative/explanatory texts to examine a topic and convey ideas and information clearly. (a) Introduce a topic clearly, provide a general observation and focus, and group related information logically; include formatting (e.g., headings), illustrations, and multimedia when useful to aiding comprehension. (b) Develop the topic with facts, definitions, concrete details, quotations, or other information and examples related to the topic. (c) Link ideas within and across categories of information using words, phrases, and clauses (e.g., in contrast, especially). (d) Use precise language and domain-specific vocabulary to inform about or explain the topic. (e) Provide a concluding statement or section related to the information or explanation presented. English language learners communicate information, ideas and concepts necessary for academic success in the content area of Mathematics. 9-6: Enrichment 9-6: Digital Math Tool Activity 9-6: Problem-Solving Reading Activity Curriculum Standards: Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. For example, create a story context for (1/3) ÷ 4, and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that (1/3) ÷ 4 = 1/12 because (1/12) × 4 = 1/3. Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for 4 ÷ (1/5), and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 × (1/5) = 4. Solve real world problems involving division of unit fractions by non- zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins? Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. Interpret division of a whole number by a unit fraction, and compute such quotients. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. For example, create a story context for (1/3) ÷ 4, and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that (1/3) ÷ 4 = 1/12 because (1/12) × 4 = 1/3. Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for 4 ÷ (1/5), and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 × (1/5) = 4. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins? Use models to divide whole numbers and unit fractions. Check your answer using multiplication. Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. For example, create a story context for (1/3) ÷ 4, and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that (1/3) ÷ 4 = 1/12 because (1/12) × 4 = 1/3. Divide unit fractions by whole numbers and whole numbers by unit fractions. 9-6: Another Look Curriculum Standards: Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. For example, create a story context for (1/3) ÷ 4, and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that (1/3) ÷ 4 = 1/12 because (1/12) × 4 = 1/3. Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for 4 ÷ (1/5), and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 × (1/5) = 4. Solve real world problems involving division of unit fractions by non- zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins? Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. Interpret division of a whole number by a unit fraction, and compute such quotients. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. For example, create a story context for (1/3) ÷ 4, and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that (1/3) ÷ 4 = 1/12 because (1/12) × 4 = 1/3. Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for 4 ÷ (1/5), and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 × (1/5) = 4. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins? Use models to divide whole numbers and unit fractions. Check your answer using multiplication. Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. For example, create a story context for (1/3) ÷ 4, and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that (1/3) ÷ 4 = 1/12 because (1/12) × 4 = 1/3. Divide unit fractions by whole numbers and whole numbers by unit fractions. Spanish Resources 9-6: eText del Libro del estudiante 9-6: Repaso diario 9-6: Aprendizaje visual 9-6: Amigo de práctica: Práctica adicional 9-6: Práctica adicional interactiva 9-6: Refuerzo para mejorar la comprensión 9-6: Desarrollar la competencia matemática 9-6: Ampliación 9-7: Solve Problems Using Division Interactive Student Edition: Grade 5 Lesson 9-7 Math Anytime 9-7: Daily Review Topic 9: Today's Challenge Step 1: Problem-Based Learning 9-7: Solve & Share Solution Curriculum Standards: Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for 4 ÷ (1/5), and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 × (1/5) = 4. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins? Interpret division of a whole number by a unit fraction, and compute such quotients. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for 4 ÷ (1/5), and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 × (1/5) = 4. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins? Solve multi-step problems involving division with unit fractions. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins? Divide unit fractions by whole numbers and whole numbers by unit fractions. 9-7: Solve & Share Curriculum Standards: Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for 4 ÷ (1/5), and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 × (1/5) = 4. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins? English language learners communicate for social and instructional purposes within the school setting. Interpret division of a whole number by a unit fraction, and compute such quotients. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for 4 ÷ (1/5), and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 × (1/5) = 4. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins? Solve multi-step problems involving division with unit fractions. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins? Divide unit fractions by whole numbers and whole numbers by unit fractions. Write informative/explanatory texts to examine a topic and convey ideas and information clearly. (a) Introduce a topic clearly, provide a general observation and focus, and group related information logically; include formatting (e.g., headings), illustrations, and multimedia when useful to aiding comprehension. (b) Develop the topic with facts, definitions, concrete details, quotations, or other information and examples related to the topic. (c) Link ideas within and across categories of information using words, phrases, and clauses (e.g., in contrast, especially). (d) Use precise language and domain-specific vocabulary to inform about or explain the topic. (e) Provide a concluding statement or section related to the information or explanation presented. English language learners communicate information, ideas and concepts necessary for academic success in the content area of Mathematics. Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 5 topics and texts, building on others’ ideas and expressing their own clearly. (a) Come to discussions prepared, having read or studied required material; explicitly draw on that preparation and other information known about the topic to explore ideas under discussion. (b) Follow agreed-upon rules for discussions and carry out assigned roles. (c) Pose and respond to specific questions by making comments that contribute to the discussion and elaborate on the remarks of others. (d) Review the key ideas expressed and draw conclusions in light of information and knowledge gained from the discussions. Summarize a written text read aloud or information presented in diverse media and formats, including visually, quantitatively, and orally. Summarize the points a speaker makes and explain how each claim is supported by reasons and evidence. Step 2: Visual Learning 9-7: Visual Learning Curriculum Standards: Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for 4 ÷ (1/5), and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 × (1/5) = 4. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins? Interpret division of a whole number by a unit fraction, and compute such quotients. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for 4 ÷ (1/5), and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 × (1/5) = 4. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins? Solve multi-step problems involving division with unit fractions. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins? Divide unit fractions by whole numbers and whole numbers by unit fractions. 9-7: Convince Me! Curriculum Standards: Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for 4 ÷ (1/5), and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 × (1/5) = 4. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins? Interpret division of a whole number by a unit fraction, and compute such quotients. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for 4 ÷ (1/5), and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 × (1/5) = 4. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins? Solve multi-step problems involving division with unit fractions. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins? Divide unit fractions by whole numbers and whole numbers by unit fractions. Practice and Problem Solving 9-7: Student Edition Practice Curriculum Standards: Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for 4 ÷ (1/5), and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 × (1/5) = 4. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins? Interpret division of a whole number by a unit fraction, and compute such quotients. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for 4 ÷ (1/5), and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 × (1/5) = 4. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins? Solve multi-step problems involving division with unit fractions. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins? Divide unit fractions by whole numbers and whole numbers by unit fractions. 9-7: Practice Buddy: Independent Practice; Problem Solving Curriculum Standards: Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for 4 ÷ (1/5), and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 × (1/5) = 4. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins? Interpret division of a whole number by a unit fraction, and compute such quotients. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for 4 ÷ (1/5), and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 × (1/5) = 4. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins? Solve multi-step problems involving division with unit fractions. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins? Divide unit fractions by whole numbers and whole numbers by unit fractions. 9-7: Practice Buddy: Additional Practice Curriculum Standards: Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for 4 ÷ (1/5), and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 × (1/5) = 4. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins? Interpret division of a whole number by a unit fraction, and compute such quotients. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for 4 ÷ (1/5), and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 × (1/5) = 4. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins? Solve multi-step problems involving division with unit fractions. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins? Divide unit fractions by whole numbers and whole numbers by unit fractions. 9-7: Interactive Additional Practice Step 3: Assess & Differentiate 9-7: Practice Buddy: Additional Practice Curriculum Standards: Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for 4 ÷ (1/5), and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 × (1/5) = 4. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins? Interpret division of a whole number by a unit fraction, and compute such quotients. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for 4 ÷ (1/5), and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 × (1/5) = 4. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins? Solve multi-step problems involving division with unit fractions. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins? Divide unit fractions by whole numbers and whole numbers by unit fractions. 9-7: Enrichment Curriculum Standards: Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for 4 ÷ (1/5), and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 × (1/5) = 4. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins? Interpret division of a whole number by a unit fraction, and compute such quotients. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for 4 ÷ (1/5), and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 × (1/5) = 4. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins? Solve multi-step problems involving division with unit fractions. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins? Divide unit fractions by whole numbers and whole numbers by unit fractions. 9-7: Quick Check Curriculum Standards: Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for 4 ÷ (1/5), and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 × (1/5) = 4. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins? Interpret division of a whole number by a unit fraction, and compute such quotients. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for 4 ÷ (1/5), and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 × (1/5) = 4. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins? Solve multi-step problems involving division with unit fractions. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins? Divide unit fractions by whole numbers and whole numbers by unit fractions. 9-7: Lesson Self-Assessment 9-7: Reteach to Build Understanding Curriculum Standards: Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for 4 ÷ (1/5), and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 × (1/5) = 4. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins? Interpret division of a whole number by a unit fraction, and compute such quotients. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for 4 ÷ (1/5), and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 × (1/5) = 4. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins? Solve multi-step problems involving division with unit fractions. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins? Divide unit fractions by whole numbers and whole numbers by unit fractions. 9-7: Build Mathematical Literacy Curriculum Standards: Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 5 topics and texts, building on others’ ideas and expressing their own clearly. (a) Come to discussions prepared, having read or studied required material; explicitly draw on that preparation and other information known about the topic to explore ideas under discussion. (b) Follow agreed-upon rules for discussions and carry out assigned roles. (c) Pose and respond to specific questions by making comments that contribute to the discussion and elaborate on the remarks of others. (d) Review the key ideas expressed and draw conclusions in light of information and knowledge gained from the discussions. English language learners communicate for social and instructional purposes within the school setting. Summarize a written text read aloud or information presented in diverse media and formats, including visually, quantitatively, and orally. Summarize the points a speaker makes and explain how each claim is supported by reasons and evidence. Write informative/explanatory texts to examine a topic and convey ideas and information clearly. (a) Introduce a topic clearly, provide a general observation and focus, and group related information logically; include formatting (e.g., headings), illustrations, and multimedia when useful to aiding comprehension. (b) Develop the topic with facts, definitions, concrete details, quotations, or other information and examples related to the topic. (c) Link ideas within and across categories of information using words, phrases, and clauses (e.g., in contrast, especially). (d) Use precise language and domain-specific vocabulary to inform about or explain the topic. (e) Provide a concluding statement or section related to the information or explanation presented. English language learners communicate information, ideas and concepts necessary for academic success in the content area of Mathematics. 9-7: Enrichment Game: Factory Frenzy - Decimals 9-7: Pick a Project 9-7: Another Look Curriculum Standards: Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for 4 ÷ (1/5), and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 × (1/5) = 4. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins? Interpret division of a whole number by a unit fraction, and compute such quotients. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for 4 ÷ (1/5), and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 × (1/5) = 4. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins? Solve multi-step problems involving division with unit fractions. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins? Divide unit fractions by whole numbers and whole numbers by unit fractions. Spanish Resources 9-7: eText del Libro del estudiante 9-7: Repaso diario 9-7: Aprendizaje visual 9-7: Amigo de práctica: Práctica adicional 9-7: Práctica adicional interactiva 9-7: Refuerzo para mejorar la comprensión 9-7: Desarrollar la competencia matemática 9-7: Ampliación Topic 9: 3-Act Math: Slime Time Interactive Student Edition: Grade 5, Topic 9: 3-Act Math Mathematical Modeling Topic 9: 3-Act Math: Slime Time, Act 1 Topic 9: 3-Act Math: Slime Time, Act 2 Topic 9: 3-Act Math: Slime Time, Act 3 Topic 9: 3-Act Math: Slime Time, Sequel 9-8: Problem Solving: Repeated Reasoning Interactive Student Edition: Grade 5 Lesson 9-8 Math Anytime 9-8: Daily Review Topic 9: Today's Challenge Step 1: Problem-Based Learning 9-8: Solve & Share Curriculum Standards: Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. For example, create a story context for (1/3) ÷ 4, and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that (1/3) ÷ 4 = 1/12 because (1/12) × 4 = 1/3. Look for and express regularity in repeated reasoning. English language learners communicate for social and instructional purposes within the school setting. Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. Look for and express regularity in repeated reasoning. Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. For example, create a story context for (1/3) ÷ 4, and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that (1/3) ÷ 4 = 1/12 because (1/12) × 4 = 1/3. Look for and express regularity in repeated reasoning. Mathematically proficient students notice if calculations are repeated, and look both for general methods and for shortcuts. Upper elementary students might notice when dividing 25 by 11 that they are repeating the same calculations over and over again, and conclude they have a repeating decimal. By paying attention to the calculation of slope as they repeatedly check whether points are on the line through (1, 2) with slope 3, middle school students might abstract the equation (y – 2)/(x – 1) = 3. Noticing the regularity in the way terms cancel when expanding (x – 1)(x + 1), (x – 1)(x² + x + 1), and (x – 1)(x³ + x² + x + 1) might lead them to the general formula for the sum of a geometric series. As they work to solve a problem, mathematically proficient students maintain oversight of the process, while attending to the details. They continually evaluate the reasonableness of their intermediate results. Notice repetition in calculations and generalize about how to divide whole numbers and unit fractions. Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. For example, create a story context for (1/3) ÷ 4, and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that (1/3) ÷ 4 = 1/12 because (1/12) × 4 = 1/3. Look for and express regularity in repeated reasoning. Look for and express regularity in repeated reasoning. Divide unit fractions by whole numbers and whole numbers by unit fractions. Look for and express regularity in repeated reasoning. Write informative/explanatory texts to examine a topic and convey ideas and information clearly. (a) Introduce a topic clearly, provide a general observation and focus, and group related information logically; include formatting (e.g., headings), illustrations, and multimedia when useful to aiding comprehension. (b) Develop the topic with facts, definitions, concrete details, quotations, or other information and examples related to the topic. (c) Link ideas within and across categories of information using words, phrases, and clauses (e.g., in contrast, especially). (d) Use precise language and domain-specific vocabulary to inform about or explain the topic. (e) Provide a concluding statement or section related to the information or explanation presented. English language learners communicate information, ideas and concepts necessary for academic success in the content area of Mathematics. Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 5 topics and texts, building on others’ ideas and expressing their own clearly. (a) Come to discussions prepared, having read or studied required material; explicitly draw on that preparation and other information known about the topic to explore ideas under discussion. (b) Follow agreed-upon rules for discussions and carry out assigned roles. (c) Pose and respond to specific questions by making comments that contribute to the discussion and elaborate on the remarks of others. (d) Review the key ideas expressed and draw conclusions in light of information and knowledge gained from the discussions. Summarize a written text read aloud or information presented in diverse media and formats, including visually, quantitatively, and orally. Summarize the points a speaker makes and explain how each claim is supported by reasons and evidence. Step 2: Visual Learning 9-8: Visual Learning Curriculum Standards: Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. For example, create a story context for (1/3) ÷ 4, and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that (1/3) ÷ 4 = 1/12 because (1/12) × 4 = 1/3. Look for and express regularity in repeated reasoning. Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. Look for and express regularity in repeated reasoning. Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. For example, create a story context for (1/3) ÷ 4, and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that (1/3) ÷ 4 = 1/12 because (1/12) × 4 = 1/3. Look for and express regularity in repeated reasoning. Mathematically proficient students notice if calculations are repeated, and look both for general methods and for shortcuts. Upper elementary students might notice when dividing 25 by 11 that they are repeating the same calculations over and over again, and conclude they have a repeating decimal. By paying attention to the calculation of slope as they repeatedly check whether points are on the line through (1, 2) with slope 3, middle school students might abstract the equation (y – 2)/(x – 1) = 3. Noticing the regularity in the way terms cancel when expanding (x – 1)(x + 1), (x – 1)(x² + x + 1), and (x – 1)(x³ + x² + x + 1) might lead them to the general formula for the sum of a geometric series. As they work to solve a problem, mathematically proficient students maintain oversight of the process, while attending to the details. They continually evaluate the reasonableness of their intermediate results. Notice repetition in calculations and generalize about how to divide whole numbers and unit fractions. Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. For example, create a story context for (1/3) ÷ 4, and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that (1/3) ÷ 4 = 1/12 because (1/12) × 4 = 1/3. Look for and express regularity in repeated reasoning. Look for and express regularity in repeated reasoning. Divide unit fractions by whole numbers and whole numbers by unit fractions. Look for and express regularity in repeated reasoning. 9-8: Convince Me! Curriculum Standards: Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. For example, create a story context for (1/3) ÷ 4, and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that (1/3) ÷ 4 = 1/12 because (1/12) × 4 = 1/3. Look for and express regularity in repeated reasoning. Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. Look for and express regularity in repeated reasoning. Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. For example, create a story context for (1/3) ÷ 4, and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that (1/3) ÷ 4 = 1/12 because (1/12) × 4 = 1/3. Look for and express regularity in repeated reasoning. Mathematically proficient students notice if calculations are repeated, and look both for general methods and for shortcuts. Upper elementary students might notice when dividing 25 by 11 that they are repeating the same calculations over and over again, and conclude they have a repeating decimal. By paying attention to the calculation of slope as they repeatedly check whether points are on the line through (1, 2) with slope 3, middle school students might abstract the equation (y – 2)/(x – 1) = 3. Noticing the regularity in the way terms cancel when expanding (x – 1)(x + 1), (x – 1)(x² + x + 1), and (x – 1)(x³ + x² + x + 1) might lead them to the general formula for the sum of a geometric series. As they work to solve a problem, mathematically proficient students maintain oversight of the process, while attending to the details. They continually evaluate the reasonableness of their intermediate results. Notice repetition in calculations and generalize about how to divide whole numbers and unit fractions. Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. For example, create a story context for (1/3) ÷ 4, and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that (1/3) ÷ 4 = 1/12 because (1/12) × 4 = 1/3. Look for and express regularity in repeated reasoning. Look for and express regularity in repeated reasoning. Divide unit fractions by whole numbers and whole numbers by unit fractions. Look for and express regularity in repeated reasoning. Practice and Problem Solving 9-8: Student Edition Practice Curriculum Standards: Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. For example, create a story context for (1/3) ÷ 4, and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that (1/3) ÷ 4 = 1/12 because (1/12) × 4 = 1/3. Look for and express regularity in repeated reasoning. Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. Look for and express regularity in repeated reasoning. Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. For example, create a story context for (1/3) ÷ 4, and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that (1/3) ÷ 4 = 1/12 because (1/12) × 4 = 1/3. Look for and express regularity in repeated reasoning. Mathematically proficient students notice if calculations are repeated, and look both for general methods and for shortcuts. Upper elementary students might notice when dividing 25 by 11 that they are repeating the same calculations over and over again, and conclude they have a repeating decimal. By paying attention to the calculation of slope as they repeatedly check whether points are on the line through (1, 2) with slope 3, middle school students might abstract the equation (y – 2)/(x – 1) = 3. Noticing the regularity in the way terms cancel when expanding (x – 1)(x + 1), (x – 1)(x² + x + 1), and (x – 1)(x³ + x² + x + 1) might lead them to the general formula for the sum of a geometric series. As they work to solve a problem, mathematically proficient students maintain oversight of the process, while attending to the details. They continually evaluate the reasonableness of their intermediate results. Notice repetition in calculations and generalize about how to divide whole numbers and unit fractions. Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. For example, create a story context for (1/3) ÷ 4, and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that (1/3) ÷ 4 = 1/12 because (1/12) × 4 = 1/3. Look for and express regularity in repeated reasoning. Look for and express regularity in repeated reasoning. Divide unit fractions by whole numbers and whole numbers by unit fractions. Look for and express regularity in repeated reasoning. 9-8: Practice Buddy: Independent Practice; Problem Solving Curriculum Standards: Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. For example, create a story context for (1/3) ÷ 4, and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that (1/3) ÷ 4 = 1/12 because (1/12) × 4 = 1/3. Look for and express regularity in repeated reasoning. Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. Look for and express regularity in repeated reasoning. Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. For example, create a story context for (1/3) ÷ 4, and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that (1/3) ÷ 4 = 1/12 because (1/12) × 4 = 1/3. Look for and express regularity in repeated reasoning. Mathematically proficient students notice if calculations are repeated, and look both for general methods and for shortcuts. Upper elementary students might notice when dividing 25 by 11 that they are repeating the same calculations over and over again, and conclude they have a repeating decimal. By paying attention to the calculation of slope as they repeatedly check whether points are on the line through (1, 2) with slope 3, middle school students might abstract the equation (y – 2)/(x – 1) = 3. Noticing the regularity in the way terms cancel when expanding (x – 1)(x + 1), (x – 1)(x² + x + 1), and (x – 1)(x³ + x² + x + 1) might lead them to the general formula for the sum of a geometric series. As they work to solve a problem, mathematically proficient students maintain oversight of the process, while attending to the details. They continually evaluate the reasonableness of their intermediate results. Notice repetition in calculations and generalize about how to divide whole numbers and unit fractions. Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. For example, create a story context for (1/3) ÷ 4, and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that (1/3) ÷ 4 = 1/12 because (1/12) × 4 = 1/3. Look for and express regularity in repeated reasoning. Look for and express regularity in repeated reasoning. Divide unit fractions by whole numbers and whole numbers by unit fractions. Look for and express regularity in repeated reasoning. 9-8: Practice Buddy: Additional Practice Curriculum Standards: Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. For example, create a story context for (1/3) ÷ 4, and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that (1/3) ÷ 4 = 1/12 because (1/12) × 4 = 1/3. Look for and express regularity in repeated reasoning. Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. Look for and express regularity in repeated reasoning. Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. For example, create a story context for (1/3) ÷ 4, and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that (1/3) ÷ 4 = 1/12 because (1/12) × 4 = 1/3. Look for and express regularity in repeated reasoning. Mathematically proficient students notice if calculations are repeated, and look both for general methods and for shortcuts. Upper elementary students might notice when dividing 25 by 11 that they are repeating the same calculations over and over again, and conclude they have a repeating decimal. By paying attention to the calculation of slope as they repeatedly check whether points are on the line through (1, 2) with slope 3, middle school students might abstract the equation (y – 2)/(x – 1) = 3. Noticing the regularity in the way terms cancel when expanding (x – 1)(x + 1), (x – 1)(x² + x + 1), and (x – 1)(x³ + x² + x + 1) might lead them to the general formula for the sum of a geometric series. As they work to solve a problem, mathematically proficient students maintain oversight of the process, while attending to the details. They continually evaluate the reasonableness of their intermediate results. Notice repetition in calculations and generalize about how to divide whole numbers and unit fractions. Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. For example, create a story context for (1/3) ÷ 4, and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that (1/3) ÷ 4 = 1/12 because (1/12) × 4 = 1/3. Look for and express regularity in repeated reasoning. Look for and express regularity in repeated reasoning. Divide unit fractions by whole numbers and whole numbers by unit fractions. Look for and express regularity in repeated reasoning. 9-8: Interactive Additional Practice Step 3: Assess & Differentiate 9-8: Practice Buddy: Additional Practice Curriculum Standards: Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. For example, create a story context for (1/3) ÷ 4, and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that (1/3) ÷ 4 = 1/12 because (1/12) × 4 = 1/3. Look for and express regularity in repeated reasoning. Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. Look for and express regularity in repeated reasoning. Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. For example, create a story context for (1/3) ÷ 4, and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that (1/3) ÷ 4 = 1/12 because (1/12) × 4 = 1/3. Look for and express regularity in repeated reasoning. Mathematically proficient students notice if calculations are repeated, and look both for general methods and for shortcuts. Upper elementary students might notice when dividing 25 by 11 that they are repeating the same calculations over and over again, and conclude they have a repeating decimal. By paying attention to the calculation of slope as they repeatedly check whether points are on the line through (1, 2) with slope 3, middle school students might abstract the equation (y – 2)/(x – 1) = 3. Noticing the regularity in the way terms cancel when expanding (x – 1)(x + 1), (x – 1)(x² + x + 1), and (x – 1)(x³ + x² + x + 1) might lead them to the general formula for the sum of a geometric series. As they work to solve a problem, mathematically proficient students maintain oversight of the process, while attending to the details. They continually evaluate the reasonableness of their intermediate results. Notice repetition in calculations and generalize about how to divide whole numbers and unit fractions. Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. For example, create a story context for (1/3) ÷ 4, and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that (1/3) ÷ 4 = 1/12 because (1/12) × 4 = 1/3. Look for and express regularity in repeated reasoning. Look for and express regularity in repeated reasoning. Divide unit fractions by whole numbers and whole numbers by unit fractions. Look for and express regularity in repeated reasoning. 9-8: Enrichment Curriculum Standards: Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. For example, create a story context for (1/3) ÷ 4, and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that (1/3) ÷ 4 = 1/12 because (1/12) × 4 = 1/3. Look for and express regularity in repeated reasoning. Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. Look for and express regularity in repeated reasoning. Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. For example, create a story context for (1/3) ÷ 4, and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that (1/3) ÷ 4 = 1/12 because (1/12) × 4 = 1/3. Look for and express regularity in repeated reasoning. Mathematically proficient students notice if calculations are repeated, and look both for general methods and for shortcuts. Upper elementary students might notice when dividing 25 by 11 that they are repeating the same calculations over and over again, and conclude they have a repeating decimal. By paying attention to the calculation of slope as they repeatedly check whether points are on the line through (1, 2) with slope 3, middle school students might abstract the equation (y – 2)/(x – 1) = 3. Noticing the regularity in the way terms cancel when expanding (x – 1)(x + 1), (x – 1)(x² + x + 1), and (x – 1)(x³ + x² + x + 1) might lead them to the general formula for the sum of a geometric series. As they work to solve a problem, mathematically proficient students maintain oversight of the process, while attending to the details. They continually evaluate the reasonableness of their intermediate results. Notice repetition in calculations and generalize about how to divide whole numbers and unit fractions. Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. For example, create a story context for (1/3) ÷ 4, and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that (1/3) ÷ 4 = 1/12 because (1/12) × 4 = 1/3. Look for and express regularity in repeated reasoning. Look for and express regularity in repeated reasoning. Divide unit fractions by whole numbers and whole numbers by unit fractions. Look for and express regularity in repeated reasoning. 9-8: Quick Check Curriculum Standards: Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. For example, create a story context for (1/3) ÷ 4, and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that (1/3) ÷ 4 = 1/12 because (1/12) × 4 = 1/3. Look for and express regularity in repeated reasoning. Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. Look for and express regularity in repeated reasoning. Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. For example, create a story context for (1/3) ÷ 4, and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that (1/3) ÷ 4 = 1/12 because (1/12) × 4 = 1/3. Look for and express regularity in repeated reasoning. Mathematically proficient students notice if calculations are repeated, and look both for general methods and for shortcuts. Upper elementary students might notice when dividing 25 by 11 that they are repeating the same calculations over and over again, and conclude they have a repeating decimal. By paying attention to the calculation of slope as they repeatedly check whether points are on the line through (1, 2) with slope 3, middle school students might abstract the equation (y – 2)/(x – 1) = 3. Noticing the regularity in the way terms cancel when expanding (x – 1)(x + 1), (x – 1)(x² + x + 1), and (x – 1)(x³ + x² + x + 1) might lead them to the general formula for the sum of a geometric series. As they work to solve a problem, mathematically proficient students maintain oversight of the process, while attending to the details. They continually evaluate the reasonableness of their intermediate results. Notice repetition in calculations and generalize about how to divide whole numbers and unit fractions. Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. For example, create a story context for (1/3) ÷ 4, and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that (1/3) ÷ 4 = 1/12 because (1/12) × 4 = 1/3. Look for and express regularity in repeated reasoning. Look for and express regularity in repeated reasoning. Divide unit fractions by whole numbers and whole numbers by unit fractions. Look for and express regularity in repeated reasoning. 9-8: Lesson Self-Assessment 9-8: Reteach to Build Understanding Curriculum Standards: Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. For example, create a story context for (1/3) ÷ 4, and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that (1/3) ÷ 4 = 1/12 because (1/12) × 4 = 1/3. Look for and express regularity in repeated reasoning. Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. Look for and express regularity in repeated reasoning. Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. For example, create a story context for (1/3) ÷ 4, and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that (1/3) ÷ 4 = 1/12 because (1/12) × 4 = 1/3. Look for and express regularity in repeated reasoning. Mathematically proficient students notice if calculations are repeated, and look both for general methods and for shortcuts. Upper elementary students might notice when dividing 25 by 11 that they are repeating the same calculations over and over again, and conclude they have a repeating decimal. By paying attention to the calculation of slope as they repeatedly check whether points are on the line through (1, 2) with slope 3, middle school students might abstract the equation (y – 2)/(x – 1) = 3. Noticing the regularity in the way terms cancel when expanding (x – 1)(x + 1), (x – 1)(x² + x + 1), and (x – 1)(x³ + x² + x + 1) might lead them to the general formula for the sum of a geometric series. As they work to solve a problem, mathematically proficient students maintain oversight of the process, while attending to the details. They continually evaluate the reasonableness of their intermediate results. Notice repetition in calculations and generalize about how to divide whole numbers and unit fractions. Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. For example, create a story context for (1/3) ÷ 4, and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that (1/3) ÷ 4 = 1/12 because (1/12) × 4 = 1/3. Look for and express regularity in repeated reasoning. Look for and express regularity in repeated reasoning. Divide unit fractions by whole numbers and whole numbers by unit fractions. Look for and express regularity in repeated reasoning. 9-8: Build Mathematical Literacy Curriculum Standards: Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 5 topics and texts, building on others’ ideas and expressing their own clearly. (a) Come to discussions prepared, having read or studied required material; explicitly draw on that preparation and other information known about the topic to explore ideas under discussion. (b) Follow agreed-upon rules for discussions and carry out assigned roles. (c) Pose and respond to specific questions by making comments that contribute to the discussion and elaborate on the remarks of others. (d) Review the key ideas expressed and draw conclusions in light of information and knowledge gained from the discussions. English language learners communicate for social and instructional purposes within the school setting. Summarize a written text read aloud or information presented in diverse media and formats, including visually, quantitatively, and orally. Summarize the points a speaker makes and explain how each claim is supported by reasons and evidence. Write informative/explanatory texts to examine a topic and convey ideas and information clearly. (a) Introduce a topic clearly, provide a general observation and focus, and group related information logically; include formatting (e.g., headings), illustrations, and multimedia when useful to aiding comprehension. (b) Develop the topic with facts, definitions, concrete details, quotations, or other information and examples related to the topic. (c) Link ideas within and across categories of information using words, phrases, and clauses (e.g., in contrast, especially). (d) Use precise language and domain-specific vocabulary to inform about or explain the topic. (e) Provide a concluding statement or section related to the information or explanation presented. English language learners communicate information, ideas and concepts necessary for academic success in the content area of Mathematics. 9-8: Enrichment Game: Fluency - Multiply Multi-Digit Whole Numbers 9-8: Problem-Solving Reading Activity Curriculum Standards: Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. For example, create a story context for (1/3) ÷ 4, and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that (1/3) ÷ 4 = 1/12 because (1/12) × 4 = 1/3. Look for and express regularity in repeated reasoning. Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. Look for and express regularity in repeated reasoning. Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. For example, create a story context for (1/3) ÷ 4, and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that (1/3) ÷ 4 = 1/12 because (1/12) × 4 = 1/3. Look for and express regularity in repeated reasoning. Mathematically proficient students notice if calculations are repeated, and look both for general methods and for shortcuts. Upper elementary students might notice when dividing 25 by 11 that they are repeating the same calculations over and over again, and conclude they have a repeating decimal. By paying attention to the calculation of slope as they repeatedly check whether points are on the line through (1, 2) with slope 3, middle school students might abstract the equation (y – 2)/(x – 1) = 3. Noticing the regularity in the way terms cancel when expanding (x – 1)(x + 1), (x – 1)(x² + x + 1), and (x – 1)(x³ + x² + x + 1) might lead them to the general formula for the sum of a geometric series. As they work to solve a problem, mathematically proficient students maintain oversight of the process, while attending to the details. They continually evaluate the reasonableness of their intermediate results. Notice repetition in calculations and generalize about how to divide whole numbers and unit fractions. Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. For example, create a story context for (1/3) ÷ 4, and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that (1/3) ÷ 4 = 1/12 because (1/12) × 4 = 1/3. Look for and express regularity in repeated reasoning. Look for and express regularity in repeated reasoning. Divide unit fractions by whole numbers and whole numbers by unit fractions. Look for and express regularity in repeated reasoning. 9-8: Another Look Curriculum Standards: Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. For example, create a story context for (1/3) ÷ 4, and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that (1/3) ÷ 4 = 1/12 because (1/12) × 4 = 1/3. Look for and express regularity in repeated reasoning. Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. Look for and express regularity in repeated reasoning. Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. For example, create a story context for (1/3) ÷ 4, and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that (1/3) ÷ 4 = 1/12 because (1/12) × 4 = 1/3. Look for and express regularity in repeated reasoning. Mathematically proficient students notice if calculations are repeated, and look both for general methods and for shortcuts. Upper elementary students might notice when dividing 25 by 11 that they are repeating the same calculations over and over again, and conclude they have a repeating decimal. By paying attention to the calculation of slope as they repeatedly check whether points are on the line through (1, 2) with slope 3, middle school students might abstract the equation (y – 2)/(x – 1) = 3. Noticing the regularity in the way terms cancel when expanding (x – 1)(x + 1), (x – 1)(x² + x + 1), and (x – 1)(x³ + x² + x + 1) might lead them to the general formula for the sum of a geometric series. As they work to solve a problem, mathematically proficient students maintain oversight of the process, while attending to the details. They continually evaluate the reasonableness of their intermediate results. Notice repetition in calculations and generalize about how to divide whole numbers and unit fractions. Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. For example, create a story context for (1/3) ÷ 4, and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that (1/3) ÷ 4 = 1/12 because (1/12) × 4 = 1/3. Look for and express regularity in repeated reasoning. Look for and express regularity in repeated reasoning. Divide unit fractions by whole numbers and whole numbers by unit fractions. Look for and express regularity in repeated reasoning. Spanish Resources 9-8: eText del Libro del estudiante 9-8: Repaso diario 9-8: Aprendizaje visual 9-8: Amigo de práctica: Práctica adicional 9-8: Práctica adicional interactiva 9-8: Refuerzo para mejorar la comprensión 9-8: Desarrollar la competencia matemática 9-8: Ampliación Topic 9: End of Topic Interactive Student Edition: End of Topic 9 Topic 9: Fluency Practice Activity Interactive Student Edition: Topic 9 Assessment Practice Interactive Student Edition: Topic 9 Performance Task Topic 9 Performance Task Topic 9 Assessment 9-2: Visual Learning Curriculum Standards: Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. For example, interpret 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3, and that when 3 wholes are shared equally among 4 people each person has a share of size 3/4. If 9 people want to share a 50-pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie? Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. For example, interpret 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3, and that when 3 wholes are shared equally among 4 people each person has a share of size 3/4. If 9 people want to share a 50-pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie? Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. For example, interpret 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3, and that when 3 wholes are shared equally among 4 people each person has a share of size 3/4. If 9 people want to share a 50-pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie? Implement division of fractions to show quotients as fractions and mixed numbers. Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. For example, interpret 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3, and that when 3 wholes are shared equally among 4 people each person has a share of size 3/4. If 9 people want to share a 50-pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie? Solve word problems involving division of whole numbers leading to answers in the form of fractions (including mixed numbers). 9-5: Visual Learning Curriculum Standards: Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. For example, create a story context for (1/3) ÷ 4, and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that (1/3) ÷ 4 = 1/12 because (1/12) × 4 = 1/3. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins? Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. For example, create a story context for (1/3) ÷ 4, and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that (1/3) ÷ 4 = 1/12 because (1/12) × 4 = 1/3. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins? Use models to divide unit fractions by non-zero whole numbers. Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. For example, create a story context for (1/3) ÷ 4, and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that (1/3) ÷ 4 = 1/12 because (1/12) × 4 = 1/3. Divide unit fractions by whole numbers and whole numbers by unit fractions. 9-6: Visual Learning Curriculum Standards: Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. For example, create a story context for (1/3) ÷ 4, and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that (1/3) ÷ 4 = 1/12 because (1/12) × 4 = 1/3. Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for 4 ÷ (1/5), and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 × (1/5) = 4. Solve real world problems involving division of unit fractions by non- zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins? Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. Interpret division of a whole number by a unit fraction, and compute such quotients. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. For example, create a story context for (1/3) ÷ 4, and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that (1/3) ÷ 4 = 1/12 because (1/12) × 4 = 1/3. Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for 4 ÷ (1/5), and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 × (1/5) = 4. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins? Use models to divide whole numbers and unit fractions. Check your answer using multiplication. Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. For example, create a story context for (1/3) ÷ 4, and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that (1/3) ÷ 4 = 1/12 because (1/12) × 4 = 1/3. Divide unit fractions by whole numbers and whole numbers by unit fractions. 9-7: Visual Learning Curriculum Standards: Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for 4 ÷ (1/5), and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 × (1/5) = 4. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins? Interpret division of a whole number by a unit fraction, and compute such quotients. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for 4 ÷ (1/5), and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 × (1/5) = 4. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins? Solve multi-step problems involving division with unit fractions. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 1/3- cup servings are in 2 cups of raisins? Divide unit fractions by whole numbers and whole numbers by unit fractions. 9-4: Visual Learning Curriculum Standards: Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for 4 ÷ (1/5), and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 × (1/5) = 4. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins? Interpret division of a whole number by a unit fraction, and compute such quotients. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for 4 ÷ (1/5), and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 × (1/5) = 4. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins? Use models, such as pictorial models or a number line, to show dividing a whole number by a unit fraction. Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for 4 ÷ (1/5), and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 × (1/5) = 4. Divide unit fractions by whole numbers and whole numbers by unit fractions. 10-4: Center Games Topic 9 Online Assessment Curriculum Standards: Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. For example, create a story context for (1/3) ÷ 4, and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that (1/3) ÷ 4 = 1/12 because (1/12) × 4 = 1/3. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins? Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for 4 ÷ (1/5), and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 × (1/5) = 4. Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. For example, interpret 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3, and that when 3 wholes are shared equally among 4 people each person has a share of size 3/4. If 9 people want to share a 50-pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie? Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. For example, create a story context for (1/3) ÷ 4, and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that (1/3) ÷ 4 = 1/12 because (1/12) × 4 = 1/3. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins? Use models to divide unit fractions by non-zero whole numbers. Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. For example, create a story context for (1/3) ÷ 4, and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that (1/3) ÷ 4 = 1/12 because (1/12) × 4 = 1/3. Divide unit fractions by whole numbers and whole numbers by unit fractions. Interpret division of a whole number by a unit fraction, and compute such quotients. Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for 4 ÷ (1/5), and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 × (1/5) = 4. Use models to divide whole numbers and unit fractions. Check your answer using multiplication. Solve multi-step problems involving division with unit fractions. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins? Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. For example, interpret 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3, and that when 3 wholes are shared equally among 4 people each person has a share of size 3/4. If 9 people want to share a 50-pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie? Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. For example, interpret 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3, and that when 3 wholes are shared equally among 4 people each person has a share of size 3/4. If 9 people want to share a 50-pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie? Implement division of fractions to show quotients as fractions and mixed numbers. Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. For example, interpret 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3, and that when 3 wholes are shared equally among 4 people each person has a share of size 3/4. If 9 people want to share a 50-pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie? Solve word problems involving division of whole numbers leading to answers in the form of fractions (including mixed numbers). Use models, such as pictorial models or a number line, to show dividing a whole number by a unit fraction. Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for 4 ÷ (1/5), and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 × (1/5) = 4. Topic 9 Spanish Assessments Tema 9: Tarea de rendimento Tema 9: Evaluación Topic 10: Represent and Interpret Data Topic 10: Today's Challenge Topic 10: Beginning of Topic Interactive Student Edition: Beginning of Topic 10 Topic 10: enVision STEM Activity Grade 5 Topic 10: Review What You Know Topic 10: Vocabulary Cards 10-1: Analyze Line Plots Interactive Student Edition: Grade 5 Lesson 10-1 Math Anytime 10-1: Daily Review Topic 10: Today's Challenge Step 1: Problem-Based Learning 10-1: Solve & Share Curriculum Standards: Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Make a line plot to display a data set of measurements in fractions of a unit (1/2 , 1/4 , 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally. Read and analyze line plots. Make a line plot to display a data set of measurements in fractions of a unit (1/2 , 1/4 , 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally. Solve problems involving computation of fractions by using information presented in line plots. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. English language learners communicate for social and instructional purposes within the school setting. Write informative/explanatory texts to examine a topic and convey ideas and information clearly. (a) Introduce a topic clearly, provide a general observation and focus, and group related information logically; include formatting (e.g., headings), illustrations, and multimedia when useful to aiding comprehension. (b) Develop the topic with facts, definitions, concrete details, quotations, or other information and examples related to the topic. (c) Link ideas within and across categories of information using words, phrases, and clauses (e.g., in contrast, especially). (d) Use precise language and domain-specific vocabulary to inform about or explain the topic. (e) Provide a concluding statement or section related to the information or explanation presented. English language learners communicate information, ideas and concepts necessary for academic success in the content area of Mathematics. Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 5 topics and texts, building on others’ ideas and expressing their own clearly. (a) Come to discussions prepared, having read or studied required material; explicitly draw on that preparation and other information known about the topic to explore ideas under discussion. (b) Follow agreed-upon rules for discussions and carry out assigned roles. (c) Pose and respond to specific questions by making comments that contribute to the discussion and elaborate on the remarks of others. (d) Review the key ideas expressed and draw conclusions in light of information and knowledge gained from the discussions. Summarize a written text read aloud or information presented in diverse media and formats, including visually, quantitatively, and orally. Summarize the points a speaker makes and explain how each claim is supported by reasons and evidence. Step 2: Visual Learning 10-1: Visual Learning Curriculum Standards: Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Make a line plot to display a data set of measurements in fractions of a unit (1/2 , 1/4 , 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally. Read and analyze line plots. Make a line plot to display a data set of measurements in fractions of a unit (1/2 , 1/4 , 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally. Solve problems involving computation of fractions by using information presented in line plots. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. Collect and graph fractional data on a line plot (e.g., length of each person’s pencil in classroom, hours of exercise each week). 10-1: Convince Me! Curriculum Standards: Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Make a line plot to display a data set of measurements in fractions of a unit (1/2 , 1/4 , 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally. Read and analyze line plots. Make a line plot to display a data set of measurements in fractions of a unit (1/2 , 1/4 , 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally. Solve problems involving computation of fractions by using information presented in line plots. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. Practice and Problem Solving 10-1: Student Edition Practice Curriculum Standards: Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Make a line plot to display a data set of measurements in fractions of a unit (1/2 , 1/4 , 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally. Read and analyze line plots. Make a line plot to display a data set of measurements in fractions of a unit (1/2 , 1/4 , 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally. Solve problems involving computation of fractions by using information presented in line plots. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. 10-1: Practice Buddy: Independent Practice; Problem Solving Curriculum Standards: Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Make a line plot to display a data set of measurements in fractions of a unit (1/2 , 1/4 , 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally. Read and analyze line plots. Make a line plot to display a data set of measurements in fractions of a unit (1/2 , 1/4 , 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally. Solve problems involving computation of fractions by using information presented in line plots. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. 10-1: Practice Buddy: Additional Practice Curriculum Standards: Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Make a line plot to display a data set of measurements in fractions of a unit (1/2 , 1/4 , 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally. Read and analyze line plots. Make a line plot to display a data set of measurements in fractions of a unit (1/2 , 1/4 , 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally. Solve problems involving computation of fractions by using information presented in line plots. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. 10-1: Interactive Additional Practice Step 3: Assess & Differentiate 10-1: Practice Buddy: Additional Practice Curriculum Standards: Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Make a line plot to display a data set of measurements in fractions of a unit (1/2 , 1/4 , 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally. Read and analyze line plots. Make a line plot to display a data set of measurements in fractions of a unit (1/2 , 1/4 , 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally. Solve problems involving computation of fractions by using information presented in line plots. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. 10-1: Enrichment Curriculum Standards: Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Make a line plot to display a data set of measurements in fractions of a unit (1/2 , 1/4 , 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally. Read and analyze line plots. Make a line plot to display a data set of measurements in fractions of a unit (1/2 , 1/4 , 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally. Solve problems involving computation of fractions by using information presented in line plots. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. 10-1: Quick Check Curriculum Standards: Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Make a line plot to display a data set of measurements in fractions of a unit (1/2 , 1/4 , 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally. Read and analyze line plots. Make a line plot to display a data set of measurements in fractions of a unit (1/2 , 1/4 , 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally. Solve problems involving computation of fractions by using information presented in line plots. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. 10-1: Lesson Self-Assessment 10-1: Reteach to Build Understanding Curriculum Standards: Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Make a line plot to display a data set of measurements in fractions of a unit (1/2 , 1/4 , 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally. Read and analyze line plots. Make a line plot to display a data set of measurements in fractions of a unit (1/2 , 1/4 , 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally. Solve problems involving computation of fractions by using information presented in line plots. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. Collect and graph fractional data on a line plot (e.g., length of each person’s pencil in classroom, hours of exercise each week). 10-1: Build Mathematical Literacy Curriculum Standards: Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 5 topics and texts, building on others’ ideas and expressing their own clearly. (a) Come to discussions prepared, having read or studied required material; explicitly draw on that preparation and other information known about the topic to explore ideas under discussion. (b) Follow agreed-upon rules for discussions and carry out assigned roles. (c) Pose and respond to specific questions by making comments that contribute to the discussion and elaborate on the remarks of others. (d) Review the key ideas expressed and draw conclusions in light of information and knowledge gained from the discussions. English language learners communicate for social and instructional purposes within the school setting. Summarize a written text read aloud or information presented in diverse media and formats, including visually, quantitatively, and orally. Summarize the points a speaker makes and explain how each claim is supported by reasons and evidence. Write informative/explanatory texts to examine a topic and convey ideas and information clearly. (a) Introduce a topic clearly, provide a general observation and focus, and group related information logically; include formatting (e.g., headings), illustrations, and multimedia when useful to aiding comprehension. (b) Develop the topic with facts, definitions, concrete details, quotations, or other information and examples related to the topic. (c) Link ideas within and across categories of information using words, phrases, and clauses (e.g., in contrast, especially). (d) Use precise language and domain-specific vocabulary to inform about or explain the topic. (e) Provide a concluding statement or section related to the information or explanation presented. English language learners communicate information, ideas and concepts necessary for academic success in the content area of Mathematics. 10-1: Enrichment 10-1: Digital Math Tool Activity 10-1: enVision STEM Activity Curriculum Standards: Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Make a line plot to display a data set of measurements in fractions of a unit (1/2 , 1/4 , 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally. Read and analyze line plots. Make a line plot to display a data set of measurements in fractions of a unit (1/2 , 1/4 , 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally. Solve problems involving computation of fractions by using information presented in line plots. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. 10-1: Another Look Curriculum Standards: Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Make a line plot to display a data set of measurements in fractions of a unit (1/2 , 1/4 , 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally. Read and analyze line plots. Make a line plot to display a data set of measurements in fractions of a unit (1/2 , 1/4 , 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally. Solve problems involving computation of fractions by using information presented in line plots. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. Collect and graph fractional data on a line plot (e.g., length of each person’s pencil in classroom, hours of exercise each week). Spanish Resources 10-1: eText del Libro del estudiante 10-1: Repaso diario 10-1: Aprendizaje visual 10-1: Amigo de práctica: Práctica adicional 10-1: Práctica adicional interactiva 10-1: Refuerzo para mejorar la comprensión 10-1: Desarrollar la competencia matemática 10-1: Ampliación 10-2: Make Line Plots Interactive Student Edition: Grade 5 Lesson 10-2 Math Anytime 10-2: Daily Review Topic 10: Today's Challenge Step 1: Problem-Based Learning 10-2: Solve & Share Curriculum Standards: Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Make a line plot to display a data set of measurements in fractions of a unit (1/2 , 1/4 , 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally. Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally. Organize and display data in a line plot. Make a line plot to display a data set of measurements in fractions of a unit (1/2 , 1/4 , 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally. Solve problems involving computation of fractions by using information presented in line plots. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. English language learners communicate for social and instructional purposes within the school setting. Write informative/explanatory texts to examine a topic and convey ideas and information clearly. (a) Introduce a topic clearly, provide a general observation and focus, and group related information logically; include formatting (e.g., headings), illustrations, and multimedia when useful to aiding comprehension. (b) Develop the topic with facts, definitions, concrete details, quotations, or other information and examples related to the topic. (c) Link ideas within and across categories of information using words, phrases, and clauses (e.g., in contrast, especially). (d) Use precise language and domain- specific vocabulary to inform about or explain the topic. (e) Provide a concluding statement or section related to the information or explanation presented. English language learners communicate information, ideas and concepts necessary for academic success in the content area of Mathematics. Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 5 topics and texts, building on others’ ideas and expressing their own clearly. (a) Come to discussions prepared, having read or studied required material; explicitly draw on that preparation and other information known about the topic to explore ideas under discussion. (b) Follow agreed-upon rules for discussions and carry out assigned roles. (c) Pose and respond to specific questions by making comments that contribute to the discussion and elaborate on the remarks of others. (d) Review the key ideas expressed and draw conclusions in light of information and knowledge gained from the discussions. Summarize a written text read aloud or information presented in diverse media and formats, including visually, quantitatively, and orally. Summarize the points a speaker makes and explain how each claim is supported by reasons and evidence. Step 2: Visual Learning 10-2: Visual Learning Curriculum Standards: Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Make a line plot to display a data set of measurements in fractions of a unit (1/2 , 1/4 , 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally. Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally. Organize and display data in a line plot. Make a line plot to display a data set of measurements in fractions of a unit (1/2 , 1/4 , 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally. Solve problems involving computation of fractions by using information presented in line plots. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. Collect and graph fractional data on a line plot (e.g., length of each person’s pencil in classroom, hours of exercise each week). 10-2: Convince Me! Curriculum Standards: Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Make a line plot to display a data set of measurements in fractions of a unit (1/2 , 1/4 , 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally. Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally. Organize and display data in a line plot. Make a line plot to display a data set of measurements in fractions of a unit (1/2 , 1/4 , 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally. Solve problems involving computation of fractions by using information presented in line plots. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. Practice and Problem Solving 10-2: Student Edition Practice Curriculum Standards: Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Make a line plot to display a data set of measurements in fractions of a unit (1/2 , 1/4 , 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally. Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally. Organize and display data in a line plot. Make a line plot to display a data set of measurements in fractions of a unit (1/2 , 1/4 , 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally. Solve problems involving computation of fractions by using information presented in line plots. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. 10-2: Practice Buddy: Independent Practice; Problem Solving Curriculum Standards: Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Make a line plot to display a data set of measurements in fractions of a unit (1/2 , 1/4 , 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally. Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally. Organize and display data in a line plot. Make a line plot to display a data set of measurements in fractions of a unit (1/2 , 1/4 , 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally. Solve problems involving computation of fractions by using information presented in line plots. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. 10-2: Practice Buddy: Additional Practice Curriculum Standards: Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Make a line plot to display a data set of measurements in fractions of a unit (1/2 , 1/4 , 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally. Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally. Organize and display data in a line plot. Make a line plot to display a data set of measurements in fractions of a unit (1/2 , 1/4 , 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally. Solve problems involving computation of fractions by using information presented in line plots. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. 10-2: Interactive Additional Practice Step 3: Assess & Differentiate 10-2: Practice Buddy: Additional Practice Curriculum Standards: Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Make a line plot to display a data set of measurements in fractions of a unit (1/2 , 1/4 , 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally. Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally. Organize and display data in a line plot. Make a line plot to display a data set of measurements in fractions of a unit (1/2 , 1/4 , 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally. Solve problems involving computation of fractions by using information presented in line plots. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. 10-2: Enrichment Curriculum Standards: Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Make a line plot to display a data set of measurements in fractions of a unit (1/2 , 1/4 , 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally. Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally. Organize and display data in a line plot. Make a line plot to display a data set of measurements in fractions of a unit (1/2 , 1/4 , 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally. Solve problems involving computation of fractions by using information presented in line plots. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. 10-2: Quick Check Curriculum Standards: Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Make a line plot to display a data set of measurements in fractions of a unit (1/2 , 1/4 , 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally. Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally. Organize and display data in a line plot. Make a line plot to display a data set of measurements in fractions of a unit (1/2 , 1/4 , 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally. Solve problems involving computation of fractions by using information presented in line plots. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. 10-2: Lesson Self-Assessment 10-2: Reteach to Build Understanding Curriculum Standards: Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Make a line plot to display a data set of measurements in fractions of a unit (1/2 , 1/4 , 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally. Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally. Organize and display data in a line plot. Make a line plot to display a data set of measurements in fractions of a unit (1/2 , 1/4 , 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally. Solve problems involving computation of fractions by using information presented in line plots. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. Collect and graph fractional data on a line plot (e.g., length of each person’s pencil in classroom, hours of exercise each week). 10-2: Build Mathematical Literacy Curriculum Standards: Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 5 topics and texts, building on others’ ideas and expressing their own clearly. (a) Come to discussions prepared, having read or studied required material; explicitly draw on that preparation and other information known about the topic to explore ideas under discussion. (b) Follow agreed-upon rules for discussions and carry out assigned roles. (c) Pose and respond to specific questions by making comments that contribute to the discussion and elaborate on the remarks of others. (d) Review the key ideas expressed and draw conclusions in light of information and knowledge gained from the discussions. English language learners communicate for social and instructional purposes within the school setting. Summarize a written text read aloud or information presented in diverse media and formats, including visually, quantitatively, and orally. Summarize the points a speaker makes and explain how each claim is supported by reasons and evidence. Write informative/explanatory texts to examine a topic and convey ideas and information clearly. (a) Introduce a topic clearly, provide a general observation and focus, and group related information logically; include formatting (e.g., headings), illustrations, and multimedia when useful to aiding comprehension. (b) Develop the topic with facts, definitions, concrete details, quotations, or other information and examples related to the topic. (c) Link ideas within and across categories of information using words, phrases, and clauses (e.g., in contrast, especially). (d) Use precise language and domain-specific vocabulary to inform about or explain the topic. (e) Provide a concluding statement or section related to the information or explanation presented. English language learners communicate information, ideas and concepts necessary for academic success in the content area of Mathematics. 10-2: Enrichment 10-2: Digital Math Tool Activity 10-2 Problem-Solving Reading Activity Curriculum Standards: Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Make a line plot to display a data set of measurements in fractions of a unit (1/2 , 1/4 , 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally. Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally. Organize and display data in a line plot. Make a line plot to display a data set of measurements in fractions of a unit (1/2 , 1/4 , 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally. Solve problems involving computation of fractions by using information presented in line plots. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. 10-2: Another Look Curriculum Standards: Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Make a line plot to display a data set of measurements in fractions of a unit (1/2 , 1/4 , 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally. Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally. Organize and display data in a line plot. Make a line plot to display a data set of measurements in fractions of a unit (1/2 , 1/4 , 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally. Solve problems involving computation of fractions by using information presented in line plots. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. Collect and graph fractional data on a line plot (e.g., length of each person’s pencil in classroom, hours of exercise each week). Spanish Resources 10-2: eText del Libro del estudiante 10-2: Repaso diario 10-2: Aprendizaje visual 10-2: Amigo de práctica: Práctica adicional 10-2: Práctica adicional interactiva 10-2: Refuerzo para mejorar la comprensión 10-2: Desarrollar la competencia matemática 10-2: Ampliación 10-3: Solve Word Problems Using Measurement Data Interactive Student Edition: Grade 5 Lesson 10-3 Math Anytime 10-3: Daily Review Topic 10: Today's Challenge Step 1: Problem-Based Learning 10-3: Solve & Share Curriculum Standards: Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Make a line plot to display a data set of measurements in fractions of a unit (1/2 , 1/4 , 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally. English language learners communicate for social and instructional purposes within the school setting. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally. Solve problems using data in a line plot. Make a line plot to display a data set of measurements in fractions of a unit (1/2 , 1/4 , 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally. Add and subtract fractions (including mixed numbers) with unlike denominators. (May include multiple methods and representations.) Solve problems involving computation of fractions by using information presented in line plots. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. Write informative/explanatory texts to examine a topic and convey ideas and information clearly. (a) Introduce a topic clearly, provide a general observation and focus, and group related information logically; include formatting (e.g., headings), illustrations, and multimedia when useful to aiding comprehension. (b) Develop the topic with facts, definitions, concrete details, quotations, or other information and examples related to the topic. (c) Link ideas within and across categories of information using words, phrases, and clauses (e.g., in contrast, especially). (d) Use precise language and domain-specific vocabulary to inform about or explain the topic. (e) Provide a concluding statement or section related to the information or explanation presented. English language learners communicate information, ideas and concepts necessary for academic success in the content area of Mathematics. Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 5 topics and texts, building on others’ ideas and expressing their own clearly. (a) Come to discussions prepared, having read or studied required material; explicitly draw on that preparation and other information known about the topic to explore ideas under discussion. (b) Follow agreed-upon rules for discussions and carry out assigned roles. (c) Pose and respond to specific questions by making comments that contribute to the discussion and elaborate on the remarks of others. (d) Review the key ideas expressed and draw conclusions in light of information and knowledge gained from the discussions. Summarize a written text read aloud or information presented in diverse media and formats, including visually, quantitatively, and orally. Summarize the points a speaker makes and explain how each claim is supported by reasons and evidence. Step 2: Visual Learning 10-3: Visual Learning Curriculum Standards: Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Make a line plot to display a data set of measurements in fractions of a unit (1/2 , 1/4 , 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally. Solve problems using data in a line plot. Make a line plot to display a data set of measurements in fractions of a unit (1/2 , 1/4 , 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally. Add and subtract fractions (including mixed numbers) with unlike denominators. (May include multiple methods and representations.) Solve problems involving computation of fractions by using information presented in line plots. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. 10-3: Convince Me! Curriculum Standards: Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Make a line plot to display a data set of measurements in fractions of a unit (1/2 , 1/4 , 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally. Solve problems using data in a line plot. Make a line plot to display a data set of measurements in fractions of a unit (1/2 , 1/4 , 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally. Add and subtract fractions (including mixed numbers) with unlike denominators. (May include multiple methods and representations.) Solve problems involving computation of fractions by using information presented in line plots. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. Practice and Problem Solving 10-3: Student Edition Practice Curriculum Standards: Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Make a line plot to display a data set of measurements in fractions of a unit (1/2 , 1/4 , 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally. Solve problems using data in a line plot. Make a line plot to display a data set of measurements in fractions of a unit (1/2 , 1/4 , 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally. Add and subtract fractions (including mixed numbers) with unlike denominators. (May include multiple methods and representations.) Solve problems involving computation of fractions by using information presented in line plots. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. 10-3: Practice Buddy: Independent Practice; Problem Solving Curriculum Standards: Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Make a line plot to display a data set of measurements in fractions of a unit (1/2 , 1/4 , 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally. Solve problems using data in a line plot. Make a line plot to display a data set of measurements in fractions of a unit (1/2 , 1/4 , 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally. Add and subtract fractions (including mixed numbers) with unlike denominators. (May include multiple methods and representations.) Solve problems involving computation of fractions by using information presented in line plots. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. 10-3: Practice Buddy: Additional Practice Curriculum Standards: Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Make a line plot to display a data set of measurements in fractions of a unit (1/2 , 1/4 , 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally. Solve problems using data in a line plot. Make a line plot to display a data set of measurements in fractions of a unit (1/2 , 1/4 , 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally. Add and subtract fractions (including mixed numbers) with unlike denominators. (May include multiple methods and representations.) Solve problems involving computation of fractions by using information presented in line plots. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. 10-3: Interactive Additional Practice Step 3: Assess & Differentiate 10-3: Practice Buddy: Additional Practice Curriculum Standards: Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Make a line plot to display a data set of measurements in fractions of a unit (1/2 , 1/4 , 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally. Solve problems using data in a line plot. Make a line plot to display a data set of measurements in fractions of a unit (1/2 , 1/4 , 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally. Add and subtract fractions (including mixed numbers) with unlike denominators. (May include multiple methods and representations.) Solve problems involving computation of fractions by using information presented in line plots. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. 10-3: Enrichment Curriculum Standards: Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Make a line plot to display a data set of measurements in fractions of a unit (1/2 , 1/4 , 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally. Solve problems using data in a line plot. Make a line plot to display a data set of measurements in fractions of a unit (1/2 , 1/4 , 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally. Add and subtract fractions (including mixed numbers) with unlike denominators. (May include multiple methods and representations.) Solve problems involving computation of fractions by using information presented in line plots. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. 10-3: Quick Check Curriculum Standards: Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Make a line plot to display a data set of measurements in fractions of a unit (1/2 , 1/4 , 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally. Solve problems using data in a line plot. Make a line plot to display a data set of measurements in fractions of a unit (1/2 , 1/4 , 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally. Add and subtract fractions (including mixed numbers) with unlike denominators. (May include multiple methods and representations.) Solve problems involving computation of fractions by using information presented in line plots. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. 10-3: Lesson Self-Assessment 10-3: Reteach to Build Understanding Curriculum Standards: Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Make a line plot to display a data set of measurements in fractions of a unit (1/2 , 1/4 , 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally. Solve problems using data in a line plot. Make a line plot to display a data set of measurements in fractions of a unit (1/2 , 1/4 , 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally. Add and subtract fractions (including mixed numbers) with unlike denominators. (May include multiple methods and representations.) Solve problems involving computation of fractions by using information presented in line plots. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. 10-3: Build Mathematical Literacy Curriculum Standards: Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 5 topics and texts, building on others’ ideas and expressing their own clearly. (a) Come to discussions prepared, having read or studied required material; explicitly draw on that preparation and other information known about the topic to explore ideas under discussion. (b) Follow agreed-upon rules for discussions and carry out assigned roles. (c) Pose and respond to specific questions by making comments that contribute to the discussion and elaborate on the remarks of others. (d) Review the key ideas expressed and draw conclusions in light of information and knowledge gained from the discussions. English language learners communicate for social and instructional purposes within the school setting. Summarize a written text read aloud or information presented in diverse media and formats, including visually, quantitatively, and orally. Summarize the points a speaker makes and explain how each claim is supported by reasons and evidence. Write informative/explanatory texts to examine a topic and convey ideas and information clearly. (a) Introduce a topic clearly, provide a general observation and focus, and group related information logically; include formatting (e.g., headings), illustrations, and multimedia when useful to aiding comprehension. (b) Develop the topic with facts, definitions, concrete details, quotations, or other information and examples related to the topic. (c) Link ideas within and across categories of information using words, phrases, and clauses (e.g., in contrast, especially). (d) Use precise language and domain-specific vocabulary to inform about or explain the topic. (e) Provide a concluding statement or section related to the information or explanation presented. English language learners communicate information, ideas and concepts necessary for academic success in the content area of Mathematics. 10-3: Enrichment Game: Fluency - Multiply Multi-Digit Whole Numbers 10-3 Problem-Solving Reading Activity Curriculum Standards: Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Make a line plot to display a data set of measurements in fractions of a unit (1/2 , 1/4 , 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally. Solve problems using data in a line plot. Make a line plot to display a data set of measurements in fractions of a unit (1/2 , 1/4 , 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally. Add and subtract fractions (including mixed numbers) with unlike denominators. (May include multiple methods and representations.) Solve problems involving computation of fractions by using information presented in line plots. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. 10-3: Another Look Curriculum Standards: Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Make a line plot to display a data set of measurements in fractions of a unit (1/2 , 1/4 , 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally. Solve problems using data in a line plot. Make a line plot to display a data set of measurements in fractions of a unit (1/2 , 1/4 , 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally. Add and subtract fractions (including mixed numbers) with unlike denominators. (May include multiple methods and representations.) Solve problems involving computation of fractions by using information presented in line plots. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. Spanish Resources 10-3: eText del Libro del estudiante 10-3: Repaso diario 10-3: Aprendizaje visual 10-3: Amigo de práctica: Práctica adicional 10-3: Práctica adicional interactiva 10-3: Refuerzo para mejorar la comprensión 10-3: Desarrollar la competencia matemática 10-3: Ampliación 10-4: Problem Solving: Critique Reasoning Interactive Student Edition: Grade 5 Lesson 10-4 Math Anytime 10-4: Daily Review Topic 10: Today's Challenge Step 1: Problem-Based Learning 10-4: Solve & Share Curriculum Standards: Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Make a line plot to display a data set of measurements in fractions of a unit (1/2 , 1/4 , 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally. Construct viable arguments and critique the reasoning of others. English language learners communicate for social and instructional purposes within the school setting. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. Construct viable arguments and critique the reasoning of others. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally. Construct viable arguments and critique the reasoning of others. Mathematically proficient students understand and use stated assumptions, definitions, and previously established results in constructing arguments. They make conjectures and build a logical progression of statements to explore the truth of their conjectures. They are able to analyze situations by breaking them into cases, and can recognize and use counterexamples. They justify their conclusions, communicate them to others, and respond to the arguments of others. They reason inductively about data, making plausible arguments that take into account the context from which the data arose. Mathematically proficient students are also able to compare the effectiveness of two plausible arguments, distinguish correct logic or reasoning from that which is flawed, and—if there is a flaw in an argument—explain what it is. Elementary students can construct arguments using concrete referents such as objects, drawings, diagrams, and actions. Such arguments can make sense and be correct, even though they are not generalized or made formal until later grades. Later, students learn to determine domains to which an argument applies. Students at all grades can listen or read the arguments of others, decide whether they make sense, and ask useful questions to clarify or improve the arguments. Critique the reasoning of others using understanding of line plots and fractions. Make a line plot to display a data set of measurements in fractions of a unit (1/2 , 1/4 , 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally. Construct viable arguments and critique the reasoning of others. Construct viable arguments and critique the reasoning of others. Add and subtract fractions (including mixed numbers) with unlike denominators. (May include multiple methods and representations.) Solve problems involving computation of fractions by using information presented in line plots. Construct viable arguments and critique the reasoning of others. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. Write informative/explanatory texts to examine a topic and convey ideas and information clearly. (a) Introduce a topic clearly, provide a general observation and focus, and group related information logically; include formatting (e.g., headings), illustrations, and multimedia when useful to aiding comprehension. (b) Develop the topic with facts, definitions, concrete details, quotations, or other information and examples related to the topic. (c) Link ideas within and across categories of information using words, phrases, and clauses (e.g., in contrast, especially). (d) Use precise language and domain-specific vocabulary to inform about or explain the topic. (e) Provide a concluding statement or section related to the information or explanation presented. English language learners communicate information, ideas and concepts necessary for academic success in the content area of Mathematics. Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 5 topics and texts, building on others’ ideas and expressing their own clearly. (a) Come to discussions prepared, having read or studied required material; explicitly draw on that preparation and other information known about the topic to explore ideas under discussion. (b) Follow agreed-upon rules for discussions and carry out assigned roles. (c) Pose and respond to specific questions by making comments that contribute to the discussion and elaborate on the remarks of others. (d) Review the key ideas expressed and draw conclusions in light of information and knowledge gained from the discussions. Summarize a written text read aloud or information presented in diverse media and formats, including visually, quantitatively, and orally. Summarize the points a speaker makes and explain how each claim is supported by reasons and evidence. Step 2: Visual Learning 10-4: Visual Learning Curriculum Standards: Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Make a line plot to display a data set of measurements in fractions of a unit (1/2 , 1/4 , 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally. Construct viable arguments and critique the reasoning of others. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. Construct viable arguments and critique the reasoning of others. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally. Construct viable arguments and critique the reasoning of others. Mathematically proficient students understand and use stated assumptions, definitions, and previously established results in constructing arguments. They make conjectures and build a logical progression of statements to explore the truth of their conjectures. They are able to analyze situations by breaking them into cases, and can recognize and use counterexamples. They justify their conclusions, communicate them to others, and respond to the arguments of others. They reason inductively about data, making plausible arguments that take into account the context from which the data arose. Mathematically proficient students are also able to compare the effectiveness of two plausible arguments, distinguish correct logic or reasoning from that which is flawed, and—if there is a flaw in an argument—explain what it is. Elementary students can construct arguments using concrete referents such as objects, drawings, diagrams, and actions. Such arguments can make sense and be correct, even though they are not generalized or made formal until later grades. Later, students learn to determine domains to which an argument applies. Students at all grades can listen or read the arguments of others, decide whether they make sense, and ask useful questions to clarify or improve the arguments. Critique the reasoning of others using understanding of line plots and fractions. Make a line plot to display a data set of measurements in fractions of a unit (1/2 , 1/4 , 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally. Construct viable arguments and critique the reasoning of others. Construct viable arguments and critique the reasoning of others. Add and subtract fractions (including mixed numbers) with unlike denominators. (May include multiple methods and representations.) Solve problems involving computation of fractions by using information presented in line plots. Construct viable arguments and critique the reasoning of others. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. 10-4: Convince Me! Curriculum Standards: Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Make a line plot to display a data set of measurements in fractions of a unit (1/2 , 1/4 , 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally. Construct viable arguments and critique the reasoning of others. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. Construct viable arguments and critique the reasoning of others. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally. Construct viable arguments and critique the reasoning of others. Mathematically proficient students understand and use stated assumptions, definitions, and previously established results in constructing arguments. They make conjectures and build a logical progression of statements to explore the truth of their conjectures. They are able to analyze situations by breaking them into cases, and can recognize and use counterexamples. They justify their conclusions, communicate them to others, and respond to the arguments of others. They reason inductively about data, making plausible arguments that take into account the context from which the data arose. Mathematically proficient students are also able to compare the effectiveness of two plausible arguments, distinguish correct logic or reasoning from that which is flawed, and—if there is a flaw in an argument—explain what it is. Elementary students can construct arguments using concrete referents such as objects, drawings, diagrams, and actions. Such arguments can make sense and be correct, even though they are not generalized or made formal until later grades. Later, students learn to determine domains to which an argument applies. Students at all grades can listen or read the arguments of others, decide whether they make sense, and ask useful questions to clarify or improve the arguments. Critique the reasoning of others using understanding of line plots and fractions. Make a line plot to display a data set of measurements in fractions of a unit (1/2 , 1/4 , 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally. Construct viable arguments and critique the reasoning of others. Construct viable arguments and critique the reasoning of others. Add and subtract fractions (including mixed numbers) with unlike denominators. (May include multiple methods and representations.) Solve problems involving computation of fractions by using information presented in line plots. Construct viable arguments and critique the reasoning of others. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. Practice and Problem Solving 10-4: Student Edition Practice Curriculum Standards: Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Make a line plot to display a data set of measurements in fractions of a unit (1/2 , 1/4 , 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally. Construct viable arguments and critique the reasoning of others. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. Construct viable arguments and critique the reasoning of others. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally. Construct viable arguments and critique the reasoning of others. Mathematically proficient students understand and use stated assumptions, definitions, and previously established results in constructing arguments. They make conjectures and build a logical progression of statements to explore the truth of their conjectures. They are able to analyze situations by breaking them into cases, and can recognize and use counterexamples. They justify their conclusions, communicate them to others, and respond to the arguments of others. They reason inductively about data, making plausible arguments that take into account the context from which the data arose. Mathematically proficient students are also able to compare the effectiveness of two plausible arguments, distinguish correct logic or reasoning from that which is flawed, and—if there is a flaw in an argument—explain what it is. Elementary students can construct arguments using concrete referents such as objects, drawings, diagrams, and actions. Such arguments can make sense and be correct, even though they are not generalized or made formal until later grades. Later, students learn to determine domains to which an argument applies. Students at all grades can listen or read the arguments of others, decide whether they make sense, and ask useful questions to clarify or improve the arguments. Critique the reasoning of others using understanding of line plots and fractions. Make a line plot to display a data set of measurements in fractions of a unit (1/2 , 1/4 , 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally. Construct viable arguments and critique the reasoning of others. Construct viable arguments and critique the reasoning of others. Add and subtract fractions (including mixed numbers) with unlike denominators. (May include multiple methods and representations.) Solve problems involving computation of fractions by using information presented in line plots. Construct viable arguments and critique the reasoning of others. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. 10-4: Practice Buddy: Independent Practice; Problem Solving Curriculum Standards: Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Make a line plot to display a data set of measurements in fractions of a unit (1/2 , 1/4 , 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally. Construct viable arguments and critique the reasoning of others. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. Construct viable arguments and critique the reasoning of others. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally. Construct viable arguments and critique the reasoning of others. Mathematically proficient students understand and use stated assumptions, definitions, and previously established results in constructing arguments. They make conjectures and build a logical progression of statements to explore the truth of their conjectures. They are able to analyze situations by breaking them into cases, and can recognize and use counterexamples. They justify their conclusions, communicate them to others, and respond to the arguments of others. They reason inductively about data, making plausible arguments that take into account the context from which the data arose. Mathematically proficient students are also able to compare the effectiveness of two plausible arguments, distinguish correct logic or reasoning from that which is flawed, and—if there is a flaw in an argument—explain what it is. Elementary students can construct arguments using concrete referents such as objects, drawings, diagrams, and actions. Such arguments can make sense and be correct, even though they are not generalized or made formal until later grades. Later, students learn to determine domains to which an argument applies. Students at all grades can listen or read the arguments of others, decide whether they make sense, and ask useful questions to clarify or improve the arguments. Critique the reasoning of others using understanding of line plots and fractions. Make a line plot to display a data set of measurements in fractions of a unit (1/2 , 1/4 , 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally. Construct viable arguments and critique the reasoning of others. Construct viable arguments and critique the reasoning of others. Add and subtract fractions (including mixed numbers) with unlike denominators. (May include multiple methods and representations.) Solve problems involving computation of fractions by using information presented in line plots. Construct viable arguments and critique the reasoning of others. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. 10-4: Practice Buddy: Additional Practice Curriculum Standards: Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Make a line plot to display a data set of measurements in fractions of a unit (1/2 , 1/4 , 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally. Construct viable arguments and critique the reasoning of others. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. Construct viable arguments and critique the reasoning of others. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally. Construct viable arguments and critique the reasoning of others. Mathematically proficient students understand and use stated assumptions, definitions, and previously established results in constructing arguments. They make conjectures and build a logical progression of statements to explore the truth of their conjectures. They are able to analyze situations by breaking them into cases, and can recognize and use counterexamples. They justify their conclusions, communicate them to others, and respond to the arguments of others. They reason inductively about data, making plausible arguments that take into account the context from which the data arose. Mathematically proficient students are also able to compare the effectiveness of two plausible arguments, distinguish correct logic or reasoning from that which is flawed, and—if there is a flaw in an argument—explain what it is. Elementary students can construct arguments using concrete referents such as objects, drawings, diagrams, and actions. Such arguments can make sense and be correct, even though they are not generalized or made formal until later grades. Later, students learn to determine domains to which an argument applies. Students at all grades can listen or read the arguments of others, decide whether they make sense, and ask useful questions to clarify or improve the arguments. Critique the reasoning of others using understanding of line plots and fractions. Make a line plot to display a data set of measurements in fractions of a unit (1/2 , 1/4 , 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally. Construct viable arguments and critique the reasoning of others. Construct viable arguments and critique the reasoning of others. Add and subtract fractions (including mixed numbers) with unlike denominators. (May include multiple methods and representations.) Solve problems involving computation of fractions by using information presented in line plots. Construct viable arguments and critique the reasoning of others. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. 10-4: Interactive Additional Practice Step 3: Assess & Differentiate 10-4: Practice Buddy: Additional Practice Curriculum Standards: Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Make a line plot to display a data set of measurements in fractions of a unit (1/2 , 1/4 , 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally. Construct viable arguments and critique the reasoning of others. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. Construct viable arguments and critique the reasoning of others. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally. Construct viable arguments and critique the reasoning of others. Mathematically proficient students understand and use stated assumptions, definitions, and previously established results in constructing arguments. They make conjectures and build a logical progression of statements to explore the truth of their conjectures. They are able to analyze situations by breaking them into cases, and can recognize and use counterexamples. They justify their conclusions, communicate them to others, and respond to the arguments of others. They reason inductively about data, making plausible arguments that take into account the context from which the data arose. Mathematically proficient students are also able to compare the effectiveness of two plausible arguments, distinguish correct logic or reasoning from that which is flawed, and—if there is a flaw in an argument—explain what it is. Elementary students can construct arguments using concrete referents such as objects, drawings, diagrams, and actions. Such arguments can make sense and be correct, even though they are not generalized or made formal until later grades. Later, students learn to determine domains to which an argument applies. Students at all grades can listen or read the arguments of others, decide whether they make sense, and ask useful questions to clarify or improve the arguments. Critique the reasoning of others using understanding of line plots and fractions. Make a line plot to display a data set of measurements in fractions of a unit (1/2 , 1/4 , 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally. Construct viable arguments and critique the reasoning of others. Construct viable arguments and critique the reasoning of others. Add and subtract fractions (including mixed numbers) with unlike denominators. (May include multiple methods and representations.) Solve problems involving computation of fractions by using information presented in line plots. Construct viable arguments and critique the reasoning of others. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. 10-4: Enrichment Curriculum Standards: Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Make a line plot to display a data set of measurements in fractions of a unit (1/2 , 1/4 , 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally. Construct viable arguments and critique the reasoning of others. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. Construct viable arguments and critique the reasoning of others. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally. Construct viable arguments and critique the reasoning of others. Mathematically proficient students understand and use stated assumptions, definitions, and previously established results in constructing arguments. They make conjectures and build a logical progression of statements to explore the truth of their conjectures. They are able to analyze situations by breaking them into cases, and can recognize and use counterexamples. They justify their conclusions, communicate them to others, and respond to the arguments of others. They reason inductively about data, making plausible arguments that take into account the context from which the data arose. Mathematically proficient students are also able to compare the effectiveness of two plausible arguments, distinguish correct logic or reasoning from that which is flawed, and—if there is a flaw in an argument—explain what it is. Elementary students can construct arguments using concrete referents such as objects, drawings, diagrams, and actions. Such arguments can make sense and be correct, even though they are not generalized or made formal until later grades. Later, students learn to determine domains to which an argument applies. Students at all grades can listen or read the arguments of others, decide whether they make sense, and ask useful questions to clarify or improve the arguments. Critique the reasoning of others using understanding of line plots and fractions. Make a line plot to display a data set of measurements in fractions of a unit (1/2 , 1/4 , 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally. Construct viable arguments and critique the reasoning of others. Construct viable arguments and critique the reasoning of others. Add and subtract fractions (including mixed numbers) with unlike denominators. (May include multiple methods and representations.) Solve problems involving computation of fractions by using information presented in line plots. Construct viable arguments and critique the reasoning of others. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. 10-4: Quick Check Curriculum Standards: Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Make a line plot to display a data set of measurements in fractions of a unit (1/2 , 1/4 , 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally. Construct viable arguments and critique the reasoning of others. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. Construct viable arguments and critique the reasoning of others. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally. Construct viable arguments and critique the reasoning of others. Mathematically proficient students understand and use stated assumptions, definitions, and previously established results in constructing arguments. They make conjectures and build a logical progression of statements to explore the truth of their conjectures. They are able to analyze situations by breaking them into cases, and can recognize and use counterexamples. They justify their conclusions, communicate them to others, and respond to the arguments of others. They reason inductively about data, making plausible arguments that take into account the context from which the data arose. Mathematically proficient students are also able to compare the effectiveness of two plausible arguments, distinguish correct logic or reasoning from that which is flawed, and—if there is a flaw in an argument—explain what it is. Elementary students can construct arguments using concrete referents such as objects, drawings, diagrams, and actions. Such arguments can make sense and be correct, even though they are not generalized or made formal until later grades. Later, students learn to determine domains to which an argument applies. Students at all grades can listen or read the arguments of others, decide whether they make sense, and ask useful questions to clarify or improve the arguments. Critique the reasoning of others using understanding of line plots and fractions. Make a line plot to display a data set of measurements in fractions of a unit (1/2 , 1/4 , 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally. Construct viable arguments and critique the reasoning of others. Construct viable arguments and critique the reasoning of others. Add and subtract fractions (including mixed numbers) with unlike denominators. (May include multiple methods and representations.) Solve problems involving computation of fractions by using information presented in line plots. Construct viable arguments and critique the reasoning of others. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. 10-4: Lesson Self-Assessment 10-4: Reteach to Build Understanding Curriculum Standards: Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Make a line plot to display a data set of measurements in fractions of a unit (1/2 , 1/4 , 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally. Construct viable arguments and critique the reasoning of others. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. Construct viable arguments and critique the reasoning of others. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally. Construct viable arguments and critique the reasoning of others. Mathematically proficient students understand and use stated assumptions, definitions, and previously established results in constructing arguments. They make conjectures and build a logical progression of statements to explore the truth of their conjectures. They are able to analyze situations by breaking them into cases, and can recognize and use counterexamples. They justify their conclusions, communicate them to others, and respond to the arguments of others. They reason inductively about data, making plausible arguments that take into account the context from which the data arose. Mathematically proficient students are also able to compare the effectiveness of two plausible arguments, distinguish correct logic or reasoning from that which is flawed, and—if there is a flaw in an argument—explain what it is. Elementary students can construct arguments using concrete referents such as objects, drawings, diagrams, and actions. Such arguments can make sense and be correct, even though they are not generalized or made formal until later grades. Later, students learn to determine domains to which an argument applies. Students at all grades can listen or read the arguments of others, decide whether they make sense, and ask useful questions to clarify or improve the arguments. Critique the reasoning of others using understanding of line plots and fractions. Make a line plot to display a data set of measurements in fractions of a unit (1/2 , 1/4 , 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally. Construct viable arguments and critique the reasoning of others. Construct viable arguments and critique the reasoning of others. Add and subtract fractions (including mixed numbers) with unlike denominators. (May include multiple methods and representations.) Solve problems involving computation of fractions by using information presented in line plots. Construct viable arguments and critique the reasoning of others. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. 10-4: Build Mathematical Literacy Curriculum Standards: Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 5 topics and texts, building on others’ ideas and expressing their own clearly. (a) Come to discussions prepared, having read or studied required material; explicitly draw on that preparation and other information known about the topic to explore ideas under discussion. (b) Follow agreed-upon rules for discussions and carry out assigned roles. (c) Pose and respond to specific questions by making comments that contribute to the discussion and elaborate on the remarks of others. (d) Review the key ideas expressed and draw conclusions in light of information and knowledge gained from the discussions. English language learners communicate for social and instructional purposes within the school setting. Summarize a written text read aloud or information presented in diverse media and formats, including visually, quantitatively, and orally. Summarize the points a speaker makes and explain how each claim is supported by reasons and evidence. Write informative/explanatory texts to examine a topic and convey ideas and information clearly. (a) Introduce a topic clearly, provide a general observation and focus, and group related information logically; include formatting (e.g., headings), illustrations, and multimedia when useful to aiding comprehension. (b) Develop the topic with facts, definitions, concrete details, quotations, or other information and examples related to the topic. (c) Link ideas within and across categories of information using words, phrases, and clauses (e.g., in contrast, especially). (d) Use precise language and domain-specific vocabulary to inform about or explain the topic. (e) Provide a concluding statement or section related to the information or explanation presented. English language learners communicate information, ideas and concepts necessary for academic success in the content area of Mathematics. 10-4: Enrichment Game: Save the Word: Grade 5 Topics 1-8 10-4: Pick a Project 10-4: Another Look Curriculum Standards: Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Make a line plot to display a data set of measurements in fractions of a unit (1/2 , 1/4 , 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally. Construct viable arguments and critique the reasoning of others. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. Construct viable arguments and critique the reasoning of others. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally. Construct viable arguments and critique the reasoning of others. Mathematically proficient students understand and use stated assumptions, definitions, and previously established results in constructing arguments. They make conjectures and build a logical progression of statements to explore the truth of their conjectures. They are able to analyze situations by breaking them into cases, and can recognize and use counterexamples. They justify their conclusions, communicate them to others, and respond to the arguments of others. They reason inductively about data, making plausible arguments that take into account the context from which the data arose. Mathematically proficient students are also able to compare the effectiveness of two plausible arguments, distinguish correct logic or reasoning from that which is flawed, and—if there is a flaw in an argument—explain what it is. Elementary students can construct arguments using concrete referents such as objects, drawings, diagrams, and actions. Such arguments can make sense and be correct, even though they are not generalized or made formal until later grades. Later, students learn to determine domains to which an argument applies. Students at all grades can listen or read the arguments of others, decide whether they make sense, and ask useful questions to clarify or improve the arguments. Critique the reasoning of others using understanding of line plots and fractions. Make a line plot to display a data set of measurements in fractions of a unit (1/2 , 1/4 , 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally. Construct viable arguments and critique the reasoning of others. Construct viable arguments and critique the reasoning of others. Add and subtract fractions (including mixed numbers) with unlike denominators. (May include multiple methods and representations.) Solve problems involving computation of fractions by using information presented in line plots. Construct viable arguments and critique the reasoning of others. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. Spanish Resources 10-4: eText del Libro del estudiante 10-4: Repaso diario 10-4: Aprendizaje visual 10-4: Amigo de práctica: Práctica adicional 10-4: Práctica adicional interactiva 10-4: Refuerzo para mejorar la comprensión 10-4: Desarrollar la competencia matemática 10-4: Ampliación Topic 10: End of Topic Interactive Student Edition: End of Topic 10 Topic 10: Fluency Practice Activity Interactive Student Edition: Topic 10 Assessment Practice Interactive Student Edition: Topic 10 Performance Task Topic 10 Performance Task Topic 10 Assessment 16-1: Center Games 10-1: Visual Learning Curriculum Standards: Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Make a line plot to display a data set of measurements in fractions of a unit (1/2 , 1/4 , 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally. Read and analyze line plots. Make a line plot to display a data set of measurements in fractions of a unit (1/2 , 1/4 , 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally. Solve problems involving computation of fractions by using information presented in line plots. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. 10-2: Visual Learning Curriculum Standards: Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Make a line plot to display a data set of measurements in fractions of a unit (1/2 , 1/4 , 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally. Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally. Organize and display data in a line plot. Make a line plot to display a data set of measurements in fractions of a unit (1/2 , 1/4 , 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally. Solve problems involving computation of fractions by using information presented in line plots. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. 10-3: Visual Learning Curriculum Standards: Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Make a line plot to display a data set of measurements in fractions of a unit (1/2 , 1/4 , 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally. Solve problems using data in a line plot. Make a line plot to display a data set of measurements in fractions of a unit (1/2 , 1/4 , 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally. Add and subtract fractions (including mixed numbers) with unlike denominators. (May include multiple methods and representations.) Solve problems involving computation of fractions by using information presented in line plots. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. Topic 10 Online Assessment Curriculum Standards: Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Make a line plot to display a data set of measurements in fractions of a unit (1/2 , 1/4 , 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally. Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally. Read and analyze line plots. Make a line plot to display a data set of measurements in fractions of a unit (1/2 , 1/4 , 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally. Solve problems involving computation of fractions by using information presented in line plots. Solve real- world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. Organize and display data in a line plot. Solve problems using data in a line plot. Add and subtract fractions (including mixed numbers) with unlike denominators. (May include multiple methods and representations.) Topic 10 Spanish Assessments Tema 10: Tarea de rendimento Tema 10: Evaluación Topic 11: Understand Volume Concepts Topic 11: Today's Challenge Topic 11: Beginning of Topic Interactive Student Edition: Beginning of Topic 11 Topic 11: enVision STEM Activity Grade 5 Topic 11: Review What You Know Topic 11: Vocabulary Cards 11-1: Model Volume Interactive Student Edition: Grade 5 Lesson 11-1 Math Anytime 11-1: Daily Review Topic 11: Today's Challenge Step 1: Problem-Based Learning 11-1: Solve & Share Curriculum Standards: A cube with side length 1 unit, called a "unit cube," is said to have "one cubic unit" of volume, and can be used to measure volume. A solid figure that can be packed without gaps or overlaps using n unit cubes is said to have a volume of n cubic units. Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units. English language learners communicate for social and instructional purposes within the school setting. Write informative/explanatory texts to examine a topic and convey ideas and information clearly. (a) Introduce a topic clearly, provide a general observation and focus, and group related information logically; include formatting (e.g., headings), illustrations, and multimedia when useful to aiding comprehension. (b) Develop the topic with facts, definitions, concrete details, quotations, or other information and examples related to the topic. (c) Link ideas within and across categories of information using words, phrases, and clauses (e.g., in contrast, especially). (d) Use precise language and domain- specific vocabulary to inform about or explain the topic. (e) Provide a concluding statement or section related to the information or explanation presented. English language learners communicate information, ideas and concepts necessary for academic success in the content area of Mathematics. Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 5 topics and texts, building on others’ ideas and expressing their own clearly. (a) Come to discussions prepared, having read or studied required material; explicitly draw on that preparation and other information known about the topic to explore ideas under discussion. (b) Follow agreed-upon rules for discussions and carry out assigned roles. (c) Pose and respond to specific questions by making comments that contribute to the discussion and elaborate on the remarks of others. (d) Review the key ideas expressed and draw conclusions in light of information and knowledge gained from the discussions. Summarize a written text read aloud or information presented in diverse media and formats, including visually, quantitatively, and orally. Summarize the points a speaker makes and explain how each claim is supported by reasons and evidence. A cube with side length 1 unit, called a “unit cube,” is said to have “one cubic unit” of volume, and can be used to measure volume. A solid figure which can be packed without gaps or overlaps using n unit cubes is said to have a volume of n cubic units. Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units. A cube with side length 1 unit, called a “unit cube,” is said to have “one cubic unit” of volume, and can be used to measure volume. A solid figure which can be packed without gaps or overlaps using n unit cubes is said to have a volume of n cubic units. Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units. Find the volume of solid figures. A cube with side length 1 unit, called a unit cube, is said to have one cubic unit of volume, and can be used to measure volume. A solid figure that can be packed without gaps or overlaps using n unit cubes is said to have a volume of n cubic units. Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units. 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. Formulas will be provided. Use various tools and strategies to measure the volume and surface area of objects that are shaped like rectangular prisms. Understand that the volume of a three dimensional figure can be found by counting the total number of same-sized cubic units that fill a shape without gaps or overlaps. Use cubic units to label volume measurements. Step 2: Visual Learning 11-1: Visual Learning Curriculum Standards: A cube with side length 1 unit, called a "unit cube," is said to have "one cubic unit" of volume, and can be used to measure volume. A solid figure that can be packed without gaps or overlaps using n unit cubes is said to have a volume of n cubic units. Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units. Use packing to recognize volume of a solid figure. A cube with side length 1 unit, called a “unit cube,” is said to have “one cubic unit” of volume, and can be used to measure volume. A solid figure which can be packed without gaps or overlaps using n unit cubes is said to have a volume of n cubic units. Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units. A cube with side length 1 unit, called a “unit cube,” is said to have “one cubic unit” of volume, and can be used to measure volume. A solid figure which can be packed without gaps or overlaps using n unit cubes is said to have a volume of n cubic units. Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units. Find the volume of solid figures. A cube with side length 1 unit, called a unit cube, is said to have one cubic unit of volume, and can be used to measure volume. A solid figure that can be packed without gaps or overlaps using n unit cubes is said to have a volume of n cubic units. Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units. 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. Formulas will be provided. Use various tools and strategies to measure the volume and surface area of objects that are shaped like rectangular prisms. Understand that the volume of a three dimensional figure can be found by counting the total number of same-sized cubic units that fill a shape without gaps or overlaps. Use cubic units to label volume measurements. 11-1: Convince Me! Curriculum Standards: A cube with side length 1 unit, called a "unit cube," is said to have "one cubic unit" of volume, and can be used to measure volume. A solid figure that can be packed without gaps or overlaps using n unit cubes is said to have a volume of n cubic units. Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units. A cube with side length 1 unit, called a “unit cube,” is said to have “one cubic unit” of volume, and can be used to measure volume. A solid figure which can be packed without gaps or overlaps using n unit cubes is said to have a volume of n cubic units. Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units. A cube with side length 1 unit, called a “unit cube,” is said to have “one cubic unit” of volume, and can be used to measure volume. A solid figure which can be packed without gaps or overlaps using n unit cubes is said to have a volume of n cubic units. Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units. Find the volume of solid figures. A cube with side length 1 unit, called a unit cube, is said to have one cubic unit of volume, and can be used to measure volume. A solid figure that can be packed without gaps or overlaps using n unit cubes is said to have a volume of n cubic units. Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units. 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. Formulas will be provided. Use various tools and strategies to measure the volume and surface area of objects that are shaped like rectangular prisms. Understand that the volume of a three dimensional figure can be found by counting the total number of same-sized cubic units that fill a shape without gaps or overlaps. Use cubic units to label volume measurements. Practice and Problem Solving 11-1: Student Edition Practice Curriculum Standards: A cube with side length 1 unit, called a "unit cube," is said to have "one cubic unit" of volume, and can be used to measure volume. A solid figure that can be packed without gaps or overlaps using n unit cubes is said to have a volume of n cubic units. Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units. A cube with side length 1 unit, called a “unit cube,” is said to have “one cubic unit” of volume, and can be used to measure volume. A solid figure which can be packed without gaps or overlaps using n unit cubes is said to have a volume of n cubic units. Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units. A cube with side length 1 unit, called a “unit cube,” is said to have “one cubic unit” of volume, and can be used to measure volume. A solid figure which can be packed without gaps or overlaps using n unit cubes is said to have a volume of n cubic units. Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units. Find the volume of solid figures. A cube with side length 1 unit, called a unit cube, is said to have one cubic unit of volume, and can be used to measure volume. A solid figure that can be packed without gaps or overlaps using n unit cubes is said to have a volume of n cubic units. Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units. 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. Formulas will be provided. Use various tools and strategies to measure the volume and surface area of objects that are shaped like rectangular prisms. Understand that the volume of a three dimensional figure can be found by counting the total number of same-sized cubic units that fill a shape without gaps or overlaps. Use cubic units to label volume measurements. 11-1: Practice Buddy: Independent Practice; Problem Solving Curriculum Standards: A cube with side length 1 unit, called a "unit cube," is said to have "one cubic unit" of volume, and can be used to measure volume. A solid figure that can be packed without gaps or overlaps using n unit cubes is said to have a volume of n cubic units. Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units. A cube with side length 1 unit, called a “unit cube,” is said to have “one cubic unit” of volume, and can be used to measure volume. A solid figure which can be packed without gaps or overlaps using n unit cubes is said to have a volume of n cubic units. Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units. A cube with side length 1 unit, called a “unit cube,” is said to have “one cubic unit” of volume, and can be used to measure volume. A solid figure which can be packed without gaps or overlaps using n unit cubes is said to have a volume of n cubic units. Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units. Find the volume of solid figures. A cube with side length 1 unit, called a unit cube, is said to have one cubic unit of volume, and can be used to measure volume. A solid figure that can be packed without gaps or overlaps using n unit cubes is said to have a volume of n cubic units. Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units. 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. Formulas will be provided. Use various tools and strategies to measure the volume and surface area of objects that are shaped like rectangular prisms. Understand that the volume of a three dimensional figure can be found by counting the total number of same-sized cubic units that fill a shape without gaps or overlaps. Use cubic units to label volume measurements. 11-1: Practice Buddy: Additional Practice Curriculum Standards: A cube with side length 1 unit, called a "unit cube," is said to have "one cubic unit" of volume, and can be used to measure volume. A solid figure that can be packed without gaps or overlaps using n unit cubes is said to have a volume of n cubic units. Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units. A cube with side length 1 unit, called a “unit cube,” is said to have “one cubic unit” of volume, and can be used to measure volume. A solid figure which can be packed without gaps or overlaps using n unit cubes is said to have a volume of n cubic units. Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units. A cube with side length 1 unit, called a “unit cube,” is said to have “one cubic unit” of volume, and can be used to measure volume. A solid figure which can be packed without gaps or overlaps using n unit cubes is said to have a volume of n cubic units. Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units. Find the volume of solid figures. A cube with side length 1 unit, called a unit cube, is said to have one cubic unit of volume, and can be used to measure volume. A solid figure that can be packed without gaps or overlaps using n unit cubes is said to have a volume of n cubic units. Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units. 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. Formulas will be provided. Use various tools and strategies to measure the volume and surface area of objects that are shaped like rectangular prisms. Understand that the volume of a three dimensional figure can be found by counting the total number of same-sized cubic units that fill a shape without gaps or overlaps. Use cubic units to label volume measurements. 11-1: Interactive Additional Practice Step 3: Assess & Differentiate 11-1: Practice Buddy: Additional Practice Curriculum Standards: A cube with side length 1 unit, called a "unit cube," is said to have "one cubic unit" of volume, and can be used to measure volume. A solid figure that can be packed without gaps or overlaps using n unit cubes is said to have a volume of n cubic units. Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units. A cube with side length 1 unit, called a “unit cube,” is said to have “one cubic unit” of volume, and can be used to measure volume. A solid figure which can be packed without gaps or overlaps using n unit cubes is said to have a volume of n cubic units. Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units. A cube with side length 1 unit, called a “unit cube,” is said to have “one cubic unit” of volume, and can be used to measure volume. A solid figure which can be packed without gaps or overlaps using n unit cubes is said to have a volume of n cubic units. Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units. Find the volume of solid figures. A cube with side length 1 unit, called a unit cube, is said to have one cubic unit of volume, and can be used to measure volume. A solid figure that can be packed without gaps or overlaps using n unit cubes is said to have a volume of n cubic units. Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units. 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. Formulas will be provided. Use various tools and strategies to measure the volume and surface area of objects that are shaped like rectangular prisms. Understand that the volume of a three dimensional figure can be found by counting the total number of same-sized cubic units that fill a shape without gaps or overlaps. Use cubic units to label volume measurements. 11-1: Enrichment Curriculum Standards: A cube with side length 1 unit, called a "unit cube," is said to have "one cubic unit" of volume, and can be used to measure volume. A solid figure that can be packed without gaps or overlaps using n unit cubes is said to have a volume of n cubic units. Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units. A cube with side length 1 unit, called a “unit cube,” is said to have “one cubic unit” of volume, and can be used to measure volume. A solid figure which can be packed without gaps or overlaps using n unit cubes is said to have a volume of n cubic units. Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units. A cube with side length 1 unit, called a “unit cube,” is said to have “one cubic unit” of volume, and can be used to measure volume. A solid figure which can be packed without gaps or overlaps using n unit cubes is said to have a volume of n cubic units. Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units. Find the volume of solid figures. A cube with side length 1 unit, called a unit cube, is said to have one cubic unit of volume, and can be used to measure volume. A solid figure that can be packed without gaps or overlaps using n unit cubes is said to have a volume of n cubic units. Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units. 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. Formulas will be provided. Use various tools and strategies to measure the volume and surface area of objects that are shaped like rectangular prisms. Understand that the volume of a three dimensional figure can be found by counting the total number of same-sized cubic units that fill a shape without gaps or overlaps. Use cubic units to label volume measurements. 11-1: Quick Check Curriculum Standards: A cube with side length 1 unit, called a "unit cube," is said to have "one cubic unit" of volume, and can be used to measure volume. A solid figure that can be packed without gaps or overlaps using n unit cubes is said to have a volume of n cubic units. Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units. A cube with side length 1 unit, called a “unit cube,” is said to have “one cubic unit” of volume, and can be used to measure volume. A solid figure which can be packed without gaps or overlaps using n unit cubes is said to have a volume of n cubic units. Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units. A cube with side length 1 unit, called a “unit cube,” is said to have “one cubic unit” of volume, and can be used to measure volume. A solid figure which can be packed without gaps or overlaps using n unit cubes is said to have a volume of n cubic units. Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units. Find the volume of solid figures. A cube with side length 1 unit, called a unit cube, is said to have one cubic unit of volume, and can be used to measure volume. A solid figure that can be packed without gaps or overlaps using n unit cubes is said to have a volume of n cubic units. Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units. 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. Formulas will be provided. Use various tools and strategies to measure the volume and surface area of objects that are shaped like rectangular prisms. Understand that the volume of a three dimensional figure can be found by counting the total number of same-sized cubic units that fill a shape without gaps or overlaps. Use cubic units to label volume measurements. 11-1: Lesson Self-Assessment 11-1: Reteach to Build Understanding Curriculum Standards: A cube with side length 1 unit, called a "unit cube," is said to have "one cubic unit" of volume, and can be used to measure volume. A solid figure that can be packed without gaps or overlaps using n unit cubes is said to have a volume of n cubic units. Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units. Use packing to recognize volume of a solid figure. A cube with side length 1 unit, called a “unit cube,” is said to have “one cubic unit” of volume, and can be used to measure volume. A solid figure which can be packed without gaps or overlaps using n unit cubes is said to have a volume of n cubic units. Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units. A cube with side length 1 unit, called a “unit cube,” is said to have “one cubic unit” of volume, and can be used to measure volume. A solid figure which can be packed without gaps or overlaps using n unit cubes is said to have a volume of n cubic units. Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units. Find the volume of solid figures. A cube with side length 1 unit, called a unit cube, is said to have one cubic unit of volume, and can be used to measure volume. A solid figure that can be packed without gaps or overlaps using n unit cubes is said to have a volume of n cubic units. Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units. 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. Formulas will be provided. Use various tools and strategies to measure the volume and surface area of objects that are shaped like rectangular prisms. Understand that the volume of a three dimensional figure can be found by counting the total number of same-sized cubic units that fill a shape without gaps or overlaps. Use cubic units to label volume measurements. 11-1: Build Mathematical Literacy Curriculum Standards: Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 5 topics and texts, building on others’ ideas and expressing their own clearly. (a) Come to discussions prepared, having read or studied required material; explicitly draw on that preparation and other information known about the topic to explore ideas under discussion. (b) Follow agreed-upon rules for discussions and carry out assigned roles. (c) Pose and respond to specific questions by making comments that contribute to the discussion and elaborate on the remarks of others. (d) Review the key ideas expressed and draw conclusions in light of information and knowledge gained from the discussions. English language learners communicate for social and instructional purposes within the school setting. Summarize a written text read aloud or information presented in diverse media and formats, including visually, quantitatively, and orally. Summarize the points a speaker makes and explain how each claim is supported by reasons and evidence. Write informative/explanatory texts to examine a topic and convey ideas and information clearly. (a) Introduce a topic clearly, provide a general observation and focus, and group related information logically; include formatting (e.g., headings), illustrations, and multimedia when useful to aiding comprehension. (b) Develop the topic with facts, definitions, concrete details, quotations, or other information and examples related to the topic. (c) Link ideas within and across categories of information using words, phrases, and clauses (e.g., in contrast, especially). (d) Use precise language and domain-specific vocabulary to inform about or explain the topic. (e) Provide a concluding statement or section related to the information or explanation presented. English language learners communicate information, ideas and concepts necessary for academic success in the content area of Mathematics. 11-1: Enrichment 11-1: Digital Math Tool Activity 11-1: Problem-Solving Reading Activity Curriculum Standards: A cube with side length 1 unit, called a "unit cube," is said to have "one cubic unit" of volume, and can be used to measure volume. A solid figure that can be packed without gaps or overlaps using n unit cubes is said to have a volume of n cubic units. Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units. A cube with side length 1 unit, called a “unit cube,” is said to have “one cubic unit” of volume, and can be used to measure volume. A solid figure which can be packed without gaps or overlaps using n unit cubes is said to have a volume of n cubic units. Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units. A cube with side length 1 unit, called a “unit cube,” is said to have “one cubic unit” of volume, and can be used to measure volume. A solid figure which can be packed without gaps or overlaps using n unit cubes is said to have a volume of n cubic units. Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units. Find the volume of solid figures. A cube with side length 1 unit, called a unit cube, is said to have one cubic unit of volume, and can be used to measure volume. A solid figure that can be packed without gaps or overlaps using n unit cubes is said to have a volume of n cubic units. Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units. 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. Formulas will be provided. Use various tools and strategies to measure the volume and surface area of objects that are shaped like rectangular prisms. Understand that the volume of a three dimensional figure can be found by counting the total number of same-sized cubic units that fill a shape without gaps or overlaps. Use cubic units to label volume measurements. 11-1: Another Look Curriculum Standards: A cube with side length 1 unit, called a "unit cube," is said to have "one cubic unit" of volume, and can be used to measure volume. A solid figure that can be packed without gaps or overlaps using n unit cubes is said to have a volume of n cubic units. Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units. Use packing to recognize volume of a solid figure. A cube with side length 1 unit, called a “unit cube,” is said to have “one cubic unit” of volume, and can be used to measure volume. A solid figure which can be packed without gaps or overlaps using n unit cubes is said to have a volume of n cubic units. Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units. A cube with side length 1 unit, called a “unit cube,” is said to have “one cubic unit” of volume, and can be used to measure volume. A solid figure which can be packed without gaps or overlaps using n unit cubes is said to have a volume of n cubic units. Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units. Find the volume of solid figures. A cube with side length 1 unit, called a unit cube, is said to have one cubic unit of volume, and can be used to measure volume. A solid figure that can be packed without gaps or overlaps using n unit cubes is said to have a volume of n cubic units. Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units. 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. Formulas will be provided. Use various tools and strategies to measure the volume and surface area of objects that are shaped like rectangular prisms. Understand that the volume of a three dimensional figure can be found by counting the total number of same-sized cubic units that fill a shape without gaps or overlaps. Use cubic units to label volume measurements. Spanish Resources 11-1: eText del Libro del estudiante 11-1: Repaso diario 11-1: Aprendizaje visual 11-1: Amigo de práctica: Práctica adicional 11-1: Práctica adicional interactiva 11-1: Refuerzo para mejorar la comprensión 11-1: Desarrollar la competencia matemática 11-1: Ampliación 11-2: Develop a Volume Formula Interactive Student Edition: Grade 5 Lesson 11-2 Math Anytime 11-2: Daily Review Topic 11: Today's Challenge Step 1: Problem-Based Learning 11-2: Solve & Share Curriculum Standards: Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units. 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. 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. English language learners communicate for social and instructional purposes within the school setting. Write informative/explanatory texts to examine a topic and convey ideas and information clearly. (a) Introduce a topic clearly, provide a general observation and focus, and group related information logically; include formatting (e.g., headings), illustrations, and multimedia when useful to aiding comprehension. (b) Develop the topic with facts, definitions, concrete details, quotations, or other information and examples related to the topic. (c) Link ideas within and across categories of information using words, phrases, and clauses (e.g., in contrast, especially). (d) Use precise language and domain-specific vocabulary to inform about or explain the topic. (e) Provide a concluding statement or section related to the information or explanation presented. English language learners communicate information, ideas and concepts necessary for academic success in the content area of Mathematics. Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 5 topics and texts, building on others’ ideas and expressing their own clearly. (a) Come to discussions prepared, having read or studied required material; explicitly draw on that preparation and other information known about the topic to explore ideas under discussion. (b) Follow agreed-upon rules for discussions and carry out assigned roles. (c) Pose and respond to specific questions by making comments that contribute to the discussion and elaborate on the remarks of others. (d) Review the key ideas expressed and draw conclusions in light of information and knowledge gained from the discussions. Summarize a written text read aloud or information presented in diverse media and formats, including visually, quantitatively, and orally. Summarize the points a speaker makes and explain how each claim is supported by reasons and evidence. 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. 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. 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. 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. Find the volume of rectangular prisms using a formula. Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units. 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. 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. 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. Formulas will be provided. 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. Apply the commutative, associative and distributive properties and order of operations to generate equivalent numerical expressions and to solve problems involving whole numbers. Use various tools and strategies to measure the volume and surface area of objects that are shaped like rectangular prisms. Understand that the volume of a three dimensional figure can be found by counting the total number of same-sized cubic units that fill a shape without gaps or overlaps. Use cubic units to label volume measurements. Develop and use the formulas V = ?wh and V = Bh to determine the volume of rectangular prisms. Justify why base area B and height h are multiplied to find the volume of a ectangular prism by breaking the prism into layers of unit cubes. Step 2: Visual Learning 11-2: Visual Learning Curriculum Standards: Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units. 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. 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. Use packing to recognize volume of a solid figure. 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. 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. 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. 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. Find the volume of rectangular prisms using a formula. Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units. 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. 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. 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. Formulas will be provided. 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. Apply the commutative, associative and distributive properties and order of operations to generate equivalent numerical expressions and to solve problems involving whole numbers. Use various tools and strategies to measure the volume and surface area of objects that are shaped like rectangular prisms. Understand that the volume of a three dimensional figure can be found by counting the total number of same-sized cubic units that fill a shape without gaps or overlaps. Use cubic units to label volume measurements. Develop and use the formulas V = ?wh and V = Bh to determine the volume of rectangular prisms. Justify why base area B and height h are multiplied to find the volume of a ectangular prism by breaking the prism into layers of unit cubes. Determine the volume of a rectangular prism built by “unit cubes.” Use multiplication to represent each layer of the rectangular prism. 11-2: Convince Me! Curriculum Standards: Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units. 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. 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. 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. 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. 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. 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. Find the volume of rectangular prisms using a formula. Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units. 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. 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. 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. Formulas will be provided. 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. Apply the commutative, associative and distributive properties and order of operations to generate equivalent numerical expressions and to solve problems involving whole numbers. Use various tools and strategies to measure the volume and surface area of objects that are shaped like rectangular prisms. Understand that the volume of a three dimensional figure can be found by counting the total number of same-sized cubic units that fill a shape without gaps or overlaps. Use cubic units to label volume measurements. Develop and use the formulas V = ?wh and V = Bh to determine the volume of rectangular prisms. Justify why base area B and height h are multiplied to find the volume of a ectangular prism by breaking the prism into layers of unit cubes. Practice and Problem Solving 11-2: Student Edition Practice Curriculum Standards: Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units. 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. 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. 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. 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. 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. 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. Find the volume of rectangular prisms using a formula. Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units. 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. 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. 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. Formulas will be provided. 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. Apply the commutative, associative and distributive properties and order of operations to generate equivalent numerical expressions and to solve problems involving whole numbers. Use various tools and strategies to measure the volume and surface area of objects that are shaped like rectangular prisms. Understand that the volume of a three dimensional figure can be found by counting the total number of same-sized cubic units that fill a shape without gaps or overlaps. Use cubic units to label volume measurements. Develop and use the formulas V = ?wh and V = Bh to determine the volume of rectangular prisms. Justify why base area B and height h are multiplied to find the volume of a ectangular prism by breaking the prism into layers of unit cubes. 11-2: Practice Buddy: Independent Practice; Problem Solving Curriculum Standards: Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units. 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. 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. 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. 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. 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. 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. Find the volume of rectangular prisms using a formula. Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units. 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. 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. 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. Formulas will be provided. 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. Apply the commutative, associative and distributive properties and order of operations to generate equivalent numerical expressions and to solve problems involving whole numbers. Use various tools and strategies to measure the volume and surface area of objects that are shaped like rectangular prisms. Understand that the volume of a three dimensional figure can be found by counting the total number of same-sized cubic units that fill a shape without gaps or overlaps. Use cubic units to label volume measurements. Develop and use the formulas V = ?wh and V = Bh to determine the volume of rectangular prisms. Justify why base area B and height h are multiplied to find the volume of a ectangular prism by breaking the prism into layers of unit cubes. 11-2: Practice Buddy: Additional Practice Curriculum Standards: Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units. 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. 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. 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. 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. 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. 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. Find the volume of rectangular prisms using a formula. Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units. 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. 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. 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. Formulas will be provided. 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. Apply the commutative, associative and distributive properties and order of operations to generate equivalent numerical expressions and to solve problems involving whole numbers. Use various tools and strategies to measure the volume and surface area of objects that are shaped like rectangular prisms. Understand that the volume of a three dimensional figure can be found by counting the total number of same-sized cubic units that fill a shape without gaps or overlaps. Use cubic units to label volume measurements. Develop and use the formulas V = ?wh and V = Bh to determine the volume of rectangular prisms. Justify why base area B and height h are multiplied to find the volume of a ectangular prism by breaking the prism into layers of unit cubes. 11-2: Interactive Additional Practice Step 3: Assess & Differentiate 11-2: Practice Buddy: Additional Practice Curriculum Standards: Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units. 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. 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. 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. 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. 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. 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. Find the volume of rectangular prisms using a formula. Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units. 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. 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. 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. Formulas will be provided. 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. Apply the commutative, associative and distributive properties and order of operations to generate equivalent numerical expressions and to solve problems involving whole numbers. Use various tools and strategies to measure the volume and surface area of objects that are shaped like rectangular prisms. Understand that the volume of a three dimensional figure can be found by counting the total number of same-sized cubic units that fill a shape without gaps or overlaps. Use cubic units to label volume measurements. Develop and use the formulas V = ?wh and V = Bh to determine the volume of rectangular prisms. Justify why base area B and height h are multiplied to find the volume of a ectangular prism by breaking the prism into layers of unit cubes. 11-2: Enrichment Curriculum Standards: Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units. 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. 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. 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. 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. 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. 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. Find the volume of rectangular prisms using a formula. Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units. 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. 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. 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. Formulas will be provided. 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. Apply the commutative, associative and distributive properties and order of operations to generate equivalent numerical expressions and to solve problems involving whole numbers. Use various tools and strategies to measure the volume and surface area of objects that are shaped like rectangular prisms. Understand that the volume of a three dimensional figure can be found by counting the total number of same-sized cubic units that fill a shape without gaps or overlaps. Use cubic units to label volume measurements. Develop and use the formulas V = ?wh and V = Bh to determine the volume of rectangular prisms. Justify why base area B and height h are multiplied to find the volume of a ectangular prism by breaking the prism into layers of unit cubes. 11-2: Quick Check Curriculum Standards: Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units. 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. 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. 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. 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. 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. 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. Find the volume of rectangular prisms using a formula. Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units. 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. 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. 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. Formulas will be provided. 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. Apply the commutative, associative and distributive properties and order of operations to generate equivalent numerical expressions and to solve problems involving whole numbers. Use various tools and strategies to measure the volume and surface area of objects that are shaped like rectangular prisms. Understand that the volume of a three dimensional figure can be found by counting the total number of same-sized cubic units that fill a shape without gaps or overlaps. Use cubic units to label volume measurements. Develop and use the formulas V = ?wh and V = Bh to determine the volume of rectangular prisms. Justify why base area B and height h are multiplied to find the volume of a ectangular prism by breaking the prism into layers of unit cubes. 11-2: Lesson Self-Assessment 11-2: Reteach to Build Understanding Curriculum Standards: Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units. 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. 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. Use packing to recognize volume of a solid figure. 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. 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. 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. 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. Find the volume of rectangular prisms using a formula. Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units. 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. 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. 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. Formulas will be provided. 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. Apply the commutative, associative and distributive properties and order of operations to generate equivalent numerical expressions and to solve problems involving whole numbers. Use various tools and strategies to measure the volume and surface area of objects that are shaped like rectangular prisms. Understand that the volume of a three dimensional figure can be found by counting the total number of same-sized cubic units that fill a shape without gaps or overlaps. Use cubic units to label volume measurements. Develop and use the formulas V = ?wh and V = Bh to determine the volume of rectangular prisms. Justify why base area B and height h are multiplied to find the volume of a ectangular prism by breaking the prism into layers of unit cubes. Determine the volume of a rectangular prism built by “unit cubes.” Use multiplication to represent each layer of the rectangular prism. 11-2: Build Mathematical Literacy Curriculum Standards: Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 5 topics and texts, building on others’ ideas and expressing their own clearly. (a) Come to discussions prepared, having read or studied required material; explicitly draw on that preparation and other information known about the topic to explore ideas under discussion. (b) Follow agreed-upon rules for discussions and carry out assigned roles. (c) Pose and respond to specific questions by making comments that contribute to the discussion and elaborate on the remarks of others. (d) Review the key ideas expressed and draw conclusions in light of information and knowledge gained from the discussions. English language learners communicate for social and instructional purposes within the school setting. Summarize a written text read aloud or information presented in diverse media and formats, including visually, quantitatively, and orally. Summarize the points a speaker makes and explain how each claim is supported by reasons and evidence. Write informative/explanatory texts to examine a topic and convey ideas and information clearly. (a) Introduce a topic clearly, provide a general observation and focus, and group related information logically; include formatting (e.g., headings), illustrations, and multimedia when useful to aiding comprehension. (b) Develop the topic with facts, definitions, concrete details, quotations, or other information and examples related to the topic. (c) Link ideas within and across categories of information using words, phrases, and clauses (e.g., in contrast, especially). (d) Use precise language and domain-specific vocabulary to inform about or explain the topic. (e) Provide a concluding statement or section related to the information or explanation presented. English language learners communicate information, ideas and concepts necessary for academic success in the content area of Mathematics. 11-2: Enrichment 11-2: Digital Math Tool Activity 11-2: enVision STEM Activity Curriculum Standards: Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units. 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. 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. 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. 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. 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. 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. Find the volume of rectangular prisms using a formula. Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units. 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. 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. 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. Formulas will be provided. 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. Apply the commutative, associative and distributive properties and order of operations to generate equivalent numerical expressions and to solve problems involving whole numbers. Use various tools and strategies to measure the volume and surface area of objects that are shaped like rectangular prisms. Understand that the volume of a three dimensional figure can be found by counting the total number of same-sized cubic units that fill a shape without gaps or overlaps. Use cubic units to label volume measurements. Develop and use the formulas V = ?wh and V = Bh to determine the volume of rectangular prisms. Justify why base area B and height h are multiplied to find the volume of a ectangular prism by breaking the prism into layers of unit cubes. 11-2: Another Look Curriculum Standards: Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units. 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. 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. Use packing to recognize volume of a solid figure. 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. 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. 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. 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. Find the volume of rectangular prisms using a formula. Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units. 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. 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. 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. Formulas will be provided. 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. Apply the commutative, associative and distributive properties and order of operations to generate equivalent numerical expressions and to solve problems involving whole numbers. Use various tools and strategies to measure the volume and surface area of objects that are shaped like rectangular prisms. Understand that the volume of a three dimensional figure can be found by counting the total number of same-sized cubic units that fill a shape without gaps or overlaps. Use cubic units to label volume measurements. Develop and use the formulas V = ?wh and V = Bh to determine the volume of rectangular prisms. Justify why base area B and height h are multiplied to find the volume of a ectangular prism by breaking the prism into layers of unit cubes. Determine the volume of a rectangular prism built by “unit cubes.” Use multiplication to represent each layer of the rectangular prism. Spanish Resources 11-2: eText del Libro del estudiante 11-2: Repaso diario 11-2: Aprendizaje visual 11-2: Amigo de práctica: Práctica adicional 11-2: Práctica adicional interactiva 11-2: Refuerzo para mejorar la comprensión 11-2: Desarrollar la competencia matemática 11-2: Ampliación Topic 11: 3-Act Math: Fill'er Up Interactive Student Edition: Grade 5, Topic 11: 3-Act Math Mathematical Modeling Topic 11: 3-Act Math: Fill'er Up, Act 1 Topic 11: 3-Act Math: Fill'er Up, Act 2 Topic 11: 3-Act Math: Fill'er Up, Act 3 Topic 11: 3-Act Math: Fill'er Up, Sequel 11-3: Combine Volumes of Prisms Interactive Student Edition: Grade 5 Lesson 11-3 Math Anytime 11-3: Daily Review Topic 11: Today's Challenge Step 1: Problem-Based Learning 11-3: Solve & Share Curriculum Standards: Recognize volume as additive. 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. English language learners communicate for social and instructional purposes within the school setting. Write informative/explanatory texts to examine a topic and convey ideas and information clearly. (a) Introduce a topic clearly, provide a general observation and focus, and group related information logically; include formatting (e.g., headings), illustrations, and multimedia when useful to aiding comprehension. (b) Develop the topic with facts, definitions, concrete details, quotations, or other information and examples related to the topic. (c) Link ideas within and across categories of information using words, phrases, and clauses (e.g., in contrast, especially). (d) Use precise language and domain-specific vocabulary to inform about or explain the topic. (e) Provide a concluding statement or section related to the information or explanation presented. English language learners communicate information, ideas and concepts necessary for academic success in the content area of Mathematics. Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 5 topics and texts, building on others’ ideas and expressing their own clearly. (a) Come to discussions prepared, having read or studied required material; explicitly draw on that preparation and other information known about the topic to explore ideas under discussion. (b) Follow agreed-upon rules for discussions and carry out assigned roles. (c) Pose and respond to specific questions by making comments that contribute to the discussion and elaborate on the remarks of others. (d) Review the key ideas expressed and draw conclusions in light of information and knowledge gained from the discussions. Summarize a written text read aloud or information presented in diverse media and formats, including visually, quantitatively, and orally. Summarize the points a speaker makes and explain how each claim is supported by reasons and evidence. Recognize volume as additive. 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. Recognize volume as additive. 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. Find the volume of a solid figure that is the combination of two or more rectangular prisms. Recognize volume as additive. 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. Find volumes of solid figures composed of two nonoverlapping right rectangular prisms. 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. Use various tools and strategies to measure the volume and surface area of objects that are shaped like rectangular prisms. Understand that the volume of a three dimensional figure can be found by counting the total number of same-sized cubic units that fill a shape without gaps or overlaps. Use cubic units to label volume measurements. Develop and use the formulas V = ?wh and V = Bh to determine the volume of rectangular prisms. Justify why base area B and height h are multiplied to find the volume of a ectangular prism by breaking the prism into layers of unit cubes. Step 2: Visual Learning 11-3: Visual Learning Curriculum Standards: Recognize volume as additive. 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. Use addition to determine the length, width, and height. Recognize volume as additive. 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. Recognize volume as additive. 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. Find the volume of a solid figure that is the combination of two or more rectangular prisms. Recognize volume as additive. 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. Find volumes of solid figures composed of two nonoverlapping right rectangular prisms. 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. Use various tools and strategies to measure the volume and surface area of objects that are shaped like rectangular prisms. Understand that the volume of a three dimensional figure can be found by counting the total number of same-sized cubic units that fill a shape without gaps or overlaps. Use cubic units to label volume measurements. Develop and use the formulas V = ?wh and V = Bh to determine the volume of rectangular prisms. Justify why base area B and height h are multiplied to find the volume of a ectangular prism by breaking the prism into layers of unit cubes. 11-3: Convince Me! Curriculum Standards: Recognize volume as additive. 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. Recognize volume as additive. 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. Recognize volume as additive. 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. Find the volume of a solid figure that is the combination of two or more rectangular prisms. Recognize volume as additive. 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. Find volumes of solid figures composed of two nonoverlapping right rectangular prisms. 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. Use various tools and strategies to measure the volume and surface area of objects that are shaped like rectangular prisms. Understand that the volume of a three dimensional figure can be found by counting the total number of same-sized cubic units that fill a shape without gaps or overlaps. Use cubic units to label volume measurements. Develop and use the formulas V = ?wh and V = Bh to determine the volume of rectangular prisms. Justify why base area B and height h are multiplied to find the volume of a ectangular prism by breaking the prism into layers of unit cubes. Practice and Problem Solving 11-3: Student Edition Practice Curriculum Standards: Recognize volume as additive. 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. Recognize volume as additive. 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. Recognize volume as additive. 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. Find the volume of a solid figure that is the combination of two or more rectangular prisms. Recognize volume as additive. 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. Find volumes of solid figures composed of two nonoverlapping right rectangular prisms. 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. Use various tools and strategies to measure the volume and surface area of objects that are shaped like rectangular prisms. Understand that the volume of a three dimensional figure can be found by counting the total number of same-sized cubic units that fill a shape without gaps or overlaps. Use cubic units to label volume measurements. Develop and use the formulas V = ?wh and V = Bh to determine the volume of rectangular prisms. Justify why base area B and height h are multiplied to find the volume of a ectangular prism by breaking the prism into layers of unit cubes. 11-3: Practice Buddy: Independent Practice; Problem Solving Curriculum Standards: Recognize volume as additive. 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. Recognize volume as additive. 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. Recognize volume as additive. 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. Find the volume of a solid figure that is the combination of two or more rectangular prisms. Recognize volume as additive. 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. Find volumes of solid figures composed of two nonoverlapping right rectangular prisms. 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. Use various tools and strategies to measure the volume and surface area of objects that are shaped like rectangular prisms. Understand that the volume of a three dimensional figure can be found by counting the total number of same-sized cubic units that fill a shape without gaps or overlaps. Use cubic units to label volume measurements. Develop and use the formulas V = ?wh and V = Bh to determine the volume of rectangular prisms. Justify why base area B and height h are multiplied to find the volume of a ectangular prism by breaking the prism into layers of unit cubes. 11-3: Practice Buddy: Additional Practice Curriculum Standards: Recognize volume as additive. 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. Recognize volume as additive. 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. Recognize volume as additive. 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. Find the volume of a solid figure that is the combination of two or more rectangular prisms. Recognize volume as additive. 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. Find volumes of solid figures composed of two nonoverlapping right rectangular prisms. 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. Use various tools and strategies to measure the volume and surface area of objects that are shaped like rectangular prisms. Understand that the volume of a three dimensional figure can be found by counting the total number of same-sized cubic units that fill a shape without gaps or overlaps. Use cubic units to label volume measurements. Develop and use the formulas V = ?wh and V = Bh to determine the volume of rectangular prisms. Justify why base area B and height h are multiplied to find the volume of a ectangular prism by breaking the prism into layers of unit cubes. 11-3: Interactive Additional Practice Step 3: Assess & Differentiate 11-3: Practice Buddy: Additional Practice Curriculum Standards: Recognize volume as additive. 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. Recognize volume as additive. 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. Recognize volume as additive. 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. Find the volume of a solid figure that is the combination of two or more rectangular prisms. Recognize volume as additive. 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. Find volumes of solid figures composed of two nonoverlapping right rectangular prisms. 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. Use various tools and strategies to measure the volume and surface area of objects that are shaped like rectangular prisms. Understand that the volume of a three dimensional figure can be found by counting the total number of same-sized cubic units that fill a shape without gaps or overlaps. Use cubic units to label volume measurements. Develop and use the formulas V = ?wh and V = Bh to determine the volume of rectangular prisms. Justify why base area B and height h are multiplied to find the volume of a ectangular prism by breaking the prism into layers of unit cubes. 11-3: Enrichment Curriculum Standards: Recognize volume as additive. 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. Recognize volume as additive. 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. Recognize volume as additive. 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. Find the volume of a solid figure that is the combination of two or more rectangular prisms. Recognize volume as additive. 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. Find volumes of solid figures composed of two nonoverlapping right rectangular prisms. 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. Use various tools and strategies to measure the volume and surface area of objects that are shaped like rectangular prisms. Understand that the volume of a three dimensional figure can be found by counting the total number of same-sized cubic units that fill a shape without gaps or overlaps. Use cubic units to label volume measurements. Develop and use the formulas V = ?wh and V = Bh to determine the volume of rectangular prisms. Justify why base area B and height h are multiplied to find the volume of a ectangular prism by breaking the prism into layers of unit cubes. 11-3: Quick Check Curriculum Standards: Recognize volume as additive. 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. Recognize volume as additive. 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. Recognize volume as additive. 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. Find the volume of a solid figure that is the combination of two or more rectangular prisms. Recognize volume as additive. 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. Find volumes of solid figures composed of two nonoverlapping right rectangular prisms. 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. Use various tools and strategies to measure the volume and surface area of objects that are shaped like rectangular prisms. Understand that the volume of a three dimensional figure can be found by counting the total number of same-sized cubic units that fill a shape without gaps or overlaps. Use cubic units to label volume measurements. Develop and use the formulas V = ?wh and V = Bh to determine the volume of rectangular prisms. Justify why base area B and height h are multiplied to find the volume of a ectangular prism by breaking the prism into layers of unit cubes. 11-3: Lesson Self-Assessment 11-3: Reteach to Build Understanding Curriculum Standards: Recognize volume as additive. 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. Use addition to determine the length, width, and height. Recognize volume as additive. 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. Recognize volume as additive. 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. Find the volume of a solid figure that is the combination of two or more rectangular prisms. Recognize volume as additive. 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. Find volumes of solid figures composed of two nonoverlapping right rectangular prisms. 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. Use various tools and strategies to measure the volume and surface area of objects that are shaped like rectangular prisms. Understand that the volume of a three dimensional figure can be found by counting the total number of same-sized cubic units that fill a shape without gaps or overlaps. Use cubic units to label volume measurements. Develop and use the formulas V = ?wh and V = Bh to determine the volume of rectangular prisms. Justify why base area B and height h are multiplied to find the volume of a ectangular prism by breaking the prism into layers of unit cubes. 11-3: Build Mathematical Literacy Curriculum Standards: Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 5 topics and texts, building on others’ ideas and expressing their own clearly. (a) Come to discussions prepared, having read or studied required material; explicitly draw on that preparation and other information known about the topic to explore ideas under discussion. (b) Follow agreed-upon rules for discussions and carry out assigned roles. (c) Pose and respond to specific questions by making comments that contribute to the discussion and elaborate on the remarks of others. (d) Review the key ideas expressed and draw conclusions in light of information and knowledge gained from the discussions. English language learners communicate for social and instructional purposes within the school setting. Summarize a written text read aloud or information presented in diverse media and formats, including visually, quantitatively, and orally. Summarize the points a speaker makes and explain how each claim is supported by reasons and evidence. Write informative/explanatory texts to examine a topic and convey ideas and information clearly. (a) Introduce a topic clearly, provide a general observation and focus, and group related information logically; include formatting (e.g., headings), illustrations, and multimedia when useful to aiding comprehension. (b) Develop the topic with facts, definitions, concrete details, quotations, or other information and examples related to the topic. (c) Link ideas within and across categories of information using words, phrases, and clauses (e.g., in contrast, especially). (d) Use precise language and domain-specific vocabulary to inform about or explain the topic. (e) Provide a concluding statement or section related to the information or explanation presented. English language learners communicate information, ideas and concepts necessary for academic success in the content area of Mathematics. 11-3: Enrichment 11-3: Digital Math Tool Activity 11-3: Pick a Project 11-3: Another Look Curriculum Standards: Recognize volume as additive. 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. Use addition to determine the length, width, and height. Recognize volume as additive. 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. Recognize volume as additive. 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. Find the volume of a solid figure that is the combination of two or more rectangular prisms. Recognize volume as additive. 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. Find volumes of solid figures composed of two nonoverlapping right rectangular prisms. 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. Use various tools and strategies to measure the volume and surface area of objects that are shaped like rectangular prisms. Understand that the volume of a three dimensional figure can be found by counting the total number of same-sized cubic units that fill a shape without gaps or overlaps. Use cubic units to label volume measurements. Develop and use the formulas V = ?wh and V = Bh to determine the volume of rectangular prisms. Justify why base area B and height h are multiplied to find the volume of a ectangular prism by breaking the prism into layers of unit cubes. Spanish Resources 11-3: eText del Libro del estudiante 11-3: Repaso diario 11-3: Aprendizaje visual 11-3: Amigo de práctica: Práctica adicional 11-3: Práctica adicional interactiva 11-3: Refuerzo para mejorar la comprensión 11-3: Desarrollar la competencia matemática 11-3: Ampliación 11-4: Solve Word Problems Using Volume Interactive Student Edition: Grade 5 Lesson 11-4 Math Anytime 11-4: Daily Review Topic 11: Today's Challenge Step 1: Problem-Based Learning 11-4: Solve & Share Curriculum Standards: Recognize volume as additive. 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. English language learners communicate for social and instructional purposes within the school setting. Write informative/explanatory texts to examine a topic and convey ideas and information clearly. (a) Introduce a topic clearly, provide a general observation and focus, and group related information logically; include formatting (e.g., headings), illustrations, and multimedia when useful to aiding comprehension. (b) Develop the topic with facts, definitions, concrete details, quotations, or other information and examples related to the topic. (c) Link ideas within and across categories of information using words, phrases, and clauses (e.g., in contrast, especially). (d) Use precise language and domain-specific vocabulary to inform about or explain the topic. (e) Provide a concluding statement or section related to the information or explanation presented. English language learners communicate information, ideas and concepts necessary for academic success in the content area of Mathematics. Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 5 topics and texts, building on others’ ideas and expressing their own clearly. (a) Come to discussions prepared, having read or studied required material; explicitly draw on that preparation and other information known about the topic to explore ideas under discussion. (b) Follow agreed-upon rules for discussions and carry out assigned roles. (c) Pose and respond to specific questions by making comments that contribute to the discussion and elaborate on the remarks of others. (d) Review the key ideas expressed and draw conclusions in light of information and knowledge gained from the discussions. Summarize a written text read aloud or information presented in diverse media and formats, including visually, quantitatively, and orally. Summarize the points a speaker makes and explain how each claim is supported by reasons and evidence. Recognize volume as additive. 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. Recognize volume as additive. 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. Use models, prior knowledge of volume and previously learned strategies to solve word problems involving volume. Recognize volume as additive. 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. Find volumes of solid figures composed of two nonoverlapping right rectangular prisms. 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. Use various tools and strategies to measure the volume and surface area of objects that are shaped like rectangular prisms. Understand that the volume of a three dimensional figure can be found by counting the total number of same-sized cubic units that fill a shape without gaps or overlaps. Use cubic units to label volume measurements. Develop and use the formulas V = ?wh and V = Bh to determine the volume of rectangular prisms. Justify why base area B and height h are multiplied to find the volume of a ectangular prism by breaking the prism into layers of unit cubes. Step 2: Visual Learning 11-4: Visual Learning Curriculum Standards: Recognize volume as additive. 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. Recognize volume as additive. 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. Recognize volume as additive. 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. Use models, prior knowledge of volume and previously learned strategies to solve word problems involving volume. Recognize volume as additive. 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. Find volumes of solid figures composed of two nonoverlapping right rectangular prisms. 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. Use various tools and strategies to measure the volume and surface area of objects that are shaped like rectangular prisms. Understand that the volume of a three dimensional figure can be found by counting the total number of same-sized cubic units that fill a shape without gaps or overlaps. Use cubic units to label volume measurements. Develop and use the formulas V = ?wh and V = Bh to determine the volume of rectangular prisms. Justify why base area B and height h are multiplied to find the volume of a ectangular prism by breaking the prism into layers of unit cubes. 11-4: Convince Me! Curriculum Standards: Recognize volume as additive. 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. Recognize volume as additive. 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. Recognize volume as additive. 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. Use models, prior knowledge of volume and previously learned strategies to solve word problems involving volume. Recognize volume as additive. 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. Find volumes of solid figures composed of two nonoverlapping right rectangular prisms. 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. Use various tools and strategies to measure the volume and surface area of objects that are shaped like rectangular prisms. Understand that the volume of a three dimensional figure can be found by counting the total number of same-sized cubic units that fill a shape without gaps or overlaps. Use cubic units to label volume measurements. Develop and use the formulas V = ?wh and V = Bh to determine the volume of rectangular prisms. Justify why base area B and height h are multiplied to find the volume of a ectangular prism by breaking the prism into layers of unit cubes. Practice and Problem Solving 11-4: Student Edition Practice Curriculum Standards: Recognize volume as additive. 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. Recognize volume as additive. 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. Recognize volume as additive. 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. Use models, prior knowledge of volume and previously learned strategies to solve word problems involving volume. Recognize volume as additive. 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. Find volumes of solid figures composed of two nonoverlapping right rectangular prisms. 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. Use various tools and strategies to measure the volume and surface area of objects that are shaped like rectangular prisms. Understand that the volume of a three dimensional figure can be found by counting the total number of same-sized cubic units that fill a shape without gaps or overlaps. Use cubic units to label volume measurements. Develop and use the formulas V = ?wh and V = Bh to determine the volume of rectangular prisms. Justify why base area B and height h are multiplied to find the volume of a ectangular prism by breaking the prism into layers of unit cubes. 11-4: Practice Buddy: Independent Practice; Problem Solving Curriculum Standards: Recognize volume as additive. 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. Recognize volume as additive. 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. Recognize volume as additive. 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. Use models, prior knowledge of volume and previously learned strategies to solve word problems involving volume. Recognize volume as additive. 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. Find volumes of solid figures composed of two nonoverlapping right rectangular prisms. 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. Use various tools and strategies to measure the volume and surface area of objects that are shaped like rectangular prisms. Understand that the volume of a three dimensional figure can be found by counting the total number of same-sized cubic units that fill a shape without gaps or overlaps. Use cubic units to label volume measurements. Develop and use the formulas V = ?wh and V = Bh to determine the volume of rectangular prisms. Justify why base area B and height h are multiplied to find the volume of a ectangular prism by breaking the prism into layers of unit cubes. 11-4: Practice Buddy: Additional Practice Curriculum Standards: Recognize volume as additive. 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. Recognize volume as additive. 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. Recognize volume as additive. 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. Use models, prior knowledge of volume and previously learned strategies to solve word problems involving volume. Recognize volume as additive. 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. Find volumes of solid figures composed of two nonoverlapping right rectangular prisms. 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. Use various tools and strategies to measure the volume and surface area of objects that are shaped like rectangular prisms. Understand that the volume of a three dimensional figure can be found by counting the total number of same-sized cubic units that fill a shape without gaps or overlaps. Use cubic units to label volume measurements. Develop and use the formulas V = ?wh and V = Bh to determine the volume of rectangular prisms. Justify why base area B and height h are multiplied to find the volume of a ectangular prism by breaking the prism into layers of unit cubes. 11-4: Interactive Additional Practice Step 3: Assess & Differentiate 11-4: Practice Buddy: Additional Practice Curriculum Standards: Recognize volume as additive. 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. Recognize volume as additive. 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. Recognize volume as additive. 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. Use models, prior knowledge of volume and previously learned strategies to solve word problems involving volume. Recognize volume as additive. 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. Find volumes of solid figures composed of two nonoverlapping right rectangular prisms. 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. Use various tools and strategies to measure the volume and surface area of objects that are shaped like rectangular prisms. Understand that the volume of a three dimensional figure can be found by counting the total number of same-sized cubic units that fill a shape without gaps or overlaps. Use cubic units to label volume measurements. Develop and use the formulas V = ?wh and V = Bh to determine the volume of rectangular prisms. Justify why base area B and height h are multiplied to find the volume of a ectangular prism by breaking the prism into layers of unit cubes. 11-4: Enrichment Curriculum Standards: Recognize volume as additive. 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. Recognize volume as additive. 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. Recognize volume as additive. 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. Use models, prior knowledge of volume and previously learned strategies to solve word problems involving volume. Recognize volume as additive. 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. Find volumes of solid figures composed of two nonoverlapping right rectangular prisms. 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. Use various tools and strategies to measure the volume and surface area of objects that are shaped like rectangular prisms. Understand that the volume of a three dimensional figure can be found by counting the total number of same-sized cubic units that fill a shape without gaps or overlaps. Use cubic units to label volume measurements. Develop and use the formulas V = ?wh and V = Bh to determine the volume of rectangular prisms. Justify why base area B and height h are multiplied to find the volume of a ectangular prism by breaking the prism into layers of unit cubes. 11-4: Quick Check Curriculum Standards: Recognize volume as additive. 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. Recognize volume as additive. 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. Recognize volume as additive. 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. Use models, prior knowledge of volume and previously learned strategies to solve word problems involving volume. Recognize volume as additive. 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. Find volumes of solid figures composed of two nonoverlapping right rectangular prisms. 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. Use various tools and strategies to measure the volume and surface area of objects that are shaped like rectangular prisms. Understand that the volume of a three dimensional figure can be found by counting the total number of same-sized cubic units that fill a shape without gaps or overlaps. Use cubic units to label volume measurements. Develop and use the formulas V = ?wh and V = Bh to determine the volume of rectangular prisms. Justify why base area B and height h are multiplied to find the volume of a ectangular prism by breaking the prism into layers of unit cubes. 11-4: Lesson Self-Assessment 11-4: Reteach to Build Understanding Curriculum Standards: Recognize volume as additive. 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. Recognize volume as additive. 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. Recognize volume as additive. 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. Use models, prior knowledge of volume and previously learned strategies to solve word problems involving volume. Recognize volume as additive. 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. Find volumes of solid figures composed of two nonoverlapping right rectangular prisms. 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. Use various tools and strategies to measure the volume and surface area of objects that are shaped like rectangular prisms. Understand that the volume of a three dimensional figure can be found by counting the total number of same-sized cubic units that fill a shape without gaps or overlaps. Use cubic units to label volume measurements. Develop and use the formulas V = ?wh and V = Bh to determine the volume of rectangular prisms. Justify why base area B and height h are multiplied to find the volume of a ectangular prism by breaking the prism into layers of unit cubes. 11-4: Build Mathematical Literacy Curriculum Standards: Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 5 topics and texts, building on others’ ideas and expressing their own clearly. (a) Come to discussions prepared, having read or studied required material; explicitly draw on that preparation and other information known about the topic to explore ideas under discussion. (b) Follow agreed-upon rules for discussions and carry out assigned roles. (c) Pose and respond to specific questions by making comments that contribute to the discussion and elaborate on the remarks of others. (d) Review the key ideas expressed and draw conclusions in light of information and knowledge gained from the discussions. English language learners communicate for social and instructional purposes within the school setting. Summarize a written text read aloud or information presented in diverse media and formats, including visually, quantitatively, and orally. Summarize the points a speaker makes and explain how each claim is supported by reasons and evidence. Write informative/explanatory texts to examine a topic and convey ideas and information clearly. (a) Introduce a topic clearly, provide a general observation and focus, and group related information logically; include formatting (e.g., headings), illustrations, and multimedia when useful to aiding comprehension. (b) Develop the topic with facts, definitions, concrete details, quotations, or other information and examples related to the topic. (c) Link ideas within and across categories of information using words, phrases, and clauses (e.g., in contrast, especially). (d) Use precise language and domain-specific vocabulary to inform about or explain the topic. (e) Provide a concluding statement or section related to the information or explanation presented. English language learners communicate information, ideas and concepts necessary for academic success in the content area of Mathematics. 11-4: Enrichment Game: Fluency - Multiply Multi-Digit Whole Numbers 11-4: enVision STEM Activity Curriculum Standards: Recognize volume as additive. 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. Recognize volume as additive. 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. Recognize volume as additive. 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. Use models, prior knowledge of volume and previously learned strategies to solve word problems involving volume. Recognize volume as additive. 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. Find volumes of solid figures composed of two nonoverlapping right rectangular prisms. 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. Use various tools and strategies to measure the volume and surface area of objects that are shaped like rectangular prisms. Understand that the volume of a three dimensional figure can be found by counting the total number of same-sized cubic units that fill a shape without gaps or overlaps. Use cubic units to label volume measurements. Develop and use the formulas V = ?wh and V = Bh to determine the volume of rectangular prisms. Justify why base area B and height h are multiplied to find the volume of a ectangular prism by breaking the prism into layers of unit cubes. 11-4: Another Look Curriculum Standards: Recognize volume as additive. 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. Recognize volume as additive. 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. Recognize volume as additive. 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. Use models, prior knowledge of volume and previously learned strategies to solve word problems involving volume. Recognize volume as additive. 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. Find volumes of solid figures composed of two nonoverlapping right rectangular prisms. 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. Use various tools and strategies to measure the volume and surface area of objects that are shaped like rectangular prisms. Understand that the volume of a three dimensional figure can be found by counting the total number of same-sized cubic units that fill a shape without gaps or overlaps. Use cubic units to label volume measurements. Develop and use the formulas V = ?wh and V = Bh to determine the volume of rectangular prisms. Justify why base area B and height h are multiplied to find the volume of a ectangular prism by breaking the prism into layers of unit cubes. Spanish Resources 11-4: eText del Libro del estudiante 11-4: Repaso diario 11-4: Aprendizaje visual 11-4: Amigo de práctica: Práctica adicional 11-4: Práctica adicional interactiva 11-4: Refuerzo para mejorar la comprensión 11-4: Desarrollar la competencia matemática 11-4: Ampliación 11-5: Problem Solving: Use Appropriate Tools Interactive Student Edition: Grade 5 Lesson 11-5 Math Anytime 11-5: Daily Review Topic 11: Today's Challenge Step 1: Problem-Based Learning 11-5: Solve & Share Curriculum Standards: A cube with side length 1 unit, called a "unit cube," is said to have "one cubic unit" of volume, and can be used to measure volume. A solid figure that can be packed without gaps or overlaps using n unit cubes is said to have a volume of n cubic units. Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units. Use appropriate tools strategically. A cube with side length 1 unit, called a “unit cube,” is said to have “one cubic unit” of volume, and can be used to measure volume. Use appropriate tools strategically. A cube with side length 1 unit, called a “unit cube,” is said to have “one cubic unit” of volume, and can be used to measure volume. Use appropriate tools strategically. Mathematically proficient students consider the available tools when solving a mathematical problem. These tools might include pencil and paper, concrete models, a ruler, a protractor, a calculator, a spreadsheet, a computer algebra system, a statistical package, or dynamic geometry software. Proficient students are sufficiently familiar with tools appropriate for their grade or course to make sound decisions about when each of these tools might be helpful, recognizing both the insight to be gained and their limitations. For example, mathematically proficient high school students analyze graphs of functions and solutions generated using a graphing calculator. They detect possible errors by strategically using estimation and other mathematical knowledge. When making mathematical models, they know that technology can enable them to visualize the results of varying assumptions, explore consequences, and compare predictions with data. Mathematically proficient students at various grade levels are able to identify relevant external mathematical resources, such as digital content located on a website, and use them to pose or solve problems. They are able to use technological tools to explore and deepen their understanding of concepts. Use previously learned knowledge about volume to choose the appropriate tools to solve volume problems. A cube with side length 1 unit, called a unit cube, is said to have one cubic unit of volume, and can be used to measure volume. A solid figure that can be packed without gaps or overlaps using n unit cubes is said to have a volume of n cubic units. Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units. Use appropriate tools strategically. Use appropriate tools strategically. Find volumes of solid figures composed of two nonoverlapping right rectangular prisms. Use appropriate tools strategically. Understand that the volume of a three dimensional figure can be found by counting the total number of same-sized cubic units that fill a shape without gaps or overlaps. Use cubic units to label volume measurements. English language learners communicate for social and instructional purposes within the school setting. Write informative/explanatory texts to examine a topic and convey ideas and information clearly. (a) Introduce a topic clearly, provide a general observation and focus, and group related information logically; include formatting (e.g., headings), illustrations, and multimedia when useful to aiding comprehension. (b) Develop the topic with facts, definitions, concrete details, quotations, or other information and examples related to the topic. (c) Link ideas within and across categories of information using words, phrases, and clauses (e.g., in contrast, especially). (d) Use precise language and domain- specific vocabulary to inform about or explain the topic. (e) Provide a concluding statement or section related to the information or explanation presented. English language learners communicate information, ideas and concepts necessary for academic success in the content area of Mathematics. Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 5 topics and texts, building on others’ ideas and expressing their own clearly. (a) Come to discussions prepared, having read or studied required material; explicitly draw on that preparation and other information known about the topic to explore ideas under discussion. (b) Follow agreed-upon rules for discussions and carry out assigned roles. (c) Pose and respond to specific questions by making comments that contribute to the discussion and elaborate on the remarks of others. (d) Review the key ideas expressed and draw conclusions in light of information and knowledge gained from the discussions. Summarize a written text read aloud or information presented in diverse media and formats, including visually, quantitatively, and orally. Summarize the points a speaker makes and explain how each claim is supported by reasons and evidence. Step 2: Visual Learning 11-5: Visual Learning Curriculum Standards: A cube with side length 1 unit, called a "unit cube," is said to have "one cubic unit" of volume, and can be used to measure volume. A solid figure that can be packed without gaps or overlaps using n unit cubes is said to have a volume of n cubic units. Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units. Use appropriate tools strategically. A cube with side length 1 unit, called a “unit cube,” is said to have “one cubic unit” of volume, and can be used to measure volume. Use appropriate tools strategically. A cube with side length 1 unit, called a “unit cube,” is said to have “one cubic unit” of volume, and can be used to measure volume. Use appropriate tools strategically. Mathematically proficient students consider the available tools when solving a mathematical problem. These tools might include pencil and paper, concrete models, a ruler, a protractor, a calculator, a spreadsheet, a computer algebra system, a statistical package, or dynamic geometry software. Proficient students are sufficiently familiar with tools appropriate for their grade or course to make sound decisions about when each of these tools might be helpful, recognizing both the insight to be gained and their limitations. For example, mathematically proficient high school students analyze graphs of functions and solutions generated using a graphing calculator. They detect possible errors by strategically using estimation and other mathematical knowledge. When making mathematical models, they know that technology can enable them to visualize the results of varying assumptions, explore consequences, and compare predictions with data. Mathematically proficient students at various grade levels are able to identify relevant external mathematical resources, such as digital content located on a website, and use them to pose or solve problems. They are able to use technological tools to explore and deepen their understanding of concepts. Use previously learned knowledge about volume to choose the appropriate tools to solve volume problems. A cube with side length 1 unit, called a unit cube, is said to have one cubic unit of volume, and can be used to measure volume. A solid figure that can be packed without gaps or overlaps using n unit cubes is said to have a volume of n cubic units. Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units. Use appropriate tools strategically. Use appropriate tools strategically. Find volumes of solid figures composed of two nonoverlapping right rectangular prisms. Use appropriate tools strategically. Understand that the volume of a three dimensional figure can be found by counting the total number of same-sized cubic units that fill a shape without gaps or overlaps. Use cubic units to label volume measurements. Connect the layers to the dimensions and multiply to find the volume of the rectangular prism. 11-5: Convince Me! Curriculum Standards: A cube with side length 1 unit, called a "unit cube," is said to have "one cubic unit" of volume, and can be used to measure volume. A solid figure that can be packed without gaps or overlaps using n unit cubes is said to have a volume of n cubic units. Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units. Use appropriate tools strategically. A cube with side length 1 unit, called a “unit cube,” is said to have “one cubic unit” of volume, and can be used to measure volume. Use appropriate tools strategically. A cube with side length 1 unit, called a “unit cube,” is said to have “one cubic unit” of volume, and can be used to measure volume. Use appropriate tools strategically. Mathematically proficient students consider the available tools when solving a mathematical problem. These tools might include pencil and paper, concrete models, a ruler, a protractor, a calculator, a spreadsheet, a computer algebra system, a statistical package, or dynamic geometry software. Proficient students are sufficiently familiar with tools appropriate for their grade or course to make sound decisions about when each of these tools might be helpful, recognizing both the insight to be gained and their limitations. For example, mathematically proficient high school students analyze graphs of functions and solutions generated using a graphing calculator. They detect possible errors by strategically using estimation and other mathematical knowledge. When making mathematical models, they know that technology can enable them to visualize the results of varying assumptions, explore consequences, and compare predictions with data. Mathematically proficient students at various grade levels are able to identify relevant external mathematical resources, such as digital content located on a website, and use them to pose or solve problems. They are able to use technological tools to explore and deepen their understanding of concepts. Use previously learned knowledge about volume to choose the appropriate tools to solve volume problems. A cube with side length 1 unit, called a unit cube, is said to have one cubic unit of volume, and can be used to measure volume. A solid figure that can be packed without gaps or overlaps using n unit cubes is said to have a volume of n cubic units. Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units. Use appropriate tools strategically. Use appropriate tools strategically. Find volumes of solid figures composed of two nonoverlapping right rectangular prisms. Use appropriate tools strategically. Understand that the volume of a three dimensional figure can be found by counting the total number of same-sized cubic units that fill a shape without gaps or overlaps. Use cubic units to label volume measurements. Practice and Problem Solving 11-5: Student Edition Practice Curriculum Standards: A cube with side length 1 unit, called a "unit cube," is said to have "one cubic unit" of volume, and can be used to measure volume. A solid figure that can be packed without gaps or overlaps using n unit cubes is said to have a volume of n cubic units. Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units. Use appropriate tools strategically. A cube with side length 1 unit, called a “unit cube,” is said to have “one cubic unit” of volume, and can be used to measure volume. Use appropriate tools strategically. A cube with side length 1 unit, called a “unit cube,” is said to have “one cubic unit” of volume, and can be used to measure volume. Use appropriate tools strategically. Mathematically proficient students consider the available tools when solving a mathematical problem. These tools might include pencil and paper, concrete models, a ruler, a protractor, a calculator, a spreadsheet, a computer algebra system, a statistical package, or dynamic geometry software. Proficient students are sufficiently familiar with tools appropriate for their grade or course to make sound decisions about when each of these tools might be helpful, recognizing both the insight to be gained and their limitations. For example, mathematically proficient high school students analyze graphs of functions and solutions generated using a graphing calculator. They detect possible errors by strategically using estimation and other mathematical knowledge. When making mathematical models, they know that technology can enable them to visualize the results of varying assumptions, explore consequences, and compare predictions with data. Mathematically proficient students at various grade levels are able to identify relevant external mathematical resources, such as digital content located on a website, and use them to pose or solve problems. They are able to use technological tools to explore and deepen their understanding of concepts. Use previously learned knowledge about volume to choose the appropriate tools to solve volume problems. A cube with side length 1 unit, called a unit cube, is said to have one cubic unit of volume, and can be used to measure volume. A solid figure that can be packed without gaps or overlaps using n unit cubes is said to have a volume of n cubic units. Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units. Use appropriate tools strategically. Use appropriate tools strategically. Find volumes of solid figures composed of two nonoverlapping right rectangular prisms. Use appropriate tools strategically. Understand that the volume of a three dimensional figure can be found by counting the total number of same-sized cubic units that fill a shape without gaps or overlaps. Use cubic units to label volume measurements. 11-5: Practice Buddy: Independent Practice; Problem Solving Curriculum Standards: A cube with side length 1 unit, called a "unit cube," is said to have "one cubic unit" of volume, and can be used to measure volume. A solid figure that can be packed without gaps or overlaps using n unit cubes is said to have a volume of n cubic units. Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units. Use appropriate tools strategically. A cube with side length 1 unit, called a “unit cube,” is said to have “one cubic unit” of volume, and can be used to measure volume. Use appropriate tools strategically. A cube with side length 1 unit, called a “unit cube,” is said to have “one cubic unit” of volume, and can be used to measure volume. Use appropriate tools strategically. Mathematically proficient students consider the available tools when solving a mathematical problem. These tools might include pencil and paper, concrete models, a ruler, a protractor, a calculator, a spreadsheet, a computer algebra system, a statistical package, or dynamic geometry software. Proficient students are sufficiently familiar with tools appropriate for their grade or course to make sound decisions about when each of these tools might be helpful, recognizing both the insight to be gained and their limitations. For example, mathematically proficient high school students analyze graphs of functions and solutions generated using a graphing calculator. They detect possible errors by strategically using estimation and other mathematical knowledge. When making mathematical models, they know that technology can enable them to visualize the results of varying assumptions, explore consequences, and compare predictions with data. Mathematically proficient students at various grade levels are able to identify relevant external mathematical resources, such as digital content located on a website, and use them to pose or solve problems. They are able to use technological tools to explore and deepen their understanding of concepts. Use previously learned knowledge about volume to choose the appropriate tools to solve volume problems. A cube with side length 1 unit, called a unit cube, is said to have one cubic unit of volume, and can be used to measure volume. A solid figure that can be packed without gaps or overlaps using n unit cubes is said to have a volume of n cubic units. Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units. Use appropriate tools strategically. Use appropriate tools strategically. Find volumes of solid figures composed of two nonoverlapping right rectangular prisms. Use appropriate tools strategically. Understand that the volume of a three dimensional figure can be found by counting the total number of same-sized cubic units that fill a shape without gaps or overlaps. Use cubic units to label volume measurements. 11-5: Practice Buddy: Additional Practice Curriculum Standards: A cube with side length 1 unit, called a "unit cube," is said to have "one cubic unit" of volume, and can be used to measure volume. A solid figure that can be packed without gaps or overlaps using n unit cubes is said to have a volume of n cubic units. Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units. Use appropriate tools strategically. A cube with side length 1 unit, called a “unit cube,” is said to have “one cubic unit” of volume, and can be used to measure volume. Use appropriate tools strategically. A cube with side length 1 unit, called a “unit cube,” is said to have “one cubic unit” of volume, and can be used to measure volume. Use appropriate tools strategically. Mathematically proficient students consider the available tools when solving a mathematical problem. These tools might include pencil and paper, concrete models, a ruler, a protractor, a calculator, a spreadsheet, a computer algebra system, a statistical package, or dynamic geometry software. Proficient students are sufficiently familiar with tools appropriate for their grade or course to make sound decisions about when each of these tools might be helpful, recognizing both the insight to be gained and their limitations. For example, mathematically proficient high school students analyze graphs of functions and solutions generated using a graphing calculator. They detect possible errors by strategically using estimation and other mathematical knowledge. When making mathematical models, they know that technology can enable them to visualize the results of varying assumptions, explore consequences, and compare predictions with data. Mathematically proficient students at various grade levels are able to identify relevant external mathematical resources, such as digital content located on a website, and use them to pose or solve problems. They are able to use technological tools to explore and deepen their understanding of concepts. Use previously learned knowledge about volume to choose the appropriate tools to solve volume problems. A cube with side length 1 unit, called a unit cube, is said to have one cubic unit of volume, and can be used to measure volume. A solid figure that can be packed without gaps or overlaps using n unit cubes is said to have a volume of n cubic units. Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units. Use appropriate tools strategically. Use appropriate tools strategically. Find volumes of solid figures composed of two nonoverlapping right rectangular prisms. Use appropriate tools strategically. Understand that the volume of a three dimensional figure can be found by counting the total number of same-sized cubic units that fill a shape without gaps or overlaps. Use cubic units to label volume measurements. 11-5: Interactive Additional Practice Step 3: Assess & Differentiate 11-5: Practice Buddy: Additional Practice Curriculum Standards: A cube with side length 1 unit, called a "unit cube," is said to have "one cubic unit" of volume, and can be used to measure volume. A solid figure that can be packed without gaps or overlaps using n unit cubes is said to have a volume of n cubic units. Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units. Use appropriate tools strategically. A cube with side length 1 unit, called a “unit cube,” is said to have “one cubic unit” of volume, and can be used to measure volume. Use appropriate tools strategically. A cube with side length 1 unit, called a “unit cube,” is said to have “one cubic unit” of volume, and can be used to measure volume. Use appropriate tools strategically. Mathematically proficient students consider the available tools when solving a mathematical problem. These tools might include pencil and paper, concrete models, a ruler, a protractor, a calculator, a spreadsheet, a computer algebra system, a statistical package, or dynamic geometry software. Proficient students are sufficiently familiar with tools appropriate for their grade or course to make sound decisions about when each of these tools might be helpful, recognizing both the insight to be gained and their limitations. For example, mathematically proficient high school students analyze graphs of functions and solutions generated using a graphing calculator. They detect possible errors by strategically using estimation and other mathematical knowledge. When making mathematical models, they know that technology can enable them to visualize the results of varying assumptions, explore consequences, and compare predictions with data. Mathematically proficient students at various grade levels are able to identify relevant external mathematical resources, such as digital content located on a website, and use them to pose or solve problems. They are able to use technological tools to explore and deepen their understanding of concepts. Use previously learned knowledge about volume to choose the appropriate tools to solve volume problems. A cube with side length 1 unit, called a unit cube, is said to have one cubic unit of volume, and can be used to measure volume. A solid figure that can be packed without gaps or overlaps using n unit cubes is said to have a volume of n cubic units. Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units. Use appropriate tools strategically. Use appropriate tools strategically. Find volumes of solid figures composed of two nonoverlapping right rectangular prisms. Use appropriate tools strategically. Understand that the volume of a three dimensional figure can be found by counting the total number of same-sized cubic units that fill a shape without gaps or overlaps. Use cubic units to label volume measurements. 11-5: Enrichment Curriculum Standards: A cube with side length 1 unit, called a "unit cube," is said to have "one cubic unit" of volume, and can be used to measure volume. A solid figure that can be packed without gaps or overlaps using n unit cubes is said to have a volume of n cubic units. Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units. Use appropriate tools strategically. A cube with side length 1 unit, called a “unit cube,” is said to have “one cubic unit” of volume, and can be used to measure volume. Use appropriate tools strategically. A cube with side length 1 unit, called a “unit cube,” is said to have “one cubic unit” of volume, and can be used to measure volume. Use appropriate tools strategically. Mathematically proficient students consider the available tools when solving a mathematical problem. These tools might include pencil and paper, concrete models, a ruler, a protractor, a calculator, a spreadsheet, a computer algebra system, a statistical package, or dynamic geometry software. Proficient students are sufficiently familiar with tools appropriate for their grade or course to make sound decisions about when each of these tools might be helpful, recognizing both the insight to be gained and their limitations. For example, mathematically proficient high school students analyze graphs of functions and solutions generated using a graphing calculator. They detect possible errors by strategically using estimation and other mathematical knowledge. When making mathematical models, they know that technology can enable them to visualize the results of varying assumptions, explore consequences, and compare predictions with data. Mathematically proficient students at various grade levels are able to identify relevant external mathematical resources, such as digital content located on a website, and use them to pose or solve problems. They are able to use technological tools to explore and deepen their understanding of concepts. Use previously learned knowledge about volume to choose the appropriate tools to solve volume problems. A cube with side length 1 unit, called a unit cube, is said to have one cubic unit of volume, and can be used to measure volume. A solid figure that can be packed without gaps or overlaps using n unit cubes is said to have a volume of n cubic units. Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units. Use appropriate tools strategically. Use appropriate tools strategically. Find volumes of solid figures composed of two nonoverlapping right rectangular prisms. Use appropriate tools strategically. Understand that the volume of a three dimensional figure can be found by counting the total number of same-sized cubic units that fill a shape without gaps or overlaps. Use cubic units to label volume measurements. 11-5: Quick Check Curriculum Standards: A cube with side length 1 unit, called a "unit cube," is said to have "one cubic unit" of volume, and can be used to measure volume. A solid figure that can be packed without gaps or overlaps using n unit cubes is said to have a volume of n cubic units. Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units. Use appropriate tools strategically. A cube with side length 1 unit, called a “unit cube,” is said to have “one cubic unit” of volume, and can be used to measure volume. Use appropriate tools strategically. A cube with side length 1 unit, called a “unit cube,” is said to have “one cubic unit” of volume, and can be used to measure volume. Use appropriate tools strategically. Mathematically proficient students consider the available tools when solving a mathematical problem. These tools might include pencil and paper, concrete models, a ruler, a protractor, a calculator, a spreadsheet, a computer algebra system, a statistical package, or dynamic geometry software. Proficient students are sufficiently familiar with tools appropriate for their grade or course to make sound decisions about when each of these tools might be helpful, recognizing both the insight to be gained and their limitations. For example, mathematically proficient high school students analyze graphs of functions and solutions generated using a graphing calculator. They detect possible errors by strategically using estimation and other mathematical knowledge. When making mathematical models, they know that technology can enable them to visualize the results of varying assumptions, explore consequences, and compare predictions with data. Mathematically proficient students at various grade levels are able to identify relevant external mathematical resources, such as digital content located on a website, and use them to pose or solve problems. They are able to use technological tools to explore and deepen their understanding of concepts. Use previously learned knowledge about volume to choose the appropriate tools to solve volume problems. A cube with side length 1 unit, called a unit cube, is said to have one cubic unit of volume, and can be used to measure volume. A solid figure that can be packed without gaps or overlaps using n unit cubes is said to have a volume of n cubic units. Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units. Use appropriate tools strategically. Use appropriate tools strategically. Find volumes of solid figures composed of two nonoverlapping right rectangular prisms. Use appropriate tools strategically. Understand that the volume of a three dimensional figure can be found by counting the total number of same-sized cubic units that fill a shape without gaps or overlaps. Use cubic units to label volume measurements. 11-5: Lesson Self-Assessment 11-5: Reteach to Build Understanding Curriculum Standards: A cube with side length 1 unit, called a "unit cube," is said to have "one cubic unit" of volume, and can be used to measure volume. A solid figure that can be packed without gaps or overlaps using n unit cubes is said to have a volume of n cubic units. Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units. Use appropriate tools strategically. A cube with side length 1 unit, called a “unit cube,” is said to have “one cubic unit” of volume, and can be used to measure volume. Use appropriate tools strategically. A cube with side length 1 unit, called a “unit cube,” is said to have “one cubic unit” of volume, and can be used to measure volume. Use appropriate tools strategically. Mathematically proficient students consider the available tools when solving a mathematical problem. These tools might include pencil and paper, concrete models, a ruler, a protractor, a calculator, a spreadsheet, a computer algebra system, a statistical package, or dynamic geometry software. Proficient students are sufficiently familiar with tools appropriate for their grade or course to make sound decisions about when each of these tools might be helpful, recognizing both the insight to be gained and their limitations. For example, mathematically proficient high school students analyze graphs of functions and solutions generated using a graphing calculator. They detect possible errors by strategically using estimation and other mathematical knowledge. When making mathematical models, they know that technology can enable them to visualize the results of varying assumptions, explore consequences, and compare predictions with data. Mathematically proficient students at various grade levels are able to identify relevant external mathematical resources, such as digital content located on a website, and use them to pose or solve problems. They are able to use technological tools to explore and deepen their understanding of concepts. Use previously learned knowledge about volume to choose the appropriate tools to solve volume problems. A cube with side length 1 unit, called a unit cube, is said to have one cubic unit of volume, and can be used to measure volume. A solid figure that can be packed without gaps or overlaps using n unit cubes is said to have a volume of n cubic units. Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units. Use appropriate tools strategically. Use appropriate tools strategically. Find volumes of solid figures composed of two nonoverlapping right rectangular prisms. Use appropriate tools strategically. Understand that the volume of a three dimensional figure can be found by counting the total number of same-sized cubic units that fill a shape without gaps or overlaps. Use cubic units to label volume measurements. Connect the layers to the dimensions and multiply to find the volume of the rectangular prism. 11-5: Build Mathematical Literacy Curriculum Standards: Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 5 topics and texts, building on others’ ideas and expressing their own clearly. (a) Come to discussions prepared, having read or studied required material; explicitly draw on that preparation and other information known about the topic to explore ideas under discussion. (b) Follow agreed-upon rules for discussions and carry out assigned roles. (c) Pose and respond to specific questions by making comments that contribute to the discussion and elaborate on the remarks of others. (d) Review the key ideas expressed and draw conclusions in light of information and knowledge gained from the discussions. English language learners communicate for social and instructional purposes within the school setting. Summarize a written text read aloud or information presented in diverse media and formats, including visually, quantitatively, and orally. Summarize the points a speaker makes and explain how each claim is supported by reasons and evidence. Write informative/explanatory texts to examine a topic and convey ideas and information clearly. (a) Introduce a topic clearly, provide a general observation and focus, and group related information logically; include formatting (e.g., headings), illustrations, and multimedia when useful to aiding comprehension. (b) Develop the topic with facts, definitions, concrete details, quotations, or other information and examples related to the topic. (c) Link ideas within and across categories of information using words, phrases, and clauses (e.g., in contrast, especially). (d) Use precise language and domain-specific vocabulary to inform about or explain the topic. (e) Provide a concluding statement or section related to the information or explanation presented. English language learners communicate information, ideas and concepts necessary for academic success in the content area of Mathematics. 11-5: Enrichment Game: Save the Word: Grade 5 Topics 1-8 11-5: Problem-Solving Reading Activity Curriculum Standards: A cube with side length 1 unit, called a "unit cube," is said to have "one cubic unit" of volume, and can be used to measure volume. A solid figure that can be packed without gaps or overlaps using n unit cubes is said to have a volume of n cubic units. Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units. Use appropriate tools strategically. A cube with side length 1 unit, called a “unit cube,” is said to have “one cubic unit” of volume, and can be used to measure volume. Use appropriate tools strategically. A cube with side length 1 unit, called a “unit cube,” is said to have “one cubic unit” of volume, and can be used to measure volume. Use appropriate tools strategically. Mathematically proficient students consider the available tools when solving a mathematical problem. These tools might include pencil and paper, concrete models, a ruler, a protractor, a calculator, a spreadsheet, a computer algebra system, a statistical package, or dynamic geometry software. Proficient students are sufficiently familiar with tools appropriate for their grade or course to make sound decisions about when each of these tools might be helpful, recognizing both the insight to be gained and their limitations. For example, mathematically proficient high school students analyze graphs of functions and solutions generated using a graphing calculator. They detect possible errors by strategically using estimation and other mathematical knowledge. When making mathematical models, they know that technology can enable them to visualize the results of varying assumptions, explore consequences, and compare predictions with data. Mathematically proficient students at various grade levels are able to identify relevant external mathematical resources, such as digital content located on a website, and use them to pose or solve problems. They are able to use technological tools to explore and deepen their understanding of concepts. Use previously learned knowledge about volume to choose the appropriate tools to solve volume problems. A cube with side length 1 unit, called a unit cube, is said to have one cubic unit of volume, and can be used to measure volume. A solid figure that can be packed without gaps or overlaps using n unit cubes is said to have a volume of n cubic units. Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units. Use appropriate tools strategically. Use appropriate tools strategically. Find volumes of solid figures composed of two nonoverlapping right rectangular prisms. Use appropriate tools strategically. Understand that the volume of a three dimensional figure can be found by counting the total number of same-sized cubic units that fill a shape without gaps or overlaps. Use cubic units to label volume measurements. 11-5: Another Look Curriculum Standards: A cube with side length 1 unit, called a "unit cube," is said to have "one cubic unit" of volume, and can be used to measure volume. A solid figure that can be packed without gaps or overlaps using n unit cubes is said to have a volume of n cubic units. Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units. Use appropriate tools strategically. A cube with side length 1 unit, called a “unit cube,” is said to have “one cubic unit” of volume, and can be used to measure volume. Use appropriate tools strategically. A cube with side length 1 unit, called a “unit cube,” is said to have “one cubic unit” of volume, and can be used to measure volume. Use appropriate tools strategically. Mathematically proficient students consider the available tools when solving a mathematical problem. These tools might include pencil and paper, concrete models, a ruler, a protractor, a calculator, a spreadsheet, a computer algebra system, a statistical package, or dynamic geometry software. Proficient students are sufficiently familiar with tools appropriate for their grade or course to make sound decisions about when each of these tools might be helpful, recognizing both the insight to be gained and their limitations. For example, mathematically proficient high school students analyze graphs of functions and solutions generated using a graphing calculator. They detect possible errors by strategically using estimation and other mathematical knowledge. When making mathematical models, they know that technology can enable them to visualize the results of varying assumptions, explore consequences, and compare predictions with data. Mathematically proficient students at various grade levels are able to identify relevant external mathematical resources, such as digital content located on a website, and use them to pose or solve problems. They are able to use technological tools to explore and deepen their understanding of concepts. Use previously learned knowledge about volume to choose the appropriate tools to solve volume problems. A cube with side length 1 unit, called a unit cube, is said to have one cubic unit of volume, and can be used to measure volume. A solid figure that can be packed without gaps or overlaps using n unit cubes is said to have a volume of n cubic units. Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units. Use appropriate tools strategically. Use appropriate tools strategically. Find volumes of solid figures composed of two nonoverlapping right rectangular prisms. Use appropriate tools strategically. Understand that the volume of a three dimensional figure can be found by counting the total number of same-sized cubic units that fill a shape without gaps or overlaps. Use cubic units to label volume measurements. Connect the layers to the dimensions and multiply to find the volume of the rectangular prism. Spanish Resources 11-5: eText del Libro del estudiante 11-5: Repaso diario 11-5: Aprendizaje visual 11-5: Amigo de práctica: Práctica adicional 11-5: Práctica adicional interactiva 11-5: Refuerzo para mejorar la comprensión 11-5: Desarrollar la competencia matemática 11-5: Ampliación Topic 11: End of Topic Interactive Student Edition: End of Topic 11 Topic 11: Fluency Practice Activity Interactive Student Edition: Topic 11 Assessment Practice Interactive Student Edition: Topic 11 Performance Task Topic 11 Performance Task Topic 11 Assessment 11-2 Center Games 11-1: Visual Learning Curriculum Standards: A cube with side length 1 unit, called a "unit cube," is said to have "one cubic unit" of volume, and can be used to measure volume. A solid figure that can be packed without gaps or overlaps using n unit cubes is said to have a volume of n cubic units. Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units. A cube with side length 1 unit, called a “unit cube,” is said to have “one cubic unit” of volume, and can be used to measure volume. A solid figure which can be packed without gaps or overlaps using n unit cubes is said to have a volume of n cubic units. Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units. A cube with side length 1 unit, called a “unit cube,” is said to have “one cubic unit” of volume, and can be used to measure volume. A solid figure which can be packed without gaps or overlaps using n unit cubes is said to have a volume of n cubic units. Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units. Find the volume of solid figures. A cube with side length 1 unit, called a unit cube, is said to have one cubic unit of volume, and can be used to measure volume. A solid figure that can be packed without gaps or overlaps using n unit cubes is said to have a volume of n cubic units. Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units. 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. Formulas will be provided. Use various tools and strategies to measure the volume and surface area of objects that are shaped like rectangular prisms. Understand that the volume of a three dimensional figure can be found by counting the total number of same-sized cubic units that fill a shape without gaps or overlaps. Use cubic units to label volume measurements. 11-2: Visual Learning Curriculum Standards: Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units. 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. 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. 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. 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. 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. 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. Find the volume of rectangular prisms using a formula. Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units. 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. 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. 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. Formulas will be provided. 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. Apply the commutative, associative and distributive properties and order of operations to generate equivalent numerical expressions and to solve problems involving whole numbers. Use various tools and strategies to measure the volume and surface area of objects that are shaped like rectangular prisms. Understand that the volume of a three dimensional figure can be found by counting the total number of same-sized cubic units that fill a shape without gaps or overlaps. Use cubic units to label volume measurements. Develop and use the formulas V = ?wh and V = Bh to determine the volume of rectangular prisms. Justify why base area B and height h are multiplied to find the volume of a ectangular prism by breaking the prism into layers of unit cubes. 11-3: Visual Learning Curriculum Standards: Recognize volume as additive. 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. Recognize volume as additive. 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. Recognize volume as additive. 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. Find the volume of a solid figure that is the combination of two or more rectangular prisms. Recognize volume as additive. 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. Find volumes of solid figures composed of two nonoverlapping right rectangular prisms. 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. Use various tools and strategies to measure the volume and surface area of objects that are shaped like rectangular prisms. Understand that the volume of a three dimensional figure can be found by counting the total number of same-sized cubic units that fill a shape without gaps or overlaps. Use cubic units to label volume measurements. Develop and use the formulas V = ?wh and V = Bh to determine the volume of rectangular prisms. Justify why base area B and height h are multiplied to find the volume of a ectangular prism by breaking the prism into layers of unit cubes. 11-4: Visual Learning Curriculum Standards: Recognize volume as additive. 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. Recognize volume as additive. 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. Recognize volume as additive. 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. Use models, prior knowledge of volume and previously learned strategies to solve word problems involving volume. Recognize volume as additive. 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. Find volumes of solid figures composed of two nonoverlapping right rectangular prisms. 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. Use various tools and strategies to measure the volume and surface area of objects that are shaped like rectangular prisms. Understand that the volume of a three dimensional figure can be found by counting the total number of same-sized cubic units that fill a shape without gaps or overlaps. Use cubic units to label volume measurements. Develop and use the formulas V = ?wh and V = Bh to determine the volume of rectangular prisms. Justify why base area B and height h are multiplied to find the volume of a ectangular prism by breaking the prism into layers of unit cubes. Topic 11 Online Assessment Curriculum Standards: Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units. 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. 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. A cube with side length 1 unit, called a "unit cube," is said to have "one cubic unit" of volume, and can be used to measure volume. A solid figure that can be packed without gaps or overlaps using n unit cubes is said to have a volume of n cubic units. Recognize volume as additive. 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. 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. 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. 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. 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. Find the volume of rectangular prisms using a formula. Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units. 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. 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. 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. Formulas will be provided. 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. Apply the commutative, associative and distributive properties and order of operations to generate equivalent numerical expressions and to solve problems involving whole numbers. Use various tools and strategies to measure the volume and surface area of objects that are shaped like rectangular prisms. Understand that the volume of a three dimensional figure can be found by counting the total number of same-sized cubic units that fill a shape without gaps or overlaps. Use cubic units to label volume measurements. Develop and use the formulas V = ?wh and V = Bh to determine the volume of rectangular prisms. Justify why base area B and height h are multiplied to find the volume of a ectangular prism by breaking the prism into layers of unit cubes. A cube with side length 1 unit, called a “unit cube,” is said to have “one cubic unit” of volume, and can be used to measure volume. A solid figure which can be packed without gaps or overlaps using n unit cubes is said to have a volume of n cubic units. Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units. A cube with side length 1 unit, called a “unit cube,” is said to have “one cubic unit” of volume, and can be used to measure volume. A solid figure which can be packed without gaps or overlaps using n unit cubes is said to have a volume of n cubic units. Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units. Find the volume of solid figures. A cube with side length 1 unit, called a unit cube, is said to have one cubic unit of volume, and can be used to measure volume. A solid figure that can be packed without gaps or overlaps using n unit cubes is said to have a volume of n cubic units. Recognize volume as additive. 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. Recognize volume as additive. 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. Use models, prior knowledge of volume and previously learned strategies to solve word problems involving volume. Recognize volume as additive. 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. Find volumes of solid figures composed of two nonoverlapping right rectangular prisms. Find the volume of a solid figure that is the combination of two or more rectangular prisms. Topic 11 Spanish Assessments Tema 11: Tarea de rendimento Tema 11: Evaluación Topic 12: Convert Measurements Topic 12: Today's Challenge Topic 12: Beginning of Topic Interactive Student Edition: Beginning of Topic 12 Topic 12: enVision STEM Activity Grade 5 Topic 12: Review What You Know Topic 12: Vocabulary Cards 12-1: Convert Customary Units of Length Interactive Student Edition: Grade 5 Lesson 12-1 Math Anytime 12-1: Daily Review Topic 12: Today's Challenge Step 1: Problem-Based Learning 12-1: Solve & Share Curriculum Standards: Fluently multiply multi-digit whole numbers using the standard algorithm. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. English language learners communicate for social and instructional purposes within the school setting. Write informative/explanatory texts to examine a topic and convey ideas and information clearly. (a) Introduce a topic clearly, provide a general observation and focus, and group related information logically; include formatting (e.g., headings), illustrations, and multimedia when useful to aiding comprehension. (b) Develop the topic with facts, definitions, concrete details, quotations, or other information and examples related to the topic. (c) Link ideas within and across categories of information using words, phrases, and clauses (e.g., in contrast, especially). (d) Use precise language and domain-specific vocabulary to inform about or explain the topic. (e) Provide a concluding statement or section related to the information or explanation presented. English language learners communicate information, ideas and concepts necessary for academic success in the content area of Mathematics. Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 5 topics and texts, building on others’ ideas and expressing their own clearly. (a) Come to discussions prepared, having read or studied required material; explicitly draw on that preparation and other information known about the topic to explore ideas under discussion. (b) Follow agreed-upon rules for discussions and carry out assigned roles. (c) Pose and respond to specific questions by making comments that contribute to the discussion and elaborate on the remarks of others. (d) Review the key ideas expressed and draw conclusions in light of information and knowledge gained from the discussions. Fluently multiply multi-digit whole numbers using the standard algorithm. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Convert among different-sized standard measurement units (i.e., km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec) within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Fluently multiply multi-digit whole numbers using the standard algorithm. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Convert among different-sized standard measurement units (i.e., km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec) within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Convert customary units of length. Convert among different- sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Convert between different-sized measurement units within a given measurement system. A table of equivalencies will be provided. Divide multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Recognize that quotients can be represented in a variety of ways, including a whole number with a remainder, a fraction or mixed number, or a decimal. Consider the context in which a problem is situated to select the most useful form of the quotient for the solution and use the context to interpret the quotient appropriately. 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. Summarize a written text read aloud or information presented in diverse media and formats, including visually, quantitatively, and orally. Summarize the points a speaker makes and explain how each claim is supported by reasons and evidence. Step 2: Visual Learning 12-1: Visual Learning Curriculum Standards: Fluently multiply multi-digit whole numbers using the standard algorithm. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Convert standard measurements of length to solve real-world problems. Fluently multiply multi-digit whole numbers using the standard algorithm. Find whole- number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Convert among different-sized standard measurement units (i.e., km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec) within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Fluently multiply multi-digit whole numbers using the standard algorithm. Find whole-number quotients of whole numbers with up to four- digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Convert among different-sized standard measurement units (i.e., km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec) within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Convert customary units of length. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Convert between different-sized measurement units within a given measurement system. A table of equivalencies will be provided. Divide multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Recognize that quotients can be represented in a variety of ways, including a whole number with a remainder, a fraction or mixed number, or a decimal. Consider the context in which a problem is situated to select the most useful form of the quotient for the solution and use the context to interpret the quotient appropriately. 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. 12-1: Convince Me! Curriculum Standards: Fluently multiply multi-digit whole numbers using the standard algorithm. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Fluently multiply multi-digit whole numbers using the standard algorithm. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Convert among different-sized standard measurement units (i.e., km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec) within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Fluently multiply multi- digit whole numbers using the standard algorithm. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Convert among different-sized standard measurement units (i.e., km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec) within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Convert customary units of length. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Convert between different-sized measurement units within a given measurement system. A table of equivalencies will be provided. Divide multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Recognize that quotients can be represented in a variety of ways, including a whole number with a remainder, a fraction or mixed number, or a decimal. Consider the context in which a problem is situated to select the most useful form of the quotient for the solution and use the context to interpret the quotient appropriately. 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. Practice and Problem Solving 12-1: Student Edition Practice Curriculum Standards: Fluently multiply multi-digit whole numbers using the standard algorithm. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Fluently multiply multi-digit whole numbers using the standard algorithm. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Convert among different-sized standard measurement units (i.e., km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec) within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Fluently multiply multi- digit whole numbers using the standard algorithm. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Convert among different-sized standard measurement units (i.e., km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec) within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Convert customary units of length. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Convert between different-sized measurement units within a given measurement system. A table of equivalencies will be provided. Divide multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Recognize that quotients can be represented in a variety of ways, including a whole number with a remainder, a fraction or mixed number, or a decimal. Consider the context in which a problem is situated to select the most useful form of the quotient for the solution and use the context to interpret the quotient appropriately. 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. 12-1: Practice Buddy: Independent Practice; Problem Solving Curriculum Standards: Fluently multiply multi-digit whole numbers using the standard algorithm. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Fluently multiply multi-digit whole numbers using the standard algorithm. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Convert among different-sized standard measurement units (i.e., km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec) within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Fluently multiply multi- digit whole numbers using the standard algorithm. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Convert among different-sized standard measurement units (i.e., km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec) within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Convert customary units of length. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Convert between different-sized measurement units within a given measurement system. A table of equivalencies will be provided. Divide multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Recognize that quotients can be represented in a variety of ways, including a whole number with a remainder, a fraction or mixed number, or a decimal. Consider the context in which a problem is situated to select the most useful form of the quotient for the solution and use the context to interpret the quotient appropriately. 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. 12-1: Practice Buddy: Additional Practice Curriculum Standards: Fluently multiply multi-digit whole numbers using the standard algorithm. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Fluently multiply multi-digit whole numbers using the standard algorithm. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Convert among different-sized standard measurement units (i.e., km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec) within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Fluently multiply multi- digit whole numbers using the standard algorithm. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Convert among different-sized standard measurement units (i.e., km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec) within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Convert customary units of length. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Convert between different-sized measurement units within a given measurement system. A table of equivalencies will be provided. Divide multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Recognize that quotients can be represented in a variety of ways, including a whole number with a remainder, a fraction or mixed number, or a decimal. Consider the context in which a problem is situated to select the most useful form of the quotient for the solution and use the context to interpret the quotient appropriately. 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. 12-1: Interactive Additional Practice Step 3: Assess & Differentiate 12-1: Practice Buddy: Additional Practice Curriculum Standards: Fluently multiply multi-digit whole numbers using the standard algorithm. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Fluently multiply multi-digit whole numbers using the standard algorithm. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Convert among different-sized standard measurement units (i.e., km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec) within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Fluently multiply multi- digit whole numbers using the standard algorithm. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Convert among different-sized standard measurement units (i.e., km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec) within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Convert customary units of length. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Convert between different-sized measurement units within a given measurement system. A table of equivalencies will be provided. Divide multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Recognize that quotients can be represented in a variety of ways, including a whole number with a remainder, a fraction or mixed number, or a decimal. Consider the context in which a problem is situated to select the most useful form of the quotient for the solution and use the context to interpret the quotient appropriately. 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. 12-1: Enrichment Curriculum Standards: Fluently multiply multi-digit whole numbers using the standard algorithm. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Fluently multiply multi-digit whole numbers using the standard algorithm. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Convert among different-sized standard measurement units (i.e., km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec) within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Fluently multiply multi- digit whole numbers using the standard algorithm. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Convert among different-sized standard measurement units (i.e., km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec) within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Convert customary units of length. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Convert between different-sized measurement units within a given measurement system. A table of equivalencies will be provided. Divide multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Recognize that quotients can be represented in a variety of ways, including a whole number with a remainder, a fraction or mixed number, or a decimal. Consider the context in which a problem is situated to select the most useful form of the quotient for the solution and use the context to interpret the quotient appropriately. 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. 12-1: Quick Check Curriculum Standards: Fluently multiply multi-digit whole numbers using the standard algorithm. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Fluently multiply multi-digit whole numbers using the standard algorithm. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Convert among different-sized standard measurement units (i.e., km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec) within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Fluently multiply multi- digit whole numbers using the standard algorithm. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Convert among different-sized standard measurement units (i.e., km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec) within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Convert customary units of length. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Convert between different-sized measurement units within a given measurement system. A table of equivalencies will be provided. Divide multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Recognize that quotients can be represented in a variety of ways, including a whole number with a remainder, a fraction or mixed number, or a decimal. Consider the context in which a problem is situated to select the most useful form of the quotient for the solution and use the context to interpret the quotient appropriately. 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. 12-1: Lesson Self-Assessment 12-1: Reteach to Build Understanding Curriculum Standards: Fluently multiply multi-digit whole numbers using the standard algorithm. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Convert standard measurements of length to solve real-world problems. Fluently multiply multi-digit whole numbers using the standard algorithm. Find whole- number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Convert among different-sized standard measurement units (i.e., km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec) within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Fluently multiply multi-digit whole numbers using the standard algorithm. Find whole-number quotients of whole numbers with up to four- digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Convert among different-sized standard measurement units (i.e., km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec) within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Convert customary units of length. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Convert between different-sized measurement units within a given measurement system. A table of equivalencies will be provided. Divide multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Recognize that quotients can be represented in a variety of ways, including a whole number with a remainder, a fraction or mixed number, or a decimal. Consider the context in which a problem is situated to select the most useful form of the quotient for the solution and use the context to interpret the quotient appropriately. 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. 12-1: Build Mathematical Literacy Curriculum Standards: Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 5 topics and texts, building on others’ ideas and expressing their own clearly. (a) Come to discussions prepared, having read or studied required material; explicitly draw on that preparation and other information known about the topic to explore ideas under discussion. (b) Follow agreed-upon rules for discussions and carry out assigned roles. (c) Pose and respond to specific questions by making comments that contribute to the discussion and elaborate on the remarks of others. (d) Review the key ideas expressed and draw conclusions in light of information and knowledge gained from the discussions. English language learners communicate for social and instructional purposes within the school setting. Summarize a written text read aloud or information presented in diverse media and formats, including visually, quantitatively, and orally. Summarize the points a speaker makes and explain how each claim is supported by reasons and evidence. Write informative/explanatory texts to examine a topic and convey ideas and information clearly. (a) Introduce a topic clearly, provide a general observation and focus, and group related information logically; include formatting (e.g., headings), illustrations, and multimedia when useful to aiding comprehension. (b) Develop the topic with facts, definitions, concrete details, quotations, or other information and examples related to the topic. (c) Link ideas within and across categories of information using words, phrases, and clauses (e.g., in contrast, especially). (d) Use precise language and domain-specific vocabulary to inform about or explain the topic. (e) Provide a concluding statement or section related to the information or explanation presented. English language learners communicate information, ideas and concepts necessary for academic success in the content area of Mathematics. 12-1: Enrichment 12-1: Digital Math Tool Activity 12-1 enVision STEM Activity Curriculum Standards: Fluently multiply multi-digit whole numbers using the standard algorithm. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Fluently multiply multi-digit whole numbers using the standard algorithm. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Convert among different-sized standard measurement units (i.e., km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec) within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Fluently multiply multi- digit whole numbers using the standard algorithm. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Convert among different-sized standard measurement units (i.e., km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec) within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Convert customary units of length. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Convert between different-sized measurement units within a given measurement system. A table of equivalencies will be provided. Divide multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Recognize that quotients can be represented in a variety of ways, including a whole number with a remainder, a fraction or mixed number, or a decimal. Consider the context in which a problem is situated to select the most useful form of the quotient for the solution and use the context to interpret the quotient appropriately. 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. 12-1: Another Look Curriculum Standards: Fluently multiply multi-digit whole numbers using the standard algorithm. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Convert standard measurements of length to solve real-world problems. Fluently multiply multi-digit whole numbers using the standard algorithm. Find whole- number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Convert among different-sized standard measurement units (i.e., km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec) within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Fluently multiply multi-digit whole numbers using the standard algorithm. Find whole-number quotients of whole numbers with up to four- digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Convert among different-sized standard measurement units (i.e., km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec) within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Convert customary units of length. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Convert between different-sized measurement units within a given measurement system. A table of equivalencies will be provided. Divide multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Recognize that quotients can be represented in a variety of ways, including a whole number with a remainder, a fraction or mixed number, or a decimal. Consider the context in which a problem is situated to select the most useful form of the quotient for the solution and use the context to interpret the quotient appropriately. 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. Spanish Resources 12-1: eText del Libro del estudiante 12-1: Repaso diario 12-1: Aprendizaje visual 12-1: Amigo de práctica: Práctica adicional 12-1: Práctica adicional interactiva 12-1: Refuerzo para mejorar la comprensión 12-1: Desarrollar la competencia matemática 12-1: Ampliación 12-2: Convert Customary Units of Capacity Interactive Student Edition: Grade 5 Lesson 12-2 Math Anytime 12-2: Daily Review Topic 12: Today's Challenge Step 1: Problem-Based Learning 12-2: Solve & Share Curriculum Standards: Fluently multiply multi-digit whole numbers using the standard algorithm. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. English language learners communicate for social and instructional purposes within the school setting. Write informative/explanatory texts to examine a topic and convey ideas and information clearly. (a) Introduce a topic clearly, provide a general observation and focus, and group related information logically; include formatting (e.g., headings), illustrations, and multimedia when useful to aiding comprehension. (b) Develop the topic with facts, definitions, concrete details, quotations, or other information and examples related to the topic. (c) Link ideas within and across categories of information using words, phrases, and clauses (e.g., in contrast, especially). (d) Use precise language and domain-specific vocabulary to inform about or explain the topic. (e) Provide a concluding statement or section related to the information or explanation presented. English language learners communicate information, ideas and concepts necessary for academic success in the content area of Mathematics. Fluently multiply multi-digit whole numbers using the standard algorithm. Find whole- number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Convert among different-sized standard measurement units (i.e., km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec) within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Fluently multiply multi-digit whole numbers using the standard algorithm. Find whole-number quotients of whole numbers with up to four- digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Convert among different-sized standard measurement units (i.e., km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec) within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Convert customary units of capacity. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Convert between different-sized measurement units within a given measurement system. A table of equivalencies will be provided. Divide multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Recognize that quotients can be represented in a variety of ways, including a whole number with a remainder, a fraction or mixed number, or a decimal. Consider the context in which a problem is situated to select the most useful form of the quotient for the solution and use the context to interpret the quotient appropriately. 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. Engage effectively in a range of collaborative discussions (one-on- one, in groups, and teacher-led) with diverse partners on grade 5 topics and texts, building on others’ ideas and expressing their own clearly. (a) Come to discussions prepared, having read or studied required material; explicitly draw on that preparation and other information known about the topic to explore ideas under discussion. (b) Follow agreed-upon rules for discussions and carry out assigned roles. (c) Pose and respond to specific questions by making comments that contribute to the discussion and elaborate on the remarks of others. (d) Review the key ideas expressed and draw conclusions in light of information and knowledge gained from the discussions. Summarize a written text read aloud or information presented in diverse media and formats, including visually, quantitatively, and orally. Summarize the points a speaker makes and explain how each claim is supported by reasons and evidence. Step 2: Visual Learning 12-2: Visual Learning Curriculum Standards: Fluently multiply multi-digit whole numbers using the standard algorithm. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Fluently multiply multi-digit whole numbers using the standard algorithm. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Convert among different-sized standard measurement units (i.e., km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec) within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Fluently multiply multi- digit whole numbers using the standard algorithm. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Convert among different-sized standard measurement units (i.e., km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec) within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Convert customary units of capacity. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Convert between different-sized measurement units within a given measurement system. A table of equivalencies will be provided. Divide multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Recognize that quotients can be represented in a variety of ways, including a whole number with a remainder, a fraction or mixed number, or a decimal. Consider the context in which a problem is situated to select the most useful form of the quotient for the solution and use the context to interpret the quotient appropriately. 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. 12-2: Convince Me! Curriculum Standards: Fluently multiply multi-digit whole numbers using the standard algorithm. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Fluently multiply multi-digit whole numbers using the standard algorithm. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Convert among different-sized standard measurement units (i.e., km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec) within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Fluently multiply multi- digit whole numbers using the standard algorithm. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Convert among different-sized standard measurement units (i.e., km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec) within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Convert customary units of capacity. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Convert between different-sized measurement units within a given measurement system. A table of equivalencies will be provided. Divide multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Recognize that quotients can be represented in a variety of ways, including a whole number with a remainder, a fraction or mixed number, or a decimal. Consider the context in which a problem is situated to select the most useful form of the quotient for the solution and use the context to interpret the quotient appropriately. 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. Practice and Problem Solving 12-2: Student Edition Practice Curriculum Standards: Fluently multiply multi-digit whole numbers using the standard algorithm. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Fluently multiply multi-digit whole numbers using the standard algorithm. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Convert among different-sized standard measurement units (i.e., km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec) within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Fluently multiply multi- digit whole numbers using the standard algorithm. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Convert among different-sized standard measurement units (i.e., km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec) within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Convert customary units of capacity. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Convert between different-sized measurement units within a given measurement system. A table of equivalencies will be provided. Divide multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Recognize that quotients can be represented in a variety of ways, including a whole number with a remainder, a fraction or mixed number, or a decimal. Consider the context in which a problem is situated to select the most useful form of the quotient for the solution and use the context to interpret the quotient appropriately. 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. 12-2: Practice Buddy: Independent Practice; Problem Solving Curriculum Standards: Fluently multiply multi-digit whole numbers using the standard algorithm. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Fluently multiply multi-digit whole numbers using the standard algorithm. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Convert among different-sized standard measurement units (i.e., km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec) within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Fluently multiply multi- digit whole numbers using the standard algorithm. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Convert among different-sized standard measurement units (i.e., km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec) within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Convert customary units of capacity. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Convert between different-sized measurement units within a given measurement system. A table of equivalencies will be provided. Divide multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Recognize that quotients can be represented in a variety of ways, including a whole number with a remainder, a fraction or mixed number, or a decimal. Consider the context in which a problem is situated to select the most useful form of the quotient for the solution and use the context to interpret the quotient appropriately. 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. 12-2: Practice Buddy: Additional Practice Curriculum Standards: Fluently multiply multi-digit whole numbers using the standard algorithm. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Fluently multiply multi-digit whole numbers using the standard algorithm. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Convert among different-sized standard measurement units (i.e., km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec) within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Fluently multiply multi- digit whole numbers using the standard algorithm. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Convert among different-sized standard measurement units (i.e., km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec) within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Convert customary units of capacity. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Convert between different-sized measurement units within a given measurement system. A table of equivalencies will be provided. Divide multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Recognize that quotients can be represented in a variety of ways, including a whole number with a remainder, a fraction or mixed number, or a decimal. Consider the context in which a problem is situated to select the most useful form of the quotient for the solution and use the context to interpret the quotient appropriately. 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. 12-2: Interactive Additional Practice Step 3: Assess & Differentiate 12-2: Practice Buddy: Additional Practice Curriculum Standards: Fluently multiply multi-digit whole numbers using the standard algorithm. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Fluently multiply multi-digit whole numbers using the standard algorithm. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Convert among different-sized standard measurement units (i.e., km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec) within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Fluently multiply multi- digit whole numbers using the standard algorithm. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Convert among different-sized standard measurement units (i.e., km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec) within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Convert customary units of capacity. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Convert between different-sized measurement units within a given measurement system. A table of equivalencies will be provided. Divide multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Recognize that quotients can be represented in a variety of ways, including a whole number with a remainder, a fraction or mixed number, or a decimal. Consider the context in which a problem is situated to select the most useful form of the quotient for the solution and use the context to interpret the quotient appropriately. 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. 12-2: Enrichment Curriculum Standards: Fluently multiply multi-digit whole numbers using the standard algorithm. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Fluently multiply multi-digit whole numbers using the standard algorithm. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Convert among different-sized standard measurement units (i.e., km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec) within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Fluently multiply multi- digit whole numbers using the standard algorithm. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Convert among different-sized standard measurement units (i.e., km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec) within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Convert customary units of capacity. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Convert between different-sized measurement units within a given measurement system. A table of equivalencies will be provided. Divide multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Recognize that quotients can be represented in a variety of ways, including a whole number with a remainder, a fraction or mixed number, or a decimal. Consider the context in which a problem is situated to select the most useful form of the quotient for the solution and use the context to interpret the quotient appropriately. 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. 12-2: Quick Check Curriculum Standards: Fluently multiply multi-digit whole numbers using the standard algorithm. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Fluently multiply multi-digit whole numbers using the standard algorithm. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Convert among different-sized standard measurement units (i.e., km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec) within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Fluently multiply multi- digit whole numbers using the standard algorithm. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Convert among different-sized standard measurement units (i.e., km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec) within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Convert customary units of capacity. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Convert between different-sized measurement units within a given measurement system. A table of equivalencies will be provided. Divide multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Recognize that quotients can be represented in a variety of ways, including a whole number with a remainder, a fraction or mixed number, or a decimal. Consider the context in which a problem is situated to select the most useful form of the quotient for the solution and use the context to interpret the quotient appropriately. 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. 12-2: Lesson Self-Assessment 12-2: Reteach to Build Understanding Curriculum Standards: Fluently multiply multi-digit whole numbers using the standard algorithm. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Fluently multiply multi-digit whole numbers using the standard algorithm. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Convert among different-sized standard measurement units (i.e., km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec) within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Fluently multiply multi- digit whole numbers using the standard algorithm. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Convert among different-sized standard measurement units (i.e., km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec) within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Convert customary units of capacity. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Convert between different-sized measurement units within a given measurement system. A table of equivalencies will be provided. Divide multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Recognize that quotients can be represented in a variety of ways, including a whole number with a remainder, a fraction or mixed number, or a decimal. Consider the context in which a problem is situated to select the most useful form of the quotient for the solution and use the context to interpret the quotient appropriately. 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. 12-2: Build Mathematical Literacy Curriculum Standards: Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 5 topics and texts, building on others’ ideas and expressing their own clearly. (a) Come to discussions prepared, having read or studied required material; explicitly draw on that preparation and other information known about the topic to explore ideas under discussion. (b) Follow agreed-upon rules for discussions and carry out assigned roles. (c) Pose and respond to specific questions by making comments that contribute to the discussion and elaborate on the remarks of others. (d) Review the key ideas expressed and draw conclusions in light of information and knowledge gained from the discussions. English language learners communicate for social and instructional purposes within the school setting. Summarize a written text read aloud or information presented in diverse media and formats, including visually, quantitatively, and orally. Summarize the points a speaker makes and explain how each claim is supported by reasons and evidence. Write informative/explanatory texts to examine a topic and convey ideas and information clearly. (a) Introduce a topic clearly, provide a general observation and focus, and group related information logically; include formatting (e.g., headings), illustrations, and multimedia when useful to aiding comprehension. (b) Develop the topic with facts, definitions, concrete details, quotations, or other information and examples related to the topic. (c) Link ideas within and across categories of information using words, phrases, and clauses (e.g., in contrast, especially). (d) Use precise language and domain-specific vocabulary to inform about or explain the topic. (e) Provide a concluding statement or section related to the information or explanation presented. English language learners communicate information, ideas and concepts necessary for academic success in the content area of Mathematics. 12-2: Enrichment 12-2: Digital Math Tool Activity 12-2: Pick a Project 12-2: Another Look Curriculum Standards: Fluently multiply multi-digit whole numbers using the standard algorithm. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Fluently multiply multi-digit whole numbers using the standard algorithm. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Convert among different-sized standard measurement units (i.e., km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec) within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Fluently multiply multi- digit whole numbers using the standard algorithm. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Convert among different-sized standard measurement units (i.e., km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec) within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Convert customary units of capacity. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Convert between different-sized measurement units within a given measurement system. A table of equivalencies will be provided. Divide multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Recognize that quotients can be represented in a variety of ways, including a whole number with a remainder, a fraction or mixed number, or a decimal. Consider the context in which a problem is situated to select the most useful form of the quotient for the solution and use the context to interpret the quotient appropriately. 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. Spanish Resources 12-2: eText del Libro del estudiante 12-2: Repaso diario 12-2: Aprendizaje visual 12-2: Amigo de práctica: Práctica adicional 12-2: Práctica adicional interactiva 12-2: Refuerzo para mejorar la comprensión 12-2: Desarrollar la competencia matemática 12-2: Ampliación 12-3: Convert Customary Units of Weight Interactive Student Edition: Grade 5 Lesson 12-3 Math Anytime 12-3: Daily Review Topic 12: Today's Challenge Step 1: Problem-Based Learning 12-3: Solve & Share Curriculum Standards: Fluently multiply multi-digit whole numbers using the standard algorithm. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. English language learners communicate for social and instructional purposes within the school setting. Write informative/explanatory texts to examine a topic and convey ideas and information clearly. (a) Introduce a topic clearly, provide a general observation and focus, and group related information logically; include formatting (e.g., headings), illustrations, and multimedia when useful to aiding comprehension. (b) Develop the topic with facts, definitions, concrete details, quotations, or other information and examples related to the topic. (c) Link ideas within and across categories of information using words, phrases, and clauses (e.g., in contrast, especially). (d) Use precise language and domain-specific vocabulary to inform about or explain the topic. (e) Provide a concluding statement or section related to the information or explanation presented. English language learners communicate information, ideas and concepts necessary for academic success in the content area of Mathematics. Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 5 topics and texts, building on others’ ideas and expressing their own clearly. (a) Come to discussions prepared, having read or studied required material; explicitly draw on that preparation and other information known about the topic to explore ideas under discussion. (b) Follow agreed-upon rules for discussions and carry out assigned roles. (c) Pose and respond to specific questions by making comments that contribute to the discussion and elaborate on the remarks of others. (d) Review the key ideas expressed and draw conclusions in light of information and knowledge gained from the discussions. Summarize a written text read aloud or information presented in diverse media and formats, including visually, quantitatively, and orally. Summarize the points a speaker makes and explain how each claim is supported by reasons and evidence. Fluently multiply multi-digit whole numbers using the standard algorithm. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Convert among different-sized standard measurement units (i.e., km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec) within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Fluently multiply multi-digit whole numbers using the standard algorithm. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Convert among different-sized standard measurement units (i.e., km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec) within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Convert customary units of weight. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Convert between different-sized measurement units within a given measurement system. A table of equivalencies will be provided. Divide multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Recognize that quotients can be represented in a variety of ways, including a whole number with a remainder, a fraction or mixed number, or a decimal. Consider the context in which a problem is situated to select the most useful form of the quotient for the solution and use the context to interpret the quotient appropriately. 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. Step 2: Visual Learning 12-3: Visual Learning Curriculum Standards: Fluently multiply multi-digit whole numbers using the standard algorithm. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Fluently multiply multi-digit whole numbers using the standard algorithm. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Convert among different-sized standard measurement units (i.e., km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec) within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Fluently multiply multi- digit whole numbers using the standard algorithm. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Convert among different-sized standard measurement units (i.e., km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec) within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Convert customary units of weight. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Convert between different-sized measurement units within a given measurement system. A table of equivalencies will be provided. Divide multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Recognize that quotients can be represented in a variety of ways, including a whole number with a remainder, a fraction or mixed number, or a decimal. Consider the context in which a problem is situated to select the most useful form of the quotient for the solution and use the context to interpret the quotient appropriately. 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. Convert standard measurements of mass to solve real-world problems. 12-3: Convince Me! Curriculum Standards: Fluently multiply multi-digit whole numbers using the standard algorithm. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Fluently multiply multi-digit whole numbers using the standard algorithm. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Convert among different-sized standard measurement units (i.e., km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec) within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Fluently multiply multi- digit whole numbers using the standard algorithm. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Convert among different-sized standard measurement units (i.e., km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec) within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Convert customary units of weight. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Convert between different-sized measurement units within a given measurement system. A table of equivalencies will be provided. Divide multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Recognize that quotients can be represented in a variety of ways, including a whole number with a remainder, a fraction or mixed number, or a decimal. Consider the context in which a problem is situated to select the most useful form of the quotient for the solution and use the context to interpret the quotient appropriately. 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. Practice and Problem Solving 12-3: Student Edition Practice Curriculum Standards: Fluently multiply multi-digit whole numbers using the standard algorithm. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Fluently multiply multi-digit whole numbers using the standard algorithm. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Convert among different-sized standard measurement units (i.e., km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec) within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Fluently multiply multi- digit whole numbers using the standard algorithm. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Convert among different-sized standard measurement units (i.e., km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec) within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Convert customary units of weight. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Convert between different-sized measurement units within a given measurement system. A table of equivalencies will be provided. Divide multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Recognize that quotients can be represented in a variety of ways, including a whole number with a remainder, a fraction or mixed number, or a decimal. Consider the context in which a problem is situated to select the most useful form of the quotient for the solution and use the context to interpret the quotient appropriately. 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. 12-3: Practice Buddy: Independent Practice; Problem Solving Curriculum Standards: Fluently multiply multi-digit whole numbers using the standard algorithm. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Fluently multiply multi-digit whole numbers using the standard algorithm. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Convert among different-sized standard measurement units (i.e., km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec) within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Fluently multiply multi- digit whole numbers using the standard algorithm. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Convert among different-sized standard measurement units (i.e., km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec) within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Convert customary units of weight. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Convert between different-sized measurement units within a given measurement system. A table of equivalencies will be provided. Divide multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Recognize that quotients can be represented in a variety of ways, including a whole number with a remainder, a fraction or mixed number, or a decimal. Consider the context in which a problem is situated to select the most useful form of the quotient for the solution and use the context to interpret the quotient appropriately. 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. 12-3: Practice Buddy: Additional Practice Curriculum Standards: Fluently multiply multi-digit whole numbers using the standard algorithm. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Fluently multiply multi-digit whole numbers using the standard algorithm. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Convert among different-sized standard measurement units (i.e., km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec) within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Fluently multiply multi- digit whole numbers using the standard algorithm. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Convert among different-sized standard measurement units (i.e., km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec) within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Convert customary units of weight. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Convert between different-sized measurement units within a given measurement system. A table of equivalencies will be provided. Divide multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Recognize that quotients can be represented in a variety of ways, including a whole number with a remainder, a fraction or mixed number, or a decimal. Consider the context in which a problem is situated to select the most useful form of the quotient for the solution and use the context to interpret the quotient appropriately. 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. 12-3: Interactive Additional Practice Step 3: Assess & Differentiate 12-3: Practice Buddy: Additional Practice Curriculum Standards: Fluently multiply multi-digit whole numbers using the standard algorithm. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Fluently multiply multi-digit whole numbers using the standard algorithm. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Convert among different-sized standard measurement units (i.e., km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec) within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Fluently multiply multi- digit whole numbers using the standard algorithm. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Convert among different-sized standard measurement units (i.e., km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec) within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Convert customary units of weight. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Convert between different-sized measurement units within a given measurement system. A table of equivalencies will be provided. Divide multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Recognize that quotients can be represented in a variety of ways, including a whole number with a remainder, a fraction or mixed number, or a decimal. Consider the context in which a problem is situated to select the most useful form of the quotient for the solution and use the context to interpret the quotient appropriately. 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. 12-3: Enrichment Curriculum Standards: Fluently multiply multi-digit whole numbers using the standard algorithm. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Fluently multiply multi-digit whole numbers using the standard algorithm. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Convert among different-sized standard measurement units (i.e., km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec) within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Fluently multiply multi- digit whole numbers using the standard algorithm. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Convert among different-sized standard measurement units (i.e., km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec) within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Convert customary units of weight. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Convert between different-sized measurement units within a given measurement system. A table of equivalencies will be provided. Divide multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Recognize that quotients can be represented in a variety of ways, including a whole number with a remainder, a fraction or mixed number, or a decimal. Consider the context in which a problem is situated to select the most useful form of the quotient for the solution and use the context to interpret the quotient appropriately. 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. 12-3: Quick Check Curriculum Standards: Fluently multiply multi-digit whole numbers using the standard algorithm. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Fluently multiply multi-digit whole numbers using the standard algorithm. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Convert among different-sized standard measurement units (i.e., km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec) within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Fluently multiply multi- digit whole numbers using the standard algorithm. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Convert among different-sized standard measurement units (i.e., km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec) within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Convert customary units of weight. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Convert between different-sized measurement units within a given measurement system. A table of equivalencies will be provided. Divide multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Recognize that quotients can be represented in a variety of ways, including a whole number with a remainder, a fraction or mixed number, or a decimal. Consider the context in which a problem is situated to select the most useful form of the quotient for the solution and use the context to interpret the quotient appropriately. 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. 12-3: Lesson Self-Assessment 12-3: Reteach to Build Understanding Curriculum Standards: Fluently multiply multi-digit whole numbers using the standard algorithm. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Fluently multiply multi-digit whole numbers using the standard algorithm. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Convert among different-sized standard measurement units (i.e., km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec) within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Fluently multiply multi- digit whole numbers using the standard algorithm. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Convert among different-sized standard measurement units (i.e., km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec) within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Convert customary units of weight. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Convert between different-sized measurement units within a given measurement system. A table of equivalencies will be provided. Divide multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Recognize that quotients can be represented in a variety of ways, including a whole number with a remainder, a fraction or mixed number, or a decimal. Consider the context in which a problem is situated to select the most useful form of the quotient for the solution and use the context to interpret the quotient appropriately. 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. Convert standard measurements of mass to solve real-world problems. 12-3: Build Mathematical Literacy Curriculum Standards: Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 5 topics and texts, building on others’ ideas and expressing their own clearly. (a) Come to discussions prepared, having read or studied required material; explicitly draw on that preparation and other information known about the topic to explore ideas under discussion. (b) Follow agreed-upon rules for discussions and carry out assigned roles. (c) Pose and respond to specific questions by making comments that contribute to the discussion and elaborate on the remarks of others. (d) Review the key ideas expressed and draw conclusions in light of information and knowledge gained from the discussions. English language learners communicate for social and instructional purposes within the school setting. Summarize a written text read aloud or information presented in diverse media and formats, including visually, quantitatively, and orally. Summarize the points a speaker makes and explain how each claim is supported by reasons and evidence. Write informative/explanatory texts to examine a topic and convey ideas and information clearly. (a) Introduce a topic clearly, provide a general observation and focus, and group related information logically; include formatting (e.g., headings), illustrations, and multimedia when useful to aiding comprehension. (b) Develop the topic with facts, definitions, concrete details, quotations, or other information and examples related to the topic. (c) Link ideas within and across categories of information using words, phrases, and clauses (e.g., in contrast, especially). (d) Use precise language and domain-specific vocabulary to inform about or explain the topic. (e) Provide a concluding statement or section related to the information or explanation presented. English language learners communicate information, ideas and concepts necessary for academic success in the content area of Mathematics. 12-3: Enrichment 12-3: Digital Math Tool Activity 12-3: Pick a Project 12-3: Another Look Curriculum Standards: Fluently multiply multi-digit whole numbers using the standard algorithm. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Fluently multiply multi-digit whole numbers using the standard algorithm. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Convert among different-sized standard measurement units (i.e., km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec) within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Fluently multiply multi- digit whole numbers using the standard algorithm. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Convert among different-sized standard measurement units (i.e., km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec) within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Convert customary units of weight. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Convert between different-sized measurement units within a given measurement system. A table of equivalencies will be provided. Divide multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Recognize that quotients can be represented in a variety of ways, including a whole number with a remainder, a fraction or mixed number, or a decimal. Consider the context in which a problem is situated to select the most useful form of the quotient for the solution and use the context to interpret the quotient appropriately. 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. Convert standard measurements of mass to solve real-world problems. Spanish Resources 12-3: eText del Libro del estudiante 12-3: Repaso diario 12-3: Aprendizaje visual 12-3: Amigo de práctica: Práctica adicional 12-3: Práctica adicional interactiva 12-3: Refuerzo para mejorar la comprensión 12-3: Desarrollar la competencia matemática 12-3: Ampliación 12-4: Convert Metric Units of Length Interactive Student Edition: Grade 5 Lesson 12-4 Math Anytime 12-4: Daily Review Topic 12: Today's Challenge Step 1: Problem-Based Learning 12-4: Solve & Share Curriculum Standards: Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. English language learners communicate for social and instructional purposes within the school setting. Write informative/explanatory texts to examine a topic and convey ideas and information clearly. (a) Introduce a topic clearly, provide a general observation and focus, and group related information logically; include formatting (e.g., headings), illustrations, and multimedia when useful to aiding comprehension. (b) Develop the topic with facts, definitions, concrete details, quotations, or other information and examples related to the topic. (c) Link ideas within and across categories of information using words, phrases, and clauses (e.g., in contrast, especially). (d) Use precise language and domain- specific vocabulary to inform about or explain the topic. (e) Provide a concluding statement or section related to the information or explanation presented. English language learners communicate information, ideas and concepts necessary for academic success in the content area of Mathematics. Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 5 topics and texts, building on others’ ideas and expressing their own clearly. (a) Come to discussions prepared, having read or studied required material; explicitly draw on that preparation and other information known about the topic to explore ideas under discussion. (b) Follow agreed-upon rules for discussions and carry out assigned roles. (c) Pose and respond to specific questions by making comments that contribute to the discussion and elaborate on the remarks of others. (d) Review the key ideas expressed and draw conclusions in light of information and knowledge gained from the discussions. Summarize a written text read aloud or information presented in diverse media and formats, including visually, quantitatively, and orally. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. Convert among different-sized standard measurement units (i.e., km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec) within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole- number exponents to denote powers of 10. Convert among different-sized standard measurement units (i.e., km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec) within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Convert metric units of length. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10 and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. Convert between different-sized measurement units within a given measurement system. A table of equivalencies will be provided. Divide multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Recognize that quotients can be represented in a variety of ways, including a whole number with a remainder, a fraction or mixed number, or a decimal. Consider the context in which a problem is situated to select the most useful form of the quotient for the solution and use the context to interpret the quotient appropriately. 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. Summarize the points a speaker makes and explain how each claim is supported by reasons and evidence. Step 2: Visual Learning 12-4: Visual Learning Curriculum Standards: Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Convert standard measurements of length to solve real-world problems. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole- number exponents to denote powers of 10. Convert among different-sized standard measurement units (i.e., km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec) within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole- number exponents to denote powers of 10. Convert among different-sized standard measurement units (i.e., km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec) within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Convert metric units of length. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10 and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. Convert between different-sized measurement units within a given measurement system. A table of equivalencies will be provided. Divide multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Recognize that quotients can be represented in a variety of ways, including a whole number with a remainder, a fraction or mixed number, or a decimal. Consider the context in which a problem is situated to select the most useful form of the quotient for the solution and use the context to interpret the quotient appropriately. 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. 12-4: Convince Me! Curriculum Standards: Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. Convert among different-sized standard measurement units (i.e., km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec) within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. Convert among different-sized standard measurement units (i.e., km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec) within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Convert metric units of length. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10 and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. Convert between different-sized measurement units within a given measurement system. A table of equivalencies will be provided. Divide multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Recognize that quotients can be represented in a variety of ways, including a whole number with a remainder, a fraction or mixed number, or a decimal. Consider the context in which a problem is situated to select the most useful form of the quotient for the solution and use the context to interpret the quotient appropriately. 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. Practice and Problem Solving 12-4: Student Edition Practice Curriculum Standards: Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. Convert among different-sized standard measurement units (i.e., km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec) within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. Convert among different-sized standard measurement units (i.e., km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec) within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Convert metric units of length. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10 and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. Convert between different-sized measurement units within a given measurement system. A table of equivalencies will be provided. Divide multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Recognize that quotients can be represented in a variety of ways, including a whole number with a remainder, a fraction or mixed number, or a decimal. Consider the context in which a problem is situated to select the most useful form of the quotient for the solution and use the context to interpret the quotient appropriately. 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. 12-4: Practice Buddy: Independent Practice; Problem Solving Curriculum Standards: Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. Convert among different-sized standard measurement units (i.e., km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec) within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. Convert among different-sized standard measurement units (i.e., km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec) within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Convert metric units of length. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10 and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. Convert between different-sized measurement units within a given measurement system. A table of equivalencies will be provided. Divide multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Recognize that quotients can be represented in a variety of ways, including a whole number with a remainder, a fraction or mixed number, or a decimal. Consider the context in which a problem is situated to select the most useful form of the quotient for the solution and use the context to interpret the quotient appropriately. 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. 12-4: Practice Buddy: Additional Practice Curriculum Standards: Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. Convert among different-sized standard measurement units (i.e., km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec) within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. Convert among different-sized standard measurement units (i.e., km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec) within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Convert metric units of length. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10 and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. Convert between different-sized measurement units within a given measurement system. A table of equivalencies will be provided. Divide multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Recognize that quotients can be represented in a variety of ways, including a whole number with a remainder, a fraction or mixed number, or a decimal. Consider the context in which a problem is situated to select the most useful form of the quotient for the solution and use the context to interpret the quotient appropriately. 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. 12-4: Interactive Additional Practice Step 3: Assess & Differentiate 12-4: Practice Buddy: Additional Practice Curriculum Standards: Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. Convert among different-sized standard measurement units (i.e., km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec) within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. Convert among different-sized standard measurement units (i.e., km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec) within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Convert metric units of length. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10 and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. Convert between different-sized measurement units within a given measurement system. A table of equivalencies will be provided. Divide multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Recognize that quotients can be represented in a variety of ways, including a whole number with a remainder, a fraction or mixed number, or a decimal. Consider the context in which a problem is situated to select the most useful form of the quotient for the solution and use the context to interpret the quotient appropriately. 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. 12-4: Enrichment Curriculum Standards: Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. Convert among different-sized standard measurement units (i.e., km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec) within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. Convert among different-sized standard measurement units (i.e., km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec) within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Convert metric units of length. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10 and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. Convert between different-sized measurement units within a given measurement system. A table of equivalencies will be provided. Divide multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Recognize that quotients can be represented in a variety of ways, including a whole number with a remainder, a fraction or mixed number, or a decimal. Consider the context in which a problem is situated to select the most useful form of the quotient for the solution and use the context to interpret the quotient appropriately. 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. 12-4: Quick Check Curriculum Standards: Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. Convert among different-sized standard measurement units (i.e., km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec) within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. Convert among different-sized standard measurement units (i.e., km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec) within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Convert metric units of length. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10 and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. Convert between different-sized measurement units within a given measurement system. A table of equivalencies will be provided. Divide multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Recognize that quotients can be represented in a variety of ways, including a whole number with a remainder, a fraction or mixed number, or a decimal. Consider the context in which a problem is situated to select the most useful form of the quotient for the solution and use the context to interpret the quotient appropriately. 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. 12-4: Lesson Self-Assessment 12-4: Reteach to Build Understanding Curriculum Standards: Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Convert standard measurements of length to solve real-world problems. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole- number exponents to denote powers of 10. Convert among different-sized standard measurement units (i.e., km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec) within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole- number exponents to denote powers of 10. Convert among different-sized standard measurement units (i.e., km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec) within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Convert metric units of length. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10 and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. Convert between different-sized measurement units within a given measurement system. A table of equivalencies will be provided. Divide multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Recognize that quotients can be represented in a variety of ways, including a whole number with a remainder, a fraction or mixed number, or a decimal. Consider the context in which a problem is situated to select the most useful form of the quotient for the solution and use the context to interpret the quotient appropriately. 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. 12-4: Build Mathematical Literacy Curriculum Standards: Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 5 topics and texts, building on others’ ideas and expressing their own clearly. (a) Come to discussions prepared, having read or studied required material; explicitly draw on that preparation and other information known about the topic to explore ideas under discussion. (b) Follow agreed-upon rules for discussions and carry out assigned roles. (c) Pose and respond to specific questions by making comments that contribute to the discussion and elaborate on the remarks of others. (d) Review the key ideas expressed and draw conclusions in light of information and knowledge gained from the discussions. English language learners communicate for social and instructional purposes within the school setting. Summarize a written text read aloud or information presented in diverse media and formats, including visually, quantitatively, and orally. Summarize the points a speaker makes and explain how each claim is supported by reasons and evidence. Write informative/explanatory texts to examine a topic and convey ideas and information clearly. (a) Introduce a topic clearly, provide a general observation and focus, and group related information logically; include formatting (e.g., headings), illustrations, and multimedia when useful to aiding comprehension. (b) Develop the topic with facts, definitions, concrete details, quotations, or other information and examples related to the topic. (c) Link ideas within and across categories of information using words, phrases, and clauses (e.g., in contrast, especially). (d) Use precise language and domain-specific vocabulary to inform about or explain the topic. (e) Provide a concluding statement or section related to the information or explanation presented. English language learners communicate information, ideas and concepts necessary for academic success in the content area of Mathematics. 12-4: Enrichment 12-4: Digital Math Tool Activity 12-4 Problem-Solving Reading Activity Curriculum Standards: Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. Convert among different-sized standard measurement units (i.e., km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec) within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. Convert among different-sized standard measurement units (i.e., km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec) within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Convert metric units of length. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10 and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. Convert between different-sized measurement units within a given measurement system. A table of equivalencies will be provided. Divide multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Recognize that quotients can be represented in a variety of ways, including a whole number with a remainder, a fraction or mixed number, or a decimal. Consider the context in which a problem is situated to select the most useful form of the quotient for the solution and use the context to interpret the quotient appropriately. 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. 12-4: Another Look Curriculum Standards: Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Convert standard measurements of length to solve real-world problems. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole- number exponents to denote powers of 10. Convert among different-sized standard measurement units (i.e., km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec) within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole- number exponents to denote powers of 10. Convert among different-sized standard measurement units (i.e., km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec) within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Convert metric units of length. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10 and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. Convert between different-sized measurement units within a given measurement system. A table of equivalencies will be provided. Divide multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Recognize that quotients can be represented in a variety of ways, including a whole number with a remainder, a fraction or mixed number, or a decimal. Consider the context in which a problem is situated to select the most useful form of the quotient for the solution and use the context to interpret the quotient appropriately. 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. Spanish Resources 12-4: eText del Libro del estudiante 12-4: Repaso diario 12-4: Aprendizaje visual 12-4: Amigo de práctica: Práctica adicional 12-4: Práctica adicional interactiva 12-4: Refuerzo para mejorar la comprensión 12-4: Desarrollar la competencia matemática 12-4: Ampliación 12-5: Convert Metric Units of Capacity Interactive Student Edition: Grade 5 Lesson 12-5 Math Anytime 12-5: Daily Review Topic 12: Today's Challenge Step 1: Problem-Based Learning 12-5: Solve & Share Curriculum Standards: Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. English language learners communicate for social and instructional purposes within the school setting. Write informative/explanatory texts to examine a topic and convey ideas and information clearly. (a) Introduce a topic clearly, provide a general observation and focus, and group related information logically; include formatting (e.g., headings), illustrations, and multimedia when useful to aiding comprehension. (b) Develop the topic with facts, definitions, concrete details, quotations, or other information and examples related to the topic. (c) Link ideas within and across categories of information using words, phrases, and clauses (e.g., in contrast, especially). (d) Use precise language and domain- specific vocabulary to inform about or explain the topic. (e) Provide a concluding statement or section related to the information or explanation presented. English language learners communicate information, ideas and concepts necessary for academic success in the content area of Mathematics. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. Convert among different-sized standard measurement units (i.e., km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec) within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. Convert among different-sized standard measurement units (i.e., km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec) within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Convert metric units of capacity. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10 and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. Convert between different-sized measurement units within a given measurement system. A table of equivalencies will be provided. Divide multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Recognize that quotients can be represented in a variety of ways, including a whole number with a remainder, a fraction or mixed number, or a decimal. Consider the context in which a problem is situated to select the most useful form of the quotient for the solution and use the context to interpret the quotient appropriately. 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. Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 5 topics and texts, building on others’ ideas and expressing their own clearly. (a) Come to discussions prepared, having read or studied required material; explicitly draw on that preparation and other information known about the topic to explore ideas under discussion. (b) Follow agreed-upon rules for discussions and carry out assigned roles. (c) Pose and respond to specific questions by making comments that contribute to the discussion and elaborate on the remarks of others. (d) Review the key ideas expressed and draw conclusions in light of information and knowledge gained from the discussions. Summarize a written text read aloud or information presented in diverse media and formats, including visually, quantitatively, and orally. Summarize the points a speaker makes and explain how each claim is supported by reasons and evidence. Step 2: Visual Learning 12-5: Visual Learning Curriculum Standards: Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. Convert among different-sized standard measurement units (i.e., km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec) within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. Convert among different-sized standard measurement units (i.e., km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec) within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Convert metric units of capacity. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10 and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. Convert between different-sized measurement units within a given measurement system. A table of equivalencies will be provided. Divide multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Recognize that quotients can be represented in a variety of ways, including a whole number with a remainder, a fraction or mixed number, or a decimal. Consider the context in which a problem is situated to select the most useful form of the quotient for the solution and use the context to interpret the quotient appropriately. 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. 12-5: Convince Me! Curriculum Standards: Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. Convert among different-sized standard measurement units (i.e., km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec) within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. Convert among different-sized standard measurement units (i.e., km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec) within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Convert metric units of capacity. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10 and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. Convert between different-sized measurement units within a given measurement system. A table of equivalencies will be provided. Divide multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Recognize that quotients can be represented in a variety of ways, including a whole number with a remainder, a fraction or mixed number, or a decimal. Consider the context in which a problem is situated to select the most useful form of the quotient for the solution and use the context to interpret the quotient appropriately. 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. Practice and Problem Solving 12-5: Student Edition Practice Curriculum Standards: Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. Convert among different-sized standard measurement units (i.e., km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec) within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. Convert among different-sized standard measurement units (i.e., km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec) within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Convert metric units of capacity. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10 and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. Convert between different-sized measurement units within a given measurement system. A table of equivalencies will be provided. Divide multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Recognize that quotients can be represented in a variety of ways, including a whole number with a remainder, a fraction or mixed number, or a decimal. Consider the context in which a problem is situated to select the most useful form of the quotient for the solution and use the context to interpret the quotient appropriately. 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. 12-5: Practice Buddy: Independent Practice; Problem Solving Curriculum Standards: Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. Convert among different-sized standard measurement units (i.e., km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec) within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. Convert among different-sized standard measurement units (i.e., km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec) within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Convert metric units of capacity. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10 and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. Convert between different-sized measurement units within a given measurement system. A table of equivalencies will be provided. Divide multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Recognize that quotients can be represented in a variety of ways, including a whole number with a remainder, a fraction or mixed number, or a decimal. Consider the context in which a problem is situated to select the most useful form of the quotient for the solution and use the context to interpret the quotient appropriately. 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. 12-5: Practice Buddy: Additional Practice Curriculum Standards: Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. Convert among different-sized standard measurement units (i.e., km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec) within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. Convert among different-sized standard measurement units (i.e., km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec) within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Convert metric units of capacity. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10 and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. Convert between different-sized measurement units within a given measurement system. A table of equivalencies will be provided. Divide multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Recognize that quotients can be represented in a variety of ways, including a whole number with a remainder, a fraction or mixed number, or a decimal. Consider the context in which a problem is situated to select the most useful form of the quotient for the solution and use the context to interpret the quotient appropriately. 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. 12-5: Interactive Additional Practice Step 3: Assess & Differentiate 12-5: Practice Buddy: Additional Practice Curriculum Standards: Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. Convert among different-sized standard measurement units (i.e., km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec) within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. Convert among different-sized standard measurement units (i.e., km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec) within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Convert metric units of capacity. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10 and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. Convert between different-sized measurement units within a given measurement system. A table of equivalencies will be provided. Divide multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Recognize that quotients can be represented in a variety of ways, including a whole number with a remainder, a fraction or mixed number, or a decimal. Consider the context in which a problem is situated to select the most useful form of the quotient for the solution and use the context to interpret the quotient appropriately. 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. 12-5: Enrichment Curriculum Standards: Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. Convert among different-sized standard measurement units (i.e., km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec) within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. Convert among different-sized standard measurement units (i.e., km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec) within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Convert metric units of capacity. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10 and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. Convert between different-sized measurement units within a given measurement system. A table of equivalencies will be provided. Divide multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Recognize that quotients can be represented in a variety of ways, including a whole number with a remainder, a fraction or mixed number, or a decimal. Consider the context in which a problem is situated to select the most useful form of the quotient for the solution and use the context to interpret the quotient appropriately. 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. 12-5: Quick Check Curriculum Standards: Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. Convert among different-sized standard measurement units (i.e., km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec) within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. Convert among different-sized standard measurement units (i.e., km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec) within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Convert metric units of capacity. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10 and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. Convert between different-sized measurement units within a given measurement system. A table of equivalencies will be provided. Divide multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Recognize that quotients can be represented in a variety of ways, including a whole number with a remainder, a fraction or mixed number, or a decimal. Consider the context in which a problem is situated to select the most useful form of the quotient for the solution and use the context to interpret the quotient appropriately. 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. 12-5: Lesson Self-Assessment 12-5: Reteach to Build Understanding Curriculum Standards: Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. Convert among different-sized standard measurement units (i.e., km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec) within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. Convert among different-sized standard measurement units (i.e., km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec) within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Convert metric units of capacity. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10 and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. Convert between different-sized measurement units within a given measurement system. A table of equivalencies will be provided. Divide multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Recognize that quotients can be represented in a variety of ways, including a whole number with a remainder, a fraction or mixed number, or a decimal. Consider the context in which a problem is situated to select the most useful form of the quotient for the solution and use the context to interpret the quotient appropriately. 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. 12-5: Build Mathematical Literacy Curriculum Standards: Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 5 topics and texts, building on others’ ideas and expressing their own clearly. (a) Come to discussions prepared, having read or studied required material; explicitly draw on that preparation and other information known about the topic to explore ideas under discussion. (b) Follow agreed-upon rules for discussions and carry out assigned roles. (c) Pose and respond to specific questions by making comments that contribute to the discussion and elaborate on the remarks of others. (d) Review the key ideas expressed and draw conclusions in light of information and knowledge gained from the discussions. English language learners communicate for social and instructional purposes within the school setting. Summarize a written text read aloud or information presented in diverse media and formats, including visually, quantitatively, and orally. Summarize the points a speaker makes and explain how each claim is supported by reasons and evidence. Write informative/explanatory texts to examine a topic and convey ideas and information clearly. (a) Introduce a topic clearly, provide a general observation and focus, and group related information logically; include formatting (e.g., headings), illustrations, and multimedia when useful to aiding comprehension. (b) Develop the topic with facts, definitions, concrete details, quotations, or other information and examples related to the topic. (c) Link ideas within and across categories of information using words, phrases, and clauses (e.g., in contrast, especially). (d) Use precise language and domain-specific vocabulary to inform about or explain the topic. (e) Provide a concluding statement or section related to the information or explanation presented. English language learners communicate information, ideas and concepts necessary for academic success in the content area of Mathematics. 12-5: Enrichment 12-5: Digital Math Tool Activity 12-5: Pick a Project 12-5: Another Look Curriculum Standards: Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. Convert among different-sized standard measurement units (i.e., km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec) within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. Convert among different-sized standard measurement units (i.e., km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec) within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Convert metric units of capacity. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10 and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. Convert between different-sized measurement units within a given measurement system. A table of equivalencies will be provided. Divide multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Recognize that quotients can be represented in a variety of ways, including a whole number with a remainder, a fraction or mixed number, or a decimal. Consider the context in which a problem is situated to select the most useful form of the quotient for the solution and use the context to interpret the quotient appropriately. 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. Spanish Resources 12-5: eText del Libro del estudiante 12-5: Repaso diario 12-5: Aprendizaje visual 12-5: Amigo de práctica: Práctica adicional 12-5: Práctica adicional interactiva 12-5: Refuerzo para mejorar la comprensión 12-5: Desarrollar la competencia matemática 12-5: Ampliación 12-6: Convert Metric Units of Mass Interactive Student Edition: Grade 5 Lesson 12-6 Math Anytime 12-6: Daily Review Topic 12: Today's Challenge Step 1: Problem-Based Learning 12-6: Solve & Share Curriculum Standards: Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. English language learners communicate for social and instructional purposes within the school setting. Write informative/explanatory texts to examine a topic and convey ideas and information clearly. (a) Introduce a topic clearly, provide a general observation and focus, and group related information logically; include formatting (e.g., headings), illustrations, and multimedia when useful to aiding comprehension. (b) Develop the topic with facts, definitions, concrete details, quotations, or other information and examples related to the topic. (c) Link ideas within and across categories of information using words, phrases, and clauses (e.g., in contrast, especially). (d) Use precise language and domain- specific vocabulary to inform about or explain the topic. (e) Provide a concluding statement or section related to the information or explanation presented. English language learners communicate information, ideas and concepts necessary for academic success in the content area of Mathematics. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. Convert among different-sized standard measurement units (i.e., km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec) within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. Convert among different-sized standard measurement units (i.e., km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec) within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Convert metric units of mass. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10 and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. Convert between different-sized measurement units within a given measurement system. A table of equivalencies will be provided. Divide multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Recognize that quotients can be represented in a variety of ways, including a whole number with a remainder, a fraction or mixed number, or a decimal. Consider the context in which a problem is situated to select the most useful form of the quotient for the solution and use the context to interpret the quotient appropriately. 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. Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 5 topics and texts, building on others’ ideas and expressing their own clearly. (a) Come to discussions prepared, having read or studied required material; explicitly draw on that preparation and other information known about the topic to explore ideas under discussion. (b) Follow agreed-upon rules for discussions and carry out assigned roles. (c) Pose and respond to specific questions by making comments that contribute to the discussion and elaborate on the remarks of others. (d) Review the key ideas expressed and draw conclusions in light of information and knowledge gained from the discussions. Summarize a written text read aloud or information presented in diverse media and formats, including visually, quantitatively, and orally. Summarize the points a speaker makes and explain how each claim is supported by reasons and evidence. Step 2: Visual Learning 12-6: Visual Learning Curriculum Standards: Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. Convert among different-sized standard measurement units (i.e., km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec) within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. Convert among different-sized standard measurement units (i.e., km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec) within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Convert metric units of mass. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10 and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. Convert between different-sized measurement units within a given measurement system. A table of equivalencies will be provided. Divide multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Recognize that quotients can be represented in a variety of ways, including a whole number with a remainder, a fraction or mixed number, or a decimal. Consider the context in which a problem is situated to select the most useful form of the quotient for the solution and use the context to interpret the quotient appropriately. 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. Convert standard measurements of mass to solve real-world problems. 12-6: Convince Me! Curriculum Standards: Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. Convert among different-sized standard measurement units (i.e., km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec) within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. Convert among different-sized standard measurement units (i.e., km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec) within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Convert metric units of mass. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10 and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. Convert between different-sized measurement units within a given measurement system. A table of equivalencies will be provided. Divide multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Recognize that quotients can be represented in a variety of ways, including a whole number with a remainder, a fraction or mixed number, or a decimal. Consider the context in which a problem is situated to select the most useful form of the quotient for the solution and use the context to interpret the quotient appropriately. 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. Practice and Problem Solving 12-6: Student Edition Practice Curriculum Standards: Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. Convert among different-sized standard measurement units (i.e., km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec) within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. Convert among different-sized standard measurement units (i.e., km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec) within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Convert metric units of mass. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10 and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. Convert between different-sized measurement units within a given measurement system. A table of equivalencies will be provided. Divide multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Recognize that quotients can be represented in a variety of ways, including a whole number with a remainder, a fraction or mixed number, or a decimal. Consider the context in which a problem is situated to select the most useful form of the quotient for the solution and use the context to interpret the quotient appropriately. 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. 12-6: Practice Buddy: Independent Practice; Problem Solving Curriculum Standards: Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. Convert among different-sized standard measurement units (i.e., km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec) within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. Convert among different-sized standard measurement units (i.e., km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec) within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Convert metric units of mass. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10 and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. Convert between different-sized measurement units within a given measurement system. A table of equivalencies will be provided. Divide multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Recognize that quotients can be represented in a variety of ways, including a whole number with a remainder, a fraction or mixed number, or a decimal. Consider the context in which a problem is situated to select the most useful form of the quotient for the solution and use the context to interpret the quotient appropriately. 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. 12-6: Practice Buddy: Additional Practice Curriculum Standards: Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. Convert among different-sized standard measurement units (i.e., km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec) within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. Convert among different-sized standard measurement units (i.e., km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec) within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Convert metric units of mass. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10 and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. Convert between different-sized measurement units within a given measurement system. A table of equivalencies will be provided. Divide multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Recognize that quotients can be represented in a variety of ways, including a whole number with a remainder, a fraction or mixed number, or a decimal. Consider the context in which a problem is situated to select the most useful form of the quotient for the solution and use the context to interpret the quotient appropriately. 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. 12-6: Interactive Additional Practice Step 3: Assess & Differentiate 12-6: Practice Buddy: Additional Practice Curriculum Standards: Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. Convert among different-sized standard measurement units (i.e., km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec) within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. Convert among different-sized standard measurement units (i.e., km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec) within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Convert metric units of mass. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10 and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. Convert between different-sized measurement units within a given measurement system. A table of equivalencies will be provided. Divide multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Recognize that quotients can be represented in a variety of ways, including a whole number with a remainder, a fraction or mixed number, or a decimal. Consider the context in which a problem is situated to select the most useful form of the quotient for the solution and use the context to interpret the quotient appropriately. 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. 12-6: Enrichment Curriculum Standards: Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. Convert among different-sized standard measurement units (i.e., km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec) within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. Convert among different-sized standard measurement units (i.e., km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec) within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Convert metric units of mass. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10 and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. Convert between different-sized measurement units within a given measurement system. A table of equivalencies will be provided. Divide multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Recognize that quotients can be represented in a variety of ways, including a whole number with a remainder, a fraction or mixed number, or a decimal. Consider the context in which a problem is situated to select the most useful form of the quotient for the solution and use the context to interpret the quotient appropriately. 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. 12-6: Quick Check Curriculum Standards: Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. Convert among different-sized standard measurement units (i.e., km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec) within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. Convert among different-sized standard measurement units (i.e., km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec) within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Convert metric units of mass. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10 and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. Convert between different-sized measurement units within a given measurement system. A table of equivalencies will be provided. Divide multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Recognize that quotients can be represented in a variety of ways, including a whole number with a remainder, a fraction or mixed number, or a decimal. Consider the context in which a problem is situated to select the most useful form of the quotient for the solution and use the context to interpret the quotient appropriately. 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. 12-6: Lesson Self-Assessment 12-6: Reteach to Build Understanding Curriculum Standards: Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. Convert among different-sized standard measurement units (i.e., km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec) within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. Convert among different-sized standard measurement units (i.e., km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec) within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Convert metric units of mass. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10 and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. Convert between different-sized measurement units within a given measurement system. A table of equivalencies will be provided. Divide multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Recognize that quotients can be represented in a variety of ways, including a whole number with a remainder, a fraction or mixed number, or a decimal. Consider the context in which a problem is situated to select the most useful form of the quotient for the solution and use the context to interpret the quotient appropriately. 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. Convert standard measurements of mass to solve real-world problems. 12-6: Build Mathematical Literacy Curriculum Standards: Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 5 topics and texts, building on others’ ideas and expressing their own clearly. (a) Come to discussions prepared, having read or studied required material; explicitly draw on that preparation and other information known about the topic to explore ideas under discussion. (b) Follow agreed-upon rules for discussions and carry out assigned roles. (c) Pose and respond to specific questions by making comments that contribute to the discussion and elaborate on the remarks of others. (d) Review the key ideas expressed and draw conclusions in light of information and knowledge gained from the discussions. English language learners communicate for social and instructional purposes within the school setting. Summarize a written text read aloud or information presented in diverse media and formats, including visually, quantitatively, and orally. Summarize the points a speaker makes and explain how each claim is supported by reasons and evidence. Write informative/explanatory texts to examine a topic and convey ideas and information clearly. (a) Introduce a topic clearly, provide a general observation and focus, and group related information logically; include formatting (e.g., headings), illustrations, and multimedia when useful to aiding comprehension. (b) Develop the topic with facts, definitions, concrete details, quotations, or other information and examples related to the topic. (c) Link ideas within and across categories of information using words, phrases, and clauses (e.g., in contrast, especially). (d) Use precise language and domain-specific vocabulary to inform about or explain the topic. (e) Provide a concluding statement or section related to the information or explanation presented. English language learners communicate information, ideas and concepts necessary for academic success in the content area of Mathematics. 12-6: Enrichment 12-6: Digital Math Tool Activity 12-6: Pick a Project 12-6: Another Look Curriculum Standards: Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. Convert among different-sized standard measurement units (i.e., km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec) within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. Convert among different-sized standard measurement units (i.e., km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec) within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Convert metric units of mass. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10 and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. Convert between different-sized measurement units within a given measurement system. A table of equivalencies will be provided. Divide multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Recognize that quotients can be represented in a variety of ways, including a whole number with a remainder, a fraction or mixed number, or a decimal. Consider the context in which a problem is situated to select the most useful form of the quotient for the solution and use the context to interpret the quotient appropriately. 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. Convert standard measurements of mass to solve real-world problems. Spanish Resources 12-6: eText del Libro del estudiante 12-6: Repaso diario 12-6: Aprendizaje visual 12-6: Amigo de práctica: Práctica adicional 12-6: Práctica adicional interactiva 12-6: Refuerzo para mejorar la comprensión 12-6: Desarrollar la competencia matemática 12-6: Ampliación 12-7: Convert Units of Time Interactive Student Edition: Grade 5 Lesson 12-7 Math Anytime 12-7: Daily Review Topic 12: Today's Challenge Step 1: Problem-Based Learning 12-7: Solve & Share Curriculum Standards: Fluently multiply multi-digit whole numbers using the standard algorithm. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. English language learners communicate for social and instructional purposes within the school setting. Write informative/explanatory texts to examine a topic and convey ideas and information clearly. (a) Introduce a topic clearly, provide a general observation and focus, and group related information logically; include formatting (e.g., headings), illustrations, and multimedia when useful to aiding comprehension. (b) Develop the topic with facts, definitions, concrete details, quotations, or other information and examples related to the topic. (c) Link ideas within and across categories of information using words, phrases, and clauses (e.g., in contrast, especially). (d) Use precise language and domain-specific vocabulary to inform about or explain the topic. (e) Provide a concluding statement or section related to the information or explanation presented. English language learners communicate information, ideas and concepts necessary for academic success in the content area of Mathematics. Fluently multiply multi-digit whole numbers using the standard algorithm. Find whole- number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Convert among different-sized standard measurement units (i.e., km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec) within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Fluently multiply multi-digit whole numbers using the standard algorithm. Find whole-number quotients of whole numbers with up to four- digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Convert among different-sized standard measurement units (i.e., km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec) within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Convert units of time. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Convert between different-sized measurement units within a given measurement system. A table of equivalencies will be provided. Divide multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Recognize that quotients can be represented in a variety of ways, including a whole number with a remainder, a fraction or mixed number, or a decimal. Consider the context in which a problem is situated to select the most useful form of the quotient for the solution and use the context to interpret the quotient appropriately. 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. Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 5 topics and texts, building on others’ ideas and expressing their own clearly. (a) Come to discussions prepared, having read or studied required material; explicitly draw on that preparation and other information known about the topic to explore ideas under discussion. (b) Follow agreed-upon rules for discussions and carry out assigned roles. (c) Pose and respond to specific questions by making comments that contribute to the discussion and elaborate on the remarks of others. (d) Review the key ideas expressed and draw conclusions in light of information and knowledge gained from the discussions. Summarize a written text read aloud or information presented in diverse media and formats, including visually, quantitatively, and orally. Summarize the points a speaker makes and explain how each claim is supported by reasons and evidence. Step 2: Visual Learning 12-7: Visual Learning Curriculum Standards: Fluently multiply multi-digit whole numbers using the standard algorithm. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Convert standard measurements of time to solve real-world problems. Fluently multiply multi-digit whole numbers using the standard algorithm. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Convert among different-sized standard measurement units (i.e., km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec) within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Fluently multiply multi-digit whole numbers using the standard algorithm. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Convert among different-sized standard measurement units (i.e., km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec) within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Convert units of time. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Convert between different-sized measurement units within a given measurement system. A table of equivalencies will be provided. Divide multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Recognize that quotients can be represented in a variety of ways, including a whole number with a remainder, a fraction or mixed number, or a decimal. Consider the context in which a problem is situated to select the most useful form of the quotient for the solution and use the context to interpret the quotient appropriately. 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. 12-7: Convince Me! Curriculum Standards: Fluently multiply multi-digit whole numbers using the standard algorithm. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Fluently multiply multi-digit whole numbers using the standard algorithm. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Convert among different-sized standard measurement units (i.e., km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec) within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Fluently multiply multi- digit whole numbers using the standard algorithm. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Convert among different-sized standard measurement units (i.e., km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec) within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Convert units of time. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Convert between different-sized measurement units within a given measurement system. A table of equivalencies will be provided. Divide multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Recognize that quotients can be represented in a variety of ways, including a whole number with a remainder, a fraction or mixed number, or a decimal. Consider the context in which a problem is situated to select the most useful form of the quotient for the solution and use the context to interpret the quotient appropriately. 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. Practice and Problem Solving 12-7: Student Edition Practice Curriculum Standards: Fluently multiply multi-digit whole numbers using the standard algorithm. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Fluently multiply multi-digit whole numbers using the standard algorithm. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Convert among different-sized standard measurement units (i.e., km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec) within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Fluently multiply multi- digit whole numbers using the standard algorithm. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Convert among different-sized standard measurement units (i.e., km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec) within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Convert units of time. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Convert between different-sized measurement units within a given measurement system. A table of equivalencies will be provided. Divide multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Recognize that quotients can be represented in a variety of ways, including a whole number with a remainder, a fraction or mixed number, or a decimal. Consider the context in which a problem is situated to select the most useful form of the quotient for the solution and use the context to interpret the quotient appropriately. 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. 12-7: Practice Buddy: Independent Practice; Problem Solving Curriculum Standards: Fluently multiply multi-digit whole numbers using the standard algorithm. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Fluently multiply multi-digit whole numbers using the standard algorithm. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Convert among different-sized standard measurement units (i.e., km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec) within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Fluently multiply multi- digit whole numbers using the standard algorithm. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Convert among different-sized standard measurement units (i.e., km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec) within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Convert units of time. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Convert between different-sized measurement units within a given measurement system. A table of equivalencies will be provided. Divide multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Recognize that quotients can be represented in a variety of ways, including a whole number with a remainder, a fraction or mixed number, or a decimal. Consider the context in which a problem is situated to select the most useful form of the quotient for the solution and use the context to interpret the quotient appropriately. 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. 12-7: Practice Buddy: Additional Practice Curriculum Standards: Fluently multiply multi-digit whole numbers using the standard algorithm. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Fluently multiply multi-digit whole numbers using the standard algorithm. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Convert among different-sized standard measurement units (i.e., km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec) within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Fluently multiply multi- digit whole numbers using the standard algorithm. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Convert among different-sized standard measurement units (i.e., km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec) within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Convert units of time. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Convert between different-sized measurement units within a given measurement system. A table of equivalencies will be provided. Divide multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Recognize that quotients can be represented in a variety of ways, including a whole number with a remainder, a fraction or mixed number, or a decimal. Consider the context in which a problem is situated to select the most useful form of the quotient for the solution and use the context to interpret the quotient appropriately. 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. 12-7: Interactive Additional Practice Step 3: Assess & Differentiate 12-7: Practice Buddy: Additional Practice Curriculum Standards: Fluently multiply multi-digit whole numbers using the standard algorithm. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Fluently multiply multi-digit whole numbers using the standard algorithm. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Convert among different-sized standard measurement units (i.e., km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec) within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Fluently multiply multi- digit whole numbers using the standard algorithm. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Convert among different-sized standard measurement units (i.e., km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec) within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Convert units of time. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Convert between different-sized measurement units within a given measurement system. A table of equivalencies will be provided. Divide multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Recognize that quotients can be represented in a variety of ways, including a whole number with a remainder, a fraction or mixed number, or a decimal. Consider the context in which a problem is situated to select the most useful form of the quotient for the solution and use the context to interpret the quotient appropriately. 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. 12-7: Enrichment Curriculum Standards: Fluently multiply multi-digit whole numbers using the standard algorithm. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Fluently multiply multi-digit whole numbers using the standard algorithm. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Convert among different-sized standard measurement units (i.e., km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec) within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Fluently multiply multi- digit whole numbers using the standard algorithm. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Convert among different-sized standard measurement units (i.e., km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec) within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Convert units of time. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Convert between different-sized measurement units within a given measurement system. A table of equivalencies will be provided. Divide multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Recognize that quotients can be represented in a variety of ways, including a whole number with a remainder, a fraction or mixed number, or a decimal. Consider the context in which a problem is situated to select the most useful form of the quotient for the solution and use the context to interpret the quotient appropriately. 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. 12-7: Quick Check Curriculum Standards: Fluently multiply multi-digit whole numbers using the standard algorithm. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Fluently multiply multi-digit whole numbers using the standard algorithm. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Convert among different-sized standard measurement units (i.e., km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec) within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Fluently multiply multi- digit whole numbers using the standard algorithm. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Convert among different-sized standard measurement units (i.e., km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec) within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Convert units of time. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Convert between different-sized measurement units within a given measurement system. A table of equivalencies will be provided. Divide multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Recognize that quotients can be represented in a variety of ways, including a whole number with a remainder, a fraction or mixed number, or a decimal. Consider the context in which a problem is situated to select the most useful form of the quotient for the solution and use the context to interpret the quotient appropriately. 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. 12-7: Lesson Self-Assessment 12-7: Reteach to Build Understanding Curriculum Standards: Fluently multiply multi-digit whole numbers using the standard algorithm. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Convert standard measurements of time to solve real-world problems. Fluently multiply multi-digit whole numbers using the standard algorithm. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Convert among different-sized standard measurement units (i.e., km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec) within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Fluently multiply multi-digit whole numbers using the standard algorithm. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Convert among different-sized standard measurement units (i.e., km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec) within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Convert units of time. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Convert between different-sized measurement units within a given measurement system. A table of equivalencies will be provided. Divide multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Recognize that quotients can be represented in a variety of ways, including a whole number with a remainder, a fraction or mixed number, or a decimal. Consider the context in which a problem is situated to select the most useful form of the quotient for the solution and use the context to interpret the quotient appropriately. 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. 12-7: Build Mathematical Literacy Curriculum Standards: Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 5 topics and texts, building on others’ ideas and expressing their own clearly. (a) Come to discussions prepared, having read or studied required material; explicitly draw on that preparation and other information known about the topic to explore ideas under discussion. (b) Follow agreed-upon rules for discussions and carry out assigned roles. (c) Pose and respond to specific questions by making comments that contribute to the discussion and elaborate on the remarks of others. (d) Review the key ideas expressed and draw conclusions in light of information and knowledge gained from the discussions. English language learners communicate for social and instructional purposes within the school setting. Summarize a written text read aloud or information presented in diverse media and formats, including visually, quantitatively, and orally. Summarize the points a speaker makes and explain how each claim is supported by reasons and evidence. Write informative/explanatory texts to examine a topic and convey ideas and information clearly. (a) Introduce a topic clearly, provide a general observation and focus, and group related information logically; include formatting (e.g., headings), illustrations, and multimedia when useful to aiding comprehension. (b) Develop the topic with facts, definitions, concrete details, quotations, or other information and examples related to the topic. (c) Link ideas within and across categories of information using words, phrases, and clauses (e.g., in contrast, especially). (d) Use precise language and domain-specific vocabulary to inform about or explain the topic. (e) Provide a concluding statement or section related to the information or explanation presented. English language learners communicate information, ideas and concepts necessary for academic success in the content area of Mathematics. 12-7: Enrichment Game: Factory Frenzy Fractions 12-7: Pick a Project 12-7: Another Look Curriculum Standards: Fluently multiply multi-digit whole numbers using the standard algorithm. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Convert standard measurements of time to solve real-world problems. Fluently multiply multi-digit whole numbers using the standard algorithm. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Convert among different-sized standard measurement units (i.e., km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec) within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Fluently multiply multi-digit whole numbers using the standard algorithm. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Convert among different-sized standard measurement units (i.e., km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec) within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Convert units of time. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Convert between different-sized measurement units within a given measurement system. A table of equivalencies will be provided. Divide multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Recognize that quotients can be represented in a variety of ways, including a whole number with a remainder, a fraction or mixed number, or a decimal. Consider the context in which a problem is situated to select the most useful form of the quotient for the solution and use the context to interpret the quotient appropriately. 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. Spanish Resources 12-7: eText del Libro del estudiante 12-7: Repaso diario 12-7: Aprendizaje visual 12-7: Amigo de práctica: Práctica adicional 12-7: Práctica adicional interactiva 12-7: Refuerzo para mejorar la comprensión 12-7: Desarrollar la competencia matemática 12-7: Ampliación 12-8: Solve Word Problems Using Measurement Conversions Interactive Student Edition: Grade 5 Lesson 12-8 Math Anytime 12-8: Daily Review Topic 12: Today's Challenge Step 1: Problem-Based Learning 12-8: Solve & Share Curriculum Standards: Fluently multiply multi-digit whole numbers using the standard algorithm. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. English language learners communicate for social and instructional purposes within the school setting. Write informative/explanatory texts to examine a topic and convey ideas and information clearly. (a) Introduce a topic clearly, provide a general observation and focus, and group related information logically; include formatting (e.g., headings), illustrations, and multimedia when useful to aiding comprehension. (b) Develop the topic with facts, definitions, concrete details, quotations, or other information and examples related to the topic. (c) Link ideas within and across categories of information using words, phrases, and clauses (e.g., in contrast, especially). (d) Use precise language and domain-specific vocabulary to inform about or explain the topic. (e) Provide a concluding statement or section related to the information or explanation presented. English language learners communicate information, ideas and concepts necessary for academic success in the content area of Mathematics. Fluently multiply multi-digit whole numbers using the standard algorithm. Convert among different-sized standard measurement units (i.e., km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec) within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi- step, real world problems. Fluently multiply multi-digit whole numbers using the standard algorithm. Convert among different-sized standard measurement units (i.e., km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec) within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Solve real-world problems with measurement conversions. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Convert between different-sized measurement units within a given measurement system. A table of equivalencies will be provided. 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. Engage effectively in a range of collaborative discussions (one-on- one, in groups, and teacher-led) with diverse partners on grade 5 topics and texts, building on others’ ideas and expressing their own clearly. (a) Come to discussions prepared, having read or studied required material; explicitly draw on that preparation and other information known about the topic to explore ideas under discussion. (b) Follow agreed-upon rules for discussions and carry out assigned roles. (c) Pose and respond to specific questions by making comments that contribute to the discussion and elaborate on the remarks of others. (d) Review the key ideas expressed and draw conclusions in light of information and knowledge gained from the discussions. Summarize a written text read aloud or information presented in diverse media and formats, including visually, quantitatively, and orally. Summarize the points a speaker makes and explain how each claim is supported by reasons and evidence. Step 2: Visual Learning 12-8: Visual Learning Curriculum Standards: Fluently multiply multi-digit whole numbers using the standard algorithm. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Fluently multiply multi-digit whole numbers using the standard algorithm. Convert among different-sized standard measurement units (i.e., km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec) within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi- step, real world problems. Fluently multiply multi-digit whole numbers using the standard algorithm. Convert among different-sized standard measurement units (i.e., km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec) within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Solve real-world problems with measurement conversions. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Convert between different-sized measurement units within a given measurement system. A table of equivalencies will be provided. 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. 12-8: Convince Me! Curriculum Standards: Fluently multiply multi-digit whole numbers using the standard algorithm. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Fluently multiply multi-digit whole numbers using the standard algorithm. Convert among different-sized standard measurement units (i.e., km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec) within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi- step, real world problems. Fluently multiply multi-digit whole numbers using the standard algorithm. Convert among different-sized standard measurement units (i.e., km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec) within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Solve real-world problems with measurement conversions. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Convert between different-sized measurement units within a given measurement system. A table of equivalencies will be provided. 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. Practice and Problem Solving 12-8: Student Edition Practice Curriculum Standards: Fluently multiply multi-digit whole numbers using the standard algorithm. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Fluently multiply multi-digit whole numbers using the standard algorithm. Convert among different-sized standard measurement units (i.e., km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec) within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi- step, real world problems. Fluently multiply multi-digit whole numbers using the standard algorithm. Convert among different-sized standard measurement units (i.e., km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec) within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Solve real-world problems with measurement conversions. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Convert between different-sized measurement units within a given measurement system. A table of equivalencies will be provided. 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. 12-8: Practice Buddy: Independent Practice; Problem Solving Curriculum Standards: Fluently multiply multi-digit whole numbers using the standard algorithm. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Fluently multiply multi-digit whole numbers using the standard algorithm. Convert among different-sized standard measurement units (i.e., km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec) within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi- step, real world problems. Fluently multiply multi-digit whole numbers using the standard algorithm. Convert among different-sized standard measurement units (i.e., km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec) within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Solve real-world problems with measurement conversions. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Convert between different-sized measurement units within a given measurement system. A table of equivalencies will be provided. 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. 12-8: Practice Buddy: Additional Practice Curriculum Standards: Fluently multiply multi-digit whole numbers using the standard algorithm. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Fluently multiply multi-digit whole numbers using the standard algorithm. Convert among different-sized standard measurement units (i.e., km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec) within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi- step, real world problems. Fluently multiply multi-digit whole numbers using the standard algorithm. Convert among different-sized standard measurement units (i.e., km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec) within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Solve real-world problems with measurement conversions. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Convert between different-sized measurement units within a given measurement system. A table of equivalencies will be provided. 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. 12-8: Interactive Additional Practice Step 3: Assess & Differentiate 12-8: Practice Buddy: Additional Practice Curriculum Standards: Fluently multiply multi-digit whole numbers using the standard algorithm. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Fluently multiply multi-digit whole numbers using the standard algorithm. Convert among different-sized standard measurement units (i.e., km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec) within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi- step, real world problems. Fluently multiply multi-digit whole numbers using the standard algorithm. Convert among different-sized standard measurement units (i.e., km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec) within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Solve real-world problems with measurement conversions. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Convert between different-sized measurement units within a given measurement system. A table of equivalencies will be provided. 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. 12-8: Enrichment Curriculum Standards: Fluently multiply multi-digit whole numbers using the standard algorithm. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Fluently multiply multi-digit whole numbers using the standard algorithm. Convert among different-sized standard measurement units (i.e., km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec) within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi- step, real world problems. Fluently multiply multi-digit whole numbers using the standard algorithm. Convert among different-sized standard measurement units (i.e., km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec) within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Solve real-world problems with measurement conversions. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Convert between different-sized measurement units within a given measurement system. A table of equivalencies will be provided. 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. 12-8: Quick Check Curriculum Standards: Fluently multiply multi-digit whole numbers using the standard algorithm. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Fluently multiply multi-digit whole numbers using the standard algorithm. Convert among different-sized standard measurement units (i.e., km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec) within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi- step, real world problems. Fluently multiply multi-digit whole numbers using the standard algorithm. Convert among different-sized standard measurement units (i.e., km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec) within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Solve real-world problems with measurement conversions. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Convert between different-sized measurement units within a given measurement system. A table of equivalencies will be provided. 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. 12-8: Lesson Self-Assessment 12-8: Reteach to Build Understanding Curriculum Standards: Fluently multiply multi-digit whole numbers using the standard algorithm. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Fluently multiply multi-digit whole numbers using the standard algorithm. Convert among different-sized standard measurement units (i.e., km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec) within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi- step, real world problems. Fluently multiply multi-digit whole numbers using the standard algorithm. Convert among different-sized standard measurement units (i.e., km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec) within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Solve real-world problems with measurement conversions. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Convert between different-sized measurement units within a given measurement system. A table of equivalencies will be provided. 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. 12-8: Build Mathematical Literacy Curriculum Standards: Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 5 topics and texts, building on others’ ideas and expressing their own clearly. (a) Come to discussions prepared, having read or studied required material; explicitly draw on that preparation and other information known about the topic to explore ideas under discussion. (b) Follow agreed-upon rules for discussions and carry out assigned roles. (c) Pose and respond to specific questions by making comments that contribute to the discussion and elaborate on the remarks of others. (d) Review the key ideas expressed and draw conclusions in light of information and knowledge gained from the discussions. English language learners communicate for social and instructional purposes within the school setting. Summarize a written text read aloud or information presented in diverse media and formats, including visually, quantitatively, and orally. Summarize the points a speaker makes and explain how each claim is supported by reasons and evidence. Write informative/explanatory texts to examine a topic and convey ideas and information clearly. (a) Introduce a topic clearly, provide a general observation and focus, and group related information logically; include formatting (e.g., headings), illustrations, and multimedia when useful to aiding comprehension. (b) Develop the topic with facts, definitions, concrete details, quotations, or other information and examples related to the topic. (c) Link ideas within and across categories of information using words, phrases, and clauses (e.g., in contrast, especially). (d) Use precise language and domain-specific vocabulary to inform about or explain the topic. (e) Provide a concluding statement or section related to the information or explanation presented. English language learners communicate information, ideas and concepts necessary for academic success in the content area of Mathematics. 12-8: Enrichment Game: Factory Frenzy Fractions 12-8 Problem-Solving Reading Activity Curriculum Standards: Fluently multiply multi-digit whole numbers using the standard algorithm. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Fluently multiply multi-digit whole numbers using the standard algorithm. Convert among different-sized standard measurement units (i.e., km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec) within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi- step, real world problems. Fluently multiply multi-digit whole numbers using the standard algorithm. Convert among different-sized standard measurement units (i.e., km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec) within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Solve real-world problems with measurement conversions. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Convert between different-sized measurement units within a given measurement system. A table of equivalencies will be provided. 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. 12-8: Another Look Curriculum Standards: Fluently multiply multi-digit whole numbers using the standard algorithm. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Fluently multiply multi-digit whole numbers using the standard algorithm. Convert among different-sized standard measurement units (i.e., km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec) within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi- step, real world problems. Fluently multiply multi-digit whole numbers using the standard algorithm. Convert among different-sized standard measurement units (i.e., km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec) within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Solve real-world problems with measurement conversions. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Convert between different-sized measurement units within a given measurement system. A table of equivalencies will be provided. 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. Spanish Resources 12-8: eText del Libro del estudiante 12-8: Repaso diario 12-8: Aprendizaje visual 12-8: Amigo de práctica: Práctica adicional 12-8: Práctica adicional interactiva 12-8: Refuerzo para mejorar la comprensión 12-8: Desarrollar la competencia matemática 12-8: Ampliación 12-9: Problem Solving: Precision Interactive Student Edition: Grade 5 Lesson 12-9 Math Anytime 12-9: Daily Review Topic 12: Today's Challenge Step 1: Problem-Based Learning 12-9: Solve & Share Curriculum Standards: Fluently multiply multi-digit whole numbers using the standard algorithm. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Attend to precision. Fluently multiply multi-digit whole numbers using the standard algorithm. Convert among different-sized standard measurement units (i.e., km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec) within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Attend to precision. Fluently multiply multi-digit whole numbers using the standard algorithm. Convert among different-sized standard measurement units (i.e., km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec) within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Attend to precision. Mathematically proficient students try to communicate precisely to others. They try to use clear definitions in discussion with others and in their own reasoning. They state the meaning of the symbols they choose, including using the equal sign consistently and appropriately. They are careful about specifying units of measure, and labeling axes to clarify the correspondence with quantities in a problem. They calculate accurately and efficiently, express numerical answers with a degree of precision appropriate for the problem context. In the elementary grades, students give carefully formulated explanations to each other. By the time they reach high school they have learned to examine claims and make explicit use of definitions. Be precise when solving measurement problems. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Attend to precision. Attend to precision. Convert between different-sized measurement units within a given measurement system. A table of equivalencies will be provided. Attend to precision. Solve real-world and mathematical problems requiring addition, subtraction, multiplication and division of multi-digit whole numbers. Use various strategies, including the inverse relationships between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. English language learners communicate for social and instructional purposes within the school setting. Write informative/explanatory texts to examine a topic and convey ideas and information clearly. (a) Introduce a topic clearly, provide a general observation and focus, and group related information logically; include formatting (e.g., headings), illustrations, and multimedia when useful to aiding comprehension. (b) Develop the topic with facts, definitions, concrete details, quotations, or other information and examples related to the topic. (c) Link ideas within and across categories of information using words, phrases, and clauses (e.g., in contrast, especially). (d) Use precise language and domain-specific vocabulary to inform about or explain the topic. (e) Provide a concluding statement or section related to the information or explanation presented. English language learners communicate information, ideas and concepts necessary for academic success in the content area of Mathematics. Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 5 topics and texts, building on others’ ideas and expressing their own clearly. (a) Come to discussions prepared, having read or studied required material; explicitly draw on that preparation and other information known about the topic to explore ideas under discussion. (b) Follow agreed-upon rules for discussions and carry out assigned roles. (c) Pose and respond to specific questions by making comments that contribute to the discussion and elaborate on the remarks of others. (d) Review the key ideas expressed and draw conclusions in light of information and knowledge gained from the discussions. Summarize a written text read aloud or information presented in diverse media and formats, including visually, quantitatively, and orally. Summarize the points a speaker makes and explain how each claim is supported by reasons and evidence. Step 2: Visual Learning 12-9: Visual Learning Curriculum Standards: Fluently multiply multi-digit whole numbers using the standard algorithm. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Attend to precision. Fluently multiply multi-digit whole numbers using the standard algorithm. Convert among different-sized standard measurement units (i.e., km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec) within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Attend to precision. Fluently multiply multi-digit whole numbers using the standard algorithm. Convert among different-sized standard measurement units (i.e., km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec) within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Attend to precision. Mathematically proficient students try to communicate precisely to others. They try to use clear definitions in discussion with others and in their own reasoning. They state the meaning of the symbols they choose, including using the equal sign consistently and appropriately. They are careful about specifying units of measure, and labeling axes to clarify the correspondence with quantities in a problem. They calculate accurately and efficiently, express numerical answers with a degree of precision appropriate for the problem context. In the elementary grades, students give carefully formulated explanations to each other. By the time they reach high school they have learned to examine claims and make explicit use of definitions. Be precise when solving measurement problems. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Attend to precision. Attend to precision. Convert between different-sized measurement units within a given measurement system. A table of equivalencies will be provided. Attend to precision. Solve real-world and mathematical problems requiring addition, subtraction, multiplication and division of multi-digit whole numbers. Use various strategies, including the inverse relationships between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. 12-9: Convince Me! Curriculum Standards: Fluently multiply multi-digit whole numbers using the standard algorithm. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Attend to precision. Fluently multiply multi-digit whole numbers using the standard algorithm. Convert among different-sized standard measurement units (i.e., km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec) within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Attend to precision. Fluently multiply multi-digit whole numbers using the standard algorithm. Convert among different-sized standard measurement units (i.e., km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec) within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Attend to precision. Mathematically proficient students try to communicate precisely to others. They try to use clear definitions in discussion with others and in their own reasoning. They state the meaning of the symbols they choose, including using the equal sign consistently and appropriately. They are careful about specifying units of measure, and labeling axes to clarify the correspondence with quantities in a problem. They calculate accurately and efficiently, express numerical answers with a degree of precision appropriate for the problem context. In the elementary grades, students give carefully formulated explanations to each other. By the time they reach high school they have learned to examine claims and make explicit use of definitions. Be precise when solving measurement problems. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Attend to precision. Attend to precision. Convert between different-sized measurement units within a given measurement system. A table of equivalencies will be provided. Attend to precision. Solve real-world and mathematical problems requiring addition, subtraction, multiplication and division of multi-digit whole numbers. Use various strategies, including the inverse relationships between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. Practice and Problem Solving 12-9: Student Edition Practice Curriculum Standards: Fluently multiply multi-digit whole numbers using the standard algorithm. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Attend to precision. Fluently multiply multi-digit whole numbers using the standard algorithm. Convert among different-sized standard measurement units (i.e., km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec) within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Attend to precision. Fluently multiply multi-digit whole numbers using the standard algorithm. Convert among different-sized standard measurement units (i.e., km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec) within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Attend to precision. Mathematically proficient students try to communicate precisely to others. They try to use clear definitions in discussion with others and in their own reasoning. They state the meaning of the symbols they choose, including using the equal sign consistently and appropriately. They are careful about specifying units of measure, and labeling axes to clarify the correspondence with quantities in a problem. They calculate accurately and efficiently, express numerical answers with a degree of precision appropriate for the problem context. In the elementary grades, students give carefully formulated explanations to each other. By the time they reach high school they have learned to examine claims and make explicit use of definitions. Be precise when solving measurement problems. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Attend to precision. Attend to precision. Convert between different-sized measurement units within a given measurement system. A table of equivalencies will be provided. Attend to precision. Solve real-world and mathematical problems requiring addition, subtraction, multiplication and division of multi-digit whole numbers. Use various strategies, including the inverse relationships between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. 12-9: Practice Buddy: Independent Practice; Problem Solving Curriculum Standards: Fluently multiply multi-digit whole numbers using the standard algorithm. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Attend to precision. Fluently multiply multi-digit whole numbers using the standard algorithm. Convert among different-sized standard measurement units (i.e., km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec) within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Attend to precision. Fluently multiply multi-digit whole numbers using the standard algorithm. Convert among different-sized standard measurement units (i.e., km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec) within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Attend to precision. Mathematically proficient students try to communicate precisely to others. They try to use clear definitions in discussion with others and in their own reasoning. They state the meaning of the symbols they choose, including using the equal sign consistently and appropriately. They are careful about specifying units of measure, and labeling axes to clarify the correspondence with quantities in a problem. They calculate accurately and efficiently, express numerical answers with a degree of precision appropriate for the problem context. In the elementary grades, students give carefully formulated explanations to each other. By the time they reach high school they have learned to examine claims and make explicit use of definitions. Be precise when solving measurement problems. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Attend to precision. Attend to precision. Convert between different-sized measurement units within a given measurement system. A table of equivalencies will be provided. Attend to precision. Solve real-world and mathematical problems requiring addition, subtraction, multiplication and division of multi-digit whole numbers. Use various strategies, including the inverse relationships between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. 12-9: Practice Buddy: Additional Practice Curriculum Standards: Fluently multiply multi-digit whole numbers using the standard algorithm. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Attend to precision. Fluently multiply multi-digit whole numbers using the standard algorithm. Convert among different-sized standard measurement units (i.e., km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec) within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Attend to precision. Fluently multiply multi-digit whole numbers using the standard algorithm. Convert among different-sized standard measurement units (i.e., km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec) within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Attend to precision. Mathematically proficient students try to communicate precisely to others. They try to use clear definitions in discussion with others and in their own reasoning. They state the meaning of the symbols they choose, including using the equal sign consistently and appropriately. They are careful about specifying units of measure, and labeling axes to clarify the correspondence with quantities in a problem. They calculate accurately and efficiently, express numerical answers with a degree of precision appropriate for the problem context. In the elementary grades, students give carefully formulated explanations to each other. By the time they reach high school they have learned to examine claims and make explicit use of definitions. Be precise when solving measurement problems. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Attend to precision. Attend to precision. Convert between different-sized measurement units within a given measurement system. A table of equivalencies will be provided. Attend to precision. Solve real-world and mathematical problems requiring addition, subtraction, multiplication and division of multi-digit whole numbers. Use various strategies, including the inverse relationships between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. 12-9: Interactive Additional Practice Step 3: Assess & Differentiate 12-9: Practice Buddy: Additional Practice Curriculum Standards: Fluently multiply multi-digit whole numbers using the standard algorithm. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Attend to precision. Fluently multiply multi-digit whole numbers using the standard algorithm. Convert among different-sized standard measurement units (i.e., km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec) within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Attend to precision. Fluently multiply multi-digit whole numbers using the standard algorithm. Convert among different-sized standard measurement units (i.e., km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec) within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Attend to precision. Mathematically proficient students try to communicate precisely to others. They try to use clear definitions in discussion with others and in their own reasoning. They state the meaning of the symbols they choose, including using the equal sign consistently and appropriately. They are careful about specifying units of measure, and labeling axes to clarify the correspondence with quantities in a problem. They calculate accurately and efficiently, express numerical answers with a degree of precision appropriate for the problem context. In the elementary grades, students give carefully formulated explanations to each other. By the time they reach high school they have learned to examine claims and make explicit use of definitions. Be precise when solving measurement problems. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Attend to precision. Attend to precision. Convert between different-sized measurement units within a given measurement system. A table of equivalencies will be provided. Attend to precision. Solve real-world and mathematical problems requiring addition, subtraction, multiplication and division of multi-digit whole numbers. Use various strategies, including the inverse relationships between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. 12-9: Enrichment Curriculum Standards: Fluently multiply multi-digit whole numbers using the standard algorithm. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Attend to precision. Fluently multiply multi-digit whole numbers using the standard algorithm. Convert among different-sized standard measurement units (i.e., km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec) within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Attend to precision. Fluently multiply multi-digit whole numbers using the standard algorithm. Convert among different-sized standard measurement units (i.e., km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec) within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Attend to precision. Mathematically proficient students try to communicate precisely to others. They try to use clear definitions in discussion with others and in their own reasoning. They state the meaning of the symbols they choose, including using the equal sign consistently and appropriately. They are careful about specifying units of measure, and labeling axes to clarify the correspondence with quantities in a problem. They calculate accurately and efficiently, express numerical answers with a degree of precision appropriate for the problem context. In the elementary grades, students give carefully formulated explanations to each other. By the time they reach high school they have learned to examine claims and make explicit use of definitions. Be precise when solving measurement problems. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Attend to precision. Attend to precision. Convert between different-sized measurement units within a given measurement system. A table of equivalencies will be provided. Attend to precision. Solve real-world and mathematical problems requiring addition, subtraction, multiplication and division of multi-digit whole numbers. Use various strategies, including the inverse relationships between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. 12-9: Quick Check Curriculum Standards: Fluently multiply multi-digit whole numbers using the standard algorithm. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Attend to precision. Fluently multiply multi-digit whole numbers using the standard algorithm. Convert among different-sized standard measurement units (i.e., km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec) within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Attend to precision. Fluently multiply multi-digit whole numbers using the standard algorithm. Convert among different-sized standard measurement units (i.e., km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec) within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Attend to precision. Mathematically proficient students try to communicate precisely to others. They try to use clear definitions in discussion with others and in their own reasoning. They state the meaning of the symbols they choose, including using the equal sign consistently and appropriately. They are careful about specifying units of measure, and labeling axes to clarify the correspondence with quantities in a problem. They calculate accurately and efficiently, express numerical answers with a degree of precision appropriate for the problem context. In the elementary grades, students give carefully formulated explanations to each other. By the time they reach high school they have learned to examine claims and make explicit use of definitions. Be precise when solving measurement problems. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Attend to precision. Attend to precision. Convert between different-sized measurement units within a given measurement system. A table of equivalencies will be provided. Attend to precision. Solve real-world and mathematical problems requiring addition, subtraction, multiplication and division of multi-digit whole numbers. Use various strategies, including the inverse relationships between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. 12-9: Lesson Self-Assessment 12-9: Reteach to Build Understanding Curriculum Standards: Fluently multiply multi-digit whole numbers using the standard algorithm. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Attend to precision. Fluently multiply multi-digit whole numbers using the standard algorithm. Convert among different-sized standard measurement units (i.e., km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec) within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Attend to precision. Fluently multiply multi-digit whole numbers using the standard algorithm. Convert among different-sized standard measurement units (i.e., km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec) within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Attend to precision. Mathematically proficient students try to communicate precisely to others. They try to use clear definitions in discussion with others and in their own reasoning. They state the meaning of the symbols they choose, including using the equal sign consistently and appropriately. They are careful about specifying units of measure, and labeling axes to clarify the correspondence with quantities in a problem. They calculate accurately and efficiently, express numerical answers with a degree of precision appropriate for the problem context. In the elementary grades, students give carefully formulated explanations to each other. By the time they reach high school they have learned to examine claims and make explicit use of definitions. Be precise when solving measurement problems. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Attend to precision. Attend to precision. Convert between different-sized measurement units within a given measurement system. A table of equivalencies will be provided. Attend to precision. Solve real-world and mathematical problems requiring addition, subtraction, multiplication and division of multi-digit whole numbers. Use various strategies, including the inverse relationships between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. 12-9: Build Mathematical Literacy Curriculum Standards: Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 5 topics and texts, building on others’ ideas and expressing their own clearly. (a) Come to discussions prepared, having read or studied required material; explicitly draw on that preparation and other information known about the topic to explore ideas under discussion. (b) Follow agreed-upon rules for discussions and carry out assigned roles. (c) Pose and respond to specific questions by making comments that contribute to the discussion and elaborate on the remarks of others. (d) Review the key ideas expressed and draw conclusions in light of information and knowledge gained from the discussions. English language learners communicate for social and instructional purposes within the school setting. Summarize a written text read aloud or information presented in diverse media and formats, including visually, quantitatively, and orally. Summarize the points a speaker makes and explain how each claim is supported by reasons and evidence. Write informative/explanatory texts to examine a topic and convey ideas and information clearly. (a) Introduce a topic clearly, provide a general observation and focus, and group related information logically; include formatting (e.g., headings), illustrations, and multimedia when useful to aiding comprehension. (b) Develop the topic with facts, definitions, concrete details, quotations, or other information and examples related to the topic. (c) Link ideas within and across categories of information using words, phrases, and clauses (e.g., in contrast, especially). (d) Use precise language and domain-specific vocabulary to inform about or explain the topic. (e) Provide a concluding statement or section related to the information or explanation presented. English language learners communicate information, ideas and concepts necessary for academic success in the content area of Mathematics. 12-9: Enrichment Game: Save the Word: Grade 5 Topics 1-8 12-9: enVision STEM Activity Curriculum Standards: Fluently multiply multi-digit whole numbers using the standard algorithm. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Attend to precision. Fluently multiply multi-digit whole numbers using the standard algorithm. Convert among different-sized standard measurement units (i.e., km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec) within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Attend to precision. Fluently multiply multi-digit whole numbers using the standard algorithm. Convert among different-sized standard measurement units (i.e., km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec) within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Attend to precision. Mathematically proficient students try to communicate precisely to others. They try to use clear definitions in discussion with others and in their own reasoning. They state the meaning of the symbols they choose, including using the equal sign consistently and appropriately. They are careful about specifying units of measure, and labeling axes to clarify the correspondence with quantities in a problem. They calculate accurately and efficiently, express numerical answers with a degree of precision appropriate for the problem context. In the elementary grades, students give carefully formulated explanations to each other. By the time they reach high school they have learned to examine claims and make explicit use of definitions. Be precise when solving measurement problems. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Attend to precision. Attend to precision. Convert between different-sized measurement units within a given measurement system. A table of equivalencies will be provided. Attend to precision. Solve real-world and mathematical problems requiring addition, subtraction, multiplication and division of multi-digit whole numbers. Use various strategies, including the inverse relationships between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. 12-9: Another Look Curriculum Standards: Fluently multiply multi-digit whole numbers using the standard algorithm. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Attend to precision. Fluently multiply multi-digit whole numbers using the standard algorithm. Convert among different-sized standard measurement units (i.e., km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec) within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Attend to precision. Fluently multiply multi-digit whole numbers using the standard algorithm. Convert among different-sized standard measurement units (i.e., km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec) within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Attend to precision. Mathematically proficient students try to communicate precisely to others. They try to use clear definitions in discussion with others and in their own reasoning. They state the meaning of the symbols they choose, including using the equal sign consistently and appropriately. They are careful about specifying units of measure, and labeling axes to clarify the correspondence with quantities in a problem. They calculate accurately and efficiently, express numerical answers with a degree of precision appropriate for the problem context. In the elementary grades, students give carefully formulated explanations to each other. By the time they reach high school they have learned to examine claims and make explicit use of definitions. Be precise when solving measurement problems. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Attend to precision. Attend to precision. Convert between different-sized measurement units within a given measurement system. A table of equivalencies will be provided. Attend to precision. Solve real-world and mathematical problems requiring addition, subtraction, multiplication and division of multi-digit whole numbers. Use various strategies, including the inverse relationships between operations, the use of technology, and the context of the problem to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. Spanish Resources 12-9: eText del Libro del estudiante 12-9: Repaso diario 12-9: Aprendizaje visual 12-9: Amigo de práctica: Práctica adicional 12-9: Práctica adicional interactiva 12-9: Refuerzo para mejorar la comprensión 12-9: Desarrollar la competencia matemática 12-9: Ampliación Topic 12: End of Topic Interactive Student Edition: End of Topic 12 Topic 12: Fluency Practice Activity Interactive Student Edition: Topic 12 Assessment Practice Interactive Student Edition: Topic 12 Performance Task Topic 12 Performance Task Topic 12 Assessment 13-5 Center Games 12-1: Visual Learning Curriculum Standards: Fluently multiply multi-digit whole numbers using the standard algorithm. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Fluently multiply multi-digit whole numbers using the standard algorithm. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Convert among different-sized standard measurement units (i.e., km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec) within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Fluently multiply multi-digit whole numbers using the standard algorithm. Find whole-number quotients of whole numbers with up to four- digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Convert among different-sized standard measurement units (i.e., km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec) within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Convert customary units of length. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Convert between different-sized measurement units within a given measurement system. A table of equivalencies will be provided. Divide multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Recognize that quotients can be represented in a variety of ways, including a whole number with a remainder, a fraction or mixed number, or a decimal. Consider the context in which a problem is situated to select the most useful form of the quotient for the solution and use the context to interpret the quotient appropriately. 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. 12-2: Visual Learning Curriculum Standards: Fluently multiply multi-digit whole numbers using the standard algorithm. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Fluently multiply multi-digit whole numbers using the standard algorithm. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Convert among different-sized standard measurement units (i.e., km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec) within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Fluently multiply multi-digit whole numbers using the standard algorithm. Find whole-number quotients of whole numbers with up to four- digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Convert among different-sized standard measurement units (i.e., km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec) within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Convert customary units of capacity. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Convert between different-sized measurement units within a given measurement system. A table of equivalencies will be provided. Divide multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Recognize that quotients can be represented in a variety of ways, including a whole number with a remainder, a fraction or mixed number, or a decimal. Consider the context in which a problem is situated to select the most useful form of the quotient for the solution and use the context to interpret the quotient appropriately. 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. 12-3: Visual Learning Curriculum Standards: Fluently multiply multi-digit whole numbers using the standard algorithm. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Fluently multiply multi-digit whole numbers using the standard algorithm. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Convert among different-sized standard measurement units (i.e., km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec) within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Fluently multiply multi-digit whole numbers using the standard algorithm. Find whole-number quotients of whole numbers with up to four- digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Convert among different-sized standard measurement units (i.e., km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec) within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Convert customary units of weight. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Convert between different-sized measurement units within a given measurement system. A table of equivalencies will be provided. Divide multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Recognize that quotients can be represented in a variety of ways, including a whole number with a remainder, a fraction or mixed number, or a decimal. Consider the context in which a problem is situated to select the most useful form of the quotient for the solution and use the context to interpret the quotient appropriately. 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. 12-4: Visual Learning Curriculum Standards: Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole- number exponents to denote powers of 10. Convert among different-sized standard measurement units (i.e., km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec) within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole- number exponents to denote powers of 10. Convert among different-sized standard measurement units (i.e., km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec) within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Convert metric units of length. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10 and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. Convert between different-sized measurement units within a given measurement system. A table of equivalencies will be provided. Divide multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Recognize that quotients can be represented in a variety of ways, including a whole number with a remainder, a fraction or mixed number, or a decimal. Consider the context in which a problem is situated to select the most useful form of the quotient for the solution and use the context to interpret the quotient appropriately. 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. 12-5: Visual Learning Curriculum Standards: Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole- number exponents to denote powers of 10. Convert among different-sized standard measurement units (i.e., km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec) within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole- number exponents to denote powers of 10. Convert among different-sized standard measurement units (i.e., km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec) within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Convert metric units of capacity. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10 and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. Convert between different- sized measurement units within a given measurement system. A table of equivalencies will be provided. Divide multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Recognize that quotients can be represented in a variety of ways, including a whole number with a remainder, a fraction or mixed number, or a decimal. Consider the context in which a problem is situated to select the most useful form of the quotient for the solution and use the context to interpret the quotient appropriately. 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. 12-6: Visual Learning Curriculum Standards: Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole- number exponents to denote powers of 10. Convert among different-sized standard measurement units (i.e., km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec) within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole- number exponents to denote powers of 10. Convert among different-sized standard measurement units (i.e., km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec) within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Convert metric units of mass. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10 and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. Convert between different-sized measurement units within a given measurement system. A table of equivalencies will be provided. Divide multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Recognize that quotients can be represented in a variety of ways, including a whole number with a remainder, a fraction or mixed number, or a decimal. Consider the context in which a problem is situated to select the most useful form of the quotient for the solution and use the context to interpret the quotient appropriately. 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. 12-8: Visual Learning Curriculum Standards: Fluently multiply multi-digit whole numbers using the standard algorithm. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Fluently multiply multi-digit whole numbers using the standard algorithm. Convert among different-sized standard measurement units (i.e., km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec) within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Fluently multiply multi-digit whole numbers using the standard algorithm. Convert among different-sized standard measurement units (i.e., km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec) within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Solve real-world problems with measurement conversions. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Convert between different-sized measurement units within a given measurement system. A table of equivalencies will be provided. 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. Topic 12 Online Assessment Curriculum Standards: Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Fluently multiply multi-digit whole numbers using the standard algorithm. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole- number exponents to denote powers of 10. Convert among different-sized standard measurement units (i.e., km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec) within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole- number exponents to denote powers of 10. Convert among different-sized standard measurement units (i.e., km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec) within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Convert metric units of mass. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10 and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. Convert between different-sized measurement units within a given measurement system. A table of equivalencies will be provided. Divide multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Recognize that quotients can be represented in a variety of ways, including a whole number with a remainder, a fraction or mixed number, or a decimal. Consider the context in which a problem is situated to select the most useful form of the quotient for the solution and use the context to interpret the quotient appropriately. 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. Convert metric units of capacity. Fluently multiply multi-digit whole numbers using the standard algorithm. Fluently multiply multi-digit whole numbers using the standard algorithm. Solve real-world problems with measurement conversions. 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. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Convert customary units of capacity. Convert customary units of length. Convert metric units of length. Convert customary units of weight. Topic 12 Spanish Assessments Tema 12: Tarea de rendimento Tema 12: Evaluación Topics 1–12: Cumulative/Benchmark Assessments Topics 1–12: Cumulative/Benchmark Assessment 7-7: Another Look Curriculum Standards: Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Add mixed numbers using models. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Add and subtract fractions (including mixed numbers) with unlike denominators. (May include multiple methods and representations.) Add and subtract decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Model addition and subtraction of fractions and decimals using a variety of representations. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. 4-1: Another Look Curriculum Standards: Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Use knowledge about place value and patterns to find the product of a decimal number and a power of 10. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10 and 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. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). 8-1: Another Look Curriculum Standards: Interpret the product a/b x q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = (ac)/(bd). Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Interpret the product (a/b) × q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction. Interpret the product (a/b) × q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = ac/bd.) Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Multiply a fraction by a whole number. Interpret the product a/b x q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = (ac)/(bd). 4-4: Another Look Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Use place-value understanding and an algorithm for multiplying whole numbers to multiply a decimal and a whole number. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). 5-4: Another Look Curriculum Standards: 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. 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. 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. Solve division problems using partial quotients. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors. Divide multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Recognize that quotients can be represented in a variety of ways, including a whole number with a remainder, a fraction or mixed number, or a decimal. Estimate solutions to arithmetic problems in order to assess the reasonableness of results. 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. 4-5: Another Look Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Use grids to model decimals and find the product of a decimal and a decimal. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). 2-4: Another Look Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add decimals to hundredths using familiar strategies, such as partial sums. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). Add and subtract decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Model addition and subtraction of fractions and decimals using a variety of representations. Estimate sums and differences of decimals and fractions to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. 7-3: Another Look Curriculum Standards: Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Add fractions with unlike denominators using equivalent fractions with a common denominator. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Add and subtract fractions (including mixed numbers) with unlike denominators. (May include multiple methods and representations.) Add and subtract decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Model addition and subtraction of fractions and decimals using a variety of representations. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. 6-3: Another Look Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Use models to help find quotients in problems involving decimals. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). 3-5: Another Look Curriculum Standards: Fluently multiply multi-digit whole numbers using the standard algorithm. Fluently multiply multi-digit whole numbers using the standard algorithm. Fluently multiply multi-digit whole numbers using the standard algorithm. Multiply 3-digit by 2-digit numbers by adding partial products or by using the standard algorithm. Fluently multiply multi-digit whole numbers using the standard algorithm. Multiply multi-digit whole numbers (not to exceed three-digit by three-digit). Estimate solutions to arithmetic problems in order to assess the reasonableness of results. Solve real- world and mathematical problems requiring addition, subtraction, multiplication and division of multi- digit whole numbers. Use various strategies, including the inverse relationships between operations, the use of technology, and the context of the problem to assess the reasonableness of results. 9-4: Another Look Curriculum Standards: Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for 4 ÷ (1/5), and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 × (1/5) = 4. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins? Interpret division of a whole number by a unit fraction, and compute such quotients. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for 4 ÷ (1/5), and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 × (1/5) = 4. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins? Use models, such as pictorial models or a number line, to show dividing a whole number by a unit fraction. Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for 4 ÷ (1/5), and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 × (1/5) = 4. Divide unit fractions by whole numbers and whole numbers by unit fractions. 10-2: Another Look Curriculum Standards: Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Make a line plot to display a data set of measurements in fractions of a unit (1/2 , 1/4 , 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally. Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally. Organize and display data in a line plot. Make a line plot to display a data set of measurements in fractions of a unit (1/2 , 1/4 , 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally. Solve problems involving computation of fractions by using information presented in line plots. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. 11-4: Another Look Curriculum Standards: Recognize volume as additive. 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. Recognize volume as additive. 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. Recognize volume as additive. 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. Use models, prior knowledge of volume and previously learned strategies to solve word problems involving volume. Recognize volume as additive. 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. Find volumes of solid figures composed of two nonoverlapping right rectangular prisms. 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. Use various tools and strategies to measure the volume and surface area of objects that are shaped like rectangular prisms. Understand that the volume of a three dimensional figure can be found by counting the total number of same-sized cubic units that fill a shape without gaps or overlaps. Use cubic units to label volume measurements. Develop and use the formulas V = ?wh and V = Bh to determine the volume of rectangular prisms. Justify why base area B and height h are multiplied to find the volume of a ectangular prism by breaking the prism into layers of unit cubes. 12-1: Another Look Curriculum Standards: Fluently multiply multi-digit whole numbers using the standard algorithm. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Fluently multiply multi-digit whole numbers using the standard algorithm. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Convert among different-sized standard measurement units (i.e., km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec) within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Fluently multiply multi-digit whole numbers using the standard algorithm. Find whole-number quotients of whole numbers with up to four- digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Convert among different-sized standard measurement units (i.e., km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec) within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Convert customary units of length. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Convert between different-sized measurement units within a given measurement system. A table of equivalencies will be provided. Divide multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Recognize that quotients can be represented in a variety of ways, including a whole number with a remainder, a fraction or mixed number, or a decimal. Consider the context in which a problem is situated to select the most useful form of the quotient for the solution and use the context to interpret the quotient appropriately. 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. 11-3 Center Games 5-1: Another Look Curriculum Standards: 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. 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. 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. Use place-value patterns and mental math to find quotients. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors. 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. 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. 11-1: Another Look Curriculum Standards: A cube with side length 1 unit, called a "unit cube," is said to have "one cubic unit" of volume, and can be used to measure volume. A solid figure that can be packed without gaps or overlaps using n unit cubes is said to have a volume of n cubic units. Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units. A cube with side length 1 unit, called a “unit cube,” is said to have “one cubic unit” of volume, and can be used to measure volume. A solid figure which can be packed without gaps or overlaps using n unit cubes is said to have a volume of n cubic units. Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units. A cube with side length 1 unit, called a “unit cube,” is said to have “one cubic unit” of volume, and can be used to measure volume. A solid figure which can be packed without gaps or overlaps using n unit cubes is said to have a volume of n cubic units. Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units. Find the volume of solid figures. A cube with side length 1 unit, called a unit cube, is said to have one cubic unit of volume, and can be used to measure volume. A solid figure that can be packed without gaps or overlaps using n unit cubes is said to have a volume of n cubic units. Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units. 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. Formulas will be provided. Use various tools and strategies to measure the volume and surface area of objects that are shaped like rectangular prisms. Understand that the volume of a three dimensional figure can be found by counting the total number of same-sized cubic units that fill a shape without gaps or overlaps. Use cubic units to label volume measurements. 10-1: Another Look Curriculum Standards: Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Make a line plot to display a data set of measurements in fractions of a unit (1/2 , 1/4 , 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally. Read and analyze line plots. Make a line plot to display a data set of measurements in fractions of a unit (1/2 , 1/4 , 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally. Solve problems involving computation of fractions by using information presented in line plots. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. 9-2: Another Look Curriculum Standards: Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. For example, interpret 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3, and that when 3 wholes are shared equally among 4 people each person has a share of size 3/4. If 9 people want to share a 50-pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie? Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. For example, interpret 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3, and that when 3 wholes are shared equally among 4 people each person has a share of size 3/4. If 9 people want to share a 50-pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie? Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. For example, interpret 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3, and that when 3 wholes are shared equally among 4 people each person has a share of size 3/4. If 9 people want to share a 50-pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie? Implement division of fractions to show quotients as fractions and mixed numbers. Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. For example, interpret 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3, and that when 3 wholes are shared equally among 4 people each person has a share of size 3/4. If 9 people want to share a 50-pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie? Solve word problems involving division of whole numbers leading to answers in the form of fractions (including mixed numbers). 12-3: Another Look Curriculum Standards: Fluently multiply multi-digit whole numbers using the standard algorithm. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Fluently multiply multi-digit whole numbers using the standard algorithm. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Convert among different-sized standard measurement units (i.e., km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec) within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Fluently multiply multi-digit whole numbers using the standard algorithm. Find whole-number quotients of whole numbers with up to four- digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Convert among different-sized standard measurement units (i.e., km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec) within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Convert customary units of weight. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Convert between different-sized measurement units within a given measurement system. A table of equivalencies will be provided. Divide multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Recognize that quotients can be represented in a variety of ways, including a whole number with a remainder, a fraction or mixed number, or a decimal. Consider the context in which a problem is situated to select the most useful form of the quotient for the solution and use the context to interpret the quotient appropriately. 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. 11-3: Another Look Curriculum Standards: Recognize volume as additive. 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. Recognize volume as additive. 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. Recognize volume as additive. 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. Find the volume of a solid figure that is the combination of two or more rectangular prisms. Recognize volume as additive. 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. Find volumes of solid figures composed of two nonoverlapping right rectangular prisms. 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. Use various tools and strategies to measure the volume and surface area of objects that are shaped like rectangular prisms. Understand that the volume of a three dimensional figure can be found by counting the total number of same-sized cubic units that fill a shape without gaps or overlaps. Use cubic units to label volume measurements. Develop and use the formulas V = ?wh and V = Bh to determine the volume of rectangular prisms. Justify why base area B and height h are multiplied to find the volume of a ectangular prism by breaking the prism into layers of unit cubes. 12-4: Another Look Curriculum Standards: Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole- number exponents to denote powers of 10. Convert among different-sized standard measurement units (i.e., km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec) within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole- number exponents to denote powers of 10. Convert among different-sized standard measurement units (i.e., km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec) within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Convert metric units of length. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10 and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. Convert between different-sized measurement units within a given measurement system. A table of equivalencies will be provided. Divide multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Recognize that quotients can be represented in a variety of ways, including a whole number with a remainder, a fraction or mixed number, or a decimal. Consider the context in which a problem is situated to select the most useful form of the quotient for the solution and use the context to interpret the quotient appropriately. 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. 10-4: Another Look Curriculum Standards: Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Make a line plot to display a data set of measurements in fractions of a unit (1/2 , 1/4 , 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally. Construct viable arguments and critique the reasoning of others. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. Construct viable arguments and critique the reasoning of others. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally. Construct viable arguments and critique the reasoning of others. Mathematically proficient students understand and use stated assumptions, definitions, and previously established results in constructing arguments. They make conjectures and build a logical progression of statements to explore the truth of their conjectures. They are able to analyze situations by breaking them into cases, and can recognize and use counterexamples. They justify their conclusions, communicate them to others, and respond to the arguments of others. They reason inductively about data, making plausible arguments that take into account the context from which the data arose. Mathematically proficient students are also able to compare the effectiveness of two plausible arguments, distinguish correct logic or reasoning from that which is flawed, and—if there is a flaw in an argument—explain what it is. Elementary students can construct arguments using concrete referents such as objects, drawings, diagrams, and actions. Such arguments can make sense and be correct, even though they are not generalized or made formal until later grades. Later, students learn to determine domains to which an argument applies. Students at all grades can listen or read the arguments of others, decide whether they make sense, and ask useful questions to clarify or improve the arguments. Critique the reasoning of others using understanding of line plots and fractions. Make a line plot to display a data set of measurements in fractions of a unit (1/2 , 1/4 , 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally. Construct viable arguments and critique the reasoning of others. Construct viable arguments and critique the reasoning of others. Add and subtract fractions (including mixed numbers) with unlike denominators. (May include multiple methods and representations.) Solve problems involving computation of fractions by using information presented in line plots. Construct viable arguments and critique the reasoning of others. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. 12-2: Another Look Curriculum Standards: Fluently multiply multi-digit whole numbers using the standard algorithm. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Fluently multiply multi-digit whole numbers using the standard algorithm. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Convert among different-sized standard measurement units (i.e., km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec) within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Fluently multiply multi-digit whole numbers using the standard algorithm. Find whole-number quotients of whole numbers with up to four- digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Convert among different-sized standard measurement units (i.e., km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec) within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Convert customary units of capacity. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Convert between different-sized measurement units within a given measurement system. A table of equivalencies will be provided. Divide multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Recognize that quotients can be represented in a variety of ways, including a whole number with a remainder, a fraction or mixed number, or a decimal. Consider the context in which a problem is situated to select the most useful form of the quotient for the solution and use the context to interpret the quotient appropriately. 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. 9-1: Another Look Curriculum Standards: Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. For example, interpret 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3, and that when 3 wholes are shared equally among 4 people each person has a share of size 3/4. If 9 people want to share a 50-pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie? Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. For example, interpret 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3, and that when 3 wholes are shared equally among 4 people each person has a share of size 3/4. If 9 people want to share a 50-pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie? Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. For example, interpret 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3, and that when 3 wholes are shared equally among 4 people each person has a share of size 3/4. If 9 people want to share a 50-pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie? Understand how fractions are related to division. Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. For example, interpret 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3, and that when 3 wholes are shared equally among 4 people each person has a share of size 3/4. If 9 people want to share a 50-pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie? Solve word problems involving division of whole numbers leading to answers in the form of fractions (including mixed numbers). 12-6: Another Look Curriculum Standards: Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole- number exponents to denote powers of 10. Convert among different-sized standard measurement units (i.e., km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec) within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole- number exponents to denote powers of 10. Convert among different-sized standard measurement units (i.e., km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec) within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Convert metric units of mass. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10 and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. Convert between different-sized measurement units within a given measurement system. A table of equivalencies will be provided. Divide multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Recognize that quotients can be represented in a variety of ways, including a whole number with a remainder, a fraction or mixed number, or a decimal. Consider the context in which a problem is situated to select the most useful form of the quotient for the solution and use the context to interpret the quotient appropriately. 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. 11-2: Another Look Curriculum Standards: Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units. 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. 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. 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. 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. 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. 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. Find the volume of rectangular prisms using a formula. Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units. 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. 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. 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. Formulas will be provided. 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. Apply the commutative, associative and distributive properties and order of operations to generate equivalent numerical expressions and to solve problems involving whole numbers. Use various tools and strategies to measure the volume and surface area of objects that are shaped like rectangular prisms. Understand that the volume of a three dimensional figure can be found by counting the total number of same-sized cubic units that fill a shape without gaps or overlaps. Use cubic units to label volume measurements. Develop and use the formulas V = ?wh and V = Bh to determine the volume of rectangular prisms. Justify why base area B and height h are multiplied to find the volume of a ectangular prism by breaking the prism into layers of unit cubes. Topics 1–12: Online Cumulative/Benchmark Assessment Curriculum Standards: Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units. 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. 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. A cube with side length 1 unit, called a "unit cube," is said to have "one cubic unit" of volume, and can be used to measure volume. A solid figure that can be packed without gaps or overlaps using n unit cubes is said to have a volume of n cubic units. Recognize volume as additive. 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. Fluently multiply multi-digit whole numbers using the standard algorithm. Interpret the product a/b x q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = (ac)/(bd). Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Make a line plot to display a data set of measurements in fractions of a unit (1/2 , 1/4 , 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally. 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. Construct viable arguments and critique the reasoning of others. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. For example, interpret 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3, and that when 3 wholes are shared equally among 4 people each person has a share of size 3/4. If 9 people want to share a 50-pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie? Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for 4 ÷ (1/5), and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 × (1/5) = 4. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins? Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Use knowledge about place value and patterns to find the product of a decimal number and a power of 10. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10 and 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. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). Use place-value understanding and an algorithm for multiplying whole numbers to multiply a decimal and a whole number. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Use grids to model decimals and find the product of a decimal and a decimal. 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. 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. 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. 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. Find the volume of rectangular prisms using a formula. Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units. 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. 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. 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. Formulas will be provided. 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. Apply the commutative, associative and distributive properties and order of operations to generate equivalent numerical expressions and to solve problems involving whole numbers. Use various tools and strategies to measure the volume and surface area of objects that are shaped like rectangular prisms. Understand that the volume of a three dimensional figure can be found by counting the total number of same-sized cubic units that fill a shape without gaps or overlaps. Use cubic units to label volume measurements. Develop and use the formulas V = ?wh and V = Bh to determine the volume of rectangular prisms. Justify why base area B and height h are multiplied to find the volume of a ectangular prism by breaking the prism into layers of unit cubes. A cube with side length 1 unit, called a “unit cube,” is said to have “one cubic unit” of volume, and can be used to measure volume. A solid figure which can be packed without gaps or overlaps using n unit cubes is said to have a volume of n cubic units. Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units. A cube with side length 1 unit, called a “unit cube,” is said to have “one cubic unit” of volume, and can be used to measure volume. A solid figure which can be packed without gaps or overlaps using n unit cubes is said to have a volume of n cubic units. Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units. Find the volume of solid figures. A cube with side length 1 unit, called a unit cube, is said to have one cubic unit of volume, and can be used to measure volume. A solid figure that can be packed without gaps or overlaps using n unit cubes is said to have a volume of n cubic units. Recognize volume as additive. 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. Recognize volume as additive. 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. Use models, prior knowledge of volume and previously learned strategies to solve word problems involving volume. Recognize volume as additive. 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. Find volumes of solid figures composed of two nonoverlapping right rectangular prisms. Use models to help find quotients in problems involving decimals. Find the volume of a solid figure that is the combination of two or more rectangular prisms. Fluently multiply multi-digit whole numbers using the standard algorithm. Fluently multiply multi-digit whole numbers using the standard algorithm. Multiply 3-digit by 2-digit numbers by adding partial products or by using the standard algorithm. Fluently multiply multi-digit whole numbers using the standard algorithm. Multiply multi-digit whole numbers (not to exceed three-digit by three-digit). Estimate solutions to arithmetic problems in order to assess the reasonableness of results. Interpret the product (a/b) × q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction. Interpret the product (a/b) × q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = ac/bd.) Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Multiply a fraction by a whole number. Interpret the product a/b x q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = (ac)/(bd). Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally. Read and analyze line plots. Make a line plot to display a data set of measurements in fractions of a unit (1/2 , 1/4 , 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally. Solve problems involving computation of fractions by using information presented in line plots. Solve real- world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. 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. 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. Use place-value patterns and mental math to find quotients. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors. 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. Organize and display data in a line plot. Solve division problems using partial quotients. Construct viable arguments and critique the reasoning of others. Construct viable arguments and critique the reasoning of others. Mathematically proficient students understand and use stated assumptions, definitions, and previously established results in constructing arguments. They make conjectures and build a logical progression of statements to explore the truth of their conjectures. They are able to analyze situations by breaking them into cases, and can recognize and use counterexamples. They justify their conclusions, communicate them to others, and respond to the arguments of others. They reason inductively about data, making plausible arguments that take into account the context from which the data arose. Mathematically proficient students are also able to compare the effectiveness of two plausible arguments, distinguish correct logic or reasoning from that which is flawed, and—if there is a flaw in an argument—explain what it is. Elementary students can construct arguments using concrete referents such as objects, drawings, diagrams, and actions. Such arguments can make sense and be correct, even though they are not generalized or made formal until later grades. Later, students learn to determine domains to which an argument applies. Students at all grades can listen or read the arguments of others, decide whether they make sense, and ask useful questions to clarify or improve the arguments. Critique the reasoning of others using understanding of line plots and fractions. Construct viable arguments and critique the reasoning of others. Construct viable arguments and critique the reasoning of others. Add and subtract fractions (including mixed numbers) with unlike denominators. (May include multiple methods and representations.) Construct viable arguments and critique the reasoning of others. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Add mixed numbers using models. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Add and subtract decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Model addition and subtraction of fractions and decimals using a variety of representations. Convert among different-sized standard measurement units (i.e., km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec) within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Convert among different-sized standard measurement units (i.e., km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec) within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Convert metric units of mass. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Convert between different-sized measurement units within a given measurement system. A table of equivalencies will be provided. 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. Convert metric units of capacity. Add fractions with unlike denominators using equivalent fractions with a common denominator. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Convert customary units of capacity. Convert customary units of length. Convert metric units of length. Convert customary units of weight. Add decimals to hundredths using familiar strategies, such as partial sums. Estimate sums and differences of decimals and fractions to assess the reasonableness of results. Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. For example, interpret 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3, and that when 3 wholes are shared equally among 4 people each person has a share of size 3/4. If 9 people want to share a 50-pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie? Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. For example, interpret 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3, and that when 3 wholes are shared equally among 4 people each person has a share of size 3/4. If 9 people want to share a 50-pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie? Understand how fractions are related to division. Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. For example, interpret 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3, and that when 3 wholes are shared equally among 4 people each person has a share of size 3/4. If 9 people want to share a 50-pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie? Solve word problems involving division of whole numbers leading to answers in the form of fractions (including mixed numbers). Implement division of fractions to show quotients as fractions and mixed numbers. Interpret division of a whole number by a unit fraction, and compute such quotients. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for 4 ÷ (1/5), and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 × (1/5) = 4. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins? Use models, such as pictorial models or a number line, to show dividing a whole number by a unit fraction. Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for 4 ÷ (1/5), and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 × (1/5) = 4. Divide unit fractions by whole numbers and whole numbers by unit fractions. Topic 13: Write and Interpret Numerical Expressions Topic 13: Today's Challenge Topic 13: Beginning of Topic Interactive Student Edition: Beginning of Topic 13 Topic 13: enVision STEM Activity Grade 5 Topic 13: Review What You Know Topic 13: Vocabulary Cards 13-1: Evaluate Expressions Interactive Student Edition: Grade 5 Lesson 13-1 Math Anytime 13-1: Daily Review Topic 13: Today's Challenge Step 1: Problem-Based Learning 13-1: Solve & Share Curriculum Standards: Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. English language learners communicate for social and instructional purposes within the school setting. Write informative/explanatory texts to examine a topic and convey ideas and information clearly. (a) Introduce a topic clearly, provide a general observation and focus, and group related information logically; include formatting (e.g., headings), illustrations, and multimedia when useful to aiding comprehension. (b) Develop the topic with facts, definitions, concrete details, quotations, or other information and examples related to the topic. (c) Link ideas within and across categories of information using words, phrases, and clauses (e.g., in contrast, especially). (d) Use precise language and domain-specific vocabulary to inform about or explain the topic. (e) Provide a concluding statement or section related to the information or explanation presented. English language learners communicate information, ideas and concepts necessary for academic success in the content area of Mathematics. Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. Use the order of operations to evaluate expressions. Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. Use multiple grouping symbols (parentheses, brackets, or braces) in numerical expressions and evaluate expressions containing these symbols. Apply the commutative, associative and distributive properties and order of operations to generate equivalent numerical expressions and to solve problems involving whole numbers. Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 5 topics and texts, building on others’ ideas and expressing their own clearly. (a) Come to discussions prepared, having read or studied required material; explicitly draw on that preparation and other information known about the topic to explore ideas under discussion. (b) Follow agreed-upon rules for discussions and carry out assigned roles. (c) Pose and respond to specific questions by making comments that contribute to the discussion and elaborate on the remarks of others. (d) Review the key ideas expressed and draw conclusions in light of information and knowledge gained from the discussions. Summarize a written text read aloud or information presented in diverse media and formats, including visually, quantitatively, and orally. Summarize the points a speaker makes and explain how each claim is supported by reasons and evidence. Step 2: Visual Learning 13-1: Visual Learning Curriculum Standards: Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. Use the order of operations to evaluate expressions. Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. Use multiple grouping symbols (parentheses, brackets, or braces) in numerical expressions and evaluate expressions containing these symbols. Apply the commutative, associative and distributive properties and order of operations to generate equivalent numerical expressions and to solve problems involving whole numbers. Evaluate a simple expression involving one set of parenthesis. 13-1: Convince Me! Curriculum Standards: Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. Use the order of operations to evaluate expressions. Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. Use multiple grouping symbols (parentheses, brackets, or braces) in numerical expressions and evaluate expressions containing these symbols. Apply the commutative, associative and distributive properties and order of operations to generate equivalent numerical expressions and to solve problems involving whole numbers. Practice and Problem Solving 13-1: Student Edition Practice Curriculum Standards: Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. Use the order of operations to evaluate expressions. Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. Use multiple grouping symbols (parentheses, brackets, or braces) in numerical expressions and evaluate expressions containing these symbols. Apply the commutative, associative and distributive properties and order of operations to generate equivalent numerical expressions and to solve problems involving whole numbers. 13-1: Practice Buddy: Independent Practice; Problem Solving Curriculum Standards: Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. Use the order of operations to evaluate expressions. Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. Use multiple grouping symbols (parentheses, brackets, or braces) in numerical expressions and evaluate expressions containing these symbols. Apply the commutative, associative and distributive properties and order of operations to generate equivalent numerical expressions and to solve problems involving whole numbers. 13-1: Practice Buddy: Additional Practice Curriculum Standards: Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. Use the order of operations to evaluate expressions. Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. Use multiple grouping symbols (parentheses, brackets, or braces) in numerical expressions and evaluate expressions containing these symbols. Apply the commutative, associative and distributive properties and order of operations to generate equivalent numerical expressions and to solve problems involving whole numbers. 13-1: Interactive Additional Practice Step 3: Assess & Differentiate 13-1: Practice Buddy: Additional Practice Curriculum Standards: Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. Use the order of operations to evaluate expressions. Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. Use multiple grouping symbols (parentheses, brackets, or braces) in numerical expressions and evaluate expressions containing these symbols. Apply the commutative, associative and distributive properties and order of operations to generate equivalent numerical expressions and to solve problems involving whole numbers. 13-1: Enrichment Curriculum Standards: Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. Use the order of operations to evaluate expressions. Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. Use multiple grouping symbols (parentheses, brackets, or braces) in numerical expressions and evaluate expressions containing these symbols. Apply the commutative, associative and distributive properties and order of operations to generate equivalent numerical expressions and to solve problems involving whole numbers. 13-1: Quick Check Curriculum Standards: Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. Use the order of operations to evaluate expressions. Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. Use multiple grouping symbols (parentheses, brackets, or braces) in numerical expressions and evaluate expressions containing these symbols. Apply the commutative, associative and distributive properties and order of operations to generate equivalent numerical expressions and to solve problems involving whole numbers. 13-1: Lesson Self-Assessment 13-1: Reteach to Build Understanding Curriculum Standards: Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. Use the order of operations to evaluate expressions. Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. Use multiple grouping symbols (parentheses, brackets, or braces) in numerical expressions and evaluate expressions containing these symbols. Apply the commutative, associative and distributive properties and order of operations to generate equivalent numerical expressions and to solve problems involving whole numbers. Evaluate a simple expression involving one set of parenthesis. 13-1: Build Mathematical Literacy Curriculum Standards: Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 5 topics and texts, building on others’ ideas and expressing their own clearly. (a) Come to discussions prepared, having read or studied required material; explicitly draw on that preparation and other information known about the topic to explore ideas under discussion. (b) Follow agreed-upon rules for discussions and carry out assigned roles. (c) Pose and respond to specific questions by making comments that contribute to the discussion and elaborate on the remarks of others. (d) Review the key ideas expressed and draw conclusions in light of information and knowledge gained from the discussions. English language learners communicate for social and instructional purposes within the school setting. Summarize a written text read aloud or information presented in diverse media and formats, including visually, quantitatively, and orally. Summarize the points a speaker makes and explain how each claim is supported by reasons and evidence. Write informative/explanatory texts to examine a topic and convey ideas and information clearly. (a) Introduce a topic clearly, provide a general observation and focus, and group related information logically; include formatting (e.g., headings), illustrations, and multimedia when useful to aiding comprehension. (b) Develop the topic with facts, definitions, concrete details, quotations, or other information and examples related to the topic. (c) Link ideas within and across categories of information using words, phrases, and clauses (e.g., in contrast, especially). (d) Use precise language and domain-specific vocabulary to inform about or explain the topic. (e) Provide a concluding statement or section related to the information or explanation presented. English language learners communicate information, ideas and concepts necessary for academic success in the content area of Mathematics. 13-1: Enrichment 13-1: Digital Math Tool Activity 13-1: enVision STEM Activity Curriculum Standards: Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. Use the order of operations to evaluate expressions. Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. Use multiple grouping symbols (parentheses, brackets, or braces) in numerical expressions and evaluate expressions containing these symbols. Apply the commutative, associative and distributive properties and order of operations to generate equivalent numerical expressions and to solve problems involving whole numbers. 13-1: Another Look Curriculum Standards: Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. Use the order of operations to evaluate expressions. Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. Use multiple grouping symbols (parentheses, brackets, or braces) in numerical expressions and evaluate expressions containing these symbols. Apply the commutative, associative and distributive properties and order of operations to generate equivalent numerical expressions and to solve problems involving whole numbers. Evaluate a simple expression involving one set of parenthesis. Spanish Resources 13-1: eText del Libro del estudiante 13-1: Repaso diario 13-1: Aprendizaje visual 13-1: Amigo de práctica: Práctica adicional 13-1: Práctica adicional interactiva 13-1: Refuerzo para mejorar la comprensión 13-1: Desarrollar la competencia matemática 13-1: Ampliación 13-2: Write Numerical Expressions Interactive Student Edition: Grade 5 Lesson 13-2 Math Anytime 13-2: Daily Review Topic 13: Today's Challenge Step 1: Problem-Based Learning 13-2: Solve & Share Curriculum Standards: Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. For example, 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. English language learners communicate for social and instructional purposes within the school setting. Write informative/explanatory texts to examine a topic and convey ideas and information clearly. (a) Introduce a topic clearly, provide a general observation and focus, and group related information logically; include formatting (e.g., headings), illustrations, and multimedia when useful to aiding comprehension. (b) Develop the topic with facts, definitions, concrete details, quotations, or other information and examples related to the topic. (c) Link ideas within and across categories of information using words, phrases, and clauses (e.g., in contrast, especially). (d) Use precise language and domain- specific vocabulary to inform about or explain the topic. (e) Provide a concluding statement or section related to the information or explanation presented. English language learners communicate information, ideas and concepts necessary for academic success in the content area of Mathematics. Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. For example, 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. Write simple expressions that show calculations with numbers. Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. For example, 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. Write simple expressions that model calculations with numbers and interpret numerical expressions without evaluating them. Apply the commutative, associative and distributive properties and order of operations to generate equivalent numerical expressions and to solve problems involving whole numbers. Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 5 topics and texts, building on others’ ideas and expressing their own clearly. (a) Come to discussions prepared, having read or studied required material; explicitly draw on that preparation and other information known about the topic to explore ideas under discussion. (b) Follow agreed-upon rules for discussions and carry out assigned roles. (c) Pose and respond to specific questions by making comments that contribute to the discussion and elaborate on the remarks of others. (d) Review the key ideas expressed and draw conclusions in light of information and knowledge gained from the discussions. Summarize a written text read aloud or information presented in diverse media and formats, including visually, quantitatively, and orally. Summarize the points a speaker makes and explain how each claim is supported by reasons and evidence. Step 2: Visual Learning 13-2: Visual Learning Curriculum Standards: Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. For example, 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. Write a simple expression for a calculation. Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. For example, 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. Write simple expressions that show calculations with numbers. Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. For example, 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. Write simple expressions that model calculations with numbers and interpret numerical expressions without evaluating them. Apply the commutative, associative and distributive properties and order of operations to generate equivalent numerical expressions and to solve problems involving whole numbers. 13-2: Convince Me! Curriculum Standards: Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. For example, 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. Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. For example, 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. Write simple expressions that show calculations with numbers. Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. For example, 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. Write simple expressions that model calculations with numbers and interpret numerical expressions without evaluating them. Apply the commutative, associative and distributive properties and order of operations to generate equivalent numerical expressions and to solve problems involving whole numbers. Practice and Problem Solving 13-2: Student Edition Practice Curriculum Standards: Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. For example, 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. Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. For example, 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. Write simple expressions that show calculations with numbers. Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. For example, 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. Write simple expressions that model calculations with numbers and interpret numerical expressions without evaluating them. Apply the commutative, associative and distributive properties and order of operations to generate equivalent numerical expressions and to solve problems involving whole numbers. 13-2: Practice Buddy: Independent Practice; Problem Solving Curriculum Standards: Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. For example, 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. Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. For example, 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. Write simple expressions that show calculations with numbers. Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. For example, 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. Write simple expressions that model calculations with numbers and interpret numerical expressions without evaluating them. Apply the commutative, associative and distributive properties and order of operations to generate equivalent numerical expressions and to solve problems involving whole numbers. 13-2: Practice Buddy: Additional Practice Curriculum Standards: Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. For example, 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. Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. For example, 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. Write simple expressions that show calculations with numbers. Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. For example, 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. Write simple expressions that model calculations with numbers and interpret numerical expressions without evaluating them. Apply the commutative, associative and distributive properties and order of operations to generate equivalent numerical expressions and to solve problems involving whole numbers. 13-2: Interactive Additional Practice Step 3: Assess & Differentiate 13-2: Practice Buddy: Additional Practice Curriculum Standards: Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. For example, 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. Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. For example, 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. Write simple expressions that show calculations with numbers. Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. For example, 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. Write simple expressions that model calculations with numbers and interpret numerical expressions without evaluating them. Apply the commutative, associative and distributive properties and order of operations to generate equivalent numerical expressions and to solve problems involving whole numbers. 13-2: Enrichment Curriculum Standards: Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. For example, 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. Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. For example, 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. Write simple expressions that show calculations with numbers. Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. For example, 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. Write simple expressions that model calculations with numbers and interpret numerical expressions without evaluating them. Apply the commutative, associative and distributive properties and order of operations to generate equivalent numerical expressions and to solve problems involving whole numbers. 13-2: Quick Check Curriculum Standards: Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. For example, 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. Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. For example, 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. Write simple expressions that show calculations with numbers. Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. For example, 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. Write simple expressions that model calculations with numbers and interpret numerical expressions without evaluating them. Apply the commutative, associative and distributive properties and order of operations to generate equivalent numerical expressions and to solve problems involving whole numbers. 13-2: Lesson Self-Assessment 13-2: Reteach to Build Understanding Curriculum Standards: Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. For example, 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. Write a simple expression for a calculation. Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. For example, 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. Write simple expressions that show calculations with numbers. Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. For example, 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. Write simple expressions that model calculations with numbers and interpret numerical expressions without evaluating them. Apply the commutative, associative and distributive properties and order of operations to generate equivalent numerical expressions and to solve problems involving whole numbers. 13-2: Build Mathematical Literacy Curriculum Standards: Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 5 topics and texts, building on others’ ideas and expressing their own clearly. (a) Come to discussions prepared, having read or studied required material; explicitly draw on that preparation and other information known about the topic to explore ideas under discussion. (b) Follow agreed-upon rules for discussions and carry out assigned roles. (c) Pose and respond to specific questions by making comments that contribute to the discussion and elaborate on the remarks of others. (d) Review the key ideas expressed and draw conclusions in light of information and knowledge gained from the discussions. English language learners communicate for social and instructional purposes within the school setting. Summarize a written text read aloud or information presented in diverse media and formats, including visually, quantitatively, and orally. Summarize the points a speaker makes and explain how each claim is supported by reasons and evidence. Write informative/explanatory texts to examine a topic and convey ideas and information clearly. (a) Introduce a topic clearly, provide a general observation and focus, and group related information logically; include formatting (e.g., headings), illustrations, and multimedia when useful to aiding comprehension. (b) Develop the topic with facts, definitions, concrete details, quotations, or other information and examples related to the topic. (c) Link ideas within and across categories of information using words, phrases, and clauses (e.g., in contrast, especially). (d) Use precise language and domain-specific vocabulary to inform about or explain the topic. (e) Provide a concluding statement or section related to the information or explanation presented. English language learners communicate information, ideas and concepts necessary for academic success in the content area of Mathematics. 13-2: Enrichment 13-2: Digital Math Tool Activity 13-2 Problem-Solving Reading Activity Curriculum Standards: Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. For example, 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. Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. For example, 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. Write simple expressions that show calculations with numbers. Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. For example, 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. Write simple expressions that model calculations with numbers and interpret numerical expressions without evaluating them. Apply the commutative, associative and distributive properties and order of operations to generate equivalent numerical expressions and to solve problems involving whole numbers. 13-2: Another Look Curriculum Standards: Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. For example, 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. Write a simple expression for a calculation. Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. For example, 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. Write simple expressions that show calculations with numbers. Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. For example, 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. Write simple expressions that model calculations with numbers and interpret numerical expressions without evaluating them. Apply the commutative, associative and distributive properties and order of operations to generate equivalent numerical expressions and to solve problems involving whole numbers. Spanish Resources 13-2: eText del Libro del estudiante 13-2: Repaso diario 13-2: Aprendizaje visual 13-2: Amigo de práctica: Práctica adicional 13-2: Práctica adicional interactiva 13-2: Refuerzo para mejorar la comprensión 13-2: Desarrollar la competencia matemática 13-2: Ampliación 13-3: Interpret Numerical Expressions Interactive Student Edition: Grade 5 Lesson 13-3 Math Anytime 13-3: Daily Review Topic 13: Today's Challenge Step 1: Problem-Based Learning 13-3: Solve & Share Curriculum Standards: Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. For example, 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. English language learners communicate for social and instructional purposes within the school setting. Write informative/explanatory texts to examine a topic and convey ideas and information clearly. (a) Introduce a topic clearly, provide a general observation and focus, and group related information logically; include formatting (e.g., headings), illustrations, and multimedia when useful to aiding comprehension. (b) Develop the topic with facts, definitions, concrete details, quotations, or other information and examples related to the topic. (c) Link ideas within and across categories of information using words, phrases, and clauses (e.g., in contrast, especially). (d) Use precise language and domain- specific vocabulary to inform about or explain the topic. (e) Provide a concluding statement or section related to the information or explanation presented. English language learners communicate information, ideas and concepts necessary for academic success in the content area of Mathematics. Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. For example, 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. Interpret numerical expressions without evaluating them. Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. For example, 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. Write simple expressions that model calculations with numbers and interpret numerical expressions without evaluating them. Apply the commutative, associative and distributive properties and order of operations to generate equivalent numerical expressions and to solve problems involving whole numbers. Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 5 topics and texts, building on others’ ideas and expressing their own clearly. (a) Come to discussions prepared, having read or studied required material; explicitly draw on that preparation and other information known about the topic to explore ideas under discussion. (b) Follow agreed-upon rules for discussions and carry out assigned roles. (c) Pose and respond to specific questions by making comments that contribute to the discussion and elaborate on the remarks of others. (d) Review the key ideas expressed and draw conclusions in light of information and knowledge gained from the discussions. Summarize a written text read aloud or information presented in diverse media and formats, including visually, quantitatively, and orally. Summarize the points a speaker makes and explain how each claim is supported by reasons and evidence. Step 2: Visual Learning 13-3: Visual Learning Curriculum Standards: Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. For example, 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. Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. For example, 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. Interpret numerical expressions without evaluating them. Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. For example, 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. Write simple expressions that model calculations with numbers and interpret numerical expressions without evaluating them. Apply the commutative, associative and distributive properties and order of operations to generate equivalent numerical expressions and to solve problems involving whole numbers. 13-3: Convince Me! Curriculum Standards: Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. For example, 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. Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. For example, 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. Interpret numerical expressions without evaluating them. Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. For example, 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. Write simple expressions that model calculations with numbers and interpret numerical expressions without evaluating them. Apply the commutative, associative and distributive properties and order of operations to generate equivalent numerical expressions and to solve problems involving whole numbers. Practice and Problem Solving 13-3: Student Edition Practice Curriculum Standards: Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. For example, 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. Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. For example, 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. Interpret numerical expressions without evaluating them. Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. For example, 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. Write simple expressions that model calculations with numbers and interpret numerical expressions without evaluating them. Apply the commutative, associative and distributive properties and order of operations to generate equivalent numerical expressions and to solve problems involving whole numbers. 13-3: Practice Buddy: Independent Practice; Problem Solving Curriculum Standards: Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. For example, 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. Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. For example, 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. Interpret numerical expressions without evaluating them. Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. For example, 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. Write simple expressions that model calculations with numbers and interpret numerical expressions without evaluating them. Apply the commutative, associative and distributive properties and order of operations to generate equivalent numerical expressions and to solve problems involving whole numbers. 13-3: Practice Buddy: Additional Practice Curriculum Standards: Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. For example, 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. Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. For example, 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. Interpret numerical expressions without evaluating them. Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. For example, 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. Write simple expressions that model calculations with numbers and interpret numerical expressions without evaluating them. Apply the commutative, associative and distributive properties and order of operations to generate equivalent numerical expressions and to solve problems involving whole numbers. 13-3: Interactive Additional Practice Step 3: Assess & Differentiate 13-3: Practice Buddy: Additional Practice Curriculum Standards: Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. For example, 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. Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. For example, 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. Interpret numerical expressions without evaluating them. Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. For example, 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. Write simple expressions that model calculations with numbers and interpret numerical expressions without evaluating them. Apply the commutative, associative and distributive properties and order of operations to generate equivalent numerical expressions and to solve problems involving whole numbers. 13-3: Enrichment Curriculum Standards: Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. For example, 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. Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. For example, 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. Interpret numerical expressions without evaluating them. Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. For example, 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. Write simple expressions that model calculations with numbers and interpret numerical expressions without evaluating them. Apply the commutative, associative and distributive properties and order of operations to generate equivalent numerical expressions and to solve problems involving whole numbers. 13-3: Quick Check Curriculum Standards: Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. For example, 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. Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. For example, 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. Interpret numerical expressions without evaluating them. Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. For example, 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. Write simple expressions that model calculations with numbers and interpret numerical expressions without evaluating them. Apply the commutative, associative and distributive properties and order of operations to generate equivalent numerical expressions and to solve problems involving whole numbers. 13-3: Lesson Self-Assessment 13-3: Reteach to Build Understanding Curriculum Standards: Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. For example, 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. Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. For example, 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. Interpret numerical expressions without evaluating them. Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. For example, 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. Write simple expressions that model calculations with numbers and interpret numerical expressions without evaluating them. Apply the commutative, associative and distributive properties and order of operations to generate equivalent numerical expressions and to solve problems involving whole numbers. 13-3: Build Mathematical Literacy Curriculum Standards: Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 5 topics and texts, building on others’ ideas and expressing their own clearly. (a) Come to discussions prepared, having read or studied required material; explicitly draw on that preparation and other information known about the topic to explore ideas under discussion. (b) Follow agreed-upon rules for discussions and carry out assigned roles. (c) Pose and respond to specific questions by making comments that contribute to the discussion and elaborate on the remarks of others. (d) Review the key ideas expressed and draw conclusions in light of information and knowledge gained from the discussions. English language learners communicate for social and instructional purposes within the school setting. Summarize a written text read aloud or information presented in diverse media and formats, including visually, quantitatively, and orally. Summarize the points a speaker makes and explain how each claim is supported by reasons and evidence. Write informative/explanatory texts to examine a topic and convey ideas and information clearly. (a) Introduce a topic clearly, provide a general observation and focus, and group related information logically; include formatting (e.g., headings), illustrations, and multimedia when useful to aiding comprehension. (b) Develop the topic with facts, definitions, concrete details, quotations, or other information and examples related to the topic. (c) Link ideas within and across categories of information using words, phrases, and clauses (e.g., in contrast, especially). (d) Use precise language and domain-specific vocabulary to inform about or explain the topic. (e) Provide a concluding statement or section related to the information or explanation presented. English language learners communicate information, ideas and concepts necessary for academic success in the content area of Mathematics. 13-3: Enrichment Game: Launch that Sheep - Multiply and Divide 2-Digit Numbers 13-3: Problem-Solving Reading Activity Curriculum Standards: Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. For example, 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. Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. For example, 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. Interpret numerical expressions without evaluating them. Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. For example, 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. Write simple expressions that model calculations with numbers and interpret numerical expressions without evaluating them. Apply the commutative, associative and distributive properties and order of operations to generate equivalent numerical expressions and to solve problems involving whole numbers. 13-3: Another Look Curriculum Standards: Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. For example, 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. Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. For example, 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. Interpret numerical expressions without evaluating them. Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. For example, 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. Write simple expressions that model calculations with numbers and interpret numerical expressions without evaluating them. Apply the commutative, associative and distributive properties and order of operations to generate equivalent numerical expressions and to solve problems involving whole numbers. Spanish Resources 13-3: eText del Libro del estudiante 13-3: Repaso diario 13-3: Aprendizaje visual 13-3: Amigo de práctica: Práctica adicional 13-3: Práctica adicional interactiva 13-3: Refuerzo para mejorar la comprensión 13-3: Desarrollar la competencia matemática 13-3: Ampliación Topic 13: 3-Act Math: Measure Me! Interactive Student Edition: Grade 5 Topic 13: 3-Act Math Mathematical Modeling Topic 13: 3-Act Math: Measure Me!, Act 1 Topic 13: 3-Act Math: Measure Me!, Act 2 Topic 13: 3-Act Math: Measure Me!, Act 3 Topic 13: 3-Act Math: Measure Me!, Sequel 13-4: Problem Solving: Reasoning Interactive Student Edition: Grade 5 Lesson 13-4 Math Anytime 13-4: Daily Review Topic 13: Today's Challenge Step 1: Problem-Based Learning 13-4: Solve & Share Curriculum Standards: Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. Reason abstractly and quantitatively. English language learners communicate for social and instructional purposes within the school setting. Write informative/explanatory texts to examine a topic and convey ideas and information clearly. (a) Introduce a topic clearly, provide a general observation and focus, and group related information logically; include formatting (e.g., headings), illustrations, and multimedia when useful to aiding comprehension. (b) Develop the topic with facts, definitions, concrete details, quotations, or other information and examples related to the topic. (c) Link ideas within and across categories of information using words, phrases, and clauses (e.g., in contrast, especially). (d) Use precise language and domain- specific vocabulary to inform about or explain the topic. (e) Provide a concluding statement or section related to the information or explanation presented. English language learners communicate information, ideas and concepts necessary for academic success in the content area of Mathematics. Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. Reason abstractly and quantitatively. Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. Reason abstractly and quantitatively. Mathematically proficient students make sense of quantities and their relationships in problem situations. They bring two complementary abilities to bear on problems involving quantitative relationships: the ability to decontextualize—to abstract a given situation and represent it symbolically and manipulate the representing symbols as if they have a life of their own, without necessarily attending to their referents—and the ability to contextualize, to pause as needed during the manipulation process in order to probe into the referents for the symbols involved. Quantitative reasoning entails habits of creating a coherent representation of the problem at hand; considering the units involved; attending to the meaning of quantities, not just how to compute them; and knowing and flexibly using different properties of operations and objects. Use reasoning to solve problems by making sense of quantities and relationships in the situation. Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. Reason abstractly and quantitatively. Reason abstractly and quantitatively. Use multiple grouping symbols (parentheses, brackets, or braces) in numerical expressions and evaluate expressions containing these symbols. Reason abstractly and quantitatively. Apply the commutative, associative and distributive properties and order of operations to generate equivalent numerical expressions and to solve problems involving whole numbers. Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 5 topics and texts, building on others’ ideas and expressing their own clearly. (a) Come to discussions prepared, having read or studied required material; explicitly draw on that preparation and other information known about the topic to explore ideas under discussion. (b) Follow agreed-upon rules for discussions and carry out assigned roles. (c) Pose and respond to specific questions by making comments that contribute to the discussion and elaborate on the remarks of others. (d) Review the key ideas expressed and draw conclusions in light of information and knowledge gained from the discussions. Summarize a written text read aloud or information presented in diverse media and formats, including visually, quantitatively, and orally. Summarize the points a speaker makes and explain how each claim is supported by reasons and evidence. Step 2: Visual Learning 13-4: Visual Learning Curriculum Standards: Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. Reason abstractly and quantitatively. Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. Reason abstractly and quantitatively. Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. Reason abstractly and quantitatively. Mathematically proficient students make sense of quantities and their relationships in problem situations. They bring two complementary abilities to bear on problems involving quantitative relationships: the ability to decontextualize—to abstract a given situation and represent it symbolically and manipulate the representing symbols as if they have a life of their own, without necessarily attending to their referents—and the ability to contextualize, to pause as needed during the manipulation process in order to probe into the referents for the symbols involved. Quantitative reasoning entails habits of creating a coherent representation of the problem at hand; considering the units involved; attending to the meaning of quantities, not just how to compute them; and knowing and flexibly using different properties of operations and objects. Use reasoning to solve problems by making sense of quantities and relationships in the situation. Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. Reason abstractly and quantitatively. Reason abstractly and quantitatively. Use multiple grouping symbols (parentheses, brackets, or braces) in numerical expressions and evaluate expressions containing these symbols. Reason abstractly and quantitatively. Apply the commutative, associative and distributive properties and order of operations to generate equivalent numerical expressions and to solve problems involving whole numbers. 13-4: Convince Me! Curriculum Standards: Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. Reason abstractly and quantitatively. Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. Reason abstractly and quantitatively. Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. Reason abstractly and quantitatively. Mathematically proficient students make sense of quantities and their relationships in problem situations. They bring two complementary abilities to bear on problems involving quantitative relationships: the ability to decontextualize—to abstract a given situation and represent it symbolically and manipulate the representing symbols as if they have a life of their own, without necessarily attending to their referents—and the ability to contextualize, to pause as needed during the manipulation process in order to probe into the referents for the symbols involved. Quantitative reasoning entails habits of creating a coherent representation of the problem at hand; considering the units involved; attending to the meaning of quantities, not just how to compute them; and knowing and flexibly using different properties of operations and objects. Use reasoning to solve problems by making sense of quantities and relationships in the situation. Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. Reason abstractly and quantitatively. Reason abstractly and quantitatively. Use multiple grouping symbols (parentheses, brackets, or braces) in numerical expressions and evaluate expressions containing these symbols. Reason abstractly and quantitatively. Apply the commutative, associative and distributive properties and order of operations to generate equivalent numerical expressions and to solve problems involving whole numbers. Practice and Problem Solving 13-4: Student Edition Practice Curriculum Standards: Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. Reason abstractly and quantitatively. Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. Reason abstractly and quantitatively. Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. Reason abstractly and quantitatively. Mathematically proficient students make sense of quantities and their relationships in problem situations. They bring two complementary abilities to bear on problems involving quantitative relationships: the ability to decontextualize—to abstract a given situation and represent it symbolically and manipulate the representing symbols as if they have a life of their own, without necessarily attending to their referents—and the ability to contextualize, to pause as needed during the manipulation process in order to probe into the referents for the symbols involved. Quantitative reasoning entails habits of creating a coherent representation of the problem at hand; considering the units involved; attending to the meaning of quantities, not just how to compute them; and knowing and flexibly using different properties of operations and objects. Use reasoning to solve problems by making sense of quantities and relationships in the situation. Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. Reason abstractly and quantitatively. Reason abstractly and quantitatively. Use multiple grouping symbols (parentheses, brackets, or braces) in numerical expressions and evaluate expressions containing these symbols. Reason abstractly and quantitatively. Apply the commutative, associative and distributive properties and order of operations to generate equivalent numerical expressions and to solve problems involving whole numbers. 13-4: Practice Buddy: Independent Practice; Problem Solving Curriculum Standards: Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. Reason abstractly and quantitatively. Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. Reason abstractly and quantitatively. Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. Reason abstractly and quantitatively. Mathematically proficient students make sense of quantities and their relationships in problem situations. They bring two complementary abilities to bear on problems involving quantitative relationships: the ability to decontextualize—to abstract a given situation and represent it symbolically and manipulate the representing symbols as if they have a life of their own, without necessarily attending to their referents—and the ability to contextualize, to pause as needed during the manipulation process in order to probe into the referents for the symbols involved. Quantitative reasoning entails habits of creating a coherent representation of the problem at hand; considering the units involved; attending to the meaning of quantities, not just how to compute them; and knowing and flexibly using different properties of operations and objects. Use reasoning to solve problems by making sense of quantities and relationships in the situation. Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. Reason abstractly and quantitatively. Reason abstractly and quantitatively. Use multiple grouping symbols (parentheses, brackets, or braces) in numerical expressions and evaluate expressions containing these symbols. Reason abstractly and quantitatively. Apply the commutative, associative and distributive properties and order of operations to generate equivalent numerical expressions and to solve problems involving whole numbers. 13-4: Practice Buddy: Additional Practice Curriculum Standards: Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. Reason abstractly and quantitatively. Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. Reason abstractly and quantitatively. Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. Reason abstractly and quantitatively. Mathematically proficient students make sense of quantities and their relationships in problem situations. They bring two complementary abilities to bear on problems involving quantitative relationships: the ability to decontextualize—to abstract a given situation and represent it symbolically and manipulate the representing symbols as if they have a life of their own, without necessarily attending to their referents—and the ability to contextualize, to pause as needed during the manipulation process in order to probe into the referents for the symbols involved. Quantitative reasoning entails habits of creating a coherent representation of the problem at hand; considering the units involved; attending to the meaning of quantities, not just how to compute them; and knowing and flexibly using different properties of operations and objects. Use reasoning to solve problems by making sense of quantities and relationships in the situation. Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. Reason abstractly and quantitatively. Reason abstractly and quantitatively. Use multiple grouping symbols (parentheses, brackets, or braces) in numerical expressions and evaluate expressions containing these symbols. Reason abstractly and quantitatively. Apply the commutative, associative and distributive properties and order of operations to generate equivalent numerical expressions and to solve problems involving whole numbers. 13-4: Interactive Additional Practice Step 3: Assess & Differentiate 13-4: Practice Buddy: Additional Practice Curriculum Standards: Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. Reason abstractly and quantitatively. Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. Reason abstractly and quantitatively. Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. Reason abstractly and quantitatively. Mathematically proficient students make sense of quantities and their relationships in problem situations. They bring two complementary abilities to bear on problems involving quantitative relationships: the ability to decontextualize—to abstract a given situation and represent it symbolically and manipulate the representing symbols as if they have a life of their own, without necessarily attending to their referents—and the ability to contextualize, to pause as needed during the manipulation process in order to probe into the referents for the symbols involved. Quantitative reasoning entails habits of creating a coherent representation of the problem at hand; considering the units involved; attending to the meaning of quantities, not just how to compute them; and knowing and flexibly using different properties of operations and objects. Use reasoning to solve problems by making sense of quantities and relationships in the situation. Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. Reason abstractly and quantitatively. Reason abstractly and quantitatively. Use multiple grouping symbols (parentheses, brackets, or braces) in numerical expressions and evaluate expressions containing these symbols. Reason abstractly and quantitatively. Apply the commutative, associative and distributive properties and order of operations to generate equivalent numerical expressions and to solve problems involving whole numbers. 13-4: Enrichment Curriculum Standards: Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. Reason abstractly and quantitatively. Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. Reason abstractly and quantitatively. Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. Reason abstractly and quantitatively. Mathematically proficient students make sense of quantities and their relationships in problem situations. They bring two complementary abilities to bear on problems involving quantitative relationships: the ability to decontextualize—to abstract a given situation and represent it symbolically and manipulate the representing symbols as if they have a life of their own, without necessarily attending to their referents—and the ability to contextualize, to pause as needed during the manipulation process in order to probe into the referents for the symbols involved. Quantitative reasoning entails habits of creating a coherent representation of the problem at hand; considering the units involved; attending to the meaning of quantities, not just how to compute them; and knowing and flexibly using different properties of operations and objects. Use reasoning to solve problems by making sense of quantities and relationships in the situation. Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. Reason abstractly and quantitatively. Reason abstractly and quantitatively. Use multiple grouping symbols (parentheses, brackets, or braces) in numerical expressions and evaluate expressions containing these symbols. Reason abstractly and quantitatively. Apply the commutative, associative and distributive properties and order of operations to generate equivalent numerical expressions and to solve problems involving whole numbers. 13-4: Quick Check Curriculum Standards: Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. Reason abstractly and quantitatively. Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. Reason abstractly and quantitatively. Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. Reason abstractly and quantitatively. Mathematically proficient students make sense of quantities and their relationships in problem situations. They bring two complementary abilities to bear on problems involving quantitative relationships: the ability to decontextualize—to abstract a given situation and represent it symbolically and manipulate the representing symbols as if they have a life of their own, without necessarily attending to their referents—and the ability to contextualize, to pause as needed during the manipulation process in order to probe into the referents for the symbols involved. Quantitative reasoning entails habits of creating a coherent representation of the problem at hand; considering the units involved; attending to the meaning of quantities, not just how to compute them; and knowing and flexibly using different properties of operations and objects. Use reasoning to solve problems by making sense of quantities and relationships in the situation. Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. Reason abstractly and quantitatively. Reason abstractly and quantitatively. Use multiple grouping symbols (parentheses, brackets, or braces) in numerical expressions and evaluate expressions containing these symbols. Reason abstractly and quantitatively. Apply the commutative, associative and distributive properties and order of operations to generate equivalent numerical expressions and to solve problems involving whole numbers. 13-4: Lesson Self-Assessment 13-4: Reteach to Build Understanding Curriculum Standards: Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. Reason abstractly and quantitatively. Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. Reason abstractly and quantitatively. Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. Reason abstractly and quantitatively. Mathematically proficient students make sense of quantities and their relationships in problem situations. They bring two complementary abilities to bear on problems involving quantitative relationships: the ability to decontextualize—to abstract a given situation and represent it symbolically and manipulate the representing symbols as if they have a life of their own, without necessarily attending to their referents—and the ability to contextualize, to pause as needed during the manipulation process in order to probe into the referents for the symbols involved. Quantitative reasoning entails habits of creating a coherent representation of the problem at hand; considering the units involved; attending to the meaning of quantities, not just how to compute them; and knowing and flexibly using different properties of operations and objects. Use reasoning to solve problems by making sense of quantities and relationships in the situation. Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. Reason abstractly and quantitatively. Reason abstractly and quantitatively. Use multiple grouping symbols (parentheses, brackets, or braces) in numerical expressions and evaluate expressions containing these symbols. Reason abstractly and quantitatively. Apply the commutative, associative and distributive properties and order of operations to generate equivalent numerical expressions and to solve problems involving whole numbers. 13-4: Build Mathematical Literacy Curriculum Standards: Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 5 topics and texts, building on others’ ideas and expressing their own clearly. (a) Come to discussions prepared, having read or studied required material; explicitly draw on that preparation and other information known about the topic to explore ideas under discussion. (b) Follow agreed-upon rules for discussions and carry out assigned roles. (c) Pose and respond to specific questions by making comments that contribute to the discussion and elaborate on the remarks of others. (d) Review the key ideas expressed and draw conclusions in light of information and knowledge gained from the discussions. English language learners communicate for social and instructional purposes within the school setting. Summarize a written text read aloud or information presented in diverse media and formats, including visually, quantitatively, and orally. Summarize the points a speaker makes and explain how each claim is supported by reasons and evidence. Write informative/explanatory texts to examine a topic and convey ideas and information clearly. (a) Introduce a topic clearly, provide a general observation and focus, and group related information logically; include formatting (e.g., headings), illustrations, and multimedia when useful to aiding comprehension. (b) Develop the topic with facts, definitions, concrete details, quotations, or other information and examples related to the topic. (c) Link ideas within and across categories of information using words, phrases, and clauses (e.g., in contrast, especially). (d) Use precise language and domain-specific vocabulary to inform about or explain the topic. (e) Provide a concluding statement or section related to the information or explanation presented. English language learners communicate information, ideas and concepts necessary for academic success in the content area of Mathematics. 13-4: Enrichment Game: Save the Word: Grade 5 Topics 1-12 13-4: Pick a Project 13-4: Another Look Curriculum Standards: Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. Reason abstractly and quantitatively. Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. Reason abstractly and quantitatively. Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. Reason abstractly and quantitatively. Mathematically proficient students make sense of quantities and their relationships in problem situations. They bring two complementary abilities to bear on problems involving quantitative relationships: the ability to decontextualize—to abstract a given situation and represent it symbolically and manipulate the representing symbols as if they have a life of their own, without necessarily attending to their referents—and the ability to contextualize, to pause as needed during the manipulation process in order to probe into the referents for the symbols involved. Quantitative reasoning entails habits of creating a coherent representation of the problem at hand; considering the units involved; attending to the meaning of quantities, not just how to compute them; and knowing and flexibly using different properties of operations and objects. Use reasoning to solve problems by making sense of quantities and relationships in the situation. Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. Reason abstractly and quantitatively. Reason abstractly and quantitatively. Use multiple grouping symbols (parentheses, brackets, or braces) in numerical expressions and evaluate expressions containing these symbols. Reason abstractly and quantitatively. Apply the commutative, associative and distributive properties and order of operations to generate equivalent numerical expressions and to solve problems involving whole numbers. Spanish Resources 13-4: eText del Libro del estudiante 13-4: Repaso diario 13-4: Aprendizaje visual 13-4: Amigo de práctica: Práctica adicional 13-4: Práctica adicional interactiva 13-4: Refuerzo para mejorar la comprensión 13-4: Desarrollar la competencia matemática 13-4: Ampliación Topic 13: End of Topic Interactive Student Edition: End of Topic 13 Topic 13: Fluency Practice Activity Interactive Student Edition: Topic 13 Assessment Practice Interactive Student Edition: Topic 13 Performance Task Topic 13 Performance Task Topic 13 Assessment 1-5: Center Games 13-1: Visual Learning Curriculum Standards: Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. Use the order of operations to evaluate expressions. Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. Use multiple grouping symbols (parentheses, brackets, or braces) in numerical expressions and evaluate expressions containing these symbols. Apply the commutative, associative and distributive properties and order of operations to generate equivalent numerical expressions and to solve problems involving whole numbers. Evaluate a simple expression involving one set of parenthesis. 13-2: Visual Learning Curriculum Standards: Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. For example, 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. Write a simple expression for a calculation. Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. For example, 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. Write simple expressions that show calculations with numbers. Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. For example, 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. Write simple expressions that model calculations with numbers and interpret numerical expressions without evaluating them. Apply the commutative, associative and distributive properties and order of operations to generate equivalent numerical expressions and to solve problems involving whole numbers. 13-3: Visual Learning Curriculum Standards: Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. For example, 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. Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. For example, 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. Interpret numerical expressions without evaluating them. Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. For example, 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. Write simple expressions that model calculations with numbers and interpret numerical expressions without evaluating them. Apply the commutative, associative and distributive properties and order of operations to generate equivalent numerical expressions and to solve problems involving whole numbers. Topic 13 Online Assessment Curriculum Standards: Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. For example, 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. Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. For example, 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. Interpret numerical expressions without evaluating them. Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. For example, 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. Write simple expressions that model calculations with numbers and interpret numerical expressions without evaluating them. Apply the commutative, associative and distributive properties and order of operations to generate equivalent numerical expressions and to solve problems involving whole numbers. Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. Use the order of operations to evaluate expressions. Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. Use multiple grouping symbols (parentheses, brackets, or braces) in numerical expressions and evaluate expressions containing these symbols. Write simple expressions that show calculations with numbers. Topic 13:Spanish Assessments Tema 13: Tarea de rendimento Tema 13: Evaluación Topic 14: Graph Points on the Coordinate Plane Topic 14: Today's Challenge Topic 14: Beginning of Topic Interactive Student Edition: Beginning of Topic 14 Topic 14: enVision STEM Activity Grade 5 Topic 14: Review What You Know Topic 14: Vocabulary Cards 14-1: The Coordinate System Interactive Student Edition: Grade 5 Lesson 14-1 Math Anytime 14-1: Daily Review Topic 14: Today's Challenge Step 1: Problem-Based Learning 14-1: Solve & Share Curriculum Standards: Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x- coordinate, y-axis and y-coordinate). English language learners communicate for social and instructional purposes within the school setting. Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x- coordinate, y-axis and y-coordinate). Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x- coordinate, y-axis and y-coordinate). Locate points on a coordinate grid. Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y-coordinate). Identify parts of the coordinate plane (x-axis, y-axis, and the origin) and the ordered pair (x-coordinate and y-coordinate). Limit the coordinate plane to quadrant I. Create and use rules, tables, spreadsheets and graphs to describe patterns of change and solve problems. Use a rule or table to represent ordered pairs of positive integers and graph these ordered pairs on a coordinate system. Write informative/explanatory texts to examine a topic and convey ideas and information clearly. (a) Introduce a topic clearly, provide a general observation and focus, and group related information logically; include formatting (e.g., headings), illustrations, and multimedia when useful to aiding comprehension. (b) Develop the topic with facts, definitions, concrete details, quotations, or other information and examples related to the topic. (c) Link ideas within and across categories of information using words, phrases, and clauses (e.g., in contrast, especially). (d) Use precise language and domain-specific vocabulary to inform about or explain the topic. (e) Provide a concluding statement or section related to the information or explanation presented. English language learners communicate information, ideas and concepts necessary for academic success in the content area of Mathematics. Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 5 topics and texts, building on others’ ideas and expressing their own clearly. (a) Come to discussions prepared, having read or studied required material; explicitly draw on that preparation and other information known about the topic to explore ideas under discussion. (b) Follow agreed-upon rules for discussions and carry out assigned roles. (c) Pose and respond to specific questions by making comments that contribute to the discussion and elaborate on the remarks of others. (d) Review the key ideas expressed and draw conclusions in light of information and knowledge gained from the discussions. Summarize a written text read aloud or information presented in diverse media and formats, including visually, quantitatively, and orally. Summarize the points a speaker makes and explain how each claim is supported by reasons and evidence. Step 2: Visual Learning 14-1: Visual Learning Curriculum Standards: Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x- coordinate, y-axis and y-coordinate). Find a location on a map using given coordinates. Locate points on a coordinate plane. Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y- coordinate). Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y-coordinate). Locate points on a coordinate grid. Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y- coordinate). Identify parts of the coordinate plane (x-axis, y-axis, and the origin) and the ordered pair (x- coordinate and y-coordinate). Limit the coordinate plane to quadrant I. Create and use rules, tables, spreadsheets and graphs to describe patterns of change and solve problems. Use a rule or table to represent ordered pairs of positive integers and graph these ordered pairs on a coordinate system. Locate the x- and y-axis on a coordinate plane. Given two pattern descriptions involving the same context (e.g., collecting marbles), determine the first five terms and compare the values. 14-1: Convince Me! Curriculum Standards: Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x- coordinate, y-axis and y-coordinate). Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x- coordinate, y-axis and y-coordinate). Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x- coordinate, y-axis and y-coordinate). Locate points on a coordinate grid. Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y-coordinate). Identify parts of the coordinate plane (x-axis, y-axis, and the origin) and the ordered pair (x-coordinate and y-coordinate). Limit the coordinate plane to quadrant I. Create and use rules, tables, spreadsheets and graphs to describe patterns of change and solve problems. Use a rule or table to represent ordered pairs of positive integers and graph these ordered pairs on a coordinate system. Practice and Problem Solving 14-1: Student Edition Practice Curriculum Standards: Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x- coordinate, y-axis and y-coordinate). Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x- coordinate, y-axis and y-coordinate). Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x- coordinate, y-axis and y-coordinate). Locate points on a coordinate grid. Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y-coordinate). Identify parts of the coordinate plane (x-axis, y-axis, and the origin) and the ordered pair (x-coordinate and y-coordinate). Limit the coordinate plane to quadrant I. Create and use rules, tables, spreadsheets and graphs to describe patterns of change and solve problems. Use a rule or table to represent ordered pairs of positive integers and graph these ordered pairs on a coordinate system. 14-1: Practice Buddy: Independent Practice; Problem Solving Curriculum Standards: Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x- coordinate, y-axis and y-coordinate). Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x- coordinate, y-axis and y-coordinate). Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x- coordinate, y-axis and y-coordinate). Locate points on a coordinate grid. Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y-coordinate). Identify parts of the coordinate plane (x-axis, y-axis, and the origin) and the ordered pair (x-coordinate and y-coordinate). Limit the coordinate plane to quadrant I. Create and use rules, tables, spreadsheets and graphs to describe patterns of change and solve problems. Use a rule or table to represent ordered pairs of positive integers and graph these ordered pairs on a coordinate system. 14-1: Practice Buddy: Additional Practice Curriculum Standards: Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x- coordinate, y-axis and y-coordinate). Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x- coordinate, y-axis and y-coordinate). Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x- coordinate, y-axis and y-coordinate). Locate points on a coordinate grid. Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y-coordinate). Identify parts of the coordinate plane (x-axis, y-axis, and the origin) and the ordered pair (x-coordinate and y-coordinate). Limit the coordinate plane to quadrant I. Create and use rules, tables, spreadsheets and graphs to describe patterns of change and solve problems. Use a rule or table to represent ordered pairs of positive integers and graph these ordered pairs on a coordinate system. 14-1: Interactive Additional Practice Step 3: Assess & Differentiate 14-1: Practice Buddy: Additional Practice Curriculum Standards: Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x- coordinate, y-axis and y-coordinate). Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x- coordinate, y-axis and y-coordinate). Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x- coordinate, y-axis and y-coordinate). Locate points on a coordinate grid. Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y-coordinate). Identify parts of the coordinate plane (x-axis, y-axis, and the origin) and the ordered pair (x-coordinate and y-coordinate). Limit the coordinate plane to quadrant I. Create and use rules, tables, spreadsheets and graphs to describe patterns of change and solve problems. Use a rule or table to represent ordered pairs of positive integers and graph these ordered pairs on a coordinate system. 14-1: Enrichment Curriculum Standards: Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x- coordinate, y-axis and y-coordinate). Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x- coordinate, y-axis and y-coordinate). Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x- coordinate, y-axis and y-coordinate). Locate points on a coordinate grid. Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y-coordinate). Identify parts of the coordinate plane (x-axis, y-axis, and the origin) and the ordered pair (x-coordinate and y-coordinate). Limit the coordinate plane to quadrant I. Create and use rules, tables, spreadsheets and graphs to describe patterns of change and solve problems. Use a rule or table to represent ordered pairs of positive integers and graph these ordered pairs on a coordinate system. 14-1: Quick Check Curriculum Standards: Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x- coordinate, y-axis and y-coordinate). Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x- coordinate, y-axis and y-coordinate). Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x- coordinate, y-axis and y-coordinate). Locate points on a coordinate grid. Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y-coordinate). Identify parts of the coordinate plane (x-axis, y-axis, and the origin) and the ordered pair (x-coordinate and y-coordinate). Limit the coordinate plane to quadrant I. Create and use rules, tables, spreadsheets and graphs to describe patterns of change and solve problems. Use a rule or table to represent ordered pairs of positive integers and graph these ordered pairs on a coordinate system. 14-1: Lesson Self-Assessment 14-1: Reteach to Build Understanding Curriculum Standards: Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x- coordinate, y-axis and y-coordinate). Find a location on a map using given coordinates. Locate points on a coordinate plane. Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y- coordinate). Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y-coordinate). Locate points on a coordinate grid. Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y- coordinate). Identify parts of the coordinate plane (x-axis, y-axis, and the origin) and the ordered pair (x- coordinate and y-coordinate). Limit the coordinate plane to quadrant I. Create and use rules, tables, spreadsheets and graphs to describe patterns of change and solve problems. Use a rule or table to represent ordered pairs of positive integers and graph these ordered pairs on a coordinate system. Locate the x- and y-axis on a coordinate plane. 14-1: Build Mathematical Literacy Curriculum Standards: Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 5 topics and texts, building on others’ ideas and expressing their own clearly. (a) Come to discussions prepared, having read or studied required material; explicitly draw on that preparation and other information known about the topic to explore ideas under discussion. (b) Follow agreed-upon rules for discussions and carry out assigned roles. (c) Pose and respond to specific questions by making comments that contribute to the discussion and elaborate on the remarks of others. (d) Review the key ideas expressed and draw conclusions in light of information and knowledge gained from the discussions. English language learners communicate for social and instructional purposes within the school setting. Summarize a written text read aloud or information presented in diverse media and formats, including visually, quantitatively, and orally. Summarize the points a speaker makes and explain how each claim is supported by reasons and evidence. Write informative/explanatory texts to examine a topic and convey ideas and information clearly. (a) Introduce a topic clearly, provide a general observation and focus, and group related information logically; include formatting (e.g., headings), illustrations, and multimedia when useful to aiding comprehension. (b) Develop the topic with facts, definitions, concrete details, quotations, or other information and examples related to the topic. (c) Link ideas within and across categories of information using words, phrases, and clauses (e.g., in contrast, especially). (d) Use precise language and domain-specific vocabulary to inform about or explain the topic. (e) Provide a concluding statement or section related to the information or explanation presented. English language learners communicate information, ideas and concepts necessary for academic success in the content area of Mathematics. 14-1: Enrichment 14-1: Digital Math Tool Activity 14-1: enVision STEM Activity Curriculum Standards: Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x- coordinate, y-axis and y-coordinate). Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x- coordinate, y-axis and y-coordinate). Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x- coordinate, y-axis and y-coordinate). Locate points on a coordinate grid. Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y-coordinate). Identify parts of the coordinate plane (x-axis, y-axis, and the origin) and the ordered pair (x-coordinate and y-coordinate). Limit the coordinate plane to quadrant I. Create and use rules, tables, spreadsheets and graphs to describe patterns of change and solve problems. Use a rule or table to represent ordered pairs of positive integers and graph these ordered pairs on a coordinate system. 14-1: Another Look Curriculum Standards: Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x- coordinate, y-axis and y-coordinate). Find a location on a map using given coordinates. Locate points on a coordinate plane. Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y- coordinate). Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y-coordinate). Locate points on a coordinate grid. Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y- coordinate). Identify parts of the coordinate plane (x-axis, y-axis, and the origin) and the ordered pair (x- coordinate and y-coordinate). Limit the coordinate plane to quadrant I. Create and use rules, tables, spreadsheets and graphs to describe patterns of change and solve problems. Use a rule or table to represent ordered pairs of positive integers and graph these ordered pairs on a coordinate system. Locate the x- and y-axis on a coordinate plane. Given two pattern descriptions involving the same context (e.g., collecting marbles), determine the first five terms and compare the values. Spanish Resources 14-1: eText del Libro del estudiante 14-1: Repaso diario 14-1: Aprendizaje visual 14-1: Amigo de práctica: Práctica adicional 14-1: Práctica adicional interactiva 14-1: Refuerzo para mejorar la comprensión 14-1: Desarrollar la competencia matemática 14-1: Ampliación 14-2: Graph Data Using Ordered Pairs Interactive Student Edition: Grade 5 Lesson 14-2 Math Anytime 14-2: Daily Review Topic 14: Today's Challenge Step 1: Problem-Based Learning 14-2: Solve & Share Curriculum Standards: Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x- coordinate, y-axis and y-coordinate). Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. English language learners communicate for social and instructional purposes within the school setting. Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y- coordinate). Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y-coordinate). Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. Graph points on a coordinate grid. Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. Identify parts of the coordinate plane (x-axis, y-axis, and the origin) and the ordered pair (x-coordinate and y- coordinate). Limit the coordinate plane to quadrant I. Create and use rules, tables, spreadsheets and graphs to describe patterns of change and solve problems. Use a rule or table to represent ordered pairs of positive integers and graph these ordered pairs on a coordinate system. Write informative/explanatory texts to examine a topic and convey ideas and information clearly. (a) Introduce a topic clearly, provide a general observation and focus, and group related information logically; include formatting (e.g., headings), illustrations, and multimedia when useful to aiding comprehension. (b) Develop the topic with facts, definitions, concrete details, quotations, or other information and examples related to the topic. (c) Link ideas within and across categories of information using words, phrases, and clauses (e.g., in contrast, especially). (d) Use precise language and domain- specific vocabulary to inform about or explain the topic. (e) Provide a concluding statement or section related to the information or explanation presented. English language learners communicate information, ideas and concepts necessary for academic success in the content area of Mathematics. Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 5 topics and texts, building on others’ ideas and expressing their own clearly. (a) Come to discussions prepared, having read or studied required material; explicitly draw on that preparation and other information known about the topic to explore ideas under discussion. (b) Follow agreed-upon rules for discussions and carry out assigned roles. (c) Pose and respond to specific questions by making comments that contribute to the discussion and elaborate on the remarks of others. (d) Review the key ideas expressed and draw conclusions in light of information and knowledge gained from the discussions. Summarize a written text read aloud or information presented in diverse media and formats, including visually, quantitatively, and orally. Summarize the points a speaker makes and explain how each claim is supported by reasons and evidence. Step 2: Visual Learning 14-2: Visual Learning Curriculum Standards: Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x- coordinate, y-axis and y-coordinate). Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. Graph ordered pairs (coordinates). Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y-coordinate). Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x- coordinate, y-axis and y-coordinate). Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. Graph points on a coordinate grid. Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. Identify parts of the coordinate plane (x-axis, y-axis, and the origin) and the ordered pair (x-coordinate and y-coordinate). Limit the coordinate plane to quadrant I. Create and use rules, tables, spreadsheets and graphs to describe patterns of change and solve problems. Use a rule or table to represent ordered pairs of positive integers and graph these ordered pairs on a coordinate system. 14-2: Convince Me! Curriculum Standards: Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x- coordinate, y-axis and y-coordinate). Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y- coordinate). Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y-coordinate). Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. Graph points on a coordinate grid. Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. Identify parts of the coordinate plane (x-axis, y-axis, and the origin) and the ordered pair (x-coordinate and y- coordinate). Limit the coordinate plane to quadrant I. Create and use rules, tables, spreadsheets and graphs to describe patterns of change and solve problems. Use a rule or table to represent ordered pairs of positive integers and graph these ordered pairs on a coordinate system. Practice and Problem Solving 14-2: Student Edition Practice Curriculum Standards: Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x- coordinate, y-axis and y-coordinate). Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y- coordinate). Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y-coordinate). Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. Graph points on a coordinate grid. Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. Identify parts of the coordinate plane (x-axis, y-axis, and the origin) and the ordered pair (x-coordinate and y- coordinate). Limit the coordinate plane to quadrant I. Create and use rules, tables, spreadsheets and graphs to describe patterns of change and solve problems. Use a rule or table to represent ordered pairs of positive integers and graph these ordered pairs on a coordinate system. 14-2: Practice Buddy: Independent Practice; Problem Solving Curriculum Standards: Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x- coordinate, y-axis and y-coordinate). Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y- coordinate). Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y-coordinate). Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. Graph points on a coordinate grid. Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. Identify parts of the coordinate plane (x-axis, y-axis, and the origin) and the ordered pair (x-coordinate and y- coordinate). Limit the coordinate plane to quadrant I. Create and use rules, tables, spreadsheets and graphs to describe patterns of change and solve problems. Use a rule or table to represent ordered pairs of positive integers and graph these ordered pairs on a coordinate system. 14-2: Practice Buddy: Additional Practice Curriculum Standards: Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x- coordinate, y-axis and y-coordinate). Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y- coordinate). Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y-coordinate). Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. Graph points on a coordinate grid. Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. Identify parts of the coordinate plane (x-axis, y-axis, and the origin) and the ordered pair (x-coordinate and y- coordinate). Limit the coordinate plane to quadrant I. Create and use rules, tables, spreadsheets and graphs to describe patterns of change and solve problems. Use a rule or table to represent ordered pairs of positive integers and graph these ordered pairs on a coordinate system. 14-2: Interactive Additional Practice Step 3: Assess & Differentiate 14-2: Practice Buddy: Additional Practice Curriculum Standards: Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x- coordinate, y-axis and y-coordinate). Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y- coordinate). Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y-coordinate). Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. Graph points on a coordinate grid. Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. Identify parts of the coordinate plane (x-axis, y-axis, and the origin) and the ordered pair (x-coordinate and y- coordinate). Limit the coordinate plane to quadrant I. Create and use rules, tables, spreadsheets and graphs to describe patterns of change and solve problems. Use a rule or table to represent ordered pairs of positive integers and graph these ordered pairs on a coordinate system. 14-2: Enrichment Curriculum Standards: Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x- coordinate, y-axis and y-coordinate). Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y- coordinate). Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y-coordinate). Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. Graph points on a coordinate grid. Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. Identify parts of the coordinate plane (x-axis, y-axis, and the origin) and the ordered pair (x-coordinate and y- coordinate). Limit the coordinate plane to quadrant I. Create and use rules, tables, spreadsheets and graphs to describe patterns of change and solve problems. Use a rule or table to represent ordered pairs of positive integers and graph these ordered pairs on a coordinate system. 14-2: Quick Check Curriculum Standards: Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x- coordinate, y-axis and y-coordinate). Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y- coordinate). Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y-coordinate). Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. Graph points on a coordinate grid. Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. Identify parts of the coordinate plane (x-axis, y-axis, and the origin) and the ordered pair (x-coordinate and y- coordinate). Limit the coordinate plane to quadrant I. Create and use rules, tables, spreadsheets and graphs to describe patterns of change and solve problems. Use a rule or table to represent ordered pairs of positive integers and graph these ordered pairs on a coordinate system. 14-2: Lesson Self-Assessment 14-2: Reteach to Build Understanding Curriculum Standards: Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x- coordinate, y-axis and y-coordinate). Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. Graph ordered pairs (coordinates). Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y-coordinate). Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x- coordinate, y-axis and y-coordinate). Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. Graph points on a coordinate grid. Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. Identify parts of the coordinate plane (x-axis, y-axis, and the origin) and the ordered pair (x-coordinate and y-coordinate). Limit the coordinate plane to quadrant I. Create and use rules, tables, spreadsheets and graphs to describe patterns of change and solve problems. Use a rule or table to represent ordered pairs of positive integers and graph these ordered pairs on a coordinate system. 14-2: Build Mathematical Literacy Curriculum Standards: Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 5 topics and texts, building on others’ ideas and expressing their own clearly. (a) Come to discussions prepared, having read or studied required material; explicitly draw on that preparation and other information known about the topic to explore ideas under discussion. (b) Follow agreed-upon rules for discussions and carry out assigned roles. (c) Pose and respond to specific questions by making comments that contribute to the discussion and elaborate on the remarks of others. (d) Review the key ideas expressed and draw conclusions in light of information and knowledge gained from the discussions. English language learners communicate for social and instructional purposes within the school setting. Summarize a written text read aloud or information presented in diverse media and formats, including visually, quantitatively, and orally. Summarize the points a speaker makes and explain how each claim is supported by reasons and evidence. Write informative/explanatory texts to examine a topic and convey ideas and information clearly. (a) Introduce a topic clearly, provide a general observation and focus, and group related information logically; include formatting (e.g., headings), illustrations, and multimedia when useful to aiding comprehension. (b) Develop the topic with facts, definitions, concrete details, quotations, or other information and examples related to the topic. (c) Link ideas within and across categories of information using words, phrases, and clauses (e.g., in contrast, especially). (d) Use precise language and domain-specific vocabulary to inform about or explain the topic. (e) Provide a concluding statement or section related to the information or explanation presented. English language learners communicate information, ideas and concepts necessary for academic success in the content area of Mathematics. 14-2: Enrichment 14-2: Digital Math Tool Activity 14-2 Problem-Solving Reading Activity Curriculum Standards: Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x- coordinate, y-axis and y-coordinate). Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y- coordinate). Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y-coordinate). Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. Graph points on a coordinate grid. Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. Identify parts of the coordinate plane (x-axis, y-axis, and the origin) and the ordered pair (x-coordinate and y- coordinate). Limit the coordinate plane to quadrant I. Create and use rules, tables, spreadsheets and graphs to describe patterns of change and solve problems. Use a rule or table to represent ordered pairs of positive integers and graph these ordered pairs on a coordinate system. 14-2: Another Look Curriculum Standards: Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x- coordinate, y-axis and y-coordinate). Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. Graph ordered pairs (coordinates). Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y-coordinate). Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x- coordinate, y-axis and y-coordinate). Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. Graph points on a coordinate grid. Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. Identify parts of the coordinate plane (x-axis, y-axis, and the origin) and the ordered pair (x-coordinate and y-coordinate). Limit the coordinate plane to quadrant I. Create and use rules, tables, spreadsheets and graphs to describe patterns of change and solve problems. Use a rule or table to represent ordered pairs of positive integers and graph these ordered pairs on a coordinate system. Spanish Resources 14-2: eText del Libro del estudiante 14-2: Repaso diario 14-2: Aprendizaje visual 14-2: Amigo de práctica: Práctica adicional 14-2: Práctica adicional interactiva 14-2: Refuerzo para mejorar la comprensión 14-2: Desarrollar la competencia matemática 14-2: Ampliación 14-3: Solve Problems Using Ordered Pairs Interactive Student Edition: Grade 5 Lesson 14-3 Math Anytime 14-3: Daily Review Topic 14: Today's Challenge Step 1: Problem-Based Learning 14-3: Solve & Share Curriculum Standards: Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. Solve real- world problems by graphing points. Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. Represent real-world and mathematical problems by plotting points in quadrant I of the coordinate plane and interpret coordinate values of points in the context of the situation. Create and use rules, tables, spreadsheets and graphs to describe patterns of change and solve problems. Use a rule or table to represent ordered pairs of positive integers and graph these ordered pairs on a coordinate system. English language learners communicate for social and instructional purposes within the school setting. Write informative/explanatory texts to examine a topic and convey ideas and information clearly. (a) Introduce a topic clearly, provide a general observation and focus, and group related information logically; include formatting (e.g., headings), illustrations, and multimedia when useful to aiding comprehension. (b) Develop the topic with facts, definitions, concrete details, quotations, or other information and examples related to the topic. (c) Link ideas within and across categories of information using words, phrases, and clauses (e.g., in contrast, especially). (d) Use precise language and domain-specific vocabulary to inform about or explain the topic. (e) Provide a concluding statement or section related to the information or explanation presented. English language learners communicate information, ideas and concepts necessary for academic success in the content area of Mathematics. Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 5 topics and texts, building on others’ ideas and expressing their own clearly. (a) Come to discussions prepared, having read or studied required material; explicitly draw on that preparation and other information known about the topic to explore ideas under discussion. (b) Follow agreed-upon rules for discussions and carry out assigned roles. (c) Pose and respond to specific questions by making comments that contribute to the discussion and elaborate on the remarks of others. (d) Review the key ideas expressed and draw conclusions in light of information and knowledge gained from the discussions. Summarize a written text read aloud or information presented in diverse media and formats, including visually, quantitatively, and orally. Summarize the points a speaker makes and explain how each claim is supported by reasons and evidence. Step 2: Visual Learning 14-3: Visual Learning Curriculum Standards: Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. Solve real- world problems by graphing points. Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. Represent real-world and mathematical problems by plotting points in quadrant I of the coordinate plane and interpret coordinate values of points in the context of the situation. Create and use rules, tables, spreadsheets and graphs to describe patterns of change and solve problems. Use a rule or table to represent ordered pairs of positive integers and graph these ordered pairs on a coordinate system. 14-3: Convince Me! Curriculum Standards: Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. Solve real- world problems by graphing points. Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. Represent real-world and mathematical problems by plotting points in quadrant I of the coordinate plane and interpret coordinate values of points in the context of the situation. Create and use rules, tables, spreadsheets and graphs to describe patterns of change and solve problems. Use a rule or table to represent ordered pairs of positive integers and graph these ordered pairs on a coordinate system. Practice and Problem Solving 14-3: Student Edition Practice Curriculum Standards: Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. Solve real- world problems by graphing points. Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. Represent real-world and mathematical problems by plotting points in quadrant I of the coordinate plane and interpret coordinate values of points in the context of the situation. Create and use rules, tables, spreadsheets and graphs to describe patterns of change and solve problems. Use a rule or table to represent ordered pairs of positive integers and graph these ordered pairs on a coordinate system. 14-3: Practice Buddy: Independent Practice; Problem Solving Curriculum Standards: Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. Solve real- world problems by graphing points. Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. Represent real-world and mathematical problems by plotting points in quadrant I of the coordinate plane and interpret coordinate values of points in the context of the situation. Create and use rules, tables, spreadsheets and graphs to describe patterns of change and solve problems. Use a rule or table to represent ordered pairs of positive integers and graph these ordered pairs on a coordinate system. 14-3: Practice Buddy: Additional Practice Curriculum Standards: Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. Solve real- world problems by graphing points. Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. Represent real-world and mathematical problems by plotting points in quadrant I of the coordinate plane and interpret coordinate values of points in the context of the situation. Create and use rules, tables, spreadsheets and graphs to describe patterns of change and solve problems. Use a rule or table to represent ordered pairs of positive integers and graph these ordered pairs on a coordinate system. 14-3: Interactive Additional Practice Step 3: Assess & Differentiate 14-3: Practice Buddy: Additional Practice Curriculum Standards: Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. Solve real- world problems by graphing points. Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. Represent real-world and mathematical problems by plotting points in quadrant I of the coordinate plane and interpret coordinate values of points in the context of the situation. Create and use rules, tables, spreadsheets and graphs to describe patterns of change and solve problems. Use a rule or table to represent ordered pairs of positive integers and graph these ordered pairs on a coordinate system. 14-3: Enrichment Curriculum Standards: Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. Solve real- world problems by graphing points. Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. Represent real-world and mathematical problems by plotting points in quadrant I of the coordinate plane and interpret coordinate values of points in the context of the situation. Create and use rules, tables, spreadsheets and graphs to describe patterns of change and solve problems. Use a rule or table to represent ordered pairs of positive integers and graph these ordered pairs on a coordinate system. 14-3: Quick Check Curriculum Standards: Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. Solve real- world problems by graphing points. Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. Represent real-world and mathematical problems by plotting points in quadrant I of the coordinate plane and interpret coordinate values of points in the context of the situation. Create and use rules, tables, spreadsheets and graphs to describe patterns of change and solve problems. Use a rule or table to represent ordered pairs of positive integers and graph these ordered pairs on a coordinate system. 14-3: Lesson Self-Assessment 14-3: Reteach to Build Understanding Curriculum Standards: Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. Solve real- world problems by graphing points. Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. Represent real-world and mathematical problems by plotting points in quadrant I of the coordinate plane and interpret coordinate values of points in the context of the situation. Create and use rules, tables, spreadsheets and graphs to describe patterns of change and solve problems. Use a rule or table to represent ordered pairs of positive integers and graph these ordered pairs on a coordinate system. 14-3: Build Mathematical Literacy Curriculum Standards: Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 5 topics and texts, building on others’ ideas and expressing their own clearly. (a) Come to discussions prepared, having read or studied required material; explicitly draw on that preparation and other information known about the topic to explore ideas under discussion. (b) Follow agreed-upon rules for discussions and carry out assigned roles. (c) Pose and respond to specific questions by making comments that contribute to the discussion and elaborate on the remarks of others. (d) Review the key ideas expressed and draw conclusions in light of information and knowledge gained from the discussions. English language learners communicate for social and instructional purposes within the school setting. Summarize a written text read aloud or information presented in diverse media and formats, including visually, quantitatively, and orally. Summarize the points a speaker makes and explain how each claim is supported by reasons and evidence. Write informative/explanatory texts to examine a topic and convey ideas and information clearly. (a) Introduce a topic clearly, provide a general observation and focus, and group related information logically; include formatting (e.g., headings), illustrations, and multimedia when useful to aiding comprehension. (b) Develop the topic with facts, definitions, concrete details, quotations, or other information and examples related to the topic. (c) Link ideas within and across categories of information using words, phrases, and clauses (e.g., in contrast, especially). (d) Use precise language and domain-specific vocabulary to inform about or explain the topic. (e) Provide a concluding statement or section related to the information or explanation presented. English language learners communicate information, ideas and concepts necessary for academic success in the content area of Mathematics. 14-3: Enrichment Game: Fluency - Multiply Multi-Digit Whole Numbers 14-3 Problem-Solving Reading Activity Curriculum Standards: Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. Solve real- world problems by graphing points. Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. Represent real-world and mathematical problems by plotting points in quadrant I of the coordinate plane and interpret coordinate values of points in the context of the situation. Create and use rules, tables, spreadsheets and graphs to describe patterns of change and solve problems. Use a rule or table to represent ordered pairs of positive integers and graph these ordered pairs on a coordinate system. 14-3: Another Look Curriculum Standards: Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. Solve real- world problems by graphing points. Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. Represent real-world and mathematical problems by plotting points in quadrant I of the coordinate plane and interpret coordinate values of points in the context of the situation. Create and use rules, tables, spreadsheets and graphs to describe patterns of change and solve problems. Use a rule or table to represent ordered pairs of positive integers and graph these ordered pairs on a coordinate system. Spanish Resources 14-3: eText del Libro del estudiante 14-3: Repaso diario 14-3: Aprendizaje visual 14-3: Amigo de práctica: Práctica adicional 14-3: Práctica adicional interactiva 14-3: Refuerzo para mejorar la comprensión 14-3: Desarrollar la competencia matemática 14-3: Ampliación 14-4: Problem Solving: Reasoning Interactive Student Edition: Grade 5 Lesson 14-4 Math Anytime 14-4: Daily Review Topic 14: Today's Challenge Step 1: Problem-Based Learning 14-4: Solve & Share Curriculum Standards: Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x- coordinate, y-axis and y-coordinate). Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. Reason abstractly and quantitatively. Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y-coordinate). Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. Reason abstractly and quantitatively. Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y-coordinate). Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. Reason abstractly and quantitatively. Mathematically proficient students make sense of quantities and their relationships in problem situations. They bring two complementary abilities to bear on problems involving quantitative relationships: the ability to decontextualize—to abstract a given situation and represent it symbolically and manipulate the representing symbols as if they have a life of their own, without necessarily attending to their referents—and the ability to contextualize, to pause as needed during the manipulation process in order to probe into the referents for the symbols involved. Quantitative reasoning entails habits of creating a coherent representation of the problem at hand; considering the units involved; attending to the meaning of quantities, not just how to compute them; and knowing and flexibly using different properties of operations and objects. Use reasoning to solve problems by making sense of quantities and relationships in the situation. Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. Reason abstractly and quantitatively. Reason abstractly and quantitatively. Represent real-world and mathematical problems by plotting points in quadrant I of the coordinate plane and interpret coordinate values of points in the context of the situation. Reason abstractly and quantitatively. Create and use rules, tables, spreadsheets and graphs to describe patterns of change and solve problems. Use a rule or table to represent ordered pairs of positive integers and graph these ordered pairs on a coordinate system. English language learners communicate for social and instructional purposes within the school setting. Write informative/explanatory texts to examine a topic and convey ideas and information clearly. (a) Introduce a topic clearly, provide a general observation and focus, and group related information logically; include formatting (e.g., headings), illustrations, and multimedia when useful to aiding comprehension. (b) Develop the topic with facts, definitions, concrete details, quotations, or other information and examples related to the topic. (c) Link ideas within and across categories of information using words, phrases, and clauses (e.g., in contrast, especially). (d) Use precise language and domain-specific vocabulary to inform about or explain the topic. (e) Provide a concluding statement or section related to the information or explanation presented. English language learners communicate information, ideas and concepts necessary for academic success in the content area of Mathematics. Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 5 topics and texts, building on others’ ideas and expressing their own clearly. (a) Come to discussions prepared, having read or studied required material; explicitly draw on that preparation and other information known about the topic to explore ideas under discussion. (b) Follow agreed-upon rules for discussions and carry out assigned roles. (c) Pose and respond to specific questions by making comments that contribute to the discussion and elaborate on the remarks of others. (d) Review the key ideas expressed and draw conclusions in light of information and knowledge gained from the discussions. Summarize a written text read aloud or information presented in diverse media and formats, including visually, quantitatively, and orally. Summarize the points a speaker makes and explain how each claim is supported by reasons and evidence. Step 2: Visual Learning 14-4: Visual Learning Curriculum Standards: Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x- coordinate, y-axis and y-coordinate). Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. Reason abstractly and quantitatively. Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y-coordinate). Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. Reason abstractly and quantitatively. Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y-coordinate). Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. Reason abstractly and quantitatively. Mathematically proficient students make sense of quantities and their relationships in problem situations. They bring two complementary abilities to bear on problems involving quantitative relationships: the ability to decontextualize—to abstract a given situation and represent it symbolically and manipulate the representing symbols as if they have a life of their own, without necessarily attending to their referents—and the ability to contextualize, to pause as needed during the manipulation process in order to probe into the referents for the symbols involved. Quantitative reasoning entails habits of creating a coherent representation of the problem at hand; considering the units involved; attending to the meaning of quantities, not just how to compute them; and knowing and flexibly using different properties of operations and objects. Use reasoning to solve problems by making sense of quantities and relationships in the situation. Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. Reason abstractly and quantitatively. Reason abstractly and quantitatively. Represent real-world and mathematical problems by plotting points in quadrant I of the coordinate plane and interpret coordinate values of points in the context of the situation. Reason abstractly and quantitatively. Create and use rules, tables, spreadsheets and graphs to describe patterns of change and solve problems. Use a rule or table to represent ordered pairs of positive integers and graph these ordered pairs on a coordinate system. 14-4: Convince Me! Curriculum Standards: Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x- coordinate, y-axis and y-coordinate). Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. Reason abstractly and quantitatively. Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y-coordinate). Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. Reason abstractly and quantitatively. Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y-coordinate). Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. Reason abstractly and quantitatively. Mathematically proficient students make sense of quantities and their relationships in problem situations. They bring two complementary abilities to bear on problems involving quantitative relationships: the ability to decontextualize—to abstract a given situation and represent it symbolically and manipulate the representing symbols as if they have a life of their own, without necessarily attending to their referents—and the ability to contextualize, to pause as needed during the manipulation process in order to probe into the referents for the symbols involved. Quantitative reasoning entails habits of creating a coherent representation of the problem at hand; considering the units involved; attending to the meaning of quantities, not just how to compute them; and knowing and flexibly using different properties of operations and objects. Use reasoning to solve problems by making sense of quantities and relationships in the situation. Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. Reason abstractly and quantitatively. Reason abstractly and quantitatively. Represent real-world and mathematical problems by plotting points in quadrant I of the coordinate plane and interpret coordinate values of points in the context of the situation. Reason abstractly and quantitatively. Create and use rules, tables, spreadsheets and graphs to describe patterns of change and solve problems. Use a rule or table to represent ordered pairs of positive integers and graph these ordered pairs on a coordinate system. Practice and Problem Solving 14-4: Student Edition Practice Curriculum Standards: Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x- coordinate, y-axis and y-coordinate). Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. Reason abstractly and quantitatively. Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y-coordinate). Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. Reason abstractly and quantitatively. Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y-coordinate). Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. Reason abstractly and quantitatively. Mathematically proficient students make sense of quantities and their relationships in problem situations. They bring two complementary abilities to bear on problems involving quantitative relationships: the ability to decontextualize—to abstract a given situation and represent it symbolically and manipulate the representing symbols as if they have a life of their own, without necessarily attending to their referents—and the ability to contextualize, to pause as needed during the manipulation process in order to probe into the referents for the symbols involved. Quantitative reasoning entails habits of creating a coherent representation of the problem at hand; considering the units involved; attending to the meaning of quantities, not just how to compute them; and knowing and flexibly using different properties of operations and objects. Use reasoning to solve problems by making sense of quantities and relationships in the situation. Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. Reason abstractly and quantitatively. Reason abstractly and quantitatively. Represent real-world and mathematical problems by plotting points in quadrant I of the coordinate plane and interpret coordinate values of points in the context of the situation. Reason abstractly and quantitatively. Create and use rules, tables, spreadsheets and graphs to describe patterns of change and solve problems. Use a rule or table to represent ordered pairs of positive integers and graph these ordered pairs on a coordinate system. 14-4: Practice Buddy: Independent Practice; Problem Solving Curriculum Standards: Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x- coordinate, y-axis and y-coordinate). Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. Reason abstractly and quantitatively. Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y-coordinate). Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. Reason abstractly and quantitatively. Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y-coordinate). Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. Reason abstractly and quantitatively. Mathematically proficient students make sense of quantities and their relationships in problem situations. They bring two complementary abilities to bear on problems involving quantitative relationships: the ability to decontextualize—to abstract a given situation and represent it symbolically and manipulate the representing symbols as if they have a life of their own, without necessarily attending to their referents—and the ability to contextualize, to pause as needed during the manipulation process in order to probe into the referents for the symbols involved. Quantitative reasoning entails habits of creating a coherent representation of the problem at hand; considering the units involved; attending to the meaning of quantities, not just how to compute them; and knowing and flexibly using different properties of operations and objects. Use reasoning to solve problems by making sense of quantities and relationships in the situation. Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. Reason abstractly and quantitatively. Reason abstractly and quantitatively. Represent real-world and mathematical problems by plotting points in quadrant I of the coordinate plane and interpret coordinate values of points in the context of the situation. Reason abstractly and quantitatively. Create and use rules, tables, spreadsheets and graphs to describe patterns of change and solve problems. Use a rule or table to represent ordered pairs of positive integers and graph these ordered pairs on a coordinate system. 14-4: Practice Buddy: Additional Practice Curriculum Standards: Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x- coordinate, y-axis and y-coordinate). Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. Reason abstractly and quantitatively. Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y-coordinate). Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. Reason abstractly and quantitatively. Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y-coordinate). Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. Reason abstractly and quantitatively. Mathematically proficient students make sense of quantities and their relationships in problem situations. They bring two complementary abilities to bear on problems involving quantitative relationships: the ability to decontextualize—to abstract a given situation and represent it symbolically and manipulate the representing symbols as if they have a life of their own, without necessarily attending to their referents—and the ability to contextualize, to pause as needed during the manipulation process in order to probe into the referents for the symbols involved. Quantitative reasoning entails habits of creating a coherent representation of the problem at hand; considering the units involved; attending to the meaning of quantities, not just how to compute them; and knowing and flexibly using different properties of operations and objects. Use reasoning to solve problems by making sense of quantities and relationships in the situation. Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. Reason abstractly and quantitatively. Reason abstractly and quantitatively. Represent real-world and mathematical problems by plotting points in quadrant I of the coordinate plane and interpret coordinate values of points in the context of the situation. Reason abstractly and quantitatively. Create and use rules, tables, spreadsheets and graphs to describe patterns of change and solve problems. Use a rule or table to represent ordered pairs of positive integers and graph these ordered pairs on a coordinate system. 14-4: Interactive Additional Practice Step 3: Assess & Differentiate 14-4: Practice Buddy: Additional Practice Curriculum Standards: Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x- coordinate, y-axis and y-coordinate). Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. Reason abstractly and quantitatively. Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y-coordinate). Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. Reason abstractly and quantitatively. Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y-coordinate). Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. Reason abstractly and quantitatively. Mathematically proficient students make sense of quantities and their relationships in problem situations. They bring two complementary abilities to bear on problems involving quantitative relationships: the ability to decontextualize—to abstract a given situation and represent it symbolically and manipulate the representing symbols as if they have a life of their own, without necessarily attending to their referents—and the ability to contextualize, to pause as needed during the manipulation process in order to probe into the referents for the symbols involved. Quantitative reasoning entails habits of creating a coherent representation of the problem at hand; considering the units involved; attending to the meaning of quantities, not just how to compute them; and knowing and flexibly using different properties of operations and objects. Use reasoning to solve problems by making sense of quantities and relationships in the situation. Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. Reason abstractly and quantitatively. Reason abstractly and quantitatively. Represent real-world and mathematical problems by plotting points in quadrant I of the coordinate plane and interpret coordinate values of points in the context of the situation. Reason abstractly and quantitatively. Create and use rules, tables, spreadsheets and graphs to describe patterns of change and solve problems. Use a rule or table to represent ordered pairs of positive integers and graph these ordered pairs on a coordinate system. 14-4: Enrichment Curriculum Standards: Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x- coordinate, y-axis and y-coordinate). Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. Reason abstractly and quantitatively. Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y-coordinate). Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. Reason abstractly and quantitatively. Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y-coordinate). Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. Reason abstractly and quantitatively. Mathematically proficient students make sense of quantities and their relationships in problem situations. They bring two complementary abilities to bear on problems involving quantitative relationships: the ability to decontextualize—to abstract a given situation and represent it symbolically and manipulate the representing symbols as if they have a life of their own, without necessarily attending to their referents—and the ability to contextualize, to pause as needed during the manipulation process in order to probe into the referents for the symbols involved. Quantitative reasoning entails habits of creating a coherent representation of the problem at hand; considering the units involved; attending to the meaning of quantities, not just how to compute them; and knowing and flexibly using different properties of operations and objects. Use reasoning to solve problems by making sense of quantities and relationships in the situation. Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. Reason abstractly and quantitatively. Reason abstractly and quantitatively. Represent real-world and mathematical problems by plotting points in quadrant I of the coordinate plane and interpret coordinate values of points in the context of the situation. Reason abstractly and quantitatively. Create and use rules, tables, spreadsheets and graphs to describe patterns of change and solve problems. Use a rule or table to represent ordered pairs of positive integers and graph these ordered pairs on a coordinate system. 14-4: Quick Check Curriculum Standards: Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x- coordinate, y-axis and y-coordinate). Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. Reason abstractly and quantitatively. Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y-coordinate). Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. Reason abstractly and quantitatively. Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y-coordinate). Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. Reason abstractly and quantitatively. Mathematically proficient students make sense of quantities and their relationships in problem situations. They bring two complementary abilities to bear on problems involving quantitative relationships: the ability to decontextualize—to abstract a given situation and represent it symbolically and manipulate the representing symbols as if they have a life of their own, without necessarily attending to their referents—and the ability to contextualize, to pause as needed during the manipulation process in order to probe into the referents for the symbols involved. Quantitative reasoning entails habits of creating a coherent representation of the problem at hand; considering the units involved; attending to the meaning of quantities, not just how to compute them; and knowing and flexibly using different properties of operations and objects. Use reasoning to solve problems by making sense of quantities and relationships in the situation. Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. Reason abstractly and quantitatively. Reason abstractly and quantitatively. Represent real-world and mathematical problems by plotting points in quadrant I of the coordinate plane and interpret coordinate values of points in the context of the situation. Reason abstractly and quantitatively. Create and use rules, tables, spreadsheets and graphs to describe patterns of change and solve problems. Use a rule or table to represent ordered pairs of positive integers and graph these ordered pairs on a coordinate system. 14-4: Lesson Self-Assessment 14-4: Reteach to Build Understanding Curriculum Standards: Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x- coordinate, y-axis and y-coordinate). Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. Reason abstractly and quantitatively. Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y-coordinate). Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. Reason abstractly and quantitatively. Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y-coordinate). Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. Reason abstractly and quantitatively. Mathematically proficient students make sense of quantities and their relationships in problem situations. They bring two complementary abilities to bear on problems involving quantitative relationships: the ability to decontextualize—to abstract a given situation and represent it symbolically and manipulate the representing symbols as if they have a life of their own, without necessarily attending to their referents—and the ability to contextualize, to pause as needed during the manipulation process in order to probe into the referents for the symbols involved. Quantitative reasoning entails habits of creating a coherent representation of the problem at hand; considering the units involved; attending to the meaning of quantities, not just how to compute them; and knowing and flexibly using different properties of operations and objects. Use reasoning to solve problems by making sense of quantities and relationships in the situation. Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. Reason abstractly and quantitatively. Reason abstractly and quantitatively. Represent real-world and mathematical problems by plotting points in quadrant I of the coordinate plane and interpret coordinate values of points in the context of the situation. Reason abstractly and quantitatively. Create and use rules, tables, spreadsheets and graphs to describe patterns of change and solve problems. Use a rule or table to represent ordered pairs of positive integers and graph these ordered pairs on a coordinate system. 14-4: Build Mathematical Literacy Curriculum Standards: Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 5 topics and texts, building on others’ ideas and expressing their own clearly. (a) Come to discussions prepared, having read or studied required material; explicitly draw on that preparation and other information known about the topic to explore ideas under discussion. (b) Follow agreed-upon rules for discussions and carry out assigned roles. (c) Pose and respond to specific questions by making comments that contribute to the discussion and elaborate on the remarks of others. (d) Review the key ideas expressed and draw conclusions in light of information and knowledge gained from the discussions. English language learners communicate for social and instructional purposes within the school setting. Summarize a written text read aloud or information presented in diverse media and formats, including visually, quantitatively, and orally. Summarize the points a speaker makes and explain how each claim is supported by reasons and evidence. Write informative/explanatory texts to examine a topic and convey ideas and information clearly. (a) Introduce a topic clearly, provide a general observation and focus, and group related information logically; include formatting (e.g., headings), illustrations, and multimedia when useful to aiding comprehension. (b) Develop the topic with facts, definitions, concrete details, quotations, or other information and examples related to the topic. (c) Link ideas within and across categories of information using words, phrases, and clauses (e.g., in contrast, especially). (d) Use precise language and domain-specific vocabulary to inform about or explain the topic. (e) Provide a concluding statement or section related to the information or explanation presented. English language learners communicate information, ideas and concepts necessary for academic success in the content area of Mathematics. 14-4: Enrichment Game: Save the Word: Grade 5 Topics 1-12 14-4: Pick a Project 14-4: Another Look Curriculum Standards: Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x- coordinate, y-axis and y-coordinate). Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. Reason abstractly and quantitatively. Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y-coordinate). Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. Reason abstractly and quantitatively. Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y-coordinate). Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. Reason abstractly and quantitatively. Mathematically proficient students make sense of quantities and their relationships in problem situations. They bring two complementary abilities to bear on problems involving quantitative relationships: the ability to decontextualize—to abstract a given situation and represent it symbolically and manipulate the representing symbols as if they have a life of their own, without necessarily attending to their referents—and the ability to contextualize, to pause as needed during the manipulation process in order to probe into the referents for the symbols involved. Quantitative reasoning entails habits of creating a coherent representation of the problem at hand; considering the units involved; attending to the meaning of quantities, not just how to compute them; and knowing and flexibly using different properties of operations and objects. Use reasoning to solve problems by making sense of quantities and relationships in the situation. Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. Reason abstractly and quantitatively. Reason abstractly and quantitatively. Represent real-world and mathematical problems by plotting points in quadrant I of the coordinate plane and interpret coordinate values of points in the context of the situation. Reason abstractly and quantitatively. Create and use rules, tables, spreadsheets and graphs to describe patterns of change and solve problems. Use a rule or table to represent ordered pairs of positive integers and graph these ordered pairs on a coordinate system. Spanish Resources 14-4: eText del Libro del estudiante 14-4: Repaso diario 14-4: Aprendizaje visual 14-4: Amigo de práctica: Práctica adicional 14-4: Práctica adicional interactiva 14-4: Refuerzo para mejorar la comprensión 14-4: Desarrollar la competencia matemática 14-4: Ampliación Topic 14: End of Topic Interactive Student Edition: End of Topic 14 Topic 14: Fluency Practice Activity Interactive Student Edition: Topic 14 Assessment Practice Interactive Student Edition: Topic 14 Performance Task Topic 14 Performance Task Topic 14 Assessment 14-1: Visual Learning Curriculum Standards: Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x- coordinate, y-axis and y-coordinate). Given two pattern descriptions involving the same context (e.g., collecting marbles), determine the first five terms and compare the values. Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y-coordinate). Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y-coordinate). Locate points on a coordinate grid. Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y-coordinate). Identify parts of the coordinate plane (x-axis, y-axis, and the origin) and the ordered pair (x-coordinate and y-coordinate). Limit the coordinate plane to quadrant I. Create and use rules, tables, spreadsheets and graphs to describe patterns of change and solve problems. Use a rule or table to represent ordered pairs of positive integers and graph these ordered pairs on a coordinate system. 14-2: Visual Learning Curriculum Standards: Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x- coordinate, y-axis and y-coordinate). Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y- coordinate). Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y-coordinate). Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. Graph points on a coordinate grid. Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. Identify parts of the coordinate plane (x-axis, y-axis, and the origin) and the ordered pair (x-coordinate and y- coordinate). Limit the coordinate plane to quadrant I. Create and use rules, tables, spreadsheets and graphs to describe patterns of change and solve problems. Use a rule or table to represent ordered pairs of positive integers and graph these ordered pairs on a coordinate system. 14-3: Visual Learning Curriculum Standards: Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. Solve real- world problems by graphing points. Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. Represent real-world and mathematical problems by plotting points in quadrant I of the coordinate plane and interpret coordinate values of points in the context of the situation. Create and use rules, tables, spreadsheets and graphs to describe patterns of change and solve problems. Use a rule or table to represent ordered pairs of positive integers and graph these ordered pairs on a coordinate system. 14-4: Visual Learning Curriculum Standards: Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x- coordinate, y-axis and y-coordinate). Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. Reason abstractly and quantitatively. Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y-coordinate). Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. Reason abstractly and quantitatively. Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y-coordinate). Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. Reason abstractly and quantitatively. Mathematically proficient students make sense of quantities and their relationships in problem situations. They bring two complementary abilities to bear on problems involving quantitative relationships: the ability to decontextualize—to abstract a given situation and represent it symbolically and manipulate the representing symbols as if they have a life of their own, without necessarily attending to their referents—and the ability to contextualize, to pause as needed during the manipulation process in order to probe into the referents for the symbols involved. Quantitative reasoning entails habits of creating a coherent representation of the problem at hand; considering the units involved; attending to the meaning of quantities, not just how to compute them; and knowing and flexibly using different properties of operations and objects. Use reasoning to solve problems by making sense of quantities and relationships in the situation. Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. Reason abstractly and quantitatively. Reason abstractly and quantitatively. Represent real-world and mathematical problems by plotting points in quadrant I of the coordinate plane and interpret coordinate values of points in the context of the situation. Reason abstractly and quantitatively. Create and use rules, tables, spreadsheets and graphs to describe patterns of change and solve problems. Use a rule or table to represent ordered pairs of positive integers and graph these ordered pairs on a coordinate system. 4-4: Center Games Topic 14 Online Assessment Curriculum Standards: Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x- coordinate, y-axis and y-coordinate). Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. Reason abstractly and quantitatively. Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y-coordinate). Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. Reason abstractly and quantitatively. Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y-coordinate). Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. Reason abstractly and quantitatively. Mathematically proficient students make sense of quantities and their relationships in problem situations. They bring two complementary abilities to bear on problems involving quantitative relationships: the ability to decontextualize—to abstract a given situation and represent it symbolically and manipulate the representing symbols as if they have a life of their own, without necessarily attending to their referents—and the ability to contextualize, to pause as needed during the manipulation process in order to probe into the referents for the symbols involved. Quantitative reasoning entails habits of creating a coherent representation of the problem at hand; considering the units involved; attending to the meaning of quantities, not just how to compute them; and knowing and flexibly using different properties of operations and objects. Use reasoning to solve problems by making sense of quantities and relationships in the situation. Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. Reason abstractly and quantitatively. Reason abstractly and quantitatively. Represent real-world and mathematical problems by plotting points in quadrant I of the coordinate plane and interpret coordinate values of points in the context of the situation. Reason abstractly and quantitatively. Create and use rules, tables, spreadsheets and graphs to describe patterns of change and solve problems. Use a rule or table to represent ordered pairs of positive integers and graph these ordered pairs on a coordinate system. Solve real-world problems by graphing points. Graph points on a coordinate grid. Identify parts of the coordinate plane (x-axis, y-axis, and the origin) and the ordered pair (x-coordinate and y-coordinate). Limit the coordinate plane to quadrant I. Locate points on a coordinate grid. Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y- coordinate). Topic 14 Spanish Assessments Tema 14: Tarea de rendimento Tema 14: Evaluación Topic 15: Algebra: Analyze Patterns and Relationships Topic 15: Today's Challenge Topic 15: Beginning of Topic Interactive Student Edition: Beginning of Topic 15 Topic 15: enVision STEM Activity Grade 5 Topic 15: Review What You Know Topic 15: Vocabulary Cards 15-1: Numerical Patterns Interactive Student Edition: Grade 5 Lesson 15-1 Math Anytime 15-1: Daily Review Topic 15: Today's Challenge Step 1: Problem-Based Learning 15-1: Solve & Share Curriculum Standards: 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. For example, 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. English language learners communicate for social and instructional purposes within the school setting. Write informative/explanatory texts to examine a topic and convey ideas and information clearly. (a) Introduce a topic clearly, provide a general observation and focus, and group related information logically; include formatting (e.g., headings), illustrations, and multimedia when useful to aiding comprehension. (b) Develop the topic with facts, definitions, concrete details, quotations, or other information and examples related to the topic. (c) Link ideas within and across categories of information using words, phrases, and clauses (e.g., in contrast, especially). (d) Use precise language and domain- specific vocabulary to inform about or explain the topic. (e) Provide a concluding statement or section related to the information or explanation presented. English language learners communicate information, ideas and concepts necessary for academic success in the content area of Mathematics. 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. 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. For example, 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. Analyze numerical relationships. 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. For example, 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. Generate two numerical patterns using two given rules. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. Create and use rules, tables, spreadsheets and graphs to describe patterns of change and solve problems. Use a rule or table to represent ordered pairs of positive integers and graph these ordered pairs on a coordinate system. Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher- led) with diverse partners on grade 5 topics and texts, building on others’ ideas and expressing their own clearly. (a) Come to discussions prepared, having read or studied required material; explicitly draw on that preparation and other information known about the topic to explore ideas under discussion. (b) Follow agreed-upon rules for discussions and carry out assigned roles. (c) Pose and respond to specific questions by making comments that contribute to the discussion and elaborate on the remarks of others. (d) Review the key ideas expressed and draw conclusions in light of information and knowledge gained from the discussions. Summarize a written text read aloud or information presented in diverse media and formats, including visually, quantitatively, and orally. Summarize the points a speaker makes and explain how each claim is supported by reasons and evidence. Step 2: Visual Learning 15-1: Visual Learning Curriculum Standards: 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. For example, 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. Given two pattern descriptions involving the same context (e.g., collecting marbles), determine the first five terms and compare the values. 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. 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. For example, 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. Analyze numerical relationships. 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. For example, 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. Generate two numerical patterns using two given rules. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. Create and use rules, tables, spreadsheets and graphs to describe patterns of change and solve problems. Use a rule or table to represent ordered pairs of positive integers and graph these ordered pairs on a coordinate system. 15-1: Convince Me! Curriculum Standards: 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. For example, 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. 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. 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. For example, 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. Analyze numerical relationships. 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. For example, 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. Generate two numerical patterns using two given rules. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. Create and use rules, tables, spreadsheets and graphs to describe patterns of change and solve problems. Use a rule or table to represent ordered pairs of positive integers and graph these ordered pairs on a coordinate system. Practice and Problem Solving 15-1: Student Edition Practice Curriculum Standards: 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. For example, 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. 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. 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. For example, 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. Analyze numerical relationships. 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. For example, 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. Generate two numerical patterns using two given rules. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. Create and use rules, tables, spreadsheets and graphs to describe patterns of change and solve problems. Use a rule or table to represent ordered pairs of positive integers and graph these ordered pairs on a coordinate system. 15-1: Practice Buddy: Independent Practice; Problem Solving Curriculum Standards: 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. For example, 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. 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. 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. For example, 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. Analyze numerical relationships. 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. For example, 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. Generate two numerical patterns using two given rules. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. Create and use rules, tables, spreadsheets and graphs to describe patterns of change and solve problems. Use a rule or table to represent ordered pairs of positive integers and graph these ordered pairs on a coordinate system. 15-1: Practice Buddy: Additional Practice Curriculum Standards: 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. For example, 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. 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. 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. For example, 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. Analyze numerical relationships. 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. For example, 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. Generate two numerical patterns using two given rules. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. Create and use rules, tables, spreadsheets and graphs to describe patterns of change and solve problems. Use a rule or table to represent ordered pairs of positive integers and graph these ordered pairs on a coordinate system. 15-1: Interactive Additional Practice Step 3: Assess & Differentiate 15-1: Practice Buddy: Additional Practice Curriculum Standards: 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. For example, 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. 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. 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. For example, 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. Analyze numerical relationships. 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. For example, 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. Generate two numerical patterns using two given rules. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. Create and use rules, tables, spreadsheets and graphs to describe patterns of change and solve problems. Use a rule or table to represent ordered pairs of positive integers and graph these ordered pairs on a coordinate system. 15-1: Enrichment Curriculum Standards: 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. For example, 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. 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. 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. For example, 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. Analyze numerical relationships. 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. For example, 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. Generate two numerical patterns using two given rules. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. Create and use rules, tables, spreadsheets and graphs to describe patterns of change and solve problems. Use a rule or table to represent ordered pairs of positive integers and graph these ordered pairs on a coordinate system. 15-1: Quick Check Curriculum Standards: 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. For example, 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. 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. 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. For example, 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. Analyze numerical relationships. 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. For example, 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. Generate two numerical patterns using two given rules. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. Create and use rules, tables, spreadsheets and graphs to describe patterns of change and solve problems. Use a rule or table to represent ordered pairs of positive integers and graph these ordered pairs on a coordinate system. 15-1: Lesson Self-Assessment 15-1: Reteach to Build Understanding Curriculum Standards: 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. For example, 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. Given two pattern descriptions involving the same context (e.g., collecting marbles), determine the first five terms and compare the values. 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. 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. For example, 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. Analyze numerical relationships. 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. For example, 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. Generate two numerical patterns using two given rules. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. Create and use rules, tables, spreadsheets and graphs to describe patterns of change and solve problems. Use a rule or table to represent ordered pairs of positive integers and graph these ordered pairs on a coordinate system. 15-1: Build Mathematical Literacy Curriculum Standards: Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 5 topics and texts, building on others’ ideas and expressing their own clearly. (a) Come to discussions prepared, having read or studied required material; explicitly draw on that preparation and other information known about the topic to explore ideas under discussion. (b) Follow agreed-upon rules for discussions and carry out assigned roles. (c) Pose and respond to specific questions by making comments that contribute to the discussion and elaborate on the remarks of others. (d) Review the key ideas expressed and draw conclusions in light of information and knowledge gained from the discussions. English language learners communicate for social and instructional purposes within the school setting. Summarize a written text read aloud or information presented in diverse media and formats, including visually, quantitatively, and orally. Summarize the points a speaker makes and explain how each claim is supported by reasons and evidence. Write informative/explanatory texts to examine a topic and convey ideas and information clearly. (a) Introduce a topic clearly, provide a general observation and focus, and group related information logically; include formatting (e.g., headings), illustrations, and multimedia when useful to aiding comprehension. (b) Develop the topic with facts, definitions, concrete details, quotations, or other information and examples related to the topic. (c) Link ideas within and across categories of information using words, phrases, and clauses (e.g., in contrast, especially). (d) Use precise language and domain-specific vocabulary to inform about or explain the topic. (e) Provide a concluding statement or section related to the information or explanation presented. English language learners communicate information, ideas and concepts necessary for academic success in the content area of Mathematics. 15-1: Enrichment Game: Launch that Sheep - Multiply and Divide 2-Digit Numbers 15-1: enVision STEM Activity Curriculum Standards: 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. For example, 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. 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. 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. For example, 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. Analyze numerical relationships. 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. For example, 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. Generate two numerical patterns using two given rules. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. Create and use rules, tables, spreadsheets and graphs to describe patterns of change and solve problems. Use a rule or table to represent ordered pairs of positive integers and graph these ordered pairs on a coordinate system. 15-1: Another Look Curriculum Standards: 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. For example, 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. Given two pattern descriptions involving the same context (e.g., collecting marbles), determine the first five terms and compare the values. 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. 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. For example, 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. Analyze numerical relationships. 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. For example, 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. Generate two numerical patterns using two given rules. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. Create and use rules, tables, spreadsheets and graphs to describe patterns of change and solve problems. Use a rule or table to represent ordered pairs of positive integers and graph these ordered pairs on a coordinate system. Spanish Resources 15-1: eText del Libro del estudiante 15-1: Repaso diario 15-1: Aprendizaje visual 15-1: Amigo de práctica: Práctica adicional 15-1: Práctica adicional interactiva 15-1: Refuerzo para mejorar la comprensión 15-1: Desarrollar la competencia matemática 15-1: Ampliación 15-2: More Numerical Patterns Interactive Student Edition: Grade 5 Lesson 15-2 Math Anytime 15-2: Daily Review Topic 15: Today's Challenge Step 1: Problem-Based Learning 15-2: Solve & Share Curriculum Standards: 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. For example, 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. English language learners communicate for social and instructional purposes within the school setting. Write informative/explanatory texts to examine a topic and convey ideas and information clearly. (a) Introduce a topic clearly, provide a general observation and focus, and group related information logically; include formatting (e.g., headings), illustrations, and multimedia when useful to aiding comprehension. (b) Develop the topic with facts, definitions, concrete details, quotations, or other information and examples related to the topic. (c) Link ideas within and across categories of information using words, phrases, and clauses (e.g., in contrast, especially). (d) Use precise language and domain- specific vocabulary to inform about or explain the topic. (e) Provide a concluding statement or section related to the information or explanation presented. English language learners communicate information, ideas and concepts necessary for academic success in the content area of Mathematics. Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 5 topics and texts, building on others’ ideas and expressing their own clearly. (a) Come to discussions prepared, having read or studied required material; explicitly draw on that preparation and other information known about the topic to explore ideas under discussion. (b) Follow agreed-upon rules for discussions and carry out assigned roles. (c) Pose and respond to specific questions by making comments that contribute to the discussion and elaborate on the remarks of others. (d) Review the key ideas expressed and draw conclusions in light of information and knowledge gained from the discussions. 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. 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. For example, 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. Use tables to identify relationships between patterns. 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. For example, 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. Identify apparent relationships between corresponding terms of two patterns with the same starting numbers that follow different rules. Create and use rules, tables, spreadsheets and graphs to describe patterns of change and solve problems. Use a rule or table to represent ordered pairs of positive integers and graph these ordered pairs on a coordinate system. Summarize a written text read aloud or information presented in diverse media and formats, including visually, quantitatively, and orally. Summarize the points a speaker makes and explain how each claim is supported by reasons and evidence. Step 2: Visual Learning 15-2: Visual Learning Curriculum Standards: 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. For example, 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. Given two pattern descriptions involving the same context (e.g., collecting marbles), determine the first five terms and compare the values. 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. 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. For example, 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. Use tables to identify relationships between patterns. 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. For example, 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. Identify apparent relationships between corresponding terms of two patterns with the same starting numbers that follow different rules. Create and use rules, tables, spreadsheets and graphs to describe patterns of change and solve problems. Use a rule or table to represent ordered pairs of positive integers and graph these ordered pairs on a coordinate system. 15-2: Convince Me! Curriculum Standards: 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. For example, 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. 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. 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. For example, 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. Use tables to identify relationships between patterns. 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. For example, 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. Identify apparent relationships between corresponding terms of two patterns with the same starting numbers that follow different rules. Create and use rules, tables, spreadsheets and graphs to describe patterns of change and solve problems. Use a rule or table to represent ordered pairs of positive integers and graph these ordered pairs on a coordinate system. Practice and Problem Solving 15-2: Student Edition Practice Curriculum Standards: 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. For example, 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. 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. 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. For example, 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. Use tables to identify relationships between patterns. 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. For example, 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. Identify apparent relationships between corresponding terms of two patterns with the same starting numbers that follow different rules. Create and use rules, tables, spreadsheets and graphs to describe patterns of change and solve problems. Use a rule or table to represent ordered pairs of positive integers and graph these ordered pairs on a coordinate system. 15-2: Practice Buddy: Independent Practice; Problem Solving Curriculum Standards: 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. For example, 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. 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. 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. For example, 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. Use tables to identify relationships between patterns. 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. For example, 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. Identify apparent relationships between corresponding terms of two patterns with the same starting numbers that follow different rules. Create and use rules, tables, spreadsheets and graphs to describe patterns of change and solve problems. Use a rule or table to represent ordered pairs of positive integers and graph these ordered pairs on a coordinate system. 15-2: Practice Buddy: Additional Practice Curriculum Standards: 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. For example, 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. 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. 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. For example, 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. Use tables to identify relationships between patterns. 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. For example, 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. Identify apparent relationships between corresponding terms of two patterns with the same starting numbers that follow different rules. Create and use rules, tables, spreadsheets and graphs to describe patterns of change and solve problems. Use a rule or table to represent ordered pairs of positive integers and graph these ordered pairs on a coordinate system. 15-2: Interactive Additional Practice Step 3: Assess & Differentiate 15-2: Practice Buddy: Additional Practice Curriculum Standards: 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. For example, 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. 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. 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. For example, 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. Use tables to identify relationships between patterns. 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. For example, 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. Identify apparent relationships between corresponding terms of two patterns with the same starting numbers that follow different rules. Create and use rules, tables, spreadsheets and graphs to describe patterns of change and solve problems. Use a rule or table to represent ordered pairs of positive integers and graph these ordered pairs on a coordinate system. 15-2: Enrichment Curriculum Standards: 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. For example, 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. 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. 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. For example, 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. Use tables to identify relationships between patterns. 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. For example, 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. Identify apparent relationships between corresponding terms of two patterns with the same starting numbers that follow different rules. Create and use rules, tables, spreadsheets and graphs to describe patterns of change and solve problems. Use a rule or table to represent ordered pairs of positive integers and graph these ordered pairs on a coordinate system. 15-2: Quick Check Curriculum Standards: 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. For example, 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. 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. 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. For example, 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. Use tables to identify relationships between patterns. 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. For example, 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. Identify apparent relationships between corresponding terms of two patterns with the same starting numbers that follow different rules. Create and use rules, tables, spreadsheets and graphs to describe patterns of change and solve problems. Use a rule or table to represent ordered pairs of positive integers and graph these ordered pairs on a coordinate system. 15-2: Lesson Self-Assessment 15-2: Reteach to Build Understanding Curriculum Standards: 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. For example, 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. Given two pattern descriptions involving the same context (e.g., collecting marbles), determine the first five terms and compare the values. 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. 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. For example, 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. Use tables to identify relationships between patterns. 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. For example, 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. Identify apparent relationships between corresponding terms of two patterns with the same starting numbers that follow different rules. Create and use rules, tables, spreadsheets and graphs to describe patterns of change and solve problems. Use a rule or table to represent ordered pairs of positive integers and graph these ordered pairs on a coordinate system. 15-2: Build Mathematical Literacy Curriculum Standards: Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 5 topics and texts, building on others’ ideas and expressing their own clearly. (a) Come to discussions prepared, having read or studied required material; explicitly draw on that preparation and other information known about the topic to explore ideas under discussion. (b) Follow agreed-upon rules for discussions and carry out assigned roles. (c) Pose and respond to specific questions by making comments that contribute to the discussion and elaborate on the remarks of others. (d) Review the key ideas expressed and draw conclusions in light of information and knowledge gained from the discussions. English language learners communicate for social and instructional purposes within the school setting. Summarize a written text read aloud or information presented in diverse media and formats, including visually, quantitatively, and orally. Summarize the points a speaker makes and explain how each claim is supported by reasons and evidence. Write informative/explanatory texts to examine a topic and convey ideas and information clearly. (a) Introduce a topic clearly, provide a general observation and focus, and group related information logically; include formatting (e.g., headings), illustrations, and multimedia when useful to aiding comprehension. (b) Develop the topic with facts, definitions, concrete details, quotations, or other information and examples related to the topic. (c) Link ideas within and across categories of information using words, phrases, and clauses (e.g., in contrast, especially). (d) Use precise language and domain-specific vocabulary to inform about or explain the topic. (e) Provide a concluding statement or section related to the information or explanation presented. English language learners communicate information, ideas and concepts necessary for academic success in the content area of Mathematics. 15-2: Enrichment Game: Launch that Sheep - Multiply and Divide 2-Digit Numbers 15-2 Problem-Solving Reading Activity Curriculum Standards: 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. For example, 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. 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. 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. For example, 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. Use tables to identify relationships between patterns. 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. For example, 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. Identify apparent relationships between corresponding terms of two patterns with the same starting numbers that follow different rules. Create and use rules, tables, spreadsheets and graphs to describe patterns of change and solve problems. Use a rule or table to represent ordered pairs of positive integers and graph these ordered pairs on a coordinate system. 15-2: Another Look Curriculum Standards: 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. For example, 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. Given two pattern descriptions involving the same context (e.g., collecting marbles), determine the first five terms and compare the values. 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. 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. For example, 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. Use tables to identify relationships between patterns. 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. For example, 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. Identify apparent relationships between corresponding terms of two patterns with the same starting numbers that follow different rules. Create and use rules, tables, spreadsheets and graphs to describe patterns of change and solve problems. Use a rule or table to represent ordered pairs of positive integers and graph these ordered pairs on a coordinate system. Spanish Resources 15-2: eText del Libro del estudiante 15-2: Repaso diario 15-2: Aprendizaje visual 15-2: Amigo de práctica: Práctica adicional 15-2: Práctica adicional interactiva 15-2: Refuerzo para mejorar la comprensión 15-2: Desarrollar la competencia matemática 15-2: Ampliación 15-3: Analyze and Graph Relationships Interactive Student Edition: Grade 5 Lesson 15-3 Math Anytime 15-3: Daily Review Topic 15: Today's Challenge Step 1: Problem-Based Learning 15-3: Solve & Share Curriculum Standards: 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. For example, given the rule “Add 3” and the starting number 0, and given the rule “Add 6” and the starting number 0, generate terms in the resulting sequences, and observe that the terms in one sequence are twice the corresponding terms in the other sequence. Explain informally why this is so. Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. English language learners communicate for social and instructional purposes within the school setting. Write informative/explanatory texts to examine a topic and convey ideas and information clearly. (a) Introduce a topic clearly, provide a general observation and focus, and group related information logically; include formatting (e.g., headings), illustrations, and multimedia when useful to aiding comprehension. (b) Develop the topic with facts, definitions, concrete details, quotations, or other information and examples related to the topic. (c) Link ideas within and across categories of information using words, phrases, and clauses (e.g., in contrast, especially). (d) Use precise language and domain-specific vocabulary to inform about or explain the topic. (e) Provide a concluding statement or section related to the information or explanation presented. English language learners communicate information, ideas and concepts necessary for academic success in the content area of Mathematics. Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 5 topics and texts, building on others’ ideas and expressing their own clearly. (a) Come to discussions prepared, having read or studied required material; explicitly draw on that preparation and other information known about the topic to explore ideas under discussion. (b) Follow agreed-upon rules for discussions and carry out assigned roles. (c) Pose and respond to specific questions by making comments that contribute to the discussion and elaborate on the remarks of others. (d) Review the key ideas expressed and draw conclusions in light of information and knowledge gained from the discussions. Summarize a written text read aloud or information presented in diverse media and formats, including visually, quantitatively, and orally. 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. Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. 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. For example, given the rule “Add 3” and the starting number 0, and given the rule “Add 6” and the starting number 0, generate terms in the resulting sequences, and observe that the terms in one sequence are twice the corresponding terms in the other sequence. Explain informally why this is so. Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. Analyze patterns and graph ordered pairs generated from number sequences. Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane. For example, given the rule Add 3 and the starting number 0, and given the rule Add 6 and the starting number 0, generate terms in the resulting sequences, and observe that the terms in one sequence are twice the corresponding terms in the other sequence. Explain informally why this is so. Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. Generate two numerical patterns using two given rules. Represent real-world and mathematical problems by plotting points in quadrant I of the coordinate plane and interpret coordinate values of points in the context of the situation. Create and use rules, tables, spreadsheets and graphs to describe patterns of change and solve problems. Use a rule or table to represent ordered pairs of positive integers and graph these ordered pairs on a coordinate system. Summarize the points a speaker makes and explain how each claim is supported by reasons and evidence. Step 2: Visual Learning 15-3: Visual Learning Curriculum Standards: 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. For example, given the rule “Add 3” and the starting number 0, and given the rule “Add 6” and the starting number 0, generate terms in the resulting sequences, and observe that the terms in one sequence are twice the corresponding terms in the other sequence. Explain informally why this is so. Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. Graph ordered pairs on a coordinate plane when given a table that follows patterns rules. 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. Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. 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. For example, given the rule “Add 3” and the starting number 0, and given the rule “Add 6” and the starting number 0, generate terms in the resulting sequences, and observe that the terms in one sequence are twice the corresponding terms in the other sequence. Explain informally why this is so. Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. Analyze patterns and graph ordered pairs generated from number sequences. Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane. For example, given the rule Add 3 and the starting number 0, and given the rule Add 6 and the starting number 0, generate terms in the resulting sequences, and observe that the terms in one sequence are twice the corresponding terms in the other sequence. Explain informally why this is so. Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. Generate two numerical patterns using two given rules. Represent real-world and mathematical problems by plotting points in quadrant I of the coordinate plane and interpret coordinate values of points in the context of the situation. Create and use rules, tables, spreadsheets and graphs to describe patterns of change and solve problems. Use a rule or table to represent ordered pairs of positive integers and graph these ordered pairs on a coordinate system. 15-3: Convince Me! Curriculum Standards: 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. For example, given the rule “Add 3” and the starting number 0, and given the rule “Add 6” and the starting number 0, generate terms in the resulting sequences, and observe that the terms in one sequence are twice the corresponding terms in the other sequence. Explain informally why this is so. Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. 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. Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. 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. For example, given the rule “Add 3” and the starting number 0, and given the rule “Add 6” and the starting number 0, generate terms in the resulting sequences, and observe that the terms in one sequence are twice the corresponding terms in the other sequence. Explain informally why this is so. Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. Analyze patterns and graph ordered pairs generated from number sequences. Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane. For example, given the rule Add 3 and the starting number 0, and given the rule Add 6 and the starting number 0, generate terms in the resulting sequences, and observe that the terms in one sequence are twice the corresponding terms in the other sequence. Explain informally why this is so. Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. Generate two numerical patterns using two given rules. Represent real-world and mathematical problems by plotting points in quadrant I of the coordinate plane and interpret coordinate values of points in the context of the situation. Create and use rules, tables, spreadsheets and graphs to describe patterns of change and solve problems. Use a rule or table to represent ordered pairs of positive integers and graph these ordered pairs on a coordinate system. Practice and Problem Solving 15-3: Student Edition Practice Curriculum Standards: 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. For example, given the rule “Add 3” and the starting number 0, and given the rule “Add 6” and the starting number 0, generate terms in the resulting sequences, and observe that the terms in one sequence are twice the corresponding terms in the other sequence. Explain informally why this is so. Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. 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. Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. 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. For example, given the rule “Add 3” and the starting number 0, and given the rule “Add 6” and the starting number 0, generate terms in the resulting sequences, and observe that the terms in one sequence are twice the corresponding terms in the other sequence. Explain informally why this is so. Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. Analyze patterns and graph ordered pairs generated from number sequences. Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane. For example, given the rule Add 3 and the starting number 0, and given the rule Add 6 and the starting number 0, generate terms in the resulting sequences, and observe that the terms in one sequence are twice the corresponding terms in the other sequence. Explain informally why this is so. Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. Generate two numerical patterns using two given rules. Represent real-world and mathematical problems by plotting points in quadrant I of the coordinate plane and interpret coordinate values of points in the context of the situation. Create and use rules, tables, spreadsheets and graphs to describe patterns of change and solve problems. Use a rule or table to represent ordered pairs of positive integers and graph these ordered pairs on a coordinate system. 15-3: Practice Buddy: Independent Practice; Problem Solving Curriculum Standards: 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. For example, given the rule “Add 3” and the starting number 0, and given the rule “Add 6” and the starting number 0, generate terms in the resulting sequences, and observe that the terms in one sequence are twice the corresponding terms in the other sequence. Explain informally why this is so. Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. 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. Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. 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. For example, given the rule “Add 3” and the starting number 0, and given the rule “Add 6” and the starting number 0, generate terms in the resulting sequences, and observe that the terms in one sequence are twice the corresponding terms in the other sequence. Explain informally why this is so. Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. Analyze patterns and graph ordered pairs generated from number sequences. Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane. For example, given the rule Add 3 and the starting number 0, and given the rule Add 6 and the starting number 0, generate terms in the resulting sequences, and observe that the terms in one sequence are twice the corresponding terms in the other sequence. Explain informally why this is so. Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. Generate two numerical patterns using two given rules. Represent real-world and mathematical problems by plotting points in quadrant I of the coordinate plane and interpret coordinate values of points in the context of the situation. Create and use rules, tables, spreadsheets and graphs to describe patterns of change and solve problems. Use a rule or table to represent ordered pairs of positive integers and graph these ordered pairs on a coordinate system. 15-3: Practice Buddy: Additional Practice Curriculum Standards: 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. For example, given the rule “Add 3” and the starting number 0, and given the rule “Add 6” and the starting number 0, generate terms in the resulting sequences, and observe that the terms in one sequence are twice the corresponding terms in the other sequence. Explain informally why this is so. Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. 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. Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. 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. For example, given the rule “Add 3” and the starting number 0, and given the rule “Add 6” and the starting number 0, generate terms in the resulting sequences, and observe that the terms in one sequence are twice the corresponding terms in the other sequence. Explain informally why this is so. Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. Analyze patterns and graph ordered pairs generated from number sequences. Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane. For example, given the rule Add 3 and the starting number 0, and given the rule Add 6 and the starting number 0, generate terms in the resulting sequences, and observe that the terms in one sequence are twice the corresponding terms in the other sequence. Explain informally why this is so. Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. Generate two numerical patterns using two given rules. Represent real-world and mathematical problems by plotting points in quadrant I of the coordinate plane and interpret coordinate values of points in the context of the situation. Create and use rules, tables, spreadsheets and graphs to describe patterns of change and solve problems. Use a rule or table to represent ordered pairs of positive integers and graph these ordered pairs on a coordinate system. 15-3: Interactive Additional Practice Step 3: Assess & Differentiate 15-3: Practice Buddy: Additional Practice Curriculum Standards: 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. For example, given the rule “Add 3” and the starting number 0, and given the rule “Add 6” and the starting number 0, generate terms in the resulting sequences, and observe that the terms in one sequence are twice the corresponding terms in the other sequence. Explain informally why this is so. Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. 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. Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. 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. For example, given the rule “Add 3” and the starting number 0, and given the rule “Add 6” and the starting number 0, generate terms in the resulting sequences, and observe that the terms in one sequence are twice the corresponding terms in the other sequence. Explain informally why this is so. Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. Analyze patterns and graph ordered pairs generated from number sequences. Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane. For example, given the rule Add 3 and the starting number 0, and given the rule Add 6 and the starting number 0, generate terms in the resulting sequences, and observe that the terms in one sequence are twice the corresponding terms in the other sequence. Explain informally why this is so. Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. Generate two numerical patterns using two given rules. Represent real-world and mathematical problems by plotting points in quadrant I of the coordinate plane and interpret coordinate values of points in the context of the situation. Create and use rules, tables, spreadsheets and graphs to describe patterns of change and solve problems. Use a rule or table to represent ordered pairs of positive integers and graph these ordered pairs on a coordinate system. 15-3: Enrichment Curriculum Standards: 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. For example, given the rule “Add 3” and the starting number 0, and given the rule “Add 6” and the starting number 0, generate terms in the resulting sequences, and observe that the terms in one sequence are twice the corresponding terms in the other sequence. Explain informally why this is so. Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. 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. Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. 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. For example, given the rule “Add 3” and the starting number 0, and given the rule “Add 6” and the starting number 0, generate terms in the resulting sequences, and observe that the terms in one sequence are twice the corresponding terms in the other sequence. Explain informally why this is so. Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. Analyze patterns and graph ordered pairs generated from number sequences. Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane. For example, given the rule Add 3 and the starting number 0, and given the rule Add 6 and the starting number 0, generate terms in the resulting sequences, and observe that the terms in one sequence are twice the corresponding terms in the other sequence. Explain informally why this is so. Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. Generate two numerical patterns using two given rules. Represent real-world and mathematical problems by plotting points in quadrant I of the coordinate plane and interpret coordinate values of points in the context of the situation. Create and use rules, tables, spreadsheets and graphs to describe patterns of change and solve problems. Use a rule or table to represent ordered pairs of positive integers and graph these ordered pairs on a coordinate system. 15-3: Quick Check Curriculum Standards: 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. For example, given the rule “Add 3” and the starting number 0, and given the rule “Add 6” and the starting number 0, generate terms in the resulting sequences, and observe that the terms in one sequence are twice the corresponding terms in the other sequence. Explain informally why this is so. Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. 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. Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. 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. For example, given the rule “Add 3” and the starting number 0, and given the rule “Add 6” and the starting number 0, generate terms in the resulting sequences, and observe that the terms in one sequence are twice the corresponding terms in the other sequence. Explain informally why this is so. Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. Analyze patterns and graph ordered pairs generated from number sequences. Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane. For example, given the rule Add 3 and the starting number 0, and given the rule Add 6 and the starting number 0, generate terms in the resulting sequences, and observe that the terms in one sequence are twice the corresponding terms in the other sequence. Explain informally why this is so. Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. Generate two numerical patterns using two given rules. Represent real-world and mathematical problems by plotting points in quadrant I of the coordinate plane and interpret coordinate values of points in the context of the situation. Create and use rules, tables, spreadsheets and graphs to describe patterns of change and solve problems. Use a rule or table to represent ordered pairs of positive integers and graph these ordered pairs on a coordinate system. 15-3: Lesson Self-Assessment 15-3: Reteach to Build Understanding Curriculum Standards: 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. For example, given the rule “Add 3” and the starting number 0, and given the rule “Add 6” and the starting number 0, generate terms in the resulting sequences, and observe that the terms in one sequence are twice the corresponding terms in the other sequence. Explain informally why this is so. Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. Graph ordered pairs on a coordinate plane when given a table that follows patterns rules. 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. Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. 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. For example, given the rule “Add 3” and the starting number 0, and given the rule “Add 6” and the starting number 0, generate terms in the resulting sequences, and observe that the terms in one sequence are twice the corresponding terms in the other sequence. Explain informally why this is so. Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. Analyze patterns and graph ordered pairs generated from number sequences. Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane. For example, given the rule Add 3 and the starting number 0, and given the rule Add 6 and the starting number 0, generate terms in the resulting sequences, and observe that the terms in one sequence are twice the corresponding terms in the other sequence. Explain informally why this is so. Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. Generate two numerical patterns using two given rules. Represent real-world and mathematical problems by plotting points in quadrant I of the coordinate plane and interpret coordinate values of points in the context of the situation. Create and use rules, tables, spreadsheets and graphs to describe patterns of change and solve problems. Use a rule or table to represent ordered pairs of positive integers and graph these ordered pairs on a coordinate system. 15-3: Build Mathematical Literacy Curriculum Standards: Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 5 topics and texts, building on others’ ideas and expressing their own clearly. (a) Come to discussions prepared, having read or studied required material; explicitly draw on that preparation and other information known about the topic to explore ideas under discussion. (b) Follow agreed-upon rules for discussions and carry out assigned roles. (c) Pose and respond to specific questions by making comments that contribute to the discussion and elaborate on the remarks of others. (d) Review the key ideas expressed and draw conclusions in light of information and knowledge gained from the discussions. English language learners communicate for social and instructional purposes within the school setting. Summarize a written text read aloud or information presented in diverse media and formats, including visually, quantitatively, and orally. Summarize the points a speaker makes and explain how each claim is supported by reasons and evidence. Write informative/explanatory texts to examine a topic and convey ideas and information clearly. (a) Introduce a topic clearly, provide a general observation and focus, and group related information logically; include formatting (e.g., headings), illustrations, and multimedia when useful to aiding comprehension. (b) Develop the topic with facts, definitions, concrete details, quotations, or other information and examples related to the topic. (c) Link ideas within and across categories of information using words, phrases, and clauses (e.g., in contrast, especially). (d) Use precise language and domain-specific vocabulary to inform about or explain the topic. (e) Provide a concluding statement or section related to the information or explanation presented. English language learners communicate information, ideas and concepts necessary for academic success in the content area of Mathematics. 15-3: Enrichment 15-3: Digital Math Tool Activity 15-3 Problem-Solving Reading Activity Curriculum Standards: 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. For example, given the rule “Add 3” and the starting number 0, and given the rule “Add 6” and the starting number 0, generate terms in the resulting sequences, and observe that the terms in one sequence are twice the corresponding terms in the other sequence. Explain informally why this is so. Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. 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. Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. 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. For example, given the rule “Add 3” and the starting number 0, and given the rule “Add 6” and the starting number 0, generate terms in the resulting sequences, and observe that the terms in one sequence are twice the corresponding terms in the other sequence. Explain informally why this is so. Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. Analyze patterns and graph ordered pairs generated from number sequences. Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane. For example, given the rule Add 3 and the starting number 0, and given the rule Add 6 and the starting number 0, generate terms in the resulting sequences, and observe that the terms in one sequence are twice the corresponding terms in the other sequence. Explain informally why this is so. Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. Generate two numerical patterns using two given rules. Represent real-world and mathematical problems by plotting points in quadrant I of the coordinate plane and interpret coordinate values of points in the context of the situation. Create and use rules, tables, spreadsheets and graphs to describe patterns of change and solve problems. Use a rule or table to represent ordered pairs of positive integers and graph these ordered pairs on a coordinate system. 15-3: Another Look Curriculum Standards: 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. For example, given the rule “Add 3” and the starting number 0, and given the rule “Add 6” and the starting number 0, generate terms in the resulting sequences, and observe that the terms in one sequence are twice the corresponding terms in the other sequence. Explain informally why this is so. Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. Graph ordered pairs on a coordinate plane when given a table that follows patterns rules. 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. Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. 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. For example, given the rule “Add 3” and the starting number 0, and given the rule “Add 6” and the starting number 0, generate terms in the resulting sequences, and observe that the terms in one sequence are twice the corresponding terms in the other sequence. Explain informally why this is so. Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. Analyze patterns and graph ordered pairs generated from number sequences. Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane. For example, given the rule Add 3 and the starting number 0, and given the rule Add 6 and the starting number 0, generate terms in the resulting sequences, and observe that the terms in one sequence are twice the corresponding terms in the other sequence. Explain informally why this is so. Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. Generate two numerical patterns using two given rules. Represent real-world and mathematical problems by plotting points in quadrant I of the coordinate plane and interpret coordinate values of points in the context of the situation. Create and use rules, tables, spreadsheets and graphs to describe patterns of change and solve problems. Use a rule or table to represent ordered pairs of positive integers and graph these ordered pairs on a coordinate system. Spanish Resources 15-3: eText del Libro del estudiante 15-3: Repaso diario 15-3: Aprendizaje visual 15-3: Amigo de práctica: Práctica adicional 15-3: Práctica adicional interactiva 15-3: Refuerzo para mejorar la comprensión 15-3: Desarrollar la competencia matemática 15-3: Ampliación Topic 15: 3-Act Math: Speed Stacks Interactive Student Edition: Grade 5, Topic 15: 3-Act Math Mathematical Modeling Topic 15: 3-Act Math: Speed Stacks, Act 1 Topic 15: 3-Act Math: Speed Stacks, Act 2 Topic 15: 3-Act Math: Speed Stacks, Act 3 Topic 15: 3-Act Math: Speed Stacks, Sequel 15-4: Problem Solving: Make Sense and Persevere Interactive Student Edition: Grade 5 Lesson 15-4 Math Anytime 15-4: Daily Review Topic 15: Today's Challenge Step 1: Problem-Based Learning 15-4: Solve & Share Curriculum Standards: 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. For example, 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. Make sense of problems and persevere in solving them. English language learners communicate for social and instructional purposes within the school setting. Write informative/explanatory texts to examine a topic and convey ideas and information clearly. (a) Introduce a topic clearly, provide a general observation and focus, and group related information logically; include formatting (e.g., headings), illustrations, and multimedia when useful to aiding comprehension. (b) Develop the topic with facts, definitions, concrete details, quotations, or other information and examples related to the topic. (c) Link ideas within and across categories of information using words, phrases, and clauses (e.g., in contrast, especially). (d) Use precise language and domain-specific vocabulary to inform about or explain the topic. (e) Provide a concluding statement or section related to the information or explanation presented. English language learners communicate information, ideas and concepts necessary for academic success in the content area of Mathematics. Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 5 topics and texts, building on others’ ideas and expressing their own clearly. (a) Come to discussions prepared, having read or studied required material; explicitly draw on that preparation and other information known about the topic to explore ideas under discussion. (b) Follow agreed-upon rules for discussions and carry out assigned roles. (c) Pose and respond to specific questions by making comments that contribute to the discussion and elaborate on the remarks of others. (d) Review the key ideas expressed and draw conclusions in light of information and knowledge gained from the discussions. Summarize a written text read aloud or information presented in diverse media and formats, including visually, quantitatively, and orally. Summarize the points a speaker makes and explain how each claim is supported by reasons and evidence. 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. Make sense of problems and persevere in solving them. 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. For example, 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. Make sense of problems and persevere in solving them. Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution. They analyze givens, constraints, relationships, and goals. They make conjectures about the form and meaning of the solution and plan a solution pathway rather than simply jumping into a solution attempt. They consider analogous problems, and try special cases and simpler forms of the original problem in order to gain insight into its solution. They monitor and evaluate their progress and change course if necessary. Older students might, depending on the context of the problem, transform algebraic expressions or change the viewing window on their graphing calculator to get the information they need. Mathematically proficient students can explain correspondences between equations, verbal descriptions, tables, and graphs or draw diagrams of important features and relationships, graph data, and search for regularity or trends. Younger students might rely on using concrete objects or pictures to help conceptualize and solve a problem. Mathematically proficient students check their answers to problems using a different method, and they continually ask themselves, “Does this make sense?” They can understand the approaches of others to solving complex problems and identify correspondences between different approaches. Make sense of problems and persevere in solving them. 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. For example, 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. Make sense of problems and persevere in solving them. Make sense of problems and persevere in solving them. Generate two numerical patterns using two given rules. Construct viable arguments and critique the reasoning of others. Create and use rules, tables, spreadsheets and graphs to describe patterns of change and solve problems. Use a rule or table to represent ordered pairs of positive integers and graph these ordered pairs on a coordinate system. Step 2: Visual Learning 15-4: Visual Learning Curriculum Standards: 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. For example, 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. Make sense of problems and persevere in solving them. 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. Make sense of problems and persevere in solving them. 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. For example, 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. Make sense of problems and persevere in solving them. Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution. They analyze givens, constraints, relationships, and goals. They make conjectures about the form and meaning of the solution and plan a solution pathway rather than simply jumping into a solution attempt. They consider analogous problems, and try special cases and simpler forms of the original problem in order to gain insight into its solution. They monitor and evaluate their progress and change course if necessary. Older students might, depending on the context of the problem, transform algebraic expressions or change the viewing window on their graphing calculator to get the information they need. Mathematically proficient students can explain correspondences between equations, verbal descriptions, tables, and graphs or draw diagrams of important features and relationships, graph data, and search for regularity or trends. Younger students might rely on using concrete objects or pictures to help conceptualize and solve a problem. Mathematically proficient students check their answers to problems using a different method, and they continually ask themselves, “Does this make sense?” They can understand the approaches of others to solving complex problems and identify correspondences between different approaches. Make sense of problems and persevere in solving them. 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. For example, 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. Make sense of problems and persevere in solving them. Make sense of problems and persevere in solving them. Generate two numerical patterns using two given rules. Construct viable arguments and critique the reasoning of others. Create and use rules, tables, spreadsheets and graphs to describe patterns of change and solve problems. Use a rule or table to represent ordered pairs of positive integers and graph these ordered pairs on a coordinate system. 15-4: Convince Me! Curriculum Standards: 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. For example, 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. Make sense of problems and persevere in solving them. 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. Make sense of problems and persevere in solving them. 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. For example, 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. Make sense of problems and persevere in solving them. Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution. They analyze givens, constraints, relationships, and goals. They make conjectures about the form and meaning of the solution and plan a solution pathway rather than simply jumping into a solution attempt. They consider analogous problems, and try special cases and simpler forms of the original problem in order to gain insight into its solution. They monitor and evaluate their progress and change course if necessary. Older students might, depending on the context of the problem, transform algebraic expressions or change the viewing window on their graphing calculator to get the information they need. Mathematically proficient students can explain correspondences between equations, verbal descriptions, tables, and graphs or draw diagrams of important features and relationships, graph data, and search for regularity or trends. Younger students might rely on using concrete objects or pictures to help conceptualize and solve a problem. Mathematically proficient students check their answers to problems using a different method, and they continually ask themselves, “Does this make sense?” They can understand the approaches of others to solving complex problems and identify correspondences between different approaches. Make sense of problems and persevere in solving them. 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. For example, 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. Make sense of problems and persevere in solving them. Make sense of problems and persevere in solving them. Generate two numerical patterns using two given rules. Construct viable arguments and critique the reasoning of others. Create and use rules, tables, spreadsheets and graphs to describe patterns of change and solve problems. Use a rule or table to represent ordered pairs of positive integers and graph these ordered pairs on a coordinate system. Practice and Problem Solving 15-4: Student Edition Practice Curriculum Standards: 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. For example, 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. Make sense of problems and persevere in solving them. 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. Make sense of problems and persevere in solving them. 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. For example, 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. Make sense of problems and persevere in solving them. Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution. They analyze givens, constraints, relationships, and goals. They make conjectures about the form and meaning of the solution and plan a solution pathway rather than simply jumping into a solution attempt. They consider analogous problems, and try special cases and simpler forms of the original problem in order to gain insight into its solution. They monitor and evaluate their progress and change course if necessary. Older students might, depending on the context of the problem, transform algebraic expressions or change the viewing window on their graphing calculator to get the information they need. Mathematically proficient students can explain correspondences between equations, verbal descriptions, tables, and graphs or draw diagrams of important features and relationships, graph data, and search for regularity or trends. Younger students might rely on using concrete objects or pictures to help conceptualize and solve a problem. Mathematically proficient students check their answers to problems using a different method, and they continually ask themselves, “Does this make sense?” They can understand the approaches of others to solving complex problems and identify correspondences between different approaches. Make sense of problems and persevere in solving them. 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. For example, 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. Make sense of problems and persevere in solving them. Make sense of problems and persevere in solving them. Generate two numerical patterns using two given rules. Construct viable arguments and critique the reasoning of others. Create and use rules, tables, spreadsheets and graphs to describe patterns of change and solve problems. Use a rule or table to represent ordered pairs of positive integers and graph these ordered pairs on a coordinate system. 15-4: Practice Buddy: Independent Practice; Problem Solving Curriculum Standards: 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. For example, 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. Make sense of problems and persevere in solving them. 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. Make sense of problems and persevere in solving them. 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. For example, 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. Make sense of problems and persevere in solving them. Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution. They analyze givens, constraints, relationships, and goals. They make conjectures about the form and meaning of the solution and plan a solution pathway rather than simply jumping into a solution attempt. They consider analogous problems, and try special cases and simpler forms of the original problem in order to gain insight into its solution. They monitor and evaluate their progress and change course if necessary. Older students might, depending on the context of the problem, transform algebraic expressions or change the viewing window on their graphing calculator to get the information they need. Mathematically proficient students can explain correspondences between equations, verbal descriptions, tables, and graphs or draw diagrams of important features and relationships, graph data, and search for regularity or trends. Younger students might rely on using concrete objects or pictures to help conceptualize and solve a problem. Mathematically proficient students check their answers to problems using a different method, and they continually ask themselves, “Does this make sense?” They can understand the approaches of others to solving complex problems and identify correspondences between different approaches. Make sense of problems and persevere in solving them. 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. For example, 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. Make sense of problems and persevere in solving them. Make sense of problems and persevere in solving them. Generate two numerical patterns using two given rules. Construct viable arguments and critique the reasoning of others. Create and use rules, tables, spreadsheets and graphs to describe patterns of change and solve problems. Use a rule or table to represent ordered pairs of positive integers and graph these ordered pairs on a coordinate system. 15-4: Practice Buddy: Additional Practice Curriculum Standards: 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. For example, 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. Make sense of problems and persevere in solving them. 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. Make sense of problems and persevere in solving them. 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. For example, 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. Make sense of problems and persevere in solving them. Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution. They analyze givens, constraints, relationships, and goals. They make conjectures about the form and meaning of the solution and plan a solution pathway rather than simply jumping into a solution attempt. They consider analogous problems, and try special cases and simpler forms of the original problem in order to gain insight into its solution. They monitor and evaluate their progress and change course if necessary. Older students might, depending on the context of the problem, transform algebraic expressions or change the viewing window on their graphing calculator to get the information they need. Mathematically proficient students can explain correspondences between equations, verbal descriptions, tables, and graphs or draw diagrams of important features and relationships, graph data, and search for regularity or trends. Younger students might rely on using concrete objects or pictures to help conceptualize and solve a problem. Mathematically proficient students check their answers to problems using a different method, and they continually ask themselves, “Does this make sense?” They can understand the approaches of others to solving complex problems and identify correspondences between different approaches. Make sense of problems and persevere in solving them. 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. For example, 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. Make sense of problems and persevere in solving them. Make sense of problems and persevere in solving them. Generate two numerical patterns using two given rules. Construct viable arguments and critique the reasoning of others. Create and use rules, tables, spreadsheets and graphs to describe patterns of change and solve problems. Use a rule or table to represent ordered pairs of positive integers and graph these ordered pairs on a coordinate system. 15-4: Interactive Additional Practice Step 3: Assess & Differentiate 15-4: Practice Buddy: Additional Practice Curriculum Standards: 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. For example, 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. Make sense of problems and persevere in solving them. 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. Make sense of problems and persevere in solving them. 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. For example, 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. Make sense of problems and persevere in solving them. Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution. They analyze givens, constraints, relationships, and goals. They make conjectures about the form and meaning of the solution and plan a solution pathway rather than simply jumping into a solution attempt. They consider analogous problems, and try special cases and simpler forms of the original problem in order to gain insight into its solution. They monitor and evaluate their progress and change course if necessary. Older students might, depending on the context of the problem, transform algebraic expressions or change the viewing window on their graphing calculator to get the information they need. Mathematically proficient students can explain correspondences between equations, verbal descriptions, tables, and graphs or draw diagrams of important features and relationships, graph data, and search for regularity or trends. Younger students might rely on using concrete objects or pictures to help conceptualize and solve a problem. Mathematically proficient students check their answers to problems using a different method, and they continually ask themselves, “Does this make sense?” They can understand the approaches of others to solving complex problems and identify correspondences between different approaches. Make sense of problems and persevere in solving them. 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. For example, 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. Make sense of problems and persevere in solving them. Make sense of problems and persevere in solving them. Generate two numerical patterns using two given rules. Construct viable arguments and critique the reasoning of others. Create and use rules, tables, spreadsheets and graphs to describe patterns of change and solve problems. Use a rule or table to represent ordered pairs of positive integers and graph these ordered pairs on a coordinate system. 15-4: Enrichment Curriculum Standards: 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. For example, 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. Make sense of problems and persevere in solving them. 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. Make sense of problems and persevere in solving them. 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. For example, 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. Make sense of problems and persevere in solving them. Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution. They analyze givens, constraints, relationships, and goals. They make conjectures about the form and meaning of the solution and plan a solution pathway rather than simply jumping into a solution attempt. They consider analogous problems, and try special cases and simpler forms of the original problem in order to gain insight into its solution. They monitor and evaluate their progress and change course if necessary. Older students might, depending on the context of the problem, transform algebraic expressions or change the viewing window on their graphing calculator to get the information they need. Mathematically proficient students can explain correspondences between equations, verbal descriptions, tables, and graphs or draw diagrams of important features and relationships, graph data, and search for regularity or trends. Younger students might rely on using concrete objects or pictures to help conceptualize and solve a problem. Mathematically proficient students check their answers to problems using a different method, and they continually ask themselves, “Does this make sense?” They can understand the approaches of others to solving complex problems and identify correspondences between different approaches. Make sense of problems and persevere in solving them. 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. For example, 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. Make sense of problems and persevere in solving them. Make sense of problems and persevere in solving them. Generate two numerical patterns using two given rules. Construct viable arguments and critique the reasoning of others. Create and use rules, tables, spreadsheets and graphs to describe patterns of change and solve problems. Use a rule or table to represent ordered pairs of positive integers and graph these ordered pairs on a coordinate system. 15-4: Quick Check Curriculum Standards: 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. For example, 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. Make sense of problems and persevere in solving them. 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. Make sense of problems and persevere in solving them. 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. For example, 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. Make sense of problems and persevere in solving them. Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution. They analyze givens, constraints, relationships, and goals. They make conjectures about the form and meaning of the solution and plan a solution pathway rather than simply jumping into a solution attempt. They consider analogous problems, and try special cases and simpler forms of the original problem in order to gain insight into its solution. They monitor and evaluate their progress and change course if necessary. Older students might, depending on the context of the problem, transform algebraic expressions or change the viewing window on their graphing calculator to get the information they need. Mathematically proficient students can explain correspondences between equations, verbal descriptions, tables, and graphs or draw diagrams of important features and relationships, graph data, and search for regularity or trends. Younger students might rely on using concrete objects or pictures to help conceptualize and solve a problem. Mathematically proficient students check their answers to problems using a different method, and they continually ask themselves, “Does this make sense?” They can understand the approaches of others to solving complex problems and identify correspondences between different approaches. Make sense of problems and persevere in solving them. 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. For example, 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. Make sense of problems and persevere in solving them. Make sense of problems and persevere in solving them. Generate two numerical patterns using two given rules. Construct viable arguments and critique the reasoning of others. Create and use rules, tables, spreadsheets and graphs to describe patterns of change and solve problems. Use a rule or table to represent ordered pairs of positive integers and graph these ordered pairs on a coordinate system. 15-4: Lesson Self-Assessment 15-4: Reteach to Build Understanding Curriculum Standards: 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. For example, 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. Make sense of problems and persevere in solving them. 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. Make sense of problems and persevere in solving them. 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. For example, 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. Make sense of problems and persevere in solving them. Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution. They analyze givens, constraints, relationships, and goals. They make conjectures about the form and meaning of the solution and plan a solution pathway rather than simply jumping into a solution attempt. They consider analogous problems, and try special cases and simpler forms of the original problem in order to gain insight into its solution. They monitor and evaluate their progress and change course if necessary. Older students might, depending on the context of the problem, transform algebraic expressions or change the viewing window on their graphing calculator to get the information they need. Mathematically proficient students can explain correspondences between equations, verbal descriptions, tables, and graphs or draw diagrams of important features and relationships, graph data, and search for regularity or trends. Younger students might rely on using concrete objects or pictures to help conceptualize and solve a problem. Mathematically proficient students check their answers to problems using a different method, and they continually ask themselves, “Does this make sense?” They can understand the approaches of others to solving complex problems and identify correspondences between different approaches. Make sense of problems and persevere in solving them. 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. For example, 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. Make sense of problems and persevere in solving them. Make sense of problems and persevere in solving them. Generate two numerical patterns using two given rules. Construct viable arguments and critique the reasoning of others. Create and use rules, tables, spreadsheets and graphs to describe patterns of change and solve problems. Use a rule or table to represent ordered pairs of positive integers and graph these ordered pairs on a coordinate system. 15-4: Build Mathematical Literacy Curriculum Standards: Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 5 topics and texts, building on others’ ideas and expressing their own clearly. (a) Come to discussions prepared, having read or studied required material; explicitly draw on that preparation and other information known about the topic to explore ideas under discussion. (b) Follow agreed-upon rules for discussions and carry out assigned roles. (c) Pose and respond to specific questions by making comments that contribute to the discussion and elaborate on the remarks of others. (d) Review the key ideas expressed and draw conclusions in light of information and knowledge gained from the discussions. English language learners communicate for social and instructional purposes within the school setting. Summarize a written text read aloud or information presented in diverse media and formats, including visually, quantitatively, and orally. Summarize the points a speaker makes and explain how each claim is supported by reasons and evidence. Write informative/explanatory texts to examine a topic and convey ideas and information clearly. (a) Introduce a topic clearly, provide a general observation and focus, and group related information logically; include formatting (e.g., headings), illustrations, and multimedia when useful to aiding comprehension. (b) Develop the topic with facts, definitions, concrete details, quotations, or other information and examples related to the topic. (c) Link ideas within and across categories of information using words, phrases, and clauses (e.g., in contrast, especially). (d) Use precise language and domain-specific vocabulary to inform about or explain the topic. (e) Provide a concluding statement or section related to the information or explanation presented. English language learners communicate information, ideas and concepts necessary for academic success in the content area of Mathematics. 15-4: Enrichment Game: Fluency - Multiply Multi-Digit Whole Numbers 15-4: Pick a Project 15-4: Another Look Curriculum Standards: 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. For example, 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. Make sense of problems and persevere in solving them. 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. Make sense of problems and persevere in solving them. 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. For example, 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. Make sense of problems and persevere in solving them. Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution. They analyze givens, constraints, relationships, and goals. They make conjectures about the form and meaning of the solution and plan a solution pathway rather than simply jumping into a solution attempt. They consider analogous problems, and try special cases and simpler forms of the original problem in order to gain insight into its solution. They monitor and evaluate their progress and change course if necessary. Older students might, depending on the context of the problem, transform algebraic expressions or change the viewing window on their graphing calculator to get the information they need. Mathematically proficient students can explain correspondences between equations, verbal descriptions, tables, and graphs or draw diagrams of important features and relationships, graph data, and search for regularity or trends. Younger students might rely on using concrete objects or pictures to help conceptualize and solve a problem. Mathematically proficient students check their answers to problems using a different method, and they continually ask themselves, “Does this make sense?” They can understand the approaches of others to solving complex problems and identify correspondences between different approaches. Make sense of problems and persevere in solving them. 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. For example, 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. Make sense of problems and persevere in solving them. Make sense of problems and persevere in solving them. Generate two numerical patterns using two given rules. Construct viable arguments and critique the reasoning of others. Create and use rules, tables, spreadsheets and graphs to describe patterns of change and solve problems. Use a rule or table to represent ordered pairs of positive integers and graph these ordered pairs on a coordinate system. Spanish Resources 15-4: eText del Libro del estudiante 15-4: Repaso diario 15-4: Aprendizaje visual 15-4: Amigo de práctica: Práctica adicional 15-4: Práctica adicional interactiva 15-4: Refuerzo para mejorar la comprensión 15-4: Desarrollar la competencia matemática 15-4: Ampliación Topic 15: End of Topic Interactive Student Edition: End of Topic 15 Topic 15: Fluency Practice Activity Interactive Student Edition: Topic 15 Assessment Practice Interactive Student Edition: Topic 15 Performance Task Topic 15 Performance Task Topic 15 Assessment 15-3: Visual Learning Curriculum Standards: 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. For example, given the rule “Add 3” and the starting number 0, and given the rule “Add 6” and the starting number 0, generate terms in the resulting sequences, and observe that the terms in one sequence are twice the corresponding terms in the other sequence. Explain informally why this is so. Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. 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. Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. 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. For example, given the rule “Add 3” and the starting number 0, and given the rule “Add 6” and the starting number 0, generate terms in the resulting sequences, and observe that the terms in one sequence are twice the corresponding terms in the other sequence. Explain informally why this is so. Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. Analyze patterns and graph ordered pairs generated from number sequences. Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane. For example, given the rule Add 3 and the starting number 0, and given the rule Add 6 and the starting number 0, generate terms in the resulting sequences, and observe that the terms in one sequence are twice the corresponding terms in the other sequence. Explain informally why this is so. Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. Generate two numerical patterns using two given rules. Represent real-world and mathematical problems by plotting points in quadrant I of the coordinate plane and interpret coordinate values of points in the context of the situation. Create and use rules, tables, spreadsheets and graphs to describe patterns of change and solve problems. Use a rule or table to represent ordered pairs of positive integers and graph these ordered pairs on a coordinate system. 5-2: Center Games 15-2: Visual Learning Curriculum Standards: 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. For example, 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. Given two pattern descriptions involving the same context (e.g., collecting marbles), determine the first five terms and compare the values. 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. 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. For example, 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. Use tables to identify relationships between patterns. 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. For example, 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. Identify apparent relationships between corresponding terms of two patterns with the same starting numbers that follow different rules. Create and use rules, tables, spreadsheets and graphs to describe patterns of change and solve problems. Use a rule or table to represent ordered pairs of positive integers and graph these ordered pairs on a coordinate system. Topic 15 Online Assessment Curriculum Standards: 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. For example, given the rule “Add 3” and the starting number 0, and given the rule “Add 6” and the starting number 0, generate terms in the resulting sequences, and observe that the terms in one sequence are twice the corresponding terms in the other sequence. Explain informally why this is so. Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. 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. 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. For example, 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. Use tables to identify relationships between patterns. 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. For example, 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. Identify apparent relationships between corresponding terms of two patterns with the same starting numbers that follow different rules. Create and use rules, tables, spreadsheets and graphs to describe patterns of change and solve problems. Use a rule or table to represent ordered pairs of positive integers and graph these ordered pairs on a coordinate system. Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. Analyze patterns and graph ordered pairs generated from number sequences. Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. Generate two numerical patterns using two given rules. Represent real- world and mathematical problems by plotting points in quadrant I of the coordinate plane and interpret coordinate values of points in the context of the situation. Topic 15 Spanish Assessments Tema 15: Tarea de rendimento Tema 15: Evaluación Topic 16: Geometric Measurement: Classify Two-Dimensional Figures Topic 16: Today's Challenge Topic 16: Beginning of Topic Interactive Student Edition: Beginning of Topic 16 Topic 16: enVision STEM Activity Grade 5 Topic 16: Review What You Know Topic 16: Vocabulary Cards 16-1: Classify Triangles Interactive Student Edition: Grade 5 Lesson 16-1 Math Anytime 16-1: Daily Review Topic 16: Today's Challenge Step 1: Problem-Based Learning 16-1: Solve & Share Curriculum Standards: Understand that attributes belonging to a category of two- dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles. Classify two- dimensional figures in a hierarchy based on properties. English language learners communicate for social and instructional purposes within the school setting. Write informative/explanatory texts to examine a topic and convey ideas and information clearly. (a) Introduce a topic clearly, provide a general observation and focus, and group related information logically; include formatting (e.g., headings), illustrations, and multimedia when useful to aiding comprehension. (b) Develop the topic with facts, definitions, concrete details, quotations, or other information and examples related to the topic. (c) Link ideas within and across categories of information using words, phrases, and clauses (e.g., in contrast, especially). (d) Use precise language and domain-specific vocabulary to inform about or explain the topic. (e) Provide a concluding statement or section related to the information or explanation presented. English language learners communicate information, ideas and concepts necessary for academic success in the content area of Mathematics. Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles. Classify triangles by their angles and sides. Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles. Classify two-dimensional figures in a hierarchy based on properties. Classify two-dimensional figures in a hierarchy based on properties. Describe and classify three-dimensional figures including cubes, prisms and pyramids by the number of edges, faces or vertices as well as the types of faces. Recognize and draw a net for a three-dimensional figure. Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 5 topics and texts, building on others’ ideas and expressing their own clearly. (a) Come to discussions prepared, having read or studied required material; explicitly draw on that preparation and other information known about the topic to explore ideas under discussion. (b) Follow agreed-upon rules for discussions and carry out assigned roles. (c) Pose and respond to specific questions by making comments that contribute to the discussion and elaborate on the remarks of others. (d) Review the key ideas expressed and draw conclusions in light of information and knowledge gained from the discussions. Summarize a written text read aloud or information presented in diverse media and formats, including visually, quantitatively, and orally. Summarize the points a speaker makes and explain how each claim is supported by reasons and evidence. Step 2: Visual Learning 16-1: Visual Learning Curriculum Standards: Understand that attributes belonging to a category of two- dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles. Classify two- dimensional figures in a hierarchy based on properties. Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles. Classify triangles by their angles and sides. Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles. Classify two-dimensional figures in a hierarchy based on properties. Classify two-dimensional figures in a hierarchy based on properties. Describe and classify three-dimensional figures including cubes, prisms and pyramids by the number of edges, faces or vertices as well as the types of faces. Recognize and draw a net for a three-dimensional figure. 16-1: Convince Me! Curriculum Standards: Understand that attributes belonging to a category of two- dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles. Classify two- dimensional figures in a hierarchy based on properties. Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles. Classify triangles by their angles and sides. Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles. Classify two-dimensional figures in a hierarchy based on properties. Classify two-dimensional figures in a hierarchy based on properties. Describe and classify three-dimensional figures including cubes, prisms and pyramids by the number of edges, faces or vertices as well as the types of faces. Recognize and draw a net for a three-dimensional figure. Practice and Problem Solving 16-1: Student Edition Practice Curriculum Standards: Understand that attributes belonging to a category of two- dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles. Classify two- dimensional figures in a hierarchy based on properties. Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles. Classify triangles by their angles and sides. Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles. Classify two-dimensional figures in a hierarchy based on properties. Classify two-dimensional figures in a hierarchy based on properties. Describe and classify three-dimensional figures including cubes, prisms and pyramids by the number of edges, faces or vertices as well as the types of faces. Recognize and draw a net for a three-dimensional figure. 16-1: Practice Buddy: Independent Practice; Problem Solving Curriculum Standards: Understand that attributes belonging to a category of two- dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles. Classify two- dimensional figures in a hierarchy based on properties. Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles. Classify triangles by their angles and sides. Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles. Classify two-dimensional figures in a hierarchy based on properties. Classify two-dimensional figures in a hierarchy based on properties. Describe and classify three-dimensional figures including cubes, prisms and pyramids by the number of edges, faces or vertices as well as the types of faces. Recognize and draw a net for a three-dimensional figure. 16-1: Practice Buddy: Additional Practice Curriculum Standards: Understand that attributes belonging to a category of two- dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles. Classify two- dimensional figures in a hierarchy based on properties. Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles. Classify triangles by their angles and sides. Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles. Classify two-dimensional figures in a hierarchy based on properties. Classify two-dimensional figures in a hierarchy based on properties. Describe and classify three-dimensional figures including cubes, prisms and pyramids by the number of edges, faces or vertices as well as the types of faces. Recognize and draw a net for a three-dimensional figure. 16-1: Interactive Additional Practice Step 3: Assess & Differentiate 16-1: Practice Buddy: Additional Practice Curriculum Standards: Understand that attributes belonging to a category of two- dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles. Classify two- dimensional figures in a hierarchy based on properties. Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles. Classify triangles by their angles and sides. Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles. Classify two-dimensional figures in a hierarchy based on properties. Classify two-dimensional figures in a hierarchy based on properties. Describe and classify three-dimensional figures including cubes, prisms and pyramids by the number of edges, faces or vertices as well as the types of faces. Recognize and draw a net for a three-dimensional figure. 16-1: Enrichment Curriculum Standards: Understand that attributes belonging to a category of two- dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles. Classify two- dimensional figures in a hierarchy based on properties. Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles. Classify triangles by their angles and sides. Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles. Classify two-dimensional figures in a hierarchy based on properties. Classify two-dimensional figures in a hierarchy based on properties. Describe and classify three-dimensional figures including cubes, prisms and pyramids by the number of edges, faces or vertices as well as the types of faces. Recognize and draw a net for a three-dimensional figure. 16-1: Quick Check Curriculum Standards: Understand that attributes belonging to a category of two- dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles. Classify two- dimensional figures in a hierarchy based on properties. Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles. Classify triangles by their angles and sides. Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles. Classify two-dimensional figures in a hierarchy based on properties. Classify two-dimensional figures in a hierarchy based on properties. Describe and classify three-dimensional figures including cubes, prisms and pyramids by the number of edges, faces or vertices as well as the types of faces. Recognize and draw a net for a three-dimensional figure. 16-1: Lesson Self-Assessment 16-1: Reteach to Build Understanding Curriculum Standards: Understand that attributes belonging to a category of two- dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles. Classify two- dimensional figures in a hierarchy based on properties. Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles. Classify triangles by their angles and sides. Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles. Classify two-dimensional figures in a hierarchy based on properties. Classify two-dimensional figures in a hierarchy based on properties. Describe and classify three-dimensional figures including cubes, prisms and pyramids by the number of edges, faces or vertices as well as the types of faces. Recognize and draw a net for a three-dimensional figure. 16-1: Build Mathematical Literacy Curriculum Standards: Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 5 topics and texts, building on others’ ideas and expressing their own clearly. (a) Come to discussions prepared, having read or studied required material; explicitly draw on that preparation and other information known about the topic to explore ideas under discussion. (b) Follow agreed-upon rules for discussions and carry out assigned roles. (c) Pose and respond to specific questions by making comments that contribute to the discussion and elaborate on the remarks of others. (d) Review the key ideas expressed and draw conclusions in light of information and knowledge gained from the discussions. English language learners communicate for social and instructional purposes within the school setting. Summarize a written text read aloud or information presented in diverse media and formats, including visually, quantitatively, and orally. Summarize the points a speaker makes and explain how each claim is supported by reasons and evidence. Write informative/explanatory texts to examine a topic and convey ideas and information clearly. (a) Introduce a topic clearly, provide a general observation and focus, and group related information logically; include formatting (e.g., headings), illustrations, and multimedia when useful to aiding comprehension. (b) Develop the topic with facts, definitions, concrete details, quotations, or other information and examples related to the topic. (c) Link ideas within and across categories of information using words, phrases, and clauses (e.g., in contrast, especially). (d) Use precise language and domain-specific vocabulary to inform about or explain the topic. (e) Provide a concluding statement or section related to the information or explanation presented. English language learners communicate information, ideas and concepts necessary for academic success in the content area of Mathematics. 16-1: Enrichment 16-1: Digital Math Tool Activity 16-1 Problem-Solving Reading Activity Curriculum Standards: Understand that attributes belonging to a category of two- dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles. Classify two- dimensional figures in a hierarchy based on properties. Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles. Classify triangles by their angles and sides. Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles. Classify two-dimensional figures in a hierarchy based on properties. Classify two-dimensional figures in a hierarchy based on properties. Describe and classify three-dimensional figures including cubes, prisms and pyramids by the number of edges, faces or vertices as well as the types of faces. Recognize and draw a net for a three-dimensional figure. 16-1: Another Look Curriculum Standards: Understand that attributes belonging to a category of two- dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles. Classify two- dimensional figures in a hierarchy based on properties. Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles. Classify triangles by their angles and sides. Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles. Classify two-dimensional figures in a hierarchy based on properties. Classify two-dimensional figures in a hierarchy based on properties. Describe and classify three-dimensional figures including cubes, prisms and pyramids by the number of edges, faces or vertices as well as the types of faces. Recognize and draw a net for a three-dimensional figure. Spanish Resources 16-1: eText del Libro del estudiante 16-1: Repaso diario 16-1: Aprendizaje visual 16-1: Amigo de práctica: Práctica adicional 16-1: Práctica adicional interactiva 16-1: Refuerzo para mejorar la comprensión 16-1: Desarrollar la competencia matemática 16-1: Ampliación 16-2: Classify Quadrilaterals Interactive Student Edition: Grade 5 Lesson 16-2 Math Anytime 16-2: Daily Review Topic 16: Today's Challenge Step 1: Problem-Based Learning 16-2: Solve & Share Curriculum Standards: Understand that attributes belonging to a category of two- dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles. Classify two- dimensional figures in a hierarchy based on properties. English language learners communicate for social and instructional purposes within the school setting. Write informative/explanatory texts to examine a topic and convey ideas and information clearly. (a) Introduce a topic clearly, provide a general observation and focus, and group related information logically; include formatting (e.g., headings), illustrations, and multimedia when useful to aiding comprehension. (b) Develop the topic with facts, definitions, concrete details, quotations, or other information and examples related to the topic. (c) Link ideas within and across categories of information using words, phrases, and clauses (e.g., in contrast, especially). (d) Use precise language and domain-specific vocabulary to inform about or explain the topic. (e) Provide a concluding statement or section related to the information or explanation presented. English language learners communicate information, ideas and concepts necessary for academic success in the content area of Mathematics. Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. Classify and organize two-dimensional figures into Venn diagrams based on the attributes of the figures. Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles. Classify and organize two-dimensional figures into Venn diagrams based on the attributes of the figures. Classify quadrilaterals by their properties. Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles. Classify two-dimensional figures in a hierarchy based on properties. Classify two-dimensional figures in a hierarchy based on properties. Describe and classify three-dimensional figures including cubes, prisms and pyramids by the number of edges, faces or vertices as well as the types of faces. Recognize and draw a net for a three-dimensional figure. Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 5 topics and texts, building on others’ ideas and expressing their own clearly. (a) Come to discussions prepared, having read or studied required material; explicitly draw on that preparation and other information known about the topic to explore ideas under discussion. (b) Follow agreed-upon rules for discussions and carry out assigned roles. (c) Pose and respond to specific questions by making comments that contribute to the discussion and elaborate on the remarks of others. (d) Review the key ideas expressed and draw conclusions in light of information and knowledge gained from the discussions. Summarize a written text read aloud or information presented in diverse media and formats, including visually, quantitatively, and orally. Summarize the points a speaker makes and explain how each claim is supported by reasons and evidence. Step 2: Visual Learning 16-2: Visual Learning Curriculum Standards: Understand that attributes belonging to a category of two- dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles. Classify two- dimensional figures in a hierarchy based on properties. Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. Classify and organize two-dimensional figures into Venn diagrams based on the attributes of the figures. Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles. Classify and organize two-dimensional figures into Venn diagrams based on the attributes of the figures. Classify quadrilaterals by their properties. Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles. Classify two-dimensional figures in a hierarchy based on properties. Classify two-dimensional figures in a hierarchy based on properties. Describe and classify three-dimensional figures including cubes, prisms and pyramids by the number of edges, faces or vertices as well as the types of faces. Recognize and draw a net for a three-dimensional figure. 16-2: Convince Me! Curriculum Standards: Understand that attributes belonging to a category of two- dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles. Classify two- dimensional figures in a hierarchy based on properties. Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. Classify and organize two-dimensional figures into Venn diagrams based on the attributes of the figures. Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles. Classify and organize two-dimensional figures into Venn diagrams based on the attributes of the figures. Classify quadrilaterals by their properties. Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles. Classify two-dimensional figures in a hierarchy based on properties. Classify two-dimensional figures in a hierarchy based on properties. Describe and classify three-dimensional figures including cubes, prisms and pyramids by the number of edges, faces or vertices as well as the types of faces. Recognize and draw a net for a three-dimensional figure. Practice and Problem Solving 16-2: Student Edition Practice Curriculum Standards: Understand that attributes belonging to a category of two- dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles. Classify two- dimensional figures in a hierarchy based on properties. Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. Classify and organize two-dimensional figures into Venn diagrams based on the attributes of the figures. Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles. Classify and organize two-dimensional figures into Venn diagrams based on the attributes of the figures. Classify quadrilaterals by their properties. Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles. Classify two-dimensional figures in a hierarchy based on properties. Classify two-dimensional figures in a hierarchy based on properties. Describe and classify three-dimensional figures including cubes, prisms and pyramids by the number of edges, faces or vertices as well as the types of faces. Recognize and draw a net for a three-dimensional figure. 16-2: Practice Buddy: Independent Practice; Problem Solving Curriculum Standards: Understand that attributes belonging to a category of two- dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles. Classify two- dimensional figures in a hierarchy based on properties. Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. Classify and organize two-dimensional figures into Venn diagrams based on the attributes of the figures. Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles. Classify and organize two-dimensional figures into Venn diagrams based on the attributes of the figures. Classify quadrilaterals by their properties. Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles. Classify two-dimensional figures in a hierarchy based on properties. Classify two-dimensional figures in a hierarchy based on properties. Describe and classify three-dimensional figures including cubes, prisms and pyramids by the number of edges, faces or vertices as well as the types of faces. Recognize and draw a net for a three-dimensional figure. 16-2: Practice Buddy: Additional Practice Curriculum Standards: Understand that attributes belonging to a category of two- dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles. Classify two- dimensional figures in a hierarchy based on properties. Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. Classify and organize two-dimensional figures into Venn diagrams based on the attributes of the figures. Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles. Classify and organize two-dimensional figures into Venn diagrams based on the attributes of the figures. Classify quadrilaterals by their properties. Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles. Classify two-dimensional figures in a hierarchy based on properties. Classify two-dimensional figures in a hierarchy based on properties. Describe and classify three-dimensional figures including cubes, prisms and pyramids by the number of edges, faces or vertices as well as the types of faces. Recognize and draw a net for a three-dimensional figure. 16-2: Interactive Additional Practice Step 3: Assess & Differentiate 16-2: Practice Buddy: Additional Practice Curriculum Standards: Understand that attributes belonging to a category of two- dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles. Classify two- dimensional figures in a hierarchy based on properties. Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. Classify and organize two-dimensional figures into Venn diagrams based on the attributes of the figures. Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles. Classify and organize two-dimensional figures into Venn diagrams based on the attributes of the figures. Classify quadrilaterals by their properties. Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles. Classify two-dimensional figures in a hierarchy based on properties. Classify two-dimensional figures in a hierarchy based on properties. Describe and classify three-dimensional figures including cubes, prisms and pyramids by the number of edges, faces or vertices as well as the types of faces. Recognize and draw a net for a three-dimensional figure. 16-2: Enrichment Curriculum Standards: Understand that attributes belonging to a category of two- dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles. Classify two- dimensional figures in a hierarchy based on properties. Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. Classify and organize two-dimensional figures into Venn diagrams based on the attributes of the figures. Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles. Classify and organize two-dimensional figures into Venn diagrams based on the attributes of the figures. Classify quadrilaterals by their properties. Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles. Classify two-dimensional figures in a hierarchy based on properties. Classify two-dimensional figures in a hierarchy based on properties. Describe and classify three-dimensional figures including cubes, prisms and pyramids by the number of edges, faces or vertices as well as the types of faces. Recognize and draw a net for a three-dimensional figure. 16-2: Quick Check Curriculum Standards: Understand that attributes belonging to a category of two- dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles. Classify two- dimensional figures in a hierarchy based on properties. Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. Classify and organize two-dimensional figures into Venn diagrams based on the attributes of the figures. Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles. Classify and organize two-dimensional figures into Venn diagrams based on the attributes of the figures. Classify quadrilaterals by their properties. Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles. Classify two-dimensional figures in a hierarchy based on properties. Classify two-dimensional figures in a hierarchy based on properties. Describe and classify three-dimensional figures including cubes, prisms and pyramids by the number of edges, faces or vertices as well as the types of faces. Recognize and draw a net for a three-dimensional figure. 16-2: Lesson Self-Assessment 16-2: Reteach to Build Understanding Curriculum Standards: Understand that attributes belonging to a category of two- dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles. Classify two- dimensional figures in a hierarchy based on properties. Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. Classify and organize two-dimensional figures into Venn diagrams based on the attributes of the figures. Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles. Classify and organize two-dimensional figures into Venn diagrams based on the attributes of the figures. Classify quadrilaterals by their properties. Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles. Classify two-dimensional figures in a hierarchy based on properties. Classify two-dimensional figures in a hierarchy based on properties. Describe and classify three-dimensional figures including cubes, prisms and pyramids by the number of edges, faces or vertices as well as the types of faces. Recognize and draw a net for a three-dimensional figure. 16-2: Build Mathematical Literacy Curriculum Standards: Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 5 topics and texts, building on others’ ideas and expressing their own clearly. (a) Come to discussions prepared, having read or studied required material; explicitly draw on that preparation and other information known about the topic to explore ideas under discussion. (b) Follow agreed-upon rules for discussions and carry out assigned roles. (c) Pose and respond to specific questions by making comments that contribute to the discussion and elaborate on the remarks of others. (d) Review the key ideas expressed and draw conclusions in light of information and knowledge gained from the discussions. English language learners communicate for social and instructional purposes within the school setting. Summarize a written text read aloud or information presented in diverse media and formats, including visually, quantitatively, and orally. Summarize the points a speaker makes and explain how each claim is supported by reasons and evidence. Write informative/explanatory texts to examine a topic and convey ideas and information clearly. (a) Introduce a topic clearly, provide a general observation and focus, and group related information logically; include formatting (e.g., headings), illustrations, and multimedia when useful to aiding comprehension. (b) Develop the topic with facts, definitions, concrete details, quotations, or other information and examples related to the topic. (c) Link ideas within and across categories of information using words, phrases, and clauses (e.g., in contrast, especially). (d) Use precise language and domain-specific vocabulary to inform about or explain the topic. (e) Provide a concluding statement or section related to the information or explanation presented. English language learners communicate information, ideas and concepts necessary for academic success in the content area of Mathematics. 16-2: Enrichment 16-2: Digital Math Tool Activity 16-2: Pick a Project 16-2: Another Look Curriculum Standards: Understand that attributes belonging to a category of two- dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles. Classify two- dimensional figures in a hierarchy based on properties. Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. Classify and organize two-dimensional figures into Venn diagrams based on the attributes of the figures. Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles. Classify and organize two-dimensional figures into Venn diagrams based on the attributes of the figures. Classify quadrilaterals by their properties. Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles. Classify two-dimensional figures in a hierarchy based on properties. Classify two-dimensional figures in a hierarchy based on properties. Describe and classify three-dimensional figures including cubes, prisms and pyramids by the number of edges, faces or vertices as well as the types of faces. Recognize and draw a net for a three-dimensional figure. Spanish Resources 16-2: eText del Libro del estudiante 16-2: Repaso diario 16-2: Aprendizaje visual 16-2: Amigo de práctica: Práctica adicional 16-2: Práctica adicional interactiva 16-2: Refuerzo para mejorar la comprensión 16-2: Desarrollar la competencia matemática 16-2: Ampliación 16-3: Continue to Classify Quadrilaterals Interactive Student Edition: Grade 5 Lesson 16-3 Math Anytime 16-3: Daily Review Topic 16: Today's Challenge Step 1: Problem-Based Learning 16-3: Solve & Share Curriculum Standards: Understand that attributes belonging to a category of two- dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles. Classify two- dimensional figures in a hierarchy based on properties. English language learners communicate for social and instructional purposes within the school setting. Write informative/explanatory texts to examine a topic and convey ideas and information clearly. (a) Introduce a topic clearly, provide a general observation and focus, and group related information logically; include formatting (e.g., headings), illustrations, and multimedia when useful to aiding comprehension. (b) Develop the topic with facts, definitions, concrete details, quotations, or other information and examples related to the topic. (c) Link ideas within and across categories of information using words, phrases, and clauses (e.g., in contrast, especially). (d) Use precise language and domain-specific vocabulary to inform about or explain the topic. (e) Provide a concluding statement or section related to the information or explanation presented. English language learners communicate information, ideas and concepts necessary for academic success in the content area of Mathematics. Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. Classify and organize two-dimensional figures into Venn diagrams based on the attributes of the figures. Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles. Classify and organize two-dimensional figures into Venn diagrams based on the attributes of the figures. Classify quadrilaterals using a hierarchy. Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles. Classify two-dimensional figures in a hierarchy based on properties. Classify two-dimensional figures in a hierarchy based on properties. Describe and classify three-dimensional figures including cubes, prisms and pyramids by the number of edges, faces or vertices as well as the types of faces. Recognize and draw a net for a three-dimensional figure. Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 5 topics and texts, building on others’ ideas and expressing their own clearly. (a) Come to discussions prepared, having read or studied required material; explicitly draw on that preparation and other information known about the topic to explore ideas under discussion. (b) Follow agreed-upon rules for discussions and carry out assigned roles. (c) Pose and respond to specific questions by making comments that contribute to the discussion and elaborate on the remarks of others. (d) Review the key ideas expressed and draw conclusions in light of information and knowledge gained from the discussions. Summarize a written text read aloud or information presented in diverse media and formats, including visually, quantitatively, and orally. Summarize the points a speaker makes and explain how each claim is supported by reasons and evidence. Step 2: Visual Learning 16-3: Visual Learning Curriculum Standards: Understand that attributes belonging to a category of two- dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles. Classify two- dimensional figures in a hierarchy based on properties. Use polygon-shaped manipulatives to classify and organize two-dimensional figures into Venn diagrams based on the attributes of the figures. Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. Classify and organize two-dimensional figures into Venn diagrams based on the attributes of the figures. Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles. Classify and organize two- dimensional figures into Venn diagrams based on the attributes of the figures. Classify quadrilaterals using a hierarchy. Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles. Classify two-dimensional figures in a hierarchy based on properties. Classify two-dimensional figures in a hierarchy based on properties. Describe and classify three-dimensional figures including cubes, prisms and pyramids by the number of edges, faces or vertices as well as the types of faces. Recognize and draw a net for a three-dimensional figure. 16-3: Convince Me! Curriculum Standards: Understand that attributes belonging to a category of two- dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles. Classify two- dimensional figures in a hierarchy based on properties. Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. Classify and organize two-dimensional figures into Venn diagrams based on the attributes of the figures. Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles. Classify and organize two-dimensional figures into Venn diagrams based on the attributes of the figures. Classify quadrilaterals using a hierarchy. Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles. Classify two-dimensional figures in a hierarchy based on properties. Classify two-dimensional figures in a hierarchy based on properties. Describe and classify three-dimensional figures including cubes, prisms and pyramids by the number of edges, faces or vertices as well as the types of faces. Recognize and draw a net for a three-dimensional figure. Practice and Problem Solving 16-3: Student Edition Practice Curriculum Standards: Understand that attributes belonging to a category of two- dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles. Classify two- dimensional figures in a hierarchy based on properties. Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. Classify and organize two-dimensional figures into Venn diagrams based on the attributes of the figures. Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles. Classify and organize two-dimensional figures into Venn diagrams based on the attributes of the figures. Classify quadrilaterals using a hierarchy. Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles. Classify two-dimensional figures in a hierarchy based on properties. Classify two-dimensional figures in a hierarchy based on properties. Describe and classify three-dimensional figures including cubes, prisms and pyramids by the number of edges, faces or vertices as well as the types of faces. Recognize and draw a net for a three-dimensional figure. 16-3: Practice Buddy: Independent Practice; Problem Solving Curriculum Standards: Understand that attributes belonging to a category of two- dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles. Classify two- dimensional figures in a hierarchy based on properties. Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. Classify and organize two-dimensional figures into Venn diagrams based on the attributes of the figures. Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles. Classify and organize two-dimensional figures into Venn diagrams based on the attributes of the figures. Classify quadrilaterals using a hierarchy. Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles. Classify two-dimensional figures in a hierarchy based on properties. Classify two-dimensional figures in a hierarchy based on properties. Describe and classify three-dimensional figures including cubes, prisms and pyramids by the number of edges, faces or vertices as well as the types of faces. Recognize and draw a net for a three-dimensional figure. 16-3: Practice Buddy: Additional Practice Curriculum Standards: Understand that attributes belonging to a category of two- dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles. Classify two- dimensional figures in a hierarchy based on properties. Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. Classify and organize two-dimensional figures into Venn diagrams based on the attributes of the figures. Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles. Classify and organize two-dimensional figures into Venn diagrams based on the attributes of the figures. Classify quadrilaterals using a hierarchy. Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles. Classify two-dimensional figures in a hierarchy based on properties. Classify two-dimensional figures in a hierarchy based on properties. Describe and classify three-dimensional figures including cubes, prisms and pyramids by the number of edges, faces or vertices as well as the types of faces. Recognize and draw a net for a three-dimensional figure. 16-3: Interactive Additional Practice Step 3: Assess & Differentiate 16-3: Practice Buddy: Additional Practice Curriculum Standards: Understand that attributes belonging to a category of two- dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles. Classify two- dimensional figures in a hierarchy based on properties. Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. Classify and organize two-dimensional figures into Venn diagrams based on the attributes of the figures. Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles. Classify and organize two-dimensional figures into Venn diagrams based on the attributes of the figures. Classify quadrilaterals using a hierarchy. Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles. Classify two-dimensional figures in a hierarchy based on properties. Classify two-dimensional figures in a hierarchy based on properties. Describe and classify three-dimensional figures including cubes, prisms and pyramids by the number of edges, faces or vertices as well as the types of faces. Recognize and draw a net for a three-dimensional figure. 16-3: Enrichment Curriculum Standards: Understand that attributes belonging to a category of two- dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles. Classify two- dimensional figures in a hierarchy based on properties. Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. Classify and organize two-dimensional figures into Venn diagrams based on the attributes of the figures. Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles. Classify and organize two-dimensional figures into Venn diagrams based on the attributes of the figures. Classify quadrilaterals using a hierarchy. Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles. Classify two-dimensional figures in a hierarchy based on properties. Classify two-dimensional figures in a hierarchy based on properties. Describe and classify three-dimensional figures including cubes, prisms and pyramids by the number of edges, faces or vertices as well as the types of faces. Recognize and draw a net for a three-dimensional figure. 16-3: Quick Check Curriculum Standards: Understand that attributes belonging to a category of two- dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles. Classify two- dimensional figures in a hierarchy based on properties. Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. Classify and organize two-dimensional figures into Venn diagrams based on the attributes of the figures. Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles. Classify and organize two-dimensional figures into Venn diagrams based on the attributes of the figures. Classify quadrilaterals using a hierarchy. Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles. Classify two-dimensional figures in a hierarchy based on properties. Classify two-dimensional figures in a hierarchy based on properties. Describe and classify three-dimensional figures including cubes, prisms and pyramids by the number of edges, faces or vertices as well as the types of faces. Recognize and draw a net for a three-dimensional figure. 16-3: Lesson Self-Assessment 16-3: Reteach to Build Understanding Curriculum Standards: Understand that attributes belonging to a category of two- dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles. Classify two- dimensional figures in a hierarchy based on properties. Use polygon-shaped manipulatives to classify and organize two-dimensional figures into Venn diagrams based on the attributes of the figures. Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. Classify and organize two-dimensional figures into Venn diagrams based on the attributes of the figures. Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles. Classify and organize two- dimensional figures into Venn diagrams based on the attributes of the figures. Classify quadrilaterals using a hierarchy. Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles. Classify two-dimensional figures in a hierarchy based on properties. Classify two-dimensional figures in a hierarchy based on properties. Describe and classify three-dimensional figures including cubes, prisms and pyramids by the number of edges, faces or vertices as well as the types of faces. Recognize and draw a net for a three-dimensional figure. 16-3: Build Mathematical Literacy Curriculum Standards: Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 5 topics and texts, building on others’ ideas and expressing their own clearly. (a) Come to discussions prepared, having read or studied required material; explicitly draw on that preparation and other information known about the topic to explore ideas under discussion. (b) Follow agreed-upon rules for discussions and carry out assigned roles. (c) Pose and respond to specific questions by making comments that contribute to the discussion and elaborate on the remarks of others. (d) Review the key ideas expressed and draw conclusions in light of information and knowledge gained from the discussions. English language learners communicate for social and instructional purposes within the school setting. Summarize a written text read aloud or information presented in diverse media and formats, including visually, quantitatively, and orally. Summarize the points a speaker makes and explain how each claim is supported by reasons and evidence. Write informative/explanatory texts to examine a topic and convey ideas and information clearly. (a) Introduce a topic clearly, provide a general observation and focus, and group related information logically; include formatting (e.g., headings), illustrations, and multimedia when useful to aiding comprehension. (b) Develop the topic with facts, definitions, concrete details, quotations, or other information and examples related to the topic. (c) Link ideas within and across categories of information using words, phrases, and clauses (e.g., in contrast, especially). (d) Use precise language and domain-specific vocabulary to inform about or explain the topic. (e) Provide a concluding statement or section related to the information or explanation presented. English language learners communicate information, ideas and concepts necessary for academic success in the content area of Mathematics. 16-3: Enrichment Game: Save the Word: Grade 5 Topics 1-16 16-3 Problem-Solving Reading Activity Curriculum Standards: Understand that attributes belonging to a category of two- dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles. Classify two- dimensional figures in a hierarchy based on properties. Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. Classify and organize two-dimensional figures into Venn diagrams based on the attributes of the figures. Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles. Classify and organize two-dimensional figures into Venn diagrams based on the attributes of the figures. Classify quadrilaterals using a hierarchy. Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles. Classify two-dimensional figures in a hierarchy based on properties. Classify two-dimensional figures in a hierarchy based on properties. Describe and classify three-dimensional figures including cubes, prisms and pyramids by the number of edges, faces or vertices as well as the types of faces. Recognize and draw a net for a three-dimensional figure. 16-3: Another Look Curriculum Standards: Understand that attributes belonging to a category of two- dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles. Classify two- dimensional figures in a hierarchy based on properties. Use polygon-shaped manipulatives to classify and organize two-dimensional figures into Venn diagrams based on the attributes of the figures. Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. Classify and organize two-dimensional figures into Venn diagrams based on the attributes of the figures. Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles. Classify and organize two- dimensional figures into Venn diagrams based on the attributes of the figures. Classify quadrilaterals using a hierarchy. Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles. Classify two-dimensional figures in a hierarchy based on properties. Classify two-dimensional figures in a hierarchy based on properties. Describe and classify three-dimensional figures including cubes, prisms and pyramids by the number of edges, faces or vertices as well as the types of faces. Recognize and draw a net for a three-dimensional figure. Spanish Resources 16-3: eText del Libro del estudiante 16-3: Repaso diario 16-3: Aprendizaje visual 16-3: Amigo de práctica: Práctica adicional 16-3: Práctica adicional interactiva 16-3: Refuerzo para mejorar la comprensión 16-3: Desarrollar la competencia matemática 16-3: Ampliación 16-4: Problem Solving: Construct Arguments Interactive Student Edition: Grade 5 Lesson 16-4 Step 1: Problem-Based Learning 16-4: Solve & Share Curriculum Standards: Understand that attributes belonging to a category of two- dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles. Classify two- dimensional figures in a hierarchy based on properties. Construct viable arguments and critique the reasoning of others. English language learners communicate for social and instructional purposes within the school setting. Write informative/explanatory texts to examine a topic and convey ideas and information clearly. (a) Introduce a topic clearly, provide a general observation and focus, and group related information logically; include formatting (e.g., headings), illustrations, and multimedia when useful to aiding comprehension. (b) Develop the topic with facts, definitions, concrete details, quotations, or other information and examples related to the topic. (c) Link ideas within and across categories of information using words, phrases, and clauses (e.g., in contrast, especially). (d) Use precise language and domain-specific vocabulary to inform about or explain the topic. (e) Provide a concluding statement or section related to the information or explanation presented. English language learners communicate information, ideas and concepts necessary for academic success in the content area of Mathematics. Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. Classify and organize two-dimensional figures into Venn diagrams based on the attributes of the figures. Construct viable arguments and critique the reasoning of others. Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles. Classify and organize two-dimensional figures into Venn diagrams based on the attributes of the figures. Construct viable arguments and critique the reasoning of others. Mathematically proficient students understand and use stated assumptions, definitions, and previously established results in constructing arguments. They make conjectures and build a logical progression of statements to explore the truth of their conjectures. They are able to analyze situations by breaking them into cases, and can recognize and use counterexamples. They justify their conclusions, communicate them to others, and respond to the arguments of others. They reason inductively about data, making plausible arguments that take into account the context from which the data arose. Mathematically proficient students are also able to compare the effectiveness of two plausible arguments, distinguish correct logic or reasoning from that which is flawed, and—if there is a flaw in an argument—explain what it is. Elementary students can construct arguments using concrete referents such as objects, drawings, diagrams, and actions. Such arguments can make sense and be correct, even though they are not generalized or made formal until later grades. Later, students learn to determine domains to which an argument applies. Students at all grades can listen or read the arguments of others, decide whether they make sense, and ask useful questions to clarify or improve the arguments. Construct arguments about geometric figures. Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles. Classify two- dimensional figures in a hierarchy based on properties. Construct viable arguments and critique the reasoning of others. Construct viable arguments and critique the reasoning of others. Classify two- dimensional figures in a hierarchy based on properties. Construct viable arguments and critique the reasoning of others. Describe and classify three-dimensional figures including cubes, prisms and pyramids by the number of edges, faces or vertices as well as the types of faces. Recognize and draw a net for a three-dimensional figure. Engage effectively in a range of collaborative discussions (one-on- one, in groups, and teacher-led) with diverse partners on grade 5 topics and texts, building on others’ ideas and expressing their own clearly. (a) Come to discussions prepared, having read or studied required material; explicitly draw on that preparation and other information known about the topic to explore ideas under discussion. (b) Follow agreed-upon rules for discussions and carry out assigned roles. (c) Pose and respond to specific questions by making comments that contribute to the discussion and elaborate on the remarks of others. (d) Review the key ideas expressed and draw conclusions in light of information and knowledge gained from the discussions. Summarize a written text read aloud or information presented in diverse media and formats, including visually, quantitatively, and orally. Summarize the points a speaker makes and explain how each claim is supported by reasons and evidence. Math Anytime 16-4: Daily Review Topic 16: Today's Challenge Step 2: Visual Learning 16-4: Visual Learning Curriculum Standards: Understand that attributes belonging to a category of two- dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles. Classify two- dimensional figures in a hierarchy based on properties. Construct viable arguments and critique the reasoning of others. Recognize properties of simple plane figures using polygon-shaped manipulatives. Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. Classify and organize two-dimensional figures into Venn diagrams based on the attributes of the figures. Construct viable arguments and critique the reasoning of others. Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles. Classify and organize two-dimensional figures into Venn diagrams based on the attributes of the figures. Construct viable arguments and critique the reasoning of others. Mathematically proficient students understand and use stated assumptions, definitions, and previously established results in constructing arguments. They make conjectures and build a logical progression of statements to explore the truth of their conjectures. They are able to analyze situations by breaking them into cases, and can recognize and use counterexamples. They justify their conclusions, communicate them to others, and respond to the arguments of others. They reason inductively about data, making plausible arguments that take into account the context from which the data arose. Mathematically proficient students are also able to compare the effectiveness of two plausible arguments, distinguish correct logic or reasoning from that which is flawed, and—if there is a flaw in an argument—explain what it is. Elementary students can construct arguments using concrete referents such as objects, drawings, diagrams, and actions. Such arguments can make sense and be correct, even though they are not generalized or made formal until later grades. Later, students learn to determine domains to which an argument applies. Students at all grades can listen or read the arguments of others, decide whether they make sense, and ask useful questions to clarify or improve the arguments. Construct arguments about geometric figures. Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles. Classify two- dimensional figures in a hierarchy based on properties. Construct viable arguments and critique the reasoning of others. Construct viable arguments and critique the reasoning of others. Classify two- dimensional figures in a hierarchy based on properties. Construct viable arguments and critique the reasoning of others. Describe and classify three-dimensional figures including cubes, prisms and pyramids by the number of edges, faces or vertices as well as the types of faces. Recognize and draw a net for a three-dimensional figure. 16-4: Convince Me! Curriculum Standards: Understand that attributes belonging to a category of two- dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles. Classify two- dimensional figures in a hierarchy based on properties. Construct viable arguments and critique the reasoning of others. Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. Classify and organize two-dimensional figures into Venn diagrams based on the attributes of the figures. Construct viable arguments and critique the reasoning of others. Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles. Classify and organize two-dimensional figures into Venn diagrams based on the attributes of the figures. Construct viable arguments and critique the reasoning of others. Mathematically proficient students understand and use stated assumptions, definitions, and previously established results in constructing arguments. They make conjectures and build a logical progression of statements to explore the truth of their conjectures. They are able to analyze situations by breaking them into cases, and can recognize and use counterexamples. They justify their conclusions, communicate them to others, and respond to the arguments of others. They reason inductively about data, making plausible arguments that take into account the context from which the data arose. Mathematically proficient students are also able to compare the effectiveness of two plausible arguments, distinguish correct logic or reasoning from that which is flawed, and—if there is a flaw in an argument—explain what it is. Elementary students can construct arguments using concrete referents such as objects, drawings, diagrams, and actions. Such arguments can make sense and be correct, even though they are not generalized or made formal until later grades. Later, students learn to determine domains to which an argument applies. Students at all grades can listen or read the arguments of others, decide whether they make sense, and ask useful questions to clarify or improve the arguments. Construct arguments about geometric figures. Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles. Classify two- dimensional figures in a hierarchy based on properties. Construct viable arguments and critique the reasoning of others. Construct viable arguments and critique the reasoning of others. Classify two- dimensional figures in a hierarchy based on properties. Construct viable arguments and critique the reasoning of others. Describe and classify three-dimensional figures including cubes, prisms and pyramids by the number of edges, faces or vertices as well as the types of faces. Recognize and draw a net for a three-dimensional figure. Practice and Problem Solving 16-4: Student Edition Practice Curriculum Standards: Understand that attributes belonging to a category of two- dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles. Classify two- dimensional figures in a hierarchy based on properties. Construct viable arguments and critique the reasoning of others. Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. Classify and organize two-dimensional figures into Venn diagrams based on the attributes of the figures. Construct viable arguments and critique the reasoning of others. Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles. Classify and organize two-dimensional figures into Venn diagrams based on the attributes of the figures. Construct viable arguments and critique the reasoning of others. Mathematically proficient students understand and use stated assumptions, definitions, and previously established results in constructing arguments. They make conjectures and build a logical progression of statements to explore the truth of their conjectures. They are able to analyze situations by breaking them into cases, and can recognize and use counterexamples. They justify their conclusions, communicate them to others, and respond to the arguments of others. They reason inductively about data, making plausible arguments that take into account the context from which the data arose. Mathematically proficient students are also able to compare the effectiveness of two plausible arguments, distinguish correct logic or reasoning from that which is flawed, and—if there is a flaw in an argument—explain what it is. Elementary students can construct arguments using concrete referents such as objects, drawings, diagrams, and actions. Such arguments can make sense and be correct, even though they are not generalized or made formal until later grades. Later, students learn to determine domains to which an argument applies. Students at all grades can listen or read the arguments of others, decide whether they make sense, and ask useful questions to clarify or improve the arguments. Construct arguments about geometric figures. Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles. Classify two- dimensional figures in a hierarchy based on properties. Construct viable arguments and critique the reasoning of others. Construct viable arguments and critique the reasoning of others. Classify two- dimensional figures in a hierarchy based on properties. Construct viable arguments and critique the reasoning of others. Describe and classify three-dimensional figures including cubes, prisms and pyramids by the number of edges, faces or vertices as well as the types of faces. Recognize and draw a net for a three-dimensional figure. 16-4: Practice Buddy: Independent Practice; Problem Solving Curriculum Standards: Understand that attributes belonging to a category of two- dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles. Classify two- dimensional figures in a hierarchy based on properties. Construct viable arguments and critique the reasoning of others. Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. Classify and organize two-dimensional figures into Venn diagrams based on the attributes of the figures. Construct viable arguments and critique the reasoning of others. Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles. Classify and organize two-dimensional figures into Venn diagrams based on the attributes of the figures. Construct viable arguments and critique the reasoning of others. Mathematically proficient students understand and use stated assumptions, definitions, and previously established results in constructing arguments. They make conjectures and build a logical progression of statements to explore the truth of their conjectures. They are able to analyze situations by breaking them into cases, and can recognize and use counterexamples. They justify their conclusions, communicate them to others, and respond to the arguments of others. They reason inductively about data, making plausible arguments that take into account the context from which the data arose. Mathematically proficient students are also able to compare the effectiveness of two plausible arguments, distinguish correct logic or reasoning from that which is flawed, and—if there is a flaw in an argument—explain what it is. Elementary students can construct arguments using concrete referents such as objects, drawings, diagrams, and actions. Such arguments can make sense and be correct, even though they are not generalized or made formal until later grades. Later, students learn to determine domains to which an argument applies. Students at all grades can listen or read the arguments of others, decide whether they make sense, and ask useful questions to clarify or improve the arguments. Construct arguments about geometric figures. Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles. Classify two- dimensional figures in a hierarchy based on properties. Construct viable arguments and critique the reasoning of others. Construct viable arguments and critique the reasoning of others. Classify two- dimensional figures in a hierarchy based on properties. Construct viable arguments and critique the reasoning of others. Describe and classify three-dimensional figures including cubes, prisms and pyramids by the number of edges, faces or vertices as well as the types of faces. Recognize and draw a net for a three-dimensional figure. 16-4: Practice Buddy: Additional Practice Curriculum Standards: Understand that attributes belonging to a category of two- dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles. Classify two- dimensional figures in a hierarchy based on properties. Construct viable arguments and critique the reasoning of others. Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. Classify and organize two-dimensional figures into Venn diagrams based on the attributes of the figures. Construct viable arguments and critique the reasoning of others. Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles. Classify and organize two-dimensional figures into Venn diagrams based on the attributes of the figures. Construct viable arguments and critique the reasoning of others. Mathematically proficient students understand and use stated assumptions, definitions, and previously established results in constructing arguments. They make conjectures and build a logical progression of statements to explore the truth of their conjectures. They are able to analyze situations by breaking them into cases, and can recognize and use counterexamples. They justify their conclusions, communicate them to others, and respond to the arguments of others. They reason inductively about data, making plausible arguments that take into account the context from which the data arose. Mathematically proficient students are also able to compare the effectiveness of two plausible arguments, distinguish correct logic or reasoning from that which is flawed, and—if there is a flaw in an argument—explain what it is. Elementary students can construct arguments using concrete referents such as objects, drawings, diagrams, and actions. Such arguments can make sense and be correct, even though they are not generalized or made formal until later grades. Later, students learn to determine domains to which an argument applies. Students at all grades can listen or read the arguments of others, decide whether they make sense, and ask useful questions to clarify or improve the arguments. Construct arguments about geometric figures. Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles. Classify two- dimensional figures in a hierarchy based on properties. Construct viable arguments and critique the reasoning of others. Construct viable arguments and critique the reasoning of others. Classify two- dimensional figures in a hierarchy based on properties. Construct viable arguments and critique the reasoning of others. Describe and classify three-dimensional figures including cubes, prisms and pyramids by the number of edges, faces or vertices as well as the types of faces. Recognize and draw a net for a three-dimensional figure. 16-4: Interactive Additional Practice Step 3: Assess & Differentiate 16-4: Practice Buddy: Additional Practice Curriculum Standards: Understand that attributes belonging to a category of two- dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles. Classify two- dimensional figures in a hierarchy based on properties. Construct viable arguments and critique the reasoning of others. Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. Classify and organize two-dimensional figures into Venn diagrams based on the attributes of the figures. Construct viable arguments and critique the reasoning of others. Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles. Classify and organize two-dimensional figures into Venn diagrams based on the attributes of the figures. Construct viable arguments and critique the reasoning of others. Mathematically proficient students understand and use stated assumptions, definitions, and previously established results in constructing arguments. They make conjectures and build a logical progression of statements to explore the truth of their conjectures. They are able to analyze situations by breaking them into cases, and can recognize and use counterexamples. They justify their conclusions, communicate them to others, and respond to the arguments of others. They reason inductively about data, making plausible arguments that take into account the context from which the data arose. Mathematically proficient students are also able to compare the effectiveness of two plausible arguments, distinguish correct logic or reasoning from that which is flawed, and—if there is a flaw in an argument—explain what it is. Elementary students can construct arguments using concrete referents such as objects, drawings, diagrams, and actions. Such arguments can make sense and be correct, even though they are not generalized or made formal until later grades. Later, students learn to determine domains to which an argument applies. Students at all grades can listen or read the arguments of others, decide whether they make sense, and ask useful questions to clarify or improve the arguments. Construct arguments about geometric figures. Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles. Classify two- dimensional figures in a hierarchy based on properties. Construct viable arguments and critique the reasoning of others. Construct viable arguments and critique the reasoning of others. Classify two- dimensional figures in a hierarchy based on properties. Construct viable arguments and critique the reasoning of others. Describe and classify three-dimensional figures including cubes, prisms and pyramids by the number of edges, faces or vertices as well as the types of faces. Recognize and draw a net for a three-dimensional figure. 16-4: Enrichment Curriculum Standards: Understand that attributes belonging to a category of two- dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles. Classify two- dimensional figures in a hierarchy based on properties. Construct viable arguments and critique the reasoning of others. Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. Classify and organize two-dimensional figures into Venn diagrams based on the attributes of the figures. Construct viable arguments and critique the reasoning of others. Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles. Classify and organize two-dimensional figures into Venn diagrams based on the attributes of the figures. Construct viable arguments and critique the reasoning of others. Mathematically proficient students understand and use stated assumptions, definitions, and previously established results in constructing arguments. They make conjectures and build a logical progression of statements to explore the truth of their conjectures. They are able to analyze situations by breaking them into cases, and can recognize and use counterexamples. They justify their conclusions, communicate them to others, and respond to the arguments of others. They reason inductively about data, making plausible arguments that take into account the context from which the data arose. Mathematically proficient students are also able to compare the effectiveness of two plausible arguments, distinguish correct logic or reasoning from that which is flawed, and—if there is a flaw in an argument—explain what it is. Elementary students can construct arguments using concrete referents such as objects, drawings, diagrams, and actions. Such arguments can make sense and be correct, even though they are not generalized or made formal until later grades. Later, students learn to determine domains to which an argument applies. Students at all grades can listen or read the arguments of others, decide whether they make sense, and ask useful questions to clarify or improve the arguments. Construct arguments about geometric figures. Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles. Classify two- dimensional figures in a hierarchy based on properties. Construct viable arguments and critique the reasoning of others. Construct viable arguments and critique the reasoning of others. Classify two- dimensional figures in a hierarchy based on properties. Construct viable arguments and critique the reasoning of others. Describe and classify three-dimensional figures including cubes, prisms and pyramids by the number of edges, faces or vertices as well as the types of faces. Recognize and draw a net for a three-dimensional figure. 16-4: Quick Check Curriculum Standards: Understand that attributes belonging to a category of two- dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles. Classify two- dimensional figures in a hierarchy based on properties. Construct viable arguments and critique the reasoning of others. Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. Classify and organize two-dimensional figures into Venn diagrams based on the attributes of the figures. Construct viable arguments and critique the reasoning of others. Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles. Classify and organize two-dimensional figures into Venn diagrams based on the attributes of the figures. Construct viable arguments and critique the reasoning of others. Mathematically proficient students understand and use stated assumptions, definitions, and previously established results in constructing arguments. They make conjectures and build a logical progression of statements to explore the truth of their conjectures. They are able to analyze situations by breaking them into cases, and can recognize and use counterexamples. They justify their conclusions, communicate them to others, and respond to the arguments of others. They reason inductively about data, making plausible arguments that take into account the context from which the data arose. Mathematically proficient students are also able to compare the effectiveness of two plausible arguments, distinguish correct logic or reasoning from that which is flawed, and—if there is a flaw in an argument—explain what it is. Elementary students can construct arguments using concrete referents such as objects, drawings, diagrams, and actions. Such arguments can make sense and be correct, even though they are not generalized or made formal until later grades. Later, students learn to determine domains to which an argument applies. Students at all grades can listen or read the arguments of others, decide whether they make sense, and ask useful questions to clarify or improve the arguments. Construct arguments about geometric figures. Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles. Classify two- dimensional figures in a hierarchy based on properties. Construct viable arguments and critique the reasoning of others. Construct viable arguments and critique the reasoning of others. Classify two- dimensional figures in a hierarchy based on properties. Construct viable arguments and critique the reasoning of others. Describe and classify three-dimensional figures including cubes, prisms and pyramids by the number of edges, faces or vertices as well as the types of faces. Recognize and draw a net for a three-dimensional figure. 16-4: Lesson Self-Assessment 16-4: Reteach to Build Understanding Curriculum Standards: Understand that attributes belonging to a category of two- dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles. Classify two- dimensional figures in a hierarchy based on properties. Construct viable arguments and critique the reasoning of others. Recognize properties of simple plane figures using polygon-shaped manipulatives. Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. Classify and organize two-dimensional figures into Venn diagrams based on the attributes of the figures. Construct viable arguments and critique the reasoning of others. Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles. Classify and organize two-dimensional figures into Venn diagrams based on the attributes of the figures. Construct viable arguments and critique the reasoning of others. Mathematically proficient students understand and use stated assumptions, definitions, and previously established results in constructing arguments. They make conjectures and build a logical progression of statements to explore the truth of their conjectures. They are able to analyze situations by breaking them into cases, and can recognize and use counterexamples. They justify their conclusions, communicate them to others, and respond to the arguments of others. They reason inductively about data, making plausible arguments that take into account the context from which the data arose. Mathematically proficient students are also able to compare the effectiveness of two plausible arguments, distinguish correct logic or reasoning from that which is flawed, and—if there is a flaw in an argument—explain what it is. Elementary students can construct arguments using concrete referents such as objects, drawings, diagrams, and actions. Such arguments can make sense and be correct, even though they are not generalized or made formal until later grades. Later, students learn to determine domains to which an argument applies. Students at all grades can listen or read the arguments of others, decide whether they make sense, and ask useful questions to clarify or improve the arguments. Construct arguments about geometric figures. Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles. Classify two- dimensional figures in a hierarchy based on properties. Construct viable arguments and critique the reasoning of others. Construct viable arguments and critique the reasoning of others. Classify two- dimensional figures in a hierarchy based on properties. Construct viable arguments and critique the reasoning of others. Describe and classify three-dimensional figures including cubes, prisms and pyramids by the number of edges, faces or vertices as well as the types of faces. Recognize and draw a net for a three-dimensional figure. 16-4: Build Mathematical Literacy Curriculum Standards: Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 5 topics and texts, building on others’ ideas and expressing their own clearly. (a) Come to discussions prepared, having read or studied required material; explicitly draw on that preparation and other information known about the topic to explore ideas under discussion. (b) Follow agreed-upon rules for discussions and carry out assigned roles. (c) Pose and respond to specific questions by making comments that contribute to the discussion and elaborate on the remarks of others. (d) Review the key ideas expressed and draw conclusions in light of information and knowledge gained from the discussions. English language learners communicate for social and instructional purposes within the school setting. Summarize a written text read aloud or information presented in diverse media and formats, including visually, quantitatively, and orally. Summarize the points a speaker makes and explain how each claim is supported by reasons and evidence. Write informative/explanatory texts to examine a topic and convey ideas and information clearly. (a) Introduce a topic clearly, provide a general observation and focus, and group related information logically; include formatting (e.g., headings), illustrations, and multimedia when useful to aiding comprehension. (b) Develop the topic with facts, definitions, concrete details, quotations, or other information and examples related to the topic. (c) Link ideas within and across categories of information using words, phrases, and clauses (e.g., in contrast, especially). (d) Use precise language and domain-specific vocabulary to inform about or explain the topic. (e) Provide a concluding statement or section related to the information or explanation presented. English language learners communicate information, ideas and concepts necessary for academic success in the content area of Mathematics. 16-4: Enrichment Game: Save the Word: Grade 5 Topics 1-16 16-4: enVision STEM Activity Curriculum Standards: Understand that attributes belonging to a category of two- dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles. Classify two- dimensional figures in a hierarchy based on properties. Construct viable arguments and critique the reasoning of others. Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. Classify and organize two-dimensional figures into Venn diagrams based on the attributes of the figures. Construct viable arguments and critique the reasoning of others. Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles. Classify and organize two-dimensional figures into Venn diagrams based on the attributes of the figures. Construct viable arguments and critique the reasoning of others. Mathematically proficient students understand and use stated assumptions, definitions, and previously established results in constructing arguments. They make conjectures and build a logical progression of statements to explore the truth of their conjectures. They are able to analyze situations by breaking them into cases, and can recognize and use counterexamples. They justify their conclusions, communicate them to others, and respond to the arguments of others. They reason inductively about data, making plausible arguments that take into account the context from which the data arose. Mathematically proficient students are also able to compare the effectiveness of two plausible arguments, distinguish correct logic or reasoning from that which is flawed, and—if there is a flaw in an argument—explain what it is. Elementary students can construct arguments using concrete referents such as objects, drawings, diagrams, and actions. Such arguments can make sense and be correct, even though they are not generalized or made formal until later grades. Later, students learn to determine domains to which an argument applies. Students at all grades can listen or read the arguments of others, decide whether they make sense, and ask useful questions to clarify or improve the arguments. Construct arguments about geometric figures. Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles. Classify two- dimensional figures in a hierarchy based on properties. Construct viable arguments and critique the reasoning of others. Construct viable arguments and critique the reasoning of others. Classify two- dimensional figures in a hierarchy based on properties. Construct viable arguments and critique the reasoning of others. Describe and classify three-dimensional figures including cubes, prisms and pyramids by the number of edges, faces or vertices as well as the types of faces. Recognize and draw a net for a three-dimensional figure. 16-4: Another Look Curriculum Standards: Understand that attributes belonging to a category of two- dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles. Classify two- dimensional figures in a hierarchy based on properties. Construct viable arguments and critique the reasoning of others. Recognize properties of simple plane figures using polygon-shaped manipulatives. Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. Classify and organize two-dimensional figures into Venn diagrams based on the attributes of the figures. Construct viable arguments and critique the reasoning of others. Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles. Classify and organize two-dimensional figures into Venn diagrams based on the attributes of the figures. Construct viable arguments and critique the reasoning of others. Mathematically proficient students understand and use stated assumptions, definitions, and previously established results in constructing arguments. They make conjectures and build a logical progression of statements to explore the truth of their conjectures. They are able to analyze situations by breaking them into cases, and can recognize and use counterexamples. They justify their conclusions, communicate them to others, and respond to the arguments of others. They reason inductively about data, making plausible arguments that take into account the context from which the data arose. Mathematically proficient students are also able to compare the effectiveness of two plausible arguments, distinguish correct logic or reasoning from that which is flawed, and—if there is a flaw in an argument—explain what it is. Elementary students can construct arguments using concrete referents such as objects, drawings, diagrams, and actions. Such arguments can make sense and be correct, even though they are not generalized or made formal until later grades. Later, students learn to determine domains to which an argument applies. Students at all grades can listen or read the arguments of others, decide whether they make sense, and ask useful questions to clarify or improve the arguments. Construct arguments about geometric figures. Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles. Classify two- dimensional figures in a hierarchy based on properties. Construct viable arguments and critique the reasoning of others. Construct viable arguments and critique the reasoning of others. Classify two- dimensional figures in a hierarchy based on properties. Construct viable arguments and critique the reasoning of others. Describe and classify three-dimensional figures including cubes, prisms and pyramids by the number of edges, faces or vertices as well as the types of faces. Recognize and draw a net for a three-dimensional figure. Spanish Resources 16-4: eText del Libro del estudiante 16-4: Repaso diario 16-4: Aprendizaje visual 16-4: Amigo de práctica: Práctica adicional 16-4: Práctica adicional interactiva 16-4: Refuerzo para mejorar la comprensión 16-4: Desarrollar la competencia matemática 16-4: Ampliación Topic 16: End of Topic Interactive Student Edition: End of Topic 16 Topic 16: Fluency Practice Activity Interactive Student Edition: Topic 16 Assessment Practice Interactive Student Edition: Topic 16 Performance Task Topic 16 Performance Task Topic 16 Assessment 16-4: Visual Learning Curriculum Standards: Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles. Classify two-dimensional figures in a hierarchy based on properties. Construct viable arguments and critique the reasoning of others. Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. Classify and organize two-dimensional figures into Venn diagrams based on the attributes of the figures. Construct viable arguments and critique the reasoning of others. Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles. Classify and organize two-dimensional figures into Venn diagrams based on the attributes of the figures. Construct viable arguments and critique the reasoning of others. Mathematically proficient students understand and use stated assumptions, definitions, and previously established results in constructing arguments. They make conjectures and build a logical progression of statements to explore the truth of their conjectures. They are able to analyze situations by breaking them into cases, and can recognize and use counterexamples. They justify their conclusions, communicate them to others, and respond to the arguments of others. They reason inductively about data, making plausible arguments that take into account the context from which the data arose. Mathematically proficient students are also able to compare the effectiveness of two plausible arguments, distinguish correct logic or reasoning from that which is flawed, and—if there is a flaw in an argument—explain what it is. Elementary students can construct arguments using concrete referents such as objects, drawings, diagrams, and actions. Such arguments can make sense and be correct, even though they are not generalized or made formal until later grades. Later, students learn to determine domains to which an argument applies. Students at all grades can listen or read the arguments of others, decide whether they make sense, and ask useful questions to clarify or improve the arguments. Construct arguments about geometric figures. Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles. Classify two- dimensional figures in a hierarchy based on properties. Construct viable arguments and critique the reasoning of others. Construct viable arguments and critique the reasoning of others. Classify two- dimensional figures in a hierarchy based on properties. Construct viable arguments and critique the reasoning of others. Describe and classify three-dimensional figures including cubes, prisms and pyramids by the number of edges, faces or vertices as well as the types of faces. Recognize and draw a net for a three-dimensional figure. 13-1: Center Games 16-1: Visual Learning Curriculum Standards: Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles. Classify two-dimensional figures in a hierarchy based on properties. Understand that attributes belonging to a category of two- dimensional figures also belong to all subcategories of that category. Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles. Classify triangles by their angles and sides. Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles. Classify two- dimensional figures in a hierarchy based on properties. Classify two-dimensional figures in a hierarchy based on properties. Describe and classify three-dimensional figures including cubes, prisms and pyramids by the number of edges, faces or vertices as well as the types of faces. Recognize and draw a net for a three-dimensional figure. 16-2: Visual Learning Curriculum Standards: Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles. Classify two-dimensional figures in a hierarchy based on properties. Understand that attributes belonging to a category of two- dimensional figures also belong to all subcategories of that category. Classify and organize two- dimensional figures into Venn diagrams based on the attributes of the figures. Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles. Classify and organize two-dimensional figures into Venn diagrams based on the attributes of the figures. Classify quadrilaterals by their properties. Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles. Classify two-dimensional figures in a hierarchy based on properties. Classify two-dimensional figures in a hierarchy based on properties. Describe and classify three-dimensional figures including cubes, prisms and pyramids by the number of edges, faces or vertices as well as the types of faces. Recognize and draw a net for a three-dimensional figure. 16-3: Visual Learning Curriculum Standards: Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles. Classify two-dimensional figures in a hierarchy based on properties. Understand that attributes belonging to a category of two- dimensional figures also belong to all subcategories of that category. Classify and organize two- dimensional figures into Venn diagrams based on the attributes of the figures. Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles. Classify and organize two-dimensional figures into Venn diagrams based on the attributes of the figures. Classify quadrilaterals using a hierarchy. Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles. Classify two-dimensional figures in a hierarchy based on properties. Classify two-dimensional figures in a hierarchy based on properties. Describe and classify three-dimensional figures including cubes, prisms and pyramids by the number of edges, faces or vertices as well as the types of faces. Recognize and draw a net for a three-dimensional figure. Topic 16 Online Assessment Curriculum Standards: Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles. Classify two-dimensional figures in a hierarchy based on properties. Construct viable arguments and critique the reasoning of others. Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. Classify and organize two-dimensional figures into Venn diagrams based on the attributes of the figures. Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles. Classify and organize two- dimensional figures into Venn diagrams based on the attributes of the figures. Classify quadrilaterals by their properties. Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles. Classify two-dimensional figures in a hierarchy based on properties. Classify two-dimensional figures in a hierarchy based on properties. Describe and classify three-dimensional figures including cubes, prisms and pyramids by the number of edges, faces or vertices as well as the types of faces. Recognize and draw a net for a three-dimensional figure. Classify triangles by their angles and sides. Construct viable arguments and critique the reasoning of others. Construct viable arguments and critique the reasoning of others. Mathematically proficient students understand and use stated assumptions, definitions, and previously established results in constructing arguments. They make conjectures and build a logical progression of statements to explore the truth of their conjectures. They are able to analyze situations by breaking them into cases, and can recognize and use counterexamples. They justify their conclusions, communicate them to others, and respond to the arguments of others. They reason inductively about data, making plausible arguments that take into account the context from which the data arose. Mathematically proficient students are also able to compare the effectiveness of two plausible arguments, distinguish correct logic or reasoning from that which is flawed, and—if there is a flaw in an argument—explain what it is. Elementary students can construct arguments using concrete referents such as objects, drawings, diagrams, and actions. Such arguments can make sense and be correct, even though they are not generalized or made formal until later grades. Later, students learn to determine domains to which an argument applies. Students at all grades can listen or read the arguments of others, decide whether they make sense, and ask useful questions to clarify or improve the arguments. Construct arguments about geometric figures. Construct viable arguments and critique the reasoning of others. Construct viable arguments and critique the reasoning of others. Construct viable arguments and critique the reasoning of others. Classify quadrilaterals using a hierarchy. Topic 16 Spanish Assessments Tema 16: Tarea de rendimento Tema 16: Evaluación Topics 1–16: Cumulative/Benchmark Assessments Topics 1–16: Cumulative/Benchmark Assessment 3-5: Another Look Curriculum Standards: Fluently multiply multi-digit whole numbers using the standard algorithm. Fluently multiply multi-digit whole numbers using the standard algorithm. Fluently multiply multi-digit whole numbers using the standard algorithm. Multiply 3-digit by 2-digit numbers by adding partial products or by using the standard algorithm. Fluently multiply multi-digit whole numbers using the standard algorithm. Multiply multi-digit whole numbers (not to exceed three-digit by three-digit). Estimate solutions to arithmetic problems in order to assess the reasonableness of results. Solve real- world and mathematical problems requiring addition, subtraction, multiplication and division of multi- digit whole numbers. Use various strategies, including the inverse relationships between operations, the use of technology, and the context of the problem to assess the reasonableness of results. 8-9: Another Look Curriculum Standards: Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Make sense of problems and persevere in solving them. Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Make sense of problems and persevere in solving them. Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Make sense of problems and persevere in solving them. Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution. They analyze givens, constraints, relationships, and goals. They make conjectures about the form and meaning of the solution and plan a solution pathway rather than simply jumping into a solution attempt. They consider analogous problems, and try special cases and simpler forms of the original problem in order to gain insight into its solution. They monitor and evaluate their progress and change course if necessary. Older students might, depending on the context of the problem, transform algebraic expressions or change the viewing window on their graphing calculator to get the information they need. Mathematically proficient students can explain correspondences between equations, verbal descriptions, tables, and graphs or draw diagrams of important features and relationships, graph data, and search for regularity or trends. Younger students might rely on using concrete objects or pictures to help conceptualize and solve a problem. Mathematically proficient students check their answers to problems using a different method, and they continually ask themselves, “Does this make sense?” They can understand the approaches of others to solving complex problems and identify correspondences between different approaches. Use previously learned knowledge to make sense of problems and persevere in solving them. Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Make sense of problems and persevere in solving them. Make sense of problems and persevere in solving them. Make sense of problems and persevere in solving them. 3-8: Another Look Curriculum Standards: Fluently multiply multi-digit whole numbers using the standard algorithm. Fluently multiply multi-digit whole numbers using the standard algorithm. Fluently multiply multi-digit whole numbers using the standard algorithm. Use models and strategies to solve word problems. Fluently multiply multi-digit whole numbers using the standard algorithm. Multiply multi-digit whole numbers (not to exceed three-digit by three-digit). Estimate solutions to arithmetic problems in order to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition, subtraction, multiplication and division of multi-digit whole numbers. Use various strategies, including the inverse relationships between operations, the use of technology, and the context of the problem to assess the reasonableness of results. 10-1: Another Look Curriculum Standards: Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Make a line plot to display a data set of measurements in fractions of a unit (1/2 , 1/4 , 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally. Read and analyze line plots. Make a line plot to display a data set of measurements in fractions of a unit (1/2 , 1/4 , 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally. Solve problems involving computation of fractions by using information presented in line plots. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. 4-9: Another Look Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Model with mathematics. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Model with mathematics. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Model with mathematics. Mathematically proficient students can apply the mathematics they know to solve problems arising in everyday life, society, and the workplace. In early grades, this might be as simple as writing an addition equation to describe a situation. In middle grades, a student might apply proportional reasoning to plan a school event or analyze a problem in the community. By high school, a student might use geometry to solve a design problem or use a function to describe how one quantity of interest depends on another. Mathematically proficient students who can apply what they know are comfortable making assumptions and approximations to simplify a complicated situation, realizing that these may need revision later. They are able to identify important quantities in a practical situation and map their relationships using such tools as diagrams, two-way tables, graphs, flowcharts and formulas. They can analyze those relationships mathematically to draw conclusions. They routinely interpret their mathematical results in the context of the situation and reflect on whether the results make sense, possibly improving the model if it has not served its purpose. Use previously learned concepts and skills to represent and solve problems. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Model with mathematics. Model with mathematics. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). Model with mathematics. 11-4: Another Look Curriculum Standards: Recognize volume as additive. 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. Recognize volume as additive. 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. Recognize volume as additive. 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. Use models, prior knowledge of volume and previously learned strategies to solve word problems involving volume. Recognize volume as additive. 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. Find volumes of solid figures composed of two nonoverlapping right rectangular prisms. 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. Use various tools and strategies to measure the volume and surface area of objects that are shaped like rectangular prisms. Understand that the volume of a three dimensional figure can be found by counting the total number of same-sized cubic units that fill a shape without gaps or overlaps. Use cubic units to label volume measurements. Develop and use the formulas V = ?wh and V = Bh to determine the volume of rectangular prisms. Justify why base area B and height h are multiplied to find the volume of a ectangular prism by breaking the prism into layers of unit cubes. 13-2: Another Look Curriculum Standards: Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. For example, 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. Write a simple expression for a calculation. Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. For example, 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. Write simple expressions that show calculations with numbers. Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. For example, 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. Write simple expressions that model calculations with numbers and interpret numerical expressions without evaluating them. Apply the commutative, associative and distributive properties and order of operations to generate equivalent numerical expressions and to solve problems involving whole numbers. 6-12: Another Look 2-3: Another Look Curriculum Standards: Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Model sums and differences of decimals. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). Add and subtract decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Model addition and subtraction of fractions and decimals using a variety of representations. Estimate sums and differences of decimals and fractions to assess the reasonableness of results. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. 16-4: Another Look Curriculum Standards: Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles. Classify two-dimensional figures in a hierarchy based on properties. Construct viable arguments and critique the reasoning of others. Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. Classify and organize two-dimensional figures into Venn diagrams based on the attributes of the figures. Construct viable arguments and critique the reasoning of others. Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles. Classify and organize two-dimensional figures into Venn diagrams based on the attributes of the figures. Construct viable arguments and critique the reasoning of others. Mathematically proficient students understand and use stated assumptions, definitions, and previously established results in constructing arguments. They make conjectures and build a logical progression of statements to explore the truth of their conjectures. They are able to analyze situations by breaking them into cases, and can recognize and use counterexamples. They justify their conclusions, communicate them to others, and respond to the arguments of others. They reason inductively about data, making plausible arguments that take into account the context from which the data arose. Mathematically proficient students are also able to compare the effectiveness of two plausible arguments, distinguish correct logic or reasoning from that which is flawed, and—if there is a flaw in an argument—explain what it is. Elementary students can construct arguments using concrete referents such as objects, drawings, diagrams, and actions. Such arguments can make sense and be correct, even though they are not generalized or made formal until later grades. Later, students learn to determine domains to which an argument applies. Students at all grades can listen or read the arguments of others, decide whether they make sense, and ask useful questions to clarify or improve the arguments. Construct arguments about geometric figures. Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles. Classify two- dimensional figures in a hierarchy based on properties. Construct viable arguments and critique the reasoning of others. Construct viable arguments and critique the reasoning of others. Classify two- dimensional figures in a hierarchy based on properties. Construct viable arguments and critique the reasoning of others. Describe and classify three-dimensional figures including cubes, prisms and pyramids by the number of edges, faces or vertices as well as the types of faces. Recognize and draw a net for a three-dimensional figure. 16-3: Another Look Curriculum Standards: Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles. Classify two-dimensional figures in a hierarchy based on properties. Understand that attributes belonging to a category of two- dimensional figures also belong to all subcategories of that category. Classify and organize two- dimensional figures into Venn diagrams based on the attributes of the figures. Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles. Classify and organize two-dimensional figures into Venn diagrams based on the attributes of the figures. Classify quadrilaterals using a hierarchy. Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles. Classify two-dimensional figures in a hierarchy based on properties. Classify two-dimensional figures in a hierarchy based on properties. Describe and classify three-dimensional figures including cubes, prisms and pyramids by the number of edges, faces or vertices as well as the types of faces. Recognize and draw a net for a three-dimensional figure. 13-1: Another Look Curriculum Standards: Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. Use the order of operations to evaluate expressions. Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. Use multiple grouping symbols (parentheses, brackets, or braces) in numerical expressions and evaluate expressions containing these symbols. Apply the commutative, associative and distributive properties and order of operations to generate equivalent numerical expressions and to solve problems involving whole numbers. Evaluate a simple expression involving one set of parenthesis. 14-3: Another Look Curriculum Standards: Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. Solve real- world problems by graphing points. Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. Represent real-world and mathematical problems by plotting points in quadrant I of the coordinate plane and interpret coordinate values of points in the context of the situation. Create and use rules, tables, spreadsheets and graphs to describe patterns of change and solve problems. Use a rule or table to represent ordered pairs of positive integers and graph these ordered pairs on a coordinate system. 1-5: Another Look Curriculum Standards: Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and <, symbols to record the results of comparisons. Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. Use place value to compare decimals through thousandths. Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and <, symbols to record the results of comparisons. Compare two decimals to thousandths based on meanings of the digits in each place using >, =, and < symbols. Order fractions and decimals, including mixed numbers and improper fractions, and locate on a number line. 15-2: Another Look Curriculum Standards: 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. For example, 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. Given two pattern descriptions involving the same context (e.g., collecting marbles), determine the first five terms and compare the values. 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. 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. For example, 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. Use tables to identify relationships between patterns. 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. For example, 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. Identify apparent relationships between corresponding terms of two patterns with the same starting numbers that follow different rules. Create and use rules, tables, spreadsheets and graphs to describe patterns of change and solve problems. Use a rule or table to represent ordered pairs of positive integers and graph these ordered pairs on a coordinate system. 16-1: Another Look Curriculum Standards: Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles. Classify two-dimensional figures in a hierarchy based on properties. Understand that attributes belonging to a category of two- dimensional figures also belong to all subcategories of that category. Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles. Classify triangles by their angles and sides. Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles. Classify two- dimensional figures in a hierarchy based on properties. Classify two-dimensional figures in a hierarchy based on properties. Describe and classify three-dimensional figures including cubes, prisms and pyramids by the number of edges, faces or vertices as well as the types of faces. Recognize and draw a net for a three-dimensional figure. 14-2: Another Look Curriculum Standards: Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x- coordinate, y-axis and y-coordinate). Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y- coordinate). Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y-coordinate). Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. Graph points on a coordinate grid. Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. Identify parts of the coordinate plane (x-axis, y-axis, and the origin) and the ordered pair (x-coordinate and y- coordinate). Limit the coordinate plane to quadrant I. Create and use rules, tables, spreadsheets and graphs to describe patterns of change and solve problems. Use a rule or table to represent ordered pairs of positive integers and graph these ordered pairs on a coordinate system. 13-1: Center Games 14-4: Another Look Curriculum Standards: Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x- coordinate, y-axis and y-coordinate). Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. Reason abstractly and quantitatively. Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y-coordinate). Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. Reason abstractly and quantitatively. Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y-coordinate). Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. Reason abstractly and quantitatively. Mathematically proficient students make sense of quantities and their relationships in problem situations. They bring two complementary abilities to bear on problems involving quantitative relationships: the ability to decontextualize—to abstract a given situation and represent it symbolically and manipulate the representing symbols as if they have a life of their own, without necessarily attending to their referents—and the ability to contextualize, to pause as needed during the manipulation process in order to probe into the referents for the symbols involved. Quantitative reasoning entails habits of creating a coherent representation of the problem at hand; considering the units involved; attending to the meaning of quantities, not just how to compute them; and knowing and flexibly using different properties of operations and objects. Use reasoning to solve problems by making sense of quantities and relationships in the situation. Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. Reason abstractly and quantitatively. Reason abstractly and quantitatively. Represent real-world and mathematical problems by plotting points in quadrant I of the coordinate plane and interpret coordinate values of points in the context of the situation. Reason abstractly and quantitatively. Create and use rules, tables, spreadsheets and graphs to describe patterns of change and solve problems. Use a rule or table to represent ordered pairs of positive integers and graph these ordered pairs on a coordinate system. 7-4: Another Look Curriculum Standards: Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Subtract fractions with unlike denominators. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Add and subtract fractions (including mixed numbers) with unlike denominators. (May include multiple methods and representations.) Add and subtract decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Model addition and subtraction of fractions and decimals using a variety of representations. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. Topics 1–16: Online Cumulative/Benchmark Assessment Curriculum Standards: Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Make a line plot to display a data set of measurements in fractions of a unit (1/2 , 1/4 , 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally. Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles. Classify two-dimensional figures in a hierarchy based on properties. Construct viable arguments and critique the reasoning of others. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) 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. Model with mathematics. Recognize volume as additive. 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. Fluently multiply multi-digit whole numbers using the standard algorithm. Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y-coordinate). Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. Reason abstractly and quantitatively. Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. For example, 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. Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and <, symbols to record the results of comparisons. 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. For example, 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. Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Make sense of problems and persevere in solving them. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally. Read and analyze line plots. Make a line plot to display a data set of measurements in fractions of a unit (1/2 , 1/4 , 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally. Solve problems involving computation of fractions by using information presented in line plots. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles. Classify triangles by their angles and sides. Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles. Classify two-dimensional figures in a hierarchy based on properties. Classify two-dimensional figures in a hierarchy based on properties. Describe and classify three-dimensional figures including cubes, prisms and pyramids by the number of edges, faces or vertices as well as the types of faces. Recognize and draw a net for a three-dimensional figure. Classify and organize two-dimensional figures into Venn diagrams based on the attributes of the figures. Construct viable arguments and critique the reasoning of others. Classify and organize two-dimensional figures into Venn diagrams based on the attributes of the figures. Construct viable arguments and critique the reasoning of others. Mathematically proficient students understand and use stated assumptions, definitions, and previously established results in constructing arguments. They make conjectures and build a logical progression of statements to explore the truth of their conjectures. They are able to analyze situations by breaking them into cases, and can recognize and use counterexamples. They justify their conclusions, communicate them to others, and respond to the arguments of others. They reason inductively about data, making plausible arguments that take into account the context from which the data arose. Mathematically proficient students are also able to compare the effectiveness of two plausible arguments, distinguish correct logic or reasoning from that which is flawed, and—if there is a flaw in an argument—explain what it is. Elementary students can construct arguments using concrete referents such as objects, drawings, diagrams, and actions. Such arguments can make sense and be correct, even though they are not generalized or made formal until later grades. Later, students learn to determine domains to which an argument applies. Students at all grades can listen or read the arguments of others, decide whether they make sense, and ask useful questions to clarify or improve the arguments. Construct arguments about geometric figures. Construct viable arguments and critique the reasoning of others. Construct viable arguments and critique the reasoning of others. Construct viable arguments and critique the reasoning of others. Classify quadrilaterals using a hierarchy. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Subtract fractions with unlike denominators. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Add and subtract fractions (including mixed numbers) with unlike denominators. (May include multiple methods and representations.) Add and subtract decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Model addition and subtraction of fractions and decimals using a variety of representations. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Model with mathematics. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Model with mathematics. Mathematically proficient students can apply the mathematics they know to solve problems arising in everyday life, society, and the workplace. In early grades, this might be as simple as writing an addition equation to describe a situation. In middle grades, a student might apply proportional reasoning to plan a school event or analyze a problem in the community. By high school, a student might use geometry to solve a design problem or use a function to describe how one quantity of interest depends on another. Mathematically proficient students who can apply what they know are comfortable making assumptions and approximations to simplify a complicated situation, realizing that these may need revision later. They are able to identify important quantities in a practical situation and map their relationships using such tools as diagrams, two-way tables, graphs, flowcharts and formulas. They can analyze those relationships mathematically to draw conclusions. They routinely interpret their mathematical results in the context of the situation and reflect on whether the results make sense, possibly improving the model if it has not served its purpose. Use previously learned concepts and skills to represent and solve problems. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Model with mathematics. Model with mathematics. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). Model with mathematics. Recognize volume as additive. 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. Recognize volume as additive. 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. Use models, prior knowledge of volume and previously learned strategies to solve word problems involving volume. Recognize volume as additive. 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. Find volumes of solid figures composed of two nonoverlapping right rectangular prisms. 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. Use various tools and strategies to measure the volume and surface area of objects that are shaped like rectangular prisms. Understand that the volume of a three dimensional figure can be found by counting the total number of same-sized cubic units that fill a shape without gaps or overlaps. Use cubic units to label volume measurements. Develop and use the formulas V = ?wh and V = Bh to determine the volume of rectangular prisms. Justify why base area B and height h are multiplied to find the volume of a ectangular prism by breaking the prism into layers of unit cubes. Model sums and differences of decimals. Estimate sums and differences of decimals and fractions to assess the reasonableness of results. Fluently multiply multi-digit whole numbers using the standard algorithm. Fluently multiply multi-digit whole numbers using the standard algorithm. Use models and strategies to solve word problems. Fluently multiply multi-digit whole numbers using the standard algorithm. Multiply multi-digit whole numbers (not to exceed three-digit by three-digit). Estimate solutions to arithmetic problems in order to assess the reasonableness of results. Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y-coordinate). Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. Reason abstractly and quantitatively. Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y-coordinate). Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. Reason abstractly and quantitatively. Mathematically proficient students make sense of quantities and their relationships in problem situations. They bring two complementary abilities to bear on problems involving quantitative relationships: the ability to decontextualize—to abstract a given situation and represent it symbolically and manipulate the representing symbols as if they have a life of their own, without necessarily attending to their referents—and the ability to contextualize, to pause as needed during the manipulation process in order to probe into the referents for the symbols involved. Quantitative reasoning entails habits of creating a coherent representation of the problem at hand; considering the units involved; attending to the meaning of quantities, not just how to compute them; and knowing and flexibly using different properties of operations and objects. Use reasoning to solve problems by making sense of quantities and relationships in the situation. Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. Reason abstractly and quantitatively. Reason abstractly and quantitatively. Represent real-world and mathematical problems by plotting points in quadrant I of the coordinate plane and interpret coordinate values of points in the context of the situation. Reason abstractly and quantitatively. Create and use rules, tables, spreadsheets and graphs to describe patterns of change and solve problems. Use a rule or table to represent ordered pairs of positive integers and graph these ordered pairs on a coordinate system. Solve real-world problems by graphing points. Graph points on a coordinate grid. Identify parts of the coordinate plane (x-axis, y-axis, and the origin) and the ordered pair (x-coordinate and y-coordinate). Limit the coordinate plane to quadrant I. Multiply 3-digit by 2-digit numbers by adding partial products or by using the standard algorithm. Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. Use the order of operations to evaluate expressions. Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. Use multiple grouping symbols (parentheses, brackets, or braces) in numerical expressions and evaluate expressions containing these symbols. Apply the commutative, associative and distributive properties and order of operations to generate equivalent numerical expressions and to solve problems involving whole numbers. Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. For example, 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. Write simple expressions that show calculations with numbers. Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. For example, 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. Write simple expressions that model calculations with numbers and interpret numerical expressions without evaluating them. Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. Use place value to compare decimals through thousandths. Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and <, symbols to record the results of comparisons. Compare two decimals to thousandths based on meanings of the digits in each place using >, =, and < symbols. Order fractions and decimals, including mixed numbers and improper fractions, and locate on a number line. 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. 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. For example, 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. Use tables to identify relationships between patterns. 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. For example, 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. Identify apparent relationships between corresponding terms of two patterns with the same starting numbers that follow different rules. Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Make sense of problems and persevere in solving them. Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Make sense of problems and persevere in solving them. Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution. They analyze givens, constraints, relationships, and goals. They make conjectures about the form and meaning of the solution and plan a solution pathway rather than simply jumping into a solution attempt. They consider analogous problems, and try special cases and simpler forms of the original problem in order to gain insight into its solution. They monitor and evaluate their progress and change course if necessary. Older students might, depending on the context of the problem, transform algebraic expressions or change the viewing window on their graphing calculator to get the information they need. Mathematically proficient students can explain correspondences between equations, verbal descriptions, tables, and graphs or draw diagrams of important features and relationships, graph data, and search for regularity or trends. Younger students might rely on using concrete objects or pictures to help conceptualize and solve a problem. Mathematically proficient students check their answers to problems using a different method, and they continually ask themselves, “Does this make sense?” They can understand the approaches of others to solving complex problems and identify correspondences between different approaches. Use previously learned knowledge to make sense of problems and persevere in solving them. Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Make sense of problems and persevere in solving them. Make sense of problems and persevere in solving them. Make sense of problems and persevere in solving them. Grade 5 Progress Monitoring Assessments Grade 5 Progress Monitoring Assessment: Form A Grade 5 Online Progress Monitoring Assessment: Form A Curriculum Standards: Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Understand that attributes belonging to a category of two- dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles. Classify two- dimensional figures in a hierarchy based on properties. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Model with mathematics. Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units. 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. 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. A cube with side length 1 unit, called a "unit cube," is said to have "one cubic unit" of volume, and can be used to measure volume. A solid figure that can be packed without gaps or overlaps using n unit cubes is said to have a volume of n cubic units. Recognize volume as additive. 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. Interpret the product a/b x q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = (ac)/(bd). Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 x 100 + 4 x 10 + 7 x 1 + 3 x (1/10) + 9 x (1/100) + 2 x (1/1000). Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. For example, 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. Use place value understanding to round decimals to any place. 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. For example, 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. Make sense of problems and persevere in solving them. 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. Make a line plot to display a data set of measurements in fractions of a unit (1/2 , 1/4 , 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. For example, create a story context for (1/3) ÷ 4, and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that (1/3) ÷ 4 = 1/12 because (1/12) × 4 = 1/3. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 1/3- cup servings are in 2 cups of raisins? Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y- coordinate). Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for 4 ÷ (1/5), and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 × (1/5) = 4. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Use knowledge about place value and patterns to find the product of a decimal number and a power of 10. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10 and 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. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). Understand that attributes belonging to a category of two- dimensional figures also belong to all subcategories of that category. Classify and organize two- dimensional figures into Venn diagrams based on the attributes of the figures. Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles. Classify and organize two-dimensional figures into Venn diagrams based on the attributes of the figures. Classify quadrilaterals by their properties. Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles. Classify two-dimensional figures in a hierarchy based on properties. Classify two-dimensional figures in a hierarchy based on properties. Describe and classify three-dimensional figures including cubes, prisms and pyramids by the number of edges, faces or vertices as well as the types of faces. Recognize and draw a net for a three-dimensional figure. Classify quadrilaterals using a hierarchy. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. Model with mathematics. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Model with mathematics. Mathematically proficient students can apply the mathematics they know to solve problems arising in everyday life, society, and the workplace. In early grades, this might be as simple as writing an addition equation to describe a situation. In middle grades, a student might apply proportional reasoning to plan a school event or analyze a problem in the community. By high school, a student might use geometry to solve a design problem or use a function to describe how one quantity of interest depends on another. Mathematically proficient students who can apply what they know are comfortable making assumptions and approximations to simplify a complicated situation, realizing that these may need revision later. They are able to identify important quantities in a practical situation and map their relationships using such tools as diagrams, two-way tables, graphs, flowcharts and formulas. They can analyze those relationships mathematically to draw conclusions. They routinely interpret their mathematical results in the context of the situation and reflect on whether the results make sense, possibly improving the model if it has not served its purpose. Represent a problem situation with a mathematical model. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Model with mathematics. Model with mathematics. Add and subtract fractions (including mixed numbers) with unlike denominators. (May include multiple methods and representations.) Model with mathematics. Add and subtract decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Model addition and subtraction of fractions and decimals using a variety of representations. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. Use number sense and reasoning to place the decimal point in a product. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. 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. 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. 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. 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. Find the volume of rectangular prisms using a formula. Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units. 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. 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. 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. Formulas will be provided. 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. Apply the commutative, associative and distributive properties and order of operations to generate equivalent numerical expressions and to solve problems involving whole numbers. Use various tools and strategies to measure the volume and surface area of objects that are shaped like rectangular prisms. Understand that the volume of a three dimensional figure can be found by counting the total number of same-sized cubic units that fill a shape without gaps or overlaps. Use cubic units to label volume measurements. Develop and use the formulas V = ?wh and V = Bh to determine the volume of rectangular prisms. Justify why base area B and height h are multiplied to find the volume of a ectangular prism by breaking the prism into layers of unit cubes. A cube with side length 1 unit, called a “unit cube,” is said to have “one cubic unit” of volume, and can be used to measure volume. A solid figure which can be packed without gaps or overlaps using n unit cubes is said to have a volume of n cubic units. Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units. A cube with side length 1 unit, called a “unit cube,” is said to have “one cubic unit” of volume, and can be used to measure volume. A solid figure which can be packed without gaps or overlaps using n unit cubes is said to have a volume of n cubic units. Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units. Find the volume of solid figures. A cube with side length 1 unit, called a unit cube, is said to have one cubic unit of volume, and can be used to measure volume. A solid figure that can be packed without gaps or overlaps using n unit cubes is said to have a volume of n cubic units. Recognize volume as additive. 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. Recognize volume as additive. 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. Use models, prior knowledge of volume and previously learned strategies to solve word problems involving volume. Recognize volume as additive. 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. Find volumes of solid figures composed of two nonoverlapping right rectangular prisms. Find the volume of a solid figure that is the combination of two or more rectangular prisms. Interpret the product (a/b) × q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. Interpret the product (a/b) × q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = ac/bd.) Use models to multiply two fractions. Interpret the product a/b x q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = (ac)/(bd). Multiply a fraction (including mixed numbers) by a fraction. Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 × 100 + 4 × 10 + 7 × 1 + 3 × (1/10) + 9 × (1/100) + 2 × (1/1000). Read and write decimals to thousandths using base- ten numerals, number names, and expanded form, e.g., 347.392 = 3 × 100 + 4 × 10 + 7 × 1 + 3 × (1/10) + 9 × (1/100) + 2 × (1/1000). Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 × 100 + 4 × 10 + 7 × 1 + 3 × (1/10) + 9 × (1/100) + 2 × (1/1000). Read and write numbers with decimals through thousandths using standard form, expanded form, and number names; identify equivalent decimals. Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 x 100 + 4 x 10 + 7 x 1 + 3 x (1/10) + 9 x (1/100) + 2 x (1/1000). Read and write decimals to thousandths using base-ten numerals, word form, and expanded form. Read and write decimals using place value to describe decimals in terms of groups from millionths to millions. Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Multiply a whole number by a fraction. Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. Use the order of operations to evaluate expressions. Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. Use multiple grouping symbols (parentheses, brackets, or braces) in numerical expressions and evaluate expressions containing these symbols. Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. For example, 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. Write simple expressions that show calculations with numbers. Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. For example, 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. Write simple expressions that model calculations with numbers and interpret numerical expressions without evaluating them. Use place value understanding to round decimals to any place. Use place value understanding to round decimals to any place. Use place value to round decimals to different places. Use place value understanding to round decimals to any place. Round decimals to any place (limit rounding to ones, tenths, hundredths, or thousandths place). Round numbers to the nearest 0.1, 0.01 and 0.001. 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. 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. For example, 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. Analyze numerical relationships. 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. For example, 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. Generate two numerical patterns using two given rules. Create and use rules, tables, spreadsheets and graphs to describe patterns of change and solve problems. Use a rule or table to represent ordered pairs of positive integers and graph these ordered pairs on a coordinate system. Use models, equations and previously learned strategies to multiply mixed numbers. Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Make sense of problems and persevere in solving them. Make sense of problems and persevere in solving them. Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution. They analyze givens, constraints, relationships, and goals. They make conjectures about the form and meaning of the solution and plan a solution pathway rather than simply jumping into a solution attempt. They consider analogous problems, and try special cases and simpler forms of the original problem in order to gain insight into its solution. They monitor and evaluate their progress and change course if necessary. Older students might, depending on the context of the problem, transform algebraic expressions or change the viewing window on their graphing calculator to get the information they need. Mathematically proficient students can explain correspondences between equations, verbal descriptions, tables, and graphs or draw diagrams of important features and relationships, graph data, and search for regularity or trends. Younger students might rely on using concrete objects or pictures to help conceptualize and solve a problem. Mathematically proficient students check their answers to problems using a different method, and they continually ask themselves, “Does this make sense?” They can understand the approaches of others to solving complex problems and identify correspondences between different approaches. Use previously learned knowledge to make sense of problems and persevere in solving them. Make sense of problems and persevere in solving them. Make sense of problems and persevere in solving them. Make sense of problems and persevere in solving them. 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. 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. Use compatible numbers and place-value patterns to estimate quotients. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors. Divide multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Recognize that quotients can be represented in a variety of ways, including a whole number with a remainder, a fraction or mixed number, or a decimal. Estimate solutions to arithmetic problems in order to assess the reasonableness of results. Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally. Read and analyze line plots. Make a line plot to display a data set of measurements in fractions of a unit (1/2 , 1/4 , 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally. Solve problems involving computation of fractions by using information presented in line plots. Solve division problems using partial quotients. Convert among different-sized standard measurement units (i.e., km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec) within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Convert among different-sized standard measurement units (i.e., km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec) within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi- step, real world problems. Convert metric units of capacity. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Convert between different-sized measurement units within a given measurement system. A table of equivalencies will be provided. 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. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Add fractions with unlike denominators using equivalent fractions with a common denominator. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Make sense of problems and keep working. Construct viable arguments and critique the reasoning of others. Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. For example, create a story context for (1/3) ÷ 4, and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that (1/3) ÷ 4 = 1/12 because (1/12) × 4 = 1/3. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins? Use models to divide unit fractions by non-zero whole numbers. Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. For example, create a story context for (1/3) ÷ 4, and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that (1/3) ÷ 4 = 1/12 because (1/12) × 4 = 1/3. Divide unit fractions by whole numbers and whole numbers by unit fractions. Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. Solve real- world problems by graphing points. Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. Represent real-world and mathematical problems by plotting points in quadrant I of the coordinate plane and interpret coordinate values of points in the context of the situation. Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y-coordinate). Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y-coordinate). Locate points on a coordinate grid. Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y- coordinate). Identify parts of the coordinate plane (x-axis, y-axis, and the origin) and the ordered pair (x- coordinate and y-coordinate). Limit the coordinate plane to quadrant I. Interpret division of a whole number by a unit fraction, and compute such quotients. Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for 4 ÷ (1/5), and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 × (1/5) = 4. Use models, such as pictorial models or a number line, to show dividing a whole number by a unit fraction. Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for 4 ÷ (1/5), and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 × (1/5) = 4. Grade 5 Progress Monitoring Assessment: Form B Grade 5 Online Progress Monitoring Assessment Form B Curriculum Standards: Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Understand that attributes belonging to a category of two- dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles. Classify two- dimensional figures in a hierarchy based on properties. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Model with mathematics. Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units. 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. 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. A cube with side length 1 unit, called a "unit cube," is said to have "one cubic unit" of volume, and can be used to measure volume. A solid figure that can be packed without gaps or overlaps using n unit cubes is said to have a volume of n cubic units. Recognize volume as additive. 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. Interpret the product a/b x q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = (ac)/(bd). Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 x 100 + 4 x 10 + 7 x 1 + 3 x (1/10) + 9 x (1/100) + 2 x (1/1000). Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. For example, 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. Use place value understanding to round decimals to any place. 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. For example, 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. Make sense of problems and persevere in solving them. 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. Make a line plot to display a data set of measurements in fractions of a unit (1/2 , 1/4 , 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. For example, create a story context for (1/3) ÷ 4, and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that (1/3) ÷ 4 = 1/12 because (1/12) × 4 = 1/3. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 1/3- cup servings are in 2 cups of raisins? Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y- coordinate). Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for 4 ÷ (1/5), and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 × (1/5) = 4. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Use knowledge about place value and patterns to find the product of a decimal number and a power of 10. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10 and 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. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). Understand that attributes belonging to a category of two- dimensional figures also belong to all subcategories of that category. Classify and organize two- dimensional figures into Venn diagrams based on the attributes of the figures. Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles. Classify and organize two-dimensional figures into Venn diagrams based on the attributes of the figures. Classify quadrilaterals by their properties. Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles. Classify two-dimensional figures in a hierarchy based on properties. Classify two-dimensional figures in a hierarchy based on properties. Describe and classify three-dimensional figures including cubes, prisms and pyramids by the number of edges, faces or vertices as well as the types of faces. Recognize and draw a net for a three-dimensional figure. Classify quadrilaterals using a hierarchy. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. Model with mathematics. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Model with mathematics. Mathematically proficient students can apply the mathematics they know to solve problems arising in everyday life, society, and the workplace. In early grades, this might be as simple as writing an addition equation to describe a situation. In middle grades, a student might apply proportional reasoning to plan a school event or analyze a problem in the community. By high school, a student might use geometry to solve a design problem or use a function to describe how one quantity of interest depends on another. Mathematically proficient students who can apply what they know are comfortable making assumptions and approximations to simplify a complicated situation, realizing that these may need revision later. They are able to identify important quantities in a practical situation and map their relationships using such tools as diagrams, two-way tables, graphs, flowcharts and formulas. They can analyze those relationships mathematically to draw conclusions. They routinely interpret their mathematical results in the context of the situation and reflect on whether the results make sense, possibly improving the model if it has not served its purpose. Represent a problem situation with a mathematical model. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Model with mathematics. Model with mathematics. Add and subtract fractions (including mixed numbers) with unlike denominators. (May include multiple methods and representations.) Model with mathematics. Add and subtract decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Model addition and subtraction of fractions and decimals using a variety of representations. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. Use number sense and reasoning to place the decimal point in a product. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. 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. 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. 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. 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. Find the volume of rectangular prisms using a formula. Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units. 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. 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. 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. Formulas will be provided. 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. Apply the commutative, associative and distributive properties and order of operations to generate equivalent numerical expressions and to solve problems involving whole numbers. Use various tools and strategies to measure the volume and surface area of objects that are shaped like rectangular prisms. Understand that the volume of a three dimensional figure can be found by counting the total number of same-sized cubic units that fill a shape without gaps or overlaps. Use cubic units to label volume measurements. Develop and use the formulas V = ?wh and V = Bh to determine the volume of rectangular prisms. Justify why base area B and height h are multiplied to find the volume of a ectangular prism by breaking the prism into layers of unit cubes. A cube with side length 1 unit, called a “unit cube,” is said to have “one cubic unit” of volume, and can be used to measure volume. A solid figure which can be packed without gaps or overlaps using n unit cubes is said to have a volume of n cubic units. Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units. A cube with side length 1 unit, called a “unit cube,” is said to have “one cubic unit” of volume, and can be used to measure volume. A solid figure which can be packed without gaps or overlaps using n unit cubes is said to have a volume of n cubic units. Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units. Find the volume of solid figures. A cube with side length 1 unit, called a unit cube, is said to have one cubic unit of volume, and can be used to measure volume. A solid figure that can be packed without gaps or overlaps using n unit cubes is said to have a volume of n cubic units. Recognize volume as additive. 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. Recognize volume as additive. 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. Use models, prior knowledge of volume and previously learned strategies to solve word problems involving volume. Recognize volume as additive. 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. Find volumes of solid figures composed of two nonoverlapping right rectangular prisms. Find the volume of a solid figure that is the combination of two or more rectangular prisms. Interpret the product (a/b) × q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. Interpret the product (a/b) × q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = ac/bd.) Use models to multiply two fractions. Interpret the product a/b x q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = (ac)/(bd). Multiply a fraction (including mixed numbers) by a fraction. Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 × 100 + 4 × 10 + 7 × 1 + 3 × (1/10) + 9 × (1/100) + 2 × (1/1000). Read and write decimals to thousandths using base- ten numerals, number names, and expanded form, e.g., 347.392 = 3 × 100 + 4 × 10 + 7 × 1 + 3 × (1/10) + 9 × (1/100) + 2 × (1/1000). Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 × 100 + 4 × 10 + 7 × 1 + 3 × (1/10) + 9 × (1/100) + 2 × (1/1000). Read and write numbers with decimals through thousandths using standard form, expanded form, and number names; identify equivalent decimals. Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 x 100 + 4 x 10 + 7 x 1 + 3 x (1/10) + 9 x (1/100) + 2 x (1/1000). Read and write decimals to thousandths using base-ten numerals, word form, and expanded form. Read and write decimals using place value to describe decimals in terms of groups from millionths to millions. Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Multiply a whole number by a fraction. Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. Use the order of operations to evaluate expressions. Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. Use multiple grouping symbols (parentheses, brackets, or braces) in numerical expressions and evaluate expressions containing these symbols. Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. For example, 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. Write simple expressions that show calculations with numbers. Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. For example, 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. Write simple expressions that model calculations with numbers and interpret numerical expressions without evaluating them. Use place value understanding to round decimals to any place. Use place value understanding to round decimals to any place. Use place value to round decimals to different places. Use place value understanding to round decimals to any place. Round decimals to any place (limit rounding to ones, tenths, hundredths, or thousandths place). Round numbers to the nearest 0.1, 0.01 and 0.001. 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. 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. For example, 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. Analyze numerical relationships. 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. For example, 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. Generate two numerical patterns using two given rules. Create and use rules, tables, spreadsheets and graphs to describe patterns of change and solve problems. Use a rule or table to represent ordered pairs of positive integers and graph these ordered pairs on a coordinate system. Use models, equations and previously learned strategies to multiply mixed numbers. Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Make sense of problems and persevere in solving them. Make sense of problems and persevere in solving them. Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution. They analyze givens, constraints, relationships, and goals. They make conjectures about the form and meaning of the solution and plan a solution pathway rather than simply jumping into a solution attempt. They consider analogous problems, and try special cases and simpler forms of the original problem in order to gain insight into its solution. They monitor and evaluate their progress and change course if necessary. Older students might, depending on the context of the problem, transform algebraic expressions or change the viewing window on their graphing calculator to get the information they need. Mathematically proficient students can explain correspondences between equations, verbal descriptions, tables, and graphs or draw diagrams of important features and relationships, graph data, and search for regularity or trends. Younger students might rely on using concrete objects or pictures to help conceptualize and solve a problem. Mathematically proficient students check their answers to problems using a different method, and they continually ask themselves, “Does this make sense?” They can understand the approaches of others to solving complex problems and identify correspondences between different approaches. Use previously learned knowledge to make sense of problems and persevere in solving them. Make sense of problems and persevere in solving them. Make sense of problems and persevere in solving them. Make sense of problems and persevere in solving them. 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. 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. Use compatible numbers and place-value patterns to estimate quotients. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors. Divide multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Recognize that quotients can be represented in a variety of ways, including a whole number with a remainder, a fraction or mixed number, or a decimal. Estimate solutions to arithmetic problems in order to assess the reasonableness of results. Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally. Read and analyze line plots. Make a line plot to display a data set of measurements in fractions of a unit (1/2 , 1/4 , 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally. Solve problems involving computation of fractions by using information presented in line plots. Solve division problems using partial quotients. Convert among different-sized standard measurement units (i.e., km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec) within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Convert among different-sized standard measurement units (i.e., km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec) within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi- step, real world problems. Convert metric units of capacity. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Convert between different-sized measurement units within a given measurement system. A table of equivalencies will be provided. 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. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Add fractions with unlike denominators using equivalent fractions with a common denominator. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Make sense of problems and keep working. Construct viable arguments and critique the reasoning of others. Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. For example, create a story context for (1/3) ÷ 4, and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that (1/3) ÷ 4 = 1/12 because (1/12) × 4 = 1/3. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins? Use models to divide unit fractions by non-zero whole numbers. Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. For example, create a story context for (1/3) ÷ 4, and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that (1/3) ÷ 4 = 1/12 because (1/12) × 4 = 1/3. Divide unit fractions by whole numbers and whole numbers by unit fractions. Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. Solve real- world problems by graphing points. Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. Represent real-world and mathematical problems by plotting points in quadrant I of the coordinate plane and interpret coordinate values of points in the context of the situation. Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y-coordinate). Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y-coordinate). Locate points on a coordinate grid. Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y- coordinate). Identify parts of the coordinate plane (x-axis, y-axis, and the origin) and the ordered pair (x- coordinate and y-coordinate). Limit the coordinate plane to quadrant I. Interpret division of a whole number by a unit fraction, and compute such quotients. Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for 4 ÷ (1/5), and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 × (1/5) = 4. Use models, such as pictorial models or a number line, to show dividing a whole number by a unit fraction. Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for 4 ÷ (1/5), and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 × (1/5) = 4. Grade 5 Progress Monitoring Assessment: Form C Grade 5 Online Progress Monitoring: Form C: Answer Key Grade 5 Online Progress Monitoring Assessment: Form C Curriculum Standards: Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Understand that attributes belonging to a category of two- dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles. Classify two- dimensional figures in a hierarchy based on properties. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Model with mathematics. Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units. 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. 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. A cube with side length 1 unit, called a "unit cube," is said to have "one cubic unit" of volume, and can be used to measure volume. A solid figure that can be packed without gaps or overlaps using n unit cubes is said to have a volume of n cubic units. Recognize volume as additive. 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. Interpret the product a/b x q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = (ac)/(bd). Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 x 100 + 4 x 10 + 7 x 1 + 3 x (1/10) + 9 x (1/100) + 2 x (1/1000). Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. For example, 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. Use place value understanding to round decimals to any place. 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. For example, 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. Make sense of problems and persevere in solving them. 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. Make a line plot to display a data set of measurements in fractions of a unit (1/2 , 1/4 , 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. For example, create a story context for (1/3) ÷ 4, and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that (1/3) ÷ 4 = 1/12 because (1/12) × 4 = 1/3. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 1/3- cup servings are in 2 cups of raisins? Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y- coordinate). Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for 4 ÷ (1/5), and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 × (1/5) = 4. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Use knowledge about place value and patterns to find the product of a decimal number and a power of 10. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and 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. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10 and 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. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). Understand that attributes belonging to a category of two- dimensional figures also belong to all subcategories of that category. Classify and organize two- dimensional figures into Venn diagrams based on the attributes of the figures. Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles. Classify and organize two-dimensional figures into Venn diagrams based on the attributes of the figures. Classify quadrilaterals by their properties. Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles. Classify two-dimensional figures in a hierarchy based on properties. Classify two-dimensional figures in a hierarchy based on properties. Describe and classify three-dimensional figures including cubes, prisms and pyramids by the number of edges, faces or vertices as well as the types of faces. Recognize and draw a net for a three-dimensional figure. Classify quadrilaterals using a hierarchy. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. Model with mathematics. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Model with mathematics. Mathematically proficient students can apply the mathematics they know to solve problems arising in everyday life, society, and the workplace. In early grades, this might be as simple as writing an addition equation to describe a situation. In middle grades, a student might apply proportional reasoning to plan a school event or analyze a problem in the community. By high school, a student might use geometry to solve a design problem or use a function to describe how one quantity of interest depends on another. Mathematically proficient students who can apply what they know are comfortable making assumptions and approximations to simplify a complicated situation, realizing that these may need revision later. They are able to identify important quantities in a practical situation and map their relationships using such tools as diagrams, two-way tables, graphs, flowcharts and formulas. They can analyze those relationships mathematically to draw conclusions. They routinely interpret their mathematical results in the context of the situation and reflect on whether the results make sense, possibly improving the model if it has not served its purpose. Represent a problem situation with a mathematical model. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Model with mathematics. Model with mathematics. Add and subtract fractions (including mixed numbers) with unlike denominators. (May include multiple methods and representations.) Model with mathematics. Add and subtract decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Model addition and subtraction of fractions and decimals using a variety of representations. Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. Use number sense and reasoning to place the decimal point in a product. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. 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. 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. 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. 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. Find the volume of rectangular prisms using a formula. Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units. 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. 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. 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. Formulas will be provided. 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. Apply the commutative, associative and distributive properties and order of operations to generate equivalent numerical expressions and to solve problems involving whole numbers. Use various tools and strategies to measure the volume and surface area of objects that are shaped like rectangular prisms. Understand that the volume of a three dimensional figure can be found by counting the total number of same-sized cubic units that fill a shape without gaps or overlaps. Use cubic units to label volume measurements. Develop and use the formulas V = ?wh and V = Bh to determine the volume of rectangular prisms. Justify why base area B and height h are multiplied to find the volume of a ectangular prism by breaking the prism into layers of unit cubes. A cube with side length 1 unit, called a “unit cube,” is said to have “one cubic unit” of volume, and can be used to measure volume. A solid figure which can be packed without gaps or overlaps using n unit cubes is said to have a volume of n cubic units. Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units. A cube with side length 1 unit, called a “unit cube,” is said to have “one cubic unit” of volume, and can be used to measure volume. A solid figure which can be packed without gaps or overlaps using n unit cubes is said to have a volume of n cubic units. Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units. Find the volume of solid figures. A cube with side length 1 unit, called a unit cube, is said to have one cubic unit of volume, and can be used to measure volume. A solid figure that can be packed without gaps or overlaps using n unit cubes is said to have a volume of n cubic units. Recognize volume as additive. 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. Recognize volume as additive. 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. Use models, prior knowledge of volume and previously learned strategies to solve word problems involving volume. Recognize volume as additive. 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. Find volumes of solid figures composed of two nonoverlapping right rectangular prisms. Find the volume of a solid figure that is the combination of two or more rectangular prisms. Interpret the product (a/b) × q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. Interpret the product (a/b) × q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = ac/bd.) Use models to multiply two fractions. Interpret the product a/b x q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = (ac)/(bd). Multiply a fraction (including mixed numbers) by a fraction. Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 × 100 + 4 × 10 + 7 × 1 + 3 × (1/10) + 9 × (1/100) + 2 × (1/1000). Read and write decimals to thousandths using base- ten numerals, number names, and expanded form, e.g., 347.392 = 3 × 100 + 4 × 10 + 7 × 1 + 3 × (1/10) + 9 × (1/100) + 2 × (1/1000). Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 × 100 + 4 × 10 + 7 × 1 + 3 × (1/10) + 9 × (1/100) + 2 × (1/1000). Read and write numbers with decimals through thousandths using standard form, expanded form, and number names; identify equivalent decimals. Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 x 100 + 4 x 10 + 7 x 1 + 3 x (1/10) + 9 x (1/100) + 2 x (1/1000). Read and write decimals to thousandths using base-ten numerals, word form, and expanded form. Read and write decimals using place value to describe decimals in terms of groups from millionths to millions. Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Multiply a whole number by a fraction. Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. Use the order of operations to evaluate expressions. Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. Use multiple grouping symbols (parentheses, brackets, or braces) in numerical expressions and evaluate expressions containing these symbols. Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. For example, 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. Write simple expressions that show calculations with numbers. Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. For example, 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. Write simple expressions that model calculations with numbers and interpret numerical expressions without evaluating them. Use place value understanding to round decimals to any place. Use place value understanding to round decimals to any place. Use place value to round decimals to different places. Use place value understanding to round decimals to any place. Round decimals to any place (limit rounding to ones, tenths, hundredths, or thousandths place). Round numbers to the nearest 0.1, 0.01 and 0.001. 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. 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. For example, 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. Analyze numerical relationships. 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. For example, 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. Generate two numerical patterns using two given rules. Create and use rules, tables, spreadsheets and graphs to describe patterns of change and solve problems. Use a rule or table to represent ordered pairs of positive integers and graph these ordered pairs on a coordinate system. Use models, equations and previously learned strategies to multiply mixed numbers. Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Make sense of problems and persevere in solving them. Make sense of problems and persevere in solving them. Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution. They analyze givens, constraints, relationships, and goals. They make conjectures about the form and meaning of the solution and plan a solution pathway rather than simply jumping into a solution attempt. They consider analogous problems, and try special cases and simpler forms of the original problem in order to gain insight into its solution. They monitor and evaluate their progress and change course if necessary. Older students might, depending on the context of the problem, transform algebraic expressions or change the viewing window on their graphing calculator to get the information they need. Mathematically proficient students can explain correspondences between equations, verbal descriptions, tables, and graphs or draw diagrams of important features and relationships, graph data, and search for regularity or trends. Younger students might rely on using concrete objects or pictures to help conceptualize and solve a problem. Mathematically proficient students check their answers to problems using a different method, and they continually ask themselves, “Does this make sense?” They can understand the approaches of others to solving complex problems and identify correspondences between different approaches. Use previously learned knowledge to make sense of problems and persevere in solving them. Make sense of problems and persevere in solving them. Make sense of problems and persevere in solving them. Make sense of problems and persevere in solving them. 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. 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. Use compatible numbers and place-value patterns to estimate quotients. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors. Divide multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Recognize that quotients can be represented in a variety of ways, including a whole number with a remainder, a fraction or mixed number, or a decimal. Estimate solutions to arithmetic problems in order to assess the reasonableness of results. Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally. Read and analyze line plots. Make a line plot to display a data set of measurements in fractions of a unit (1/2 , 1/4 , 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally. Solve problems involving computation of fractions by using information presented in line plots. Solve division problems using partial quotients. Convert among different-sized standard measurement units (i.e., km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec) within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Convert among different-sized standard measurement units (i.e., km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec) within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi- step, real world problems. Convert metric units of capacity. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Convert between different-sized measurement units within a given measurement system. A table of equivalencies will be provided. 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. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Add fractions with unlike denominators using equivalent fractions with a common denominator. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Make sense of problems and keep working. Construct viable arguments and critique the reasoning of others. Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. For example, create a story context for (1/3) ÷ 4, and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that (1/3) ÷ 4 = 1/12 because (1/12) × 4 = 1/3. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins? Use models to divide unit fractions by non-zero whole numbers. Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. For example, create a story context for (1/3) ÷ 4, and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that (1/3) ÷ 4 = 1/12 because (1/12) × 4 = 1/3. Divide unit fractions by whole numbers and whole numbers by unit fractions. Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. Solve real- world problems by graphing points. Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. Represent real-world and mathematical problems by plotting points in quadrant I of the coordinate plane and interpret coordinate values of points in the context of the situation. Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y-coordinate). Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y-coordinate). Locate points on a coordinate grid. Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y- coordinate). Identify parts of the coordinate plane (x-axis, y-axis, and the origin) and the ordered pair (x- coordinate and y-coordinate). Limit the coordinate plane to quadrant I. Interpret division of a whole number by a unit fraction, and compute such quotients. Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for 4 ÷ (1/5), and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 × (1/5) = 4. Use models, such as pictorial models or a number line, to show dividing a whole number by a unit fraction. Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for 4 ÷ (1/5), and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 × (1/5) = 4. Topic 17: Step Up to Grade 6 17-1: Understand Division of Fractions Student Edition: Grade 5 Lesson 17-1 Step 1: Problem-Based Learning 17-1: Explore It! Curriculum Standards: Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. For example, create a story context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi? Understand that positive and negative numbers are used together to describe quantities having opposite directions or values (e.g., temperature above/below zero, elevation above/below sea level, credits/debits, positive/negative electric charge); use positive and negative numbers to represent quantities in real-world contexts, explaining the meaning of 0 in each situation. Recognize opposite signs of numbers as indicating locations on opposite sides of 0 on the number line; recognize that the opposite of the opposite of a number is the number itself, e.g., –(–3) = 3, and that 0 is its own opposite. Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. For example, create a story context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi?. Step 2: Visual Learning 17-1: Ex 1: Divide Whole Numbers by Fractions & Try It! Curriculum Standards: Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. For example, create a story context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi? Understand that positive and negative numbers are used together to describe quantities having opposite directions or values (e.g., temperature above/below zero, elevation above/below sea level, credits/debits, positive/negative electric charge); use positive and negative numbers to represent quantities in real-world contexts, explaining the meaning of 0 in each situation. Recognize opposite signs of numbers as indicating locations on opposite sides of 0 on the number line; recognize that the opposite of the opposite of a number is the number itself, e.g., –(–3) = 3, and that 0 is its own opposite. Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. For example, create a story context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi?. 17-1: Ex 2: Divide Fractions by Whole Numbers & Try It! Curriculum Standards: Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. For example, create a story context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi? Understand that positive and negative numbers are used together to describe quantities having opposite directions or values (e.g., temperature above/below zero, elevation above/below sea level, credits/debits, positive/negative electric charge); use positive and negative numbers to represent quantities in real-world contexts, explaining the meaning of 0 in each situation. Recognize opposite signs of numbers as indicating locations on opposite sides of 0 on the number line; recognize that the opposite of the opposite of a number is the number itself, e.g., –(–3) = 3, and that 0 is its own opposite. Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. For example, create a story context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi?. 17-1: Ex 3: Use Relationships to Divide Whole Numbers by Fractions & Try It! Curriculum Standards: Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. For example, create a story context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi? Understand that positive and negative numbers are used together to describe quantities having opposite directions or values (e.g., temperature above/below zero, elevation above/below sea level, credits/debits, positive/negative electric charge); use positive and negative numbers to represent quantities in real-world contexts, explaining the meaning of 0 in each situation. Recognize opposite signs of numbers as indicating locations on opposite sides of 0 on the number line; recognize that the opposite of the opposite of a number is the number itself, e.g., –(–3) = 3, and that 0 is its own opposite. Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. For example, create a story context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi?. 17-2: Understand Integers Student Edition: Grade 5 Lesson 17-2 Step 1: Problem-Based Learning 17-2: Explain It! Curriculum Standards: Understand that positive and negative numbers are used together to describe quantities having opposite directions or values (e.g., temperature above/below zero, elevation above/below sea level, credits/debits, positive/negative electric charge); use positive and negative numbers to represent quantities in real-world contexts, explaining the meaning of 0 in each situation. Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates. Recognize opposite signs of numbers as indicating locations on opposite sides of 0 on the number line; recognize that the opposite of the opposite of a number is the number itself, e.g., -(-3) = 3, and that 0 is its own opposite. Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates. Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane. Interpret statements of inequality as statements about the relative position of two numbers on a number line diagram. For example, interpret –3 > –7 as a statement that –3 is located to the right of –7 on a number line oriented from left to right. Write, interpret, and explain statements of order for rational numbers in real-world contexts. For example, write –3 ºC > –7 ºC to express the fact that –3 ºC is warmer than –7 ºC. Understand that positive and negative numbers are used together to describe quantities having opposite directions or values (e.g., temperature above/below zero, elevation above/below sea level, credits/debits, positive/negative electric charge); use positive and negative numbers to represent quantities in real- world contexts, explaining the meaning of 0 in each situation. Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates. Recognize opposite signs of numbers as indicating locations on opposite sides of 0 on the number line; recognize that the opposite of the opposite of a number is the number itself, e.g., -(-3) = 3, and that 0 is its own opposite. Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates. Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane. Step 2: Visual Learning 17-2: Ex 1: Define Integers and Opposites & Try It! Curriculum Standards: Understand that positive and negative numbers are used together to describe quantities having opposite directions or values (e.g., temperature above/below zero, elevation above/below sea level, credits/debits, positive/negative electric charge); use positive and negative numbers to represent quantities in real-world contexts, explaining the meaning of 0 in each situation. Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates. Recognize opposite signs of numbers as indicating locations on opposite sides of 0 on the number line; recognize that the opposite of the opposite of a number is the number itself, e.g., -(-3) = 3, and that 0 is its own opposite. Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates. Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane. Interpret statements of inequality as statements about the relative position of two numbers on a number line diagram. For example, interpret –3 > –7 as a statement that –3 is located to the right of –7 on a number line oriented from left to right. Write, interpret, and explain statements of order for rational numbers in real-world contexts. For example, write –3 ºC > –7 ºC to express the fact that –3 ºC is warmer than –7 ºC. Understand that positive and negative numbers are used together to describe quantities having opposite directions or values (e.g., temperature above/below zero, elevation above/below sea level, credits/debits, positive/negative electric charge); use positive and negative numbers to represent quantities in real- world contexts, explaining the meaning of 0 in each situation. Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates. Recognize opposite signs of numbers as indicating locations on opposite sides of 0 on the number line; recognize that the opposite of the opposite of a number is the number itself, e.g., -(-3) = 3, and that 0 is its own opposite. Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates. Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane. 17-2: Ex 2: Compare and Order Integers & Try It! Curriculum Standards: Understand that positive and negative numbers are used together to describe quantities having opposite directions or values (e.g., temperature above/below zero, elevation above/below sea level, credits/debits, positive/negative electric charge); use positive and negative numbers to represent quantities in real-world contexts, explaining the meaning of 0 in each situation. Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates. Recognize opposite signs of numbers as indicating locations on opposite sides of 0 on the number line; recognize that the opposite of the opposite of a number is the number itself, e.g., -(-3) = 3, and that 0 is its own opposite. Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates. Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane. Interpret statements of inequality as statements about the relative position of two numbers on a number line diagram. For example, interpret –3 > –7 as a statement that –3 is located to the right of –7 on a number line oriented from left to right. Write, interpret, and explain statements of order for rational numbers in real-world contexts. For example, write –3 ºC > –7 ºC to express the fact that –3 ºC is warmer than –7 ºC. Understand that positive and negative numbers are used together to describe quantities having opposite directions or values (e.g., temperature above/below zero, elevation above/below sea level, credits/debits, positive/negative electric charge); use positive and negative numbers to represent quantities in real- world contexts, explaining the meaning of 0 in each situation. Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates. Recognize opposite signs of numbers as indicating locations on opposite sides of 0 on the number line; recognize that the opposite of the opposite of a number is the number itself, e.g., -(-3) = 3, and that 0 is its own opposite. Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates. Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane. 17-2: Ex 3: Use Integers to Represent Quantities & Try It! Curriculum Standards: Understand that positive and negative numbers are used together to describe quantities having opposite directions or values (e.g., temperature above/below zero, elevation above/below sea level, credits/debits, positive/negative electric charge); use positive and negative numbers to represent quantities in real-world contexts, explaining the meaning of 0 in each situation. Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates. Recognize opposite signs of numbers as indicating locations on opposite sides of 0 on the number line; recognize that the opposite of the opposite of a number is the number itself, e.g., -(-3) = 3, and that 0 is its own opposite. Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates. Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane. Interpret statements of inequality as statements about the relative position of two numbers on a number line diagram. For example, interpret –3 > –7 as a statement that –3 is located to the right of –7 on a number line oriented from left to right. Write, interpret, and explain statements of order for rational numbers in real-world contexts. For example, write –3 ºC > –7 ºC to express the fact that –3 ºC is warmer than –7 ºC. Understand that positive and negative numbers are used together to describe quantities having opposite directions or values (e.g., temperature above/below zero, elevation above/below sea level, credits/debits, positive/negative electric charge); use positive and negative numbers to represent quantities in real- world contexts, explaining the meaning of 0 in each situation. Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates. Recognize opposite signs of numbers as indicating locations on opposite sides of 0 on the number line; recognize that the opposite of the opposite of a number is the number itself, e.g., -(-3) = 3, and that 0 is its own opposite. Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates. Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane. 17-3: Rational Numbers on the Coordinate Plane Student Edition: Grade 5 Lesson 17-3 Step 1: Problem-Based Learning 17-3: Solve & Discuss It! Curriculum Standards: Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates. Understand signs of numbers in ordered pairs as indicating locations in quadrants of the coordinate plane; recognize that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes. Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates. Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane. Understand signs of numbers in ordered pairs as indicating locations in quadrants of the coordinate plane; recognize that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes. Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane. Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates. Understand signs of numbers in ordered pairs as indicating locations in quadrants of the coordinate plane; recognize that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes. Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates. Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane. Step 2: Visual Learning 17-3: Ex 1: Graph Points with Integer Coordinates & Try It! Curriculum Standards: Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates. Understand signs of numbers in ordered pairs as indicating locations in quadrants of the coordinate plane; recognize that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes. Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates. Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane. Understand signs of numbers in ordered pairs as indicating locations in quadrants of the coordinate plane; recognize that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes. Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane. Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates. Understand signs of numbers in ordered pairs as indicating locations in quadrants of the coordinate plane; recognize that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes. Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates. Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane. 17-3: Ex 2: Locate and Identify Points with Rational Coordinates & Try It! Curriculum Standards: Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates. Understand signs of numbers in ordered pairs as indicating locations in quadrants of the coordinate plane; recognize that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes. Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates. Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane. Understand signs of numbers in ordered pairs as indicating locations in quadrants of the coordinate plane; recognize that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes. Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane. Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates. Understand signs of numbers in ordered pairs as indicating locations in quadrants of the coordinate plane; recognize that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes. Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates. Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane. 17-3: Ex 3: Reflect Points Across the Axes & Try It! Curriculum Standards: Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates. Understand signs of numbers in ordered pairs as indicating locations in quadrants of the coordinate plane; recognize that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes. Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates. Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane. Understand signs of numbers in ordered pairs as indicating locations in quadrants of the coordinate plane; recognize that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes. Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane. Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates. Understand signs of numbers in ordered pairs as indicating locations in quadrants of the coordinate plane; recognize that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes. Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates. Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane. 17-4: Understand and Represent Exponents Student Edition: Grade 5 Lesson 17-4 Step 1: Problem-Based Learning 17-4: Solve & Discuss It! Curriculum Standards: Write and evaluate numerical expressions involving whole-number exponents. Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. For example, “The ratio of wings to beaks in the bird house at the zoo was 2:1, because for every 2 wings there was 1 beak.” “For every vote candidate A received, candidate C received nearly three votes.” Write and evaluate numerical expressions involving whole-number exponents. Step 2: Visual Learning 17-4: Ex 1: Understand and Represent Exponents & Try It! Curriculum Standards: Write and evaluate numerical expressions involving whole-number exponents. Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. For example, “The ratio of wings to beaks in the bird house at the zoo was 2:1, because for every 2 wings there was 1 beak.” “For every vote candidate A received, candidate C received nearly three votes.” Write and evaluate numerical expressions involving whole-number exponents. 17-4: Ex 2: Evaluate Exponents & Try It! Curriculum Standards: Write and evaluate numerical expressions involving whole-number exponents. Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. For example, “The ratio of wings to beaks in the bird house at the zoo was 2:1, because for every 2 wings there was 1 beak.” “For every vote candidate A received, candidate C received nearly three votes.” Write and evaluate numerical expressions involving whole-number exponents. 17-4: Ex 3: Evaluate Expressions with Exponents & Try It! Curriculum Standards: Write and evaluate numerical expressions involving whole-number exponents. Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. For example, “The ratio of wings to beaks in the bird house at the zoo was 2:1, because for every 2 wings there was 1 beak.” “For every vote candidate A received, candidate C received nearly three votes.” Write and evaluate numerical expressions involving whole-number exponents. 17-5: Understand Equations and Solutions Student Edition: Grade 5 Lesson 17-5 Step 1: Problem-Based Learning 17-5: Solve & Discuss It! Curriculum Standards: Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true. Understand the concept of a unit rate a/b associated with a ratio a:b with b ? 0, and use rate language in the context of a ratio relationship. For example, “This recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there is 3/4 cup of flour for each cup of sugar.” “We paid $75 for 15 hamburgers, which is a rate of $5 per hamburger.” Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true. Step 2: Visual Learning 17-5: Ex 1: Determine Whether a Value is a Solution of an Equation & Try It! Curriculum Standards: Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true. Understand the concept of a unit rate a/b associated with a ratio a:b with b ? 0, and use rate language in the context of a ratio relationship. For example, “This recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there is 3/4 cup of flour for each cup of sugar.” “We paid $75 for 15 hamburgers, which is a rate of $5 per hamburger.” Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true. 17-5: Ex 2: Use Substitution to Show No Values are a Solution & Try It! Curriculum Standards: Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true. Understand the concept of a unit rate a/b associated with a ratio a:b with b ? 0, and use rate language in the context of a ratio relationship. For example, “This recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there is 3/4 cup of flour for each cup of sugar.” “We paid $75 for 15 hamburgers, which is a rate of $5 per hamburger.” Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true. 17-6: Understand Ratios Student Edition: Grade 5 Lesson 17-6 Step 1: Problem-Based Learning 17-6: Explore It! Curriculum Standards: Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. For example, “The ratio of wings to beaks in the bird house at the zoo was 2:1, because for every 2 wings there was 1 beak.” “For every vote candidate A received, candidate C received nearly three votes.” Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations. Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent. Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. For example, "The ratio of wings to beaks in the bird house at the zoo was 2:1, because for every 2 wings there was 1 beak." "For every vote candidate A received, candidate C received nearly three votes." Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations. Step 2: Visual Learning 17-6: Ex 1: Write Ratios to Compare Quantities & Try It! Curriculum Standards: Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. For example, “The ratio of wings to beaks in the bird house at the zoo was 2:1, because for every 2 wings there was 1 beak.” “For every vote candidate A received, candidate C received nearly three votes.” Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations. Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent. Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. For example, "The ratio of wings to beaks in the bird house at the zoo was 2:1, because for every 2 wings there was 1 beak." "For every vote candidate A received, candidate C received nearly three votes." Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations. 17-6: Ex 2: Use a Bar Diagram to Solve a Ratio Problem Curriculum Standards: Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. For example, “The ratio of wings to beaks in the bird house at the zoo was 2:1, because for every 2 wings there was 1 beak.” “For every vote candidate A received, candidate C received nearly three votes.” Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations. Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent. Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. For example, "The ratio of wings to beaks in the bird house at the zoo was 2:1, because for every 2 wings there was 1 beak." "For every vote candidate A received, candidate C received nearly three votes." Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations. 17-6: Ex 3: Use a Double Number Line Diagram to Solve a Ratio Problem & Try It! Curriculum Standards: Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. For example, “The ratio of wings to beaks in the bird house at the zoo was 2:1, because for every 2 wings there was 1 beak.” “For every vote candidate A received, candidate C received nearly three votes.” Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations. Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent. Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. For example, "The ratio of wings to beaks in the bird house at the zoo was 2:1, because for every 2 wings there was 1 beak." "For every vote candidate A received, candidate C received nearly three votes." Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations. 17-7: Understand Rates and Unit Rates Student Edition: Grade 5 Lesson 17-7 Step 1: Problem-Based Learning 17-7: Solve & Discuss It! Curriculum Standards: Understand the concept of a unit rate a/b associated with a ratio a:b with b z 0, and use rate language in the context of a ratio relationship. For example, “This recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there is 3/4 cup of flour for each cup of sugar.” “We paid $75 for 15 hamburgers, which is a rate of $5 per hamburger.” Make tables of equivalent ratios relating quantities with whole-number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios. Solve unit rate problems including those involving unit pricing and constant speed. For example, if it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed? Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent. Understand the concept of a unit rate a/b associated with a ratio a:b with b ? 0, and use rate language in the context of a ratio relationship. For example, "This recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there is 3/4 cup of flour for each cup of sugar." "We paid $75 for 15 hamburgers, which is a rate of $5 per hamburger." Make tables of equivalent ratios relating quantities with whole-number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios. Solve unit rate problems including those involving unit pricing and constant speed. For example, if it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed? Step 2: Visual Learning 17-7: Ex 1: Find Equivalent Rates & Try It! Curriculum Standards: Understand the concept of a unit rate a/b associated with a ratio a:b with b z 0, and use rate language in the context of a ratio relationship. For example, “This recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there is 3/4 cup of flour for each cup of sugar.” “We paid $75 for 15 hamburgers, which is a rate of $5 per hamburger.” Make tables of equivalent ratios relating quantities with whole-number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios. Solve unit rate problems including those involving unit pricing and constant speed. For example, if it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed? Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent. Understand the concept of a unit rate a/b associated with a ratio a:b with b ? 0, and use rate language in the context of a ratio relationship. For example, "This recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there is 3/4 cup of flour for each cup of sugar." "We paid $75 for 15 hamburgers, which is a rate of $5 per hamburger." Make tables of equivalent ratios relating quantities with whole-number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios. Solve unit rate problems including those involving unit pricing and constant speed. For example, if it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed? 17-7: Ex 2: Compare Quantities in Two Ways & Try It! Curriculum Standards: Understand the concept of a unit rate a/b associated with a ratio a:b with b z 0, and use rate language in the context of a ratio relationship. For example, “This recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there is 3/4 cup of flour for each cup of sugar.” “We paid $75 for 15 hamburgers, which is a rate of $5 per hamburger.” Make tables of equivalent ratios relating quantities with whole-number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios. Solve unit rate problems including those involving unit pricing and constant speed. For example, if it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed? Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent. Understand the concept of a unit rate a/b associated with a ratio a:b with b ? 0, and use rate language in the context of a ratio relationship. For example, "This recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there is 3/4 cup of flour for each cup of sugar." "We paid $75 for 15 hamburgers, which is a rate of $5 per hamburger." Make tables of equivalent ratios relating quantities with whole-number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios. Solve unit rate problems including those involving unit pricing and constant speed. For example, if it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed? 17-7: Ex 3: Use Unit Rates to Solve Problems & Try It! Curriculum Standards: Understand the concept of a unit rate a/b associated with a ratio a:b with b z 0, and use rate language in the context of a ratio relationship. For example, “This recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there is 3/4 cup of flour for each cup of sugar.” “We paid $75 for 15 hamburgers, which is a rate of $5 per hamburger.” Make tables of equivalent ratios relating quantities with whole-number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios. Solve unit rate problems including those involving unit pricing and constant speed. For example, if it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed? Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent. Understand the concept of a unit rate a/b associated with a ratio a:b with b ? 0, and use rate language in the context of a ratio relationship. For example, "This recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there is 3/4 cup of flour for each cup of sugar." "We paid $75 for 15 hamburgers, which is a rate of $5 per hamburger." Make tables of equivalent ratios relating quantities with whole-number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios. Solve unit rate problems including those involving unit pricing and constant speed. For example, if it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed? 17-8: Understand Percent Student Edition: Grade 5 Lesson 17-8 Step 1: Problem-Based Learning 17-8: Explain It! Curriculum Standards: Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent. Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. For example, create a story context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi? Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent. Step 2: Visual Learning 17-8: Ex 1: Represent Percents & Try It! Curriculum Standards: Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent. Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. For example, create a story context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi? Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent. 17-8: Ex 2: Examine Percents and Wholes & Try It! Curriculum Standards: Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent. Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. For example, create a story context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi? Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent. 17-8: Ex 3: Use Percents & Try It! Curriculum Standards: Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent. Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. For example, create a story context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi? Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent. 17-9: Relate Fractions, Decimals, and Percents Student Edition: Grade 5 Lesson 17-9 Step 1: Problem-Based Learning 17-9: Solve & Discuss It! Curriculum Standards: Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent. Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. For example, create a story context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi? Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent. Step 2: Visual Learning 17-9: Ex 1: Express Percents and Decimals as Parts of a Whole & Try It! Curriculum Standards: Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent. Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. For example, create a story context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi? Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent. 17-9: Ex 2: Express Fractions as Parts of a Whole Curriculum Standards: Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent. Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. For example, create a story context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi? Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent. 17-9: Ex 3: Use Division with Equivalent Rates to Express Fractions as Part of a Whole & Try It! Curriculum Standards: Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent. Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. For example, create a story context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi? Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent. 17-10: Find Areas of Parallelograms and Rhombuses Student Edition: Grade 5 Lesson 17-10 Step 1: Problem-Based Learning 17-10: Solve & Discuss It! Curriculum Standards: Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems. Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real- world and mathematical problems. Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations). For example, use the formulas V = s3 and A = 6 s2 to find the volume and surface area of a cube with sides of length s = 1/2. Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real- world and mathematical problems. Step 2: Visual Learning 17-10: Ex 1: Find the Area Formula of a Parallelogram & Try It! Curriculum Standards: Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems. Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real- world and mathematical problems. Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations). For example, use the formulas V = s3 and A = 6 s2 to find the volume and surface area of a cube with sides of length s = 1/2. Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real- world and mathematical problems. 17-10: Ex 2: Find the Area of a Rhombus Curriculum Standards: Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems. Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real- world and mathematical problems. Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations). For example, use the formulas V = s3 and A = 6 s2 to find the volume and surface area of a cube with sides of length s = 1/2. Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real- world and mathematical problems. 17-10: Ex 3: Find the Base or Height of a Parallelogram & Try It! Curriculum Standards: Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems. Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real- world and mathematical problems. Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations). For example, use the formulas V = s3 and A = 6 s2 to find the volume and surface area of a cube with sides of length s = 1/2. Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real- world and mathematical problems. Math Diagnosis and Intervention System Booklet A: Numbers, Place Value, Money, and Patterns in Grades K-3 A1: Zero to Five A2: More and Fewer A3: Six to Ten A4: Ordinal Numbers Through Tenth A5: Spatial Patterns for Numbers to 10 A6: Comparing Numbers A7: Comparing Numbers to 10 A8: Numbers to 12 A9: Ordering Numbers to 12 with a Number Line A10: 11 to 19 A11: Number Words to Twenty A12: Numbers to 30 A13: Counting to 100 A14: Counting Backward from 20 A15: Counting Backward from 100 A16: Counting by 10s to 100 A17: Using Numbers 11 to 20 A18: Making Numbers 11 to 20 A19: Counting from any Number A20: Using Skip Counting A21: Odd and Even A22: Before, After, and Between A23: Counting with Tens and Ones A24: Tens A25: Tens and Ones A26: Number Patterns to 100 A27: 1 More or Less, 10 More or Less A28: Using >, <, and = to Compare Numbers A29: Ordering Three Numbers A30: Number Words A31: Numbers to 100 on the Number Line A32: Counting by Hundreds A33: Building Numbers to 999 A34: Reading and Writing Numbers to 999 A35: Patterns with Numbers on Hundreds Charts A36: Comparing Numbers to 999 A37: Before, After, and Between A38: Ordering Numbers to 999 A39: Numbers to 999 on the Number Line A40: Skip Counting on the Number Line A41: Ways to Show Numbers A42: Place-Value Patterns A43: Reading and Writing 4-Digit Numbers A44: Comparing and Ordering Numbers A45: Rounding to the Nearest Ten and Hundred A46: Numbers Halfway Between and Rounding A47: Equal Parts A48: Understanding Fractions to Fourths A49: Halves A50: Fractions of a Set A51: Estimating Fractional Amounts A52: Equal Parts of a Whole A53: Parts of a Region A54: Parts of a Set A55: Fractions on the Number Line A56: Fractions and Length A57: Using Models to Compare Fractions A58: Comparing Fractions on the Number Line A59: Using Models to Find Equivalent Fractions A60: Comparing Fractions A61: Money A62: Pennies and Nickels A63: Dimes A64: Counting Pennies, Nickels, and Dimes A65: Quarters A66: Half-Dollars A67: Counting Sets of Coins A68: Ways to Show the Same Amount A69: Dollars A70: Counting Money A71: Find a Rule A72: Input/Output Tables A73: Geometric Growth Patterns A74: Place Value Through Thousands A75: Rounding Numbers Through Thousands A76: Comparing and Ordering Numbers Through Thousands A77: Rounding Numbers Through Millions A78: Equality and Inequality A79: Using the Distributive Property A80: Working with Unit Fractions A81: Equivalent Fractions A82: Fractions and Division A83: Equivalent Fractions and the Number Line A84: Counting Coins and Bills A85: Ways to Make 5 A86: Equal Groups A87: Ways to Make 10 A88: Making Numbers With 10 A89: Count on an Open Number Line A90: Arrays and Repeated Addition A91: Working with Dollar Bills A92: Understand the Whole A93: Comparing Fractions on a Number Line A94: Whole Numbers and Fractions Booklet B: Basic Facts in Grades K-3 B1: Addition B2: Subtraction B3: Finding Sums B4: Joining Stories B5: Stories about Joining B6: Finding Differences B7: Comparing Stories B8: Separating Stories B9: Making 6 and 7 B10: Making 8 and 9 B11: Parts of Ten B12: Adding Across and Down B13: Adding in any Order B14: Missing Parts B15: Finding the Missing Part B16: Relating Addition and Subtraction B17: Making 10 on a Ten-Frame B18: Missing Parts of 10 B19: Adding with 0, 1, 2 B20: Adding Doubles B21: Using Doubles to Add B22: Facts with 5 on a Ten-Frame B23: Subtracting with 0, 1, and 2 B24: Using Doubles to Subtract B25: Thinking Addition to 12 to Subtract B26: Doubles to 18 B27: Using Doubles to Add B28: Adding 10 B29: Making 10 to Add 9 B30: Making 10 to Add 7 and 8 B31: Adding Three Numbers B32: Stories about Separating B33: Stories about Comparing B34: Relating Addition and Subtraction to 18 B35: Fact Families B36: Thinking Addition to Subtract Doubles B37: Using Addition to 18 to Subtract B38: Subtraction Facts with 10 B39: Using Subtraction Strategies B40: Using = and ? B41: Addition Properties B42: Relating Addition and Subtraction B43: Multiplication as Repeated Addition B44: Arrays and Multiplication B45: Writing Multiplication Stories B46: Multiplying by 2 and 5 B47: Multiplying by 9 B48: Multiplying by 1 and 0 B49: Multiplying by 10 B50: Multiplying by 3 B51: Multiplying by 4 B52: Multiplying by 6 or 7 B53: Multiplying by 8 B54: Multiplying Three Numbers B55: Meanings for Division B56: Writing Division Stories B57: Relating Multiplication and Division B58: Dividing by 2 Through 5 B59: Dividing by 6 and 7 B60: Dividing by 8 and 9 B61: 0 and 1 in Division B62: Using Multiplication to Compare B63: Multiplication and Arrays B64: Breaking Apart Numbers to Multiply B65: Multiplying Two-Digit Numbers B66: Mental Math: Multiplication Patterns B67: Mental Math: Division Patterns B68: Estimating Products B69: Divisibility by 2, 3, 5, 9, and 10 B70: Divisibility B71: Mental Math: Multiplying by Multiples of 10 B72: Mental Math: Using Properties B73: Using Mental Math to Multiply B74: Adding and Subtracting on a Number Line B75: Skip Counting on the Number Line B76: Make 10 to Subtract B77: More Make 10 to Subtract B78: Use Patterns to Develop Fluency in Addition B79: Count to Add on a Number Line B80: Count to Subtract on an Open Number Line B81: Patterns on Multiplication Tables Booklet C: Computation with Whole numbers in Grades K-3 C1: Adding Tens C2: Adding on a Hundred Chart C3: Adding Tens to a Two-Digit Number C4: Adding two-Digit Numbers C5: Estimating Sums C6: Regrouping in Addition C7: Deciding When to Regroup in Addition C8: Adding Two-Digit and One-Digit Numbers C9: Adding with Regrouping C10: Two-Digit Addition C11: Adding Three Numbers C12: Subtracting Tens C13: Finding Parts of 100 C14: Subtracting on a Hundred Chart C15: Subtracting Tens from a Two-Digit Number C16: Subtracting Two-Digit Numbers C17: Estimating Differences C18: Subtracting Two-Digit and One-Digit Numbers C19: Deciding When to Regroup in Subtraction C20: Subtracting with Regrouping C21: Two-Digit Subtraction C22: Using Addition to Check Subtraction C23: Adding on a Hundred Chart C24: Subtracting on a Hundred Chart C25: Using Mental Math to Add C26: Using Mental Math to Subtract C27: Adding Two-Digit Numbers C28: Subtracting Two-Digit Numbers C29: Estimating Sums C30: Estimating Differences C31: Mental Math Strategies C32: Adding Three-Digit Numbers C33: Subtracting Three-Digit Numbers C34: Adding Three Numbers C35: Subtracting Across Zero C36: Add with Tens on an Open Number Line C37: Add Two-Digit Numbers on an Open Number Line C38: Subtract Tens on an Open Number Line C39: Subtract Two-Digit Numbers on an Open Number Line C40: Use Compensation to Add C41: Break Apart Numbers to Subtract C42: Partial Sums C43: Make 10 to Add 2-Digit Numbers C44: Counting Up to Subtract on an Open Number Line C45: Adding 10 and 100 to Numbers C46: Subtracting 10 and 100 from Numbers C47: Use an Open Number Line to Multiply Booklet D: Measurement, Geometry, Data, and Probability in Grades K-3 D1: Time to the Hour D2: Time to the Half Hour D3: Time to Five Minutes D4: Time Before and After the Hour D5: Time to the Quarter Hour D6: Telling Time D7: Units of Time D8: Elapsed Time D9: Comparing and Ordering by Length D10: Comparing and Ordering by Capacity D11: Comparing and Ordering by Weight D12: Unit Size and Measuring D13: Inches and Feet D14: Centimeters D15: Inches, Feet, and Yards D16: Inches D17: Centimeters and Meters D18: Perimeter D19: Exploring Area D20: Finding Area on a Grid D21: Area of Rectangles and Squares D22: Area of Irregular Figures D23: Rectangles with the Same Area or Perimeter D24: Using Customary Units of Capacity D25: Using Metric Units of Capacity D26: Using Metric Units of Mass D27: Using Customary Units of Weight D28: Position and Location D29: Shape D30: Properties of Plane Shapes D31: Solid Figures D32: Flat Surfaces of Solid Figures D33: Making New Shapes from Shapes D34: Cutting Shapes Apart D35: Flat Surfaces and Corners D36: Faces, Corners, and Edges D37: Solid Figures D38: Lines and Line Segments D39: Acute, Right, and Obtuse Angles D40: Polygons D41: Classifying Triangles Using Sides and Angles D42: Quadrilaterals D43: Graphing D44: Sorting and Classifying D45: Reading Picture Graphs D46: Interpreting Graphs D47: Reading Bar Graphs D48: Tallying Results D49: Real Graphs D50: Data and Picture Graphs D51: Making Bar Graphs D52: Make a Graph D53: Recording Data from a Survey D54: Making Line Plots D55: Reading and Making Pictographs D56: Reading and Making a Bar Graph D57: More Perimeter D58: Measuring Capacity or Weight D59: Solving Problems with Units of Time D60: Comparing by Length D61: Comparing by Capacity D62: Comparing by Weight D63: Indirect Measurement D64: Compose with 3-D Shapes D65: Add and Subtract with Measurements D66: Find Unknown Measurements D67: Divide Rectangles into Equal Shares D68: Equal Shares, Different Shapes D69: Area and the Distributive Property D70: Perimeter and Unknown Side Lengths Booklet E: Problem Solving in Grades K-3 E1: Analyze Given Information E2: Two-Step Problems E3: Multi-Step Problems E4: Use Data from a Table or Chart E5: Analyze Given Information E6: Two-Step Problems E7: Multi-Step Problems E8: Look for a Pattern E9: Look for a Pattern E10: Make a Table and Look for a Pattern E11: Draw a Picture E12: Make a Table E13: Use Tools E14: Act It Out E15: Make an Organized List E16: Try, Check, and Revise E17: Use Reasoning E18: Use Reasoning E19: Draw a Picture and Write a Number Sentence E20: Draw a Picture and Write a Number Sentence E21: Make a Table and Look for a Pattern E22: Act It Out E23: Make an Organized List E24: Try, Check, and Revise E25: Draw a Strip Diagram and Write a Number Sentence E26: Use Tools E27: Draw a Strip Diagram E28: Use Representations E29: Use Representations E30: Work Backward E31: Make and Test Generalizations E32: Make and Test Generalizations E33: Writing to Explain E34: Writing to Explain E35: Writing Math Stories E36: Writing Math Stories E37: Use Data from a Table or Chart E38: Work Backward E39: Draw a Picture E40: Make a Table E41: Analyze Given Information E42: Draw a Picture and Write a Number Sentence E43: Draw a Strip Diagram and Write an Equation E44: Use Representations E45: Solve a Simpler Problem E46: Use Reasoning E47: Analyze Relationships E48: Make and Test Conjectures E49: Reasonableness E50: Represent Subtraction as Taking Apart E51: Solve 2-Step Word Problems: Multiplication and Division Diagnostic Tests and Answer Keys, Grades K-3 Grade K Diagnostic Test, Form A Grade K Diagnostic Test, Form B Grade 1 Diagnostic Test, Form A Grade 1 Diagnostic Test, Form B Grade 2 Diagnostic Test, Form A Grade 2 Diagnostic Test, Form B Grade 3 Diagnostic Test, Form A Grade 3 Diagnostic Test, Form B Booklet F: Numeration, Patterns, and Relationships in Grades 4-6 F1: Ways to Show Numbers F2: Numbers to 999 on the Number Line F3: Skip Counting on the Number Line F4: Rounding to the Nearest Ten and Hundred F5: Reading and Writing 4-Digit Numbers F6: Numbers Halfway Between and Rounding F7: Comparing and Ordering Numbers F8: Place-Value Patterns Curriculum Standards: Compare the value of a number when it is represented in different place values of two three-digit numbers. F9: Place Value Through Thousands Curriculum Standards: Compare the value of a number when it is represented in different place values of two three-digit numbers. F10: Rounding Numbers Through Thousands F11: Comparing and Ordering Numbers Through Thousands F12: Place Value Through Millions F13: Rounding Numbers Through Millions F14: Comparing and Ordering Numbers Through Millions F15: Place Value Through Billions F16: Place Value Through Trillions F17: Exponents and Place Value Curriculum Standards: Identify what an exponent represents (e.g., 10³= 10X10X10). F18: Meaning of Integers F19: Comparing and Ordering Integers F20: Comparing and Ordering Rational Numbers F21: Adding Integers F22: Subtracting Integers F23: Multiplying and Dividing Integers F24: Repeating Patterns F25: Number Patterns Curriculum Standards: Given two pattern descriptions involving the same context (e.g., collecting marbles), determine the first five terms and compare the values. F26: Input/Output Tables Curriculum Standards: Graph ordered pairs on a coordinate plane when given a table that follows patterns rules. F27: Geometric Growth Patterns F28: Expressions with Addition and Subtraction F29: Expressions with Multiplication and Division F30: Find a Rule F31: Patterns and Equations F32: Graphing Ordered Pairs Curriculum Standards: Graph ordered pairs on a coordinate plane when given a table that follows patterns rules. F33: Lengths of Line Segments F34: Graphing Equations F35: Graphing Points in the Coordinate Plane Curriculum Standards: Find a location on a map using given coordinates. Locate points on a coordinate plane. Locate the x- and y-axis on a coordinate plane. Graph ordered pairs (coordinates). F36: Graphing Equations in the Coordinate Plane F37: Translating Words to Expressions F38: Equality and Inequality F39: Multiplication Properties F40: Expressions with Parentheses Curriculum Standards: Write a simple expression for a calculation. Evaluate a simple expression involving one set of parenthesis. F41: Evaluate Expressions Curriculum Standards: Evaluate a simple expression involving one set of parenthesis. F42: Using the Distributive Property F43: Properties of Operations F44: Variables and Expressions F45: More Variables and Expressions F46: Writing Expressions F47: Formulas and Equations F48: Properties of Equality F49: Solving Addition and Subtraction Equations F50: Solving Multiplication and Division Equations F51: Solving Equations with Whole Numbers F52: Solving Equations with Decimals F53: Writing Addition and Subtraction Equations F54: Writing Multiplication and Division Equations F55: Solving Equations with Fractions F56: Solving Equations with More Than One Operation F57: Perfect Squares F58: Identify Parts of Expressions F59: Write Equivalent Expressions F60: Simplify Algebraic Expressions F61: Write Inequalities F62: Solve Inequalities F63: Dependent and Independent Variables F64: Absolute Value Booklet G: Operations with Whole Numbers in Grades 4-6 G1: Addition Properties G2: Relating Addition and Subtraction G3: Using Mental Math to Add G4: Using Mental Math to Subtract G5: Estimating Sums G6: Estimating Differences G7: Adding Two-Digit Numbers G8: Subtracting Two-Digit Numbers G9: Mental Math Strategies G10: Adding Three-Digit Numbers G11: Subtracting Three-Digit Numbers G12: Adding and Subtracting Money G13: Estimating Sums and Differences of Greater Numbers G14: Adding Three Numbers G15: Subtracting Four-Digit Numbers G16: Subtracting Across Zero G17: Adding 4-Digit Numbers G18: Adding Greater Numbers G19: Subtracting Greater Numbers G20: Multiplication as Repeated Addition G21: Arrays and Multiplication G22: Using Multiplication to Compare G23: Writing Multiplication Stories G24: Multiplying by 2 and 5 G25: Multiplying by 9 G26: Multiplying by 1 or 0 G27: Multiplying by 3 G28: Multiplying by 4 G29: Multiplying by 6 or 7 G30: Multiplying by 8 G31: Multiplying by 10 G32: Multiplying Three Numbers G33: Meanings for Division G34: Writing Division Stories G35: Relating Multiplication and Division G36: Dividing by 2 Through 5 G37: Dividing by 6 and 7 G38: Dividing by 8 and 9 G39: 0 and 1 in Division G40: Mental Math: Multiplication Patterns G41: Mental Math: Division Patterns G42: Estimating Products G43: Estimating Quotients G44: Multiplication and Arrays G45: Breaking Apart Numbers to Multiply G46: Multiplying Two-Digit Numbers Curriculum Standards: Fluently multiply two-digit numbers. G47: Multiplying Three-Digit Numbers G48: Multiplying Money G49: Multiplying One-Digit and Four-Digit Numbers G50: Dividing with Objects G51: Interpret the Remainder G52: Using Objects to Divide G53: Dividing Two-Digit Numbers Curriculum Standards: Find whole number quotients up to two dividends and two divisors. Find whole number quotients of whole numbers with up to two-digit dividends and two-digit divisors. G54: Dividing Three-Digit Numbers Curriculum Standards: Find whole number quotients up to two dividends and two divisors. G55: Zeros in the Quotient G56: Dividing Greater Numbers Curriculum Standards: Find whole number quotients up to two dividends and two divisors. G57: Factoring Numbers G58: Divisibility by 2, 3, 5, 9, and 10 G59: Divisibility G60: Exponents G61: Prime Factorization G62: Greatest Common Factor G63: Least Common Multiple G64: Mental Math: Multiplying by Multiples of 10 G65: Estimating Products G66: Using Arrays to Multiply Two-Digit Factors G67: Multiplying Two-Digit Numbers by Multiples of 10 G68: Multiplying by Two-Digit Numbers G69: Multiplying Greater Numbers G70: Mental Math: Using Properties G71: Dividing by Multiples of 10 G72: Estimating Quotients with Two-Digit Divisors G73: Dividing by Two-Digit Divisors G74: One- and Two-Digit Quotients G75: Dividing Greater Numbers G76: Using Mental Math to Multiply G77: Adding and Subtracting on a Number Line G78: Skip Counting on the Number Line Booklet H: Fractions, Decimals, and Percents in Grades 4-6 H1: Equal Parts of a Whole H2: Parts of a Region H3: Fractions of a Set H4: Parts of a Set H5: Fractions and Length H6: Fractions on the Number Line H7: Working with Unit Fractions H8: Using Models to Compare Fractions H9: Using Models to Find Equivalent Fractions H10: Comparing Fractions on the Number Line H11: Comparing Fractions H12: Fractions and Decimals H13: Counting Money H14: Making Change H15: Using Money to Understand Decimals H16: Equivalent Fractions H17: Fractions and Division H18: Estimating Fractional Amounts H19: Simplest Form H20: Mixed Numbers H21: Comparing and Ordering Fractions H22: Comparing and Ordering Mixed Numbers H23: Fractions and Mixed Numbers on the Number Line H24: Place Value Through Hundredths Curriculum Standards: Read, write, or select a decimal to the hundredths place. H25: Decimals on the Number Line H26: Place Value Through Thousandths H27: Place Value Through Millionths H28: Rounding Decimals Through Hundredths Curriculum Standards: Round decimals to the next whole number. Round decimals to the tenths place. H29: Rounding Decimals Through Thousandths H30: Comparing and Ordering Decimals Through Hundredths Curriculum Standards: Compare two decimals to the hundredths place, whose values are less than 1. H31: Comparing and Ordering Decimals Through Thousandths H32: Relating Fractions and Decimals H33: Decimals to Fractions H34: Fractions to Decimals H35: Relating Fractions and Decimals to Thousandths H36: Using Models to Compare Fractions and Decimals H37: Fractions, Decimals, and the Number Line H38: Adding Fractions with Like Denominators Curriculum Standards: Solve word problems involving the addition and subtraction of fractions using visual fraction models. Add and subtract fractions with like denominators with sums greater than 1 represented by mixed numbers using visual fraction models. H39: Subtracting Fractions with Like Denominators Curriculum Standards: Solve word problems involving the addition and subtraction of fractions using visual fraction models. Add and subtract fractions with like denominators with sums greater than 1 represented by mixed numbers using visual fraction models. H40: Adding and Subtracting Fractions with Like Denominators Curriculum Standards: Solve word problems involving the addition and subtraction of fractions using visual fraction models. Add and subtract fractions with like denominators with sums greater than 1 represented by mixed numbers using visual fraction models. H41: Adding and Subtracting Fractions on a Number Line Curriculum Standards: Solve word problems involving the addition and subtraction of fractions using visual fraction models. Add and subtract fractions with like denominators with sums greater than 1 represented by mixed numbers using visual fraction models. H42: Adding Fractions with Unlike Denominators Curriculum Standards: Add or subtract fractions with unlike denominators within one whole unit on a number line. Solve word problems involving the addition and subtraction of fractions using visual fraction models. H43: Subtracting Fractions with Unlike Denominators Curriculum Standards: Add or subtract fractions with unlike denominators within one whole unit on a number line. Solve word problems involving the addition and subtraction of fractions using visual fraction models. H44: Estimating Sums and Differences of Mixed Numbers H45: Adding Mixed Numbers H46: Subtracting Mixed Numbers H47: Multiplying Fractions by Whole Numbers Curriculum Standards: Multiply a fraction by a whole or mixed number using visual fraction models. Determine whether the product will increase or decrease based on the multiple using visual fraction models. Multiply a fraction by a whole or mixed number using visual fraction models. H48: Multiplying Two Fractions Curriculum Standards: Multiply a fraction by a whole or mixed number using visual fraction models. Determine whether the product will increase or decrease based on the multiple using visual fraction models. Multiply a fraction by a whole or mixed number using visual fraction models. H49: Understanding Division with Fractions Curriculum Standards: Divide unit fractions by whole numbers and whole numbers by unit fractions using visual fraction models. Divide unit fractions by whole numbers and whole numbers by unit fractions using visual fraction models. H50: Dividing Fractions Curriculum Standards: Divide unit fractions by whole numbers and whole numbers by unit fractions using visual fraction models. Divide unit fractions by whole numbers and whole numbers by unit fractions using visual fraction models. H51: Estimating Products and Quotients of Mixed Numbers H52: Multiplying Mixed Numbers Curriculum Standards: Multiply a fraction by a whole or mixed number using visual fraction models. Determine whether the product will increase or decrease based on the multiple using visual fraction models. Multiply a fraction by a whole or mixed number using visual fraction models. H53: Dividing Mixed Numbers H54: Using Models to Add and Use Strategies to Subtract Decimals H55: Estimating Decimal Sums and Differences H56: Adding Decimals to Hundredths H57: Subtracting Decimals to Hundredths H58: More Estimation of Decimal Sums and Differences H59: Adding and Subtracting Decimals to Thousandths H60: Multiplying with Decimals and Whole Numbers H61: Multiplying Decimals by 10, 100, or 1,000 Curriculum Standards: Identify the direction the decimal point will move when multiplying or dividing by a multiple of 10. H62: Estimating the Product of a Whole Number and a Decimal H63: Multiplying Decimals Using Grids H64: Multiplying Decimals by Decimals H65: Dividing with Decimals and Whole Numbers H66: Dividing Decimals by 10, 100, or 1,000 Curriculum Standards: Identify the direction the decimal point will move when multiplying or dividing by a multiple of 10. H67: Dividing a Decimal by a Whole Number H68: Estimating the Quotient of a Decimal and a Whole Number H69: Dividing a Decimal by a Decimal H70: Understanding Ratios H71: Rates and Unit Rates H72: Comparing Rates H73: Distance, Rate, and Time H74: Equal Ratios and Proportions H75: Solving Proportions H76: Maps and Scale Drawings Curriculum Standards: Find a location on a map using given coordinates. H77: Understanding Percent H78: Relating Percents, Decimals, and Fractions H79: Percents Greater Than 100 or Less Than 1 H80: Estimating Percent of a Number H81: Finding the Percent of a Whole Number H82: Tips and Sales Tax H83: Equivalent Fractions and the Number Line H84: Counting Coins and Bills H85: Estimating Fraction Sums and Differences H86: Divide Whole Numbers by Unit Fractions H87: Divide Unit Fractions by Non-Zero Whole Numbers H88: Find the Whole Booklet I: Measurement, Geometry, Data, and Probability in Grades 4-6 I1: Solid Figures I2: Lines and Line Segments I3: Acute, Right, and Obtuse Angles I4: Polygons I5: Classifying Triangles Using Sides and Angles Curriculum Standards: Use polygon-shaped manipulatives to classify and organize two- dimensional figures into Venn diagrams based on the attributes of the figures. Recognize properties of simple plane figures using polygon-shaped manipulatives. I6: Quadrilaterals Curriculum Standards: Use polygon-shaped manipulatives to classify and organize two- dimensional figures into Venn diagrams based on the attributes of the figures. Recognize properties of simple plane figures using polygon-shaped manipulatives. I7: Making New Shapes from Shapes I8: Cutting Shapes Apart I9: Congruent Figures and Motions I10: Line Symmetry I11: Solids and Nets I12: Views of Solid Figures I13: Geometric Ideas I14: Congruent Figures I15: Circles I16: Rotational Symmetry I17: Transformations I18: Measuring and Classifying Angles I19: Angle Pairs I20: Missing Angles in Triangles and Quadrilaterals I21: Measuring Length to 1/2 and 1/4 Inch I22: Using Customary Units of Length I23: Using Metric Units of Length I24: Using Customary Units of Capacity I25: Using Metric Units of Capacity I26: Using Customary Units of Weight I27: Using Metric Units of Mass I28: Time to the Quarter Hour I29: Telling Time I30: Units of Time Curriculum Standards: Convert standard measurements of time to solve real-world problems. I31: Elapsed Time I32: Converting Customary Units of Length Curriculum Standards: Convert standard measurements of length to solve real-world problems. I33: Converting Customary Units of Capacity I34: Converting Customary Units of Weight Curriculum Standards: Convert standard measurements of mass to solve real-world problems. I35: Converting Metric Units Curriculum Standards: Convert standard measurements of length to solve real-world problems. Convert standard measurements of mass to solve real-world problems. I36: Converting Between Measurement Systems I37: Units of Measure and Precision I38: More Units of Time Curriculum Standards: Convert standard measurements of time to solve real-world problems. I39: More Elapsed Time I40: Elapsed Time in Other Units I41: Perimeter I42: Exploring Area I43: Finding Area on a Grid I44: More Perimeter I45: Area of Rectangles and Squares I46: Area of Irregular Figures I47: Rectangles with the Same Area or Perimeter I48: Area of Parallelograms I49: Area of Triangles I50: Circumference I51: Area of a Circle I52: Surface Area of Rectangular Prisms I53: Surface Area I54: Counting Cubes to Find Volume Curriculum Standards: Use packing to recognize volume of a solid figure. Connect the layers to the dimensions and multiply to find the volume of the rectangular prism. Determine the volume of a rectangular prism built by “unit cubes.” Use addition to determine the length, width, and height. Use multiplication to represent each layer of the rectangular prism. I55: Measuring Volume Curriculum Standards: Use packing to recognize volume of a solid figure. Connect the layers to the dimensions and multiply to find the volume of the rectangular prism. Determine the volume of a rectangular prism built by “unit cubes.” Use addition to determine the length, width, and height. Use multiplication to represent each layer of the rectangular prism. I56: Comparing Volume and Surface Area I57: Recording Data from a Survey I58: Reading and Making Pictographs I59: Reading and Making a Bar Graph I60: Making Line Plots Curriculum Standards: Collect and graph fractional data on a line plot (e.g., length of each person’s pencil in classroom, hours of exercise each week). I61: Interpreting Graphs I62: Stem-and-Leaf Plots I63: Histograms I64: Finding the Mean I65: Median, Mode, and Range I66: Scatterplots I67: Measuring Capacity or Weight I68: Solving Problems with Units of Time I69: Making Dot Plots I70: Converting Units I71: Line Plots Curriculum Standards: Collect and graph fractional data on a line plot (e.g., length of each person’s pencil in classroom, hours of exercise each week). I72: Combining Volumes I73: Polygons on the Coordinate Plane I74: Statistical Questions I75: Box Plots I76: Measures of Variability I77: Appropriate Use of Statistical Measures I78: Summarize Data Distributions Booklet J: Problem Solving in Grades 4-6 J1: Analyze Given Information J2: Two-Step Problems Curriculum Standards: Solve one-step problems using decimals. J3: Multi-Step Problems J4: Two-Step Problems Curriculum Standards: Solve one-step problems using decimals. J5: Multi-Step Problems J6: Make an Organized List J7: Make an Organized List J8: Analyze Given Information J9: Draw a Picture and Write a Number Sentence J10: Draw a Picture and Write a Number Sentence J11: Draw a Strip Diagram and Write an Equation J12: Draw a Strip Diagram and Write an Equation J13: Try, Check, and Revise J14: Try, Check, and Revise J15: Solve a Simpler Problem J16: Use Representations J17: Make a Table and Look for a Pattern Curriculum Standards: Given two pattern descriptions involving the same context (e.g., collecting marbles), determine the first five terms and compare the values. J18: Solve a Simpler Problem J19: Make a Table and Look for a Pattern J20: Analyze Relationships J21: Use Objects J22: Use Objects J23: Use Reasoning J24: Use Reasoning J25: Draw a Picture J26: Draw a Picture J27: Work Backward J28: Work Backward J29: Make a Graph J30: Make a Graph J31: Analyze Relationships J32: Make and Test Generalizations J33: Make and Test Conjectures J34: Reasonableness J35: Reasonableness J36: Use Representations J37: Writing to Explain J38: Writing to Explain J39: Make and Test Generalizations J40: Make and Test Conjectures Diagnostic Tests and Answer Keys, Grades 4-6 Grade 4 Diagnostic Test, Form A Grade 4 Diagnostic Test, Form B Grade 5 Diagnostic Test, Form A Grade 5 Diagnostic Test, Form B Grade 6 Diagnostic Test, Form A Grade 6 Diagnostic Test, Form B Grade 5 Spanish Assessments Evaluación de conocimientos para el Grado 5 Temas 1 a 4: Evaluación acumulativa/de referencia Temas 1 a 8: Evaluación acumulativa/de referencia Temas 1 a 12: Evaluación acumulativa/de referencia Temas 1 a 16: Evaluación acumulativa/de referencia Evaluación para observar el progreso, Forma A Evaluación para observar el progreso, Forma B Evaluación para observar el progreso, Forma C Grade 5: State-Specific Resources Minnesota Grade 5 MN-1: Find 0.1, 0.01, or 0.001 More or Less Than a Number Curriculum Standards: Find 0.1 more than a number and 0.1 less than a number. Find 0.01 more than a number and 0.01 less than a number. Find 0.001 more than a number and 0.001 less than a number. MN-2: Fractions, Mixed Numbers, and Decimals Curriculum Standards: Recognize and generate equivalent decimals, fractions, mixed numbers and improper fractions in various contexts. MN-3: Display and Interpret Data: Double Bar Graphs Curriculum Standards: 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. MN-4: Understand Mean Curriculum Standards: Know and use the definitions of the mean, median and range of a set of data. Know how to use a spreadsheet to find the mean, median and range of a data set. Understand that the mean is a “leveling out” of data. MN-5: Median, Mode, and Range Curriculum Standards: Know and use the definitions of the mean, median and range of a set of data. Know how to use a spreadsheet to find the mean, median and range of a data set. Understand that the mean is a “leveling out” of data. MN-6: Describe and Classify 3-D Figures Curriculum Standards: Describe and classify three-dimensional figures including cubes, prisms and pyramids by the number of edges, faces or vertices as well as the types of faces. MN-7: Solid Figures and Nets Curriculum Standards: Recognize and draw a net for a three-dimensional figure. MN-8: Variables and Expressions Curriculum Standards: Evaluate expressions and solve equations involving variables when values for the variables are given. MN-9: Variables, Expressions, and Equations Curriculum Standards: Evaluate expressions and solve equations involving variables when values for the variables are given. MN-10: Understand Equations and Solutions Curriculum Standards: Determine whether an equation or inequality involving a variable is true or false for a given value of the variable. Represent real-world situations using equations and inequalities involving variables. Create real-world situations corresponding to equations and inequalities. MN-11: Understand Inequalities with Variables Curriculum Standards: Determine whether an equation or inequality involving a variable is true or false for a given value of the variable. Represent real-world situations using equations and inequalities involving variables. Create real-world situations corresponding to equations and inequalities. MN-12: Display and Interpret Data: Double Line Graphs Curriculum Standards: 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. MN-14: Areas of Triangles Curriculum Standards: Develop and use formulas to determine the area of triangles, parallelograms and figures that can be decomposed into triangles. 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1-4: Daily Review: Editable Worksheet Intended Role: Instructor 1-4: Daily Review: Answer Key Intended Role: Instructor Topic 1: Today's Challenge Teacher Guide Intended Role: Instructor 1-4: Solve & Share Solution Intended Role: Instructor 1-4: Solve & Share Solution Intended Role: Instructor 1-4: Printable Additional Practice Intended Role: Instructor 1-4: Additional Practice: Editable Assessment Intended Role: Instructor 1-4: Quick Check: Answer Key Intended Role: Instructor 1-4: Printable Quick Check Intended Role: Instructor 1-4: Reteach to Build Understanding: Answer Key Intended Role: Instructor 1-4: Reteach to Build Understanding: Editable Worksheet Intended Role: Instructor 1-4: Build Mathematical Literacy: Answer Key Intended Role: Instructor 1-4: Build Mathematical Literacy: Editable Worksheet Intended Role: Instructor 1-4: Enrichment: Answer Key Intended Role: Instructor 1-4: Enrichment: Editable Worksheet Intended Role: Instructor Topic 1: Problem-Solving Leveled Reading Mat Intended Role: Instructor 1-4: eText del Libro del estudiante: Clave de respuestas Intended Role: Instructor 1-4: Repaso diario: Clave de respuestas Intended Role: Instructor 1-4: Práctica adicional Intended Role: Instructor 1-4: Práctica adicional: Clave de respuestas Intended Role: Instructor 1-4: Refuerzo para mejorar la comprensión: Clave de respuestas Intended Role: Instructor 1-4: Desarrollar la competencia matemática: Clave de respuestas Intended Role: Instructor 1-4: Ampliación: Clave de respuestas Intended Role: Instructor 1-5: Lesson Plan Intended Role: Instructor Teacher's Edition eText: Grade 5 Lesson 1-5 Intended Role: Instructor 1-5: Listen & Look For Intended Role: Instructor 1-5: Daily Review: Editable Worksheet Intended Role: Instructor 1-5: Daily Review: Answer Key Intended Role: Instructor Topic 1: Today's Challenge Teacher Guide Intended Role: Instructor 1-5: Solve & Share Solution Intended Role: Instructor 1-5: Solve & Share Solution Intended Role: Instructor 1-5: Printable Additional Practice Intended Role: Instructor 1-5: Additional Practice: Editable Assessment Intended Role: Instructor 1-5: Quick Check: Answer Key Intended Role: Instructor 1-5: Printable Quick Check Intended Role: Instructor 1-5: Reteach to Build Understanding: Answer Key Intended Role: Instructor 1-5: Reteach to Build Understanding: Editable Worksheet Intended Role: Instructor 1-5: Build Mathematical Literacy: Answer Key Intended Role: Instructor 1-5: Build Mathematical Literacy: Editable Worksheet Intended Role: Instructor 1-5: Enrichment: Answer Key Intended Role: Instructor 1-5: Enrichment: Editable Worksheet Intended Role: Instructor 1-5: eText del Libro del estudiante: Clave de respuestas Intended Role: Instructor 1-5: Repaso diario: Clave de respuestas Intended Role: Instructor 1-5: Práctica adicional Intended Role: Instructor 1-5: Práctica adicional: Clave de respuestas Intended Role: Instructor 1-5: Refuerzo para mejorar la comprensión: Clave de respuestas Intended Role: Instructor 1-5: Desarrollar la competencia matemática: Clave de respuestas Intended Role: Instructor 1-5: Ampliación: Clave de respuestas Intended Role: Instructor 1-6: Lesson Plan Intended Role: Instructor Teacher's Edition eText: Grade 5 Lesson 1-6 Intended Role: Instructor 1-6: Listen & Look For Intended Role: Instructor 1-6: Daily Review: Editable Worksheet Intended Role: Instructor 1-6: Daily Review: Answer Key Intended Role: Instructor Topic 1: Today's Challenge Teacher Guide Intended Role: Instructor 1-6: Solve & Share Solution Intended Role: Instructor 1-6: Solve & Share Solution Intended Role: Instructor 1-6: Printable Additional Practice Intended Role: Instructor 1-6: Additional Practice: Editable Assessment Intended Role: Instructor 1-6: Quick Check: Answer Key Intended Role: Instructor 1-6: Printable Quick Check Intended Role: Instructor 1-6: Reteach to Build Understanding: Answer Key Intended Role: Instructor 1-6: Reteach to Build Understanding: Editable Worksheet Intended Role: Instructor 1-6: Build Mathematical Literacy: Answer Key Intended Role: Instructor 1-6: Build Mathematical Literacy: Editable Worksheet Intended Role: Instructor 1-6: Enrichment: Answer Key Intended Role: Instructor 1-6: Enrichment: Editable Worksheet Intended Role: Instructor Topic 1: Problem-Solving Leveled Reading Mat Intended Role: Instructor 1-6: eText del Libro del estudiante: Clave de respuestas Intended Role: Instructor 1-6: Repaso diario: Clave de respuestas Intended Role: Instructor 1-6: Práctica adicional Intended Role: Instructor 1-6: Práctica adicional: Clave de respuestas Intended Role: Instructor 1-6: Refuerzo para mejorar la comprensión: Clave de respuestas Intended Role: Instructor 1-6: Desarrollar la competencia matemática: Clave de respuestas Intended Role: Instructor 1-6: Ampliación: Clave de respuestas Intended Role: Instructor 1-7: Lesson Plan Intended Role: Instructor Teacher's Edition eText: Grade 5 Lesson 1-7 Intended Role: Instructor 1-7: Listen & Look For Intended Role: Instructor 1-7: Daily Review: Editable Worksheet Intended Role: Instructor 1-7: Daily Review: Answer Key Intended Role: Instructor Topic 1: Today's Challenge Teacher Guide Intended Role: Instructor 1-7: Solve & Share Solution Intended Role: Instructor 1-7: Solve & Share Solution Intended Role: Instructor 1-7: Printable Additional Practice Intended Role: Instructor 1-7: Additional Practice: Editable Assessment Intended Role: Instructor 1-7: Quick Check: Answer Key Intended Role: Instructor 1-7: Printable Quick Check Intended Role: Instructor 1-7: Reteach to Build Understanding: Answer Key Intended Role: Instructor 1-7: Reteach to Build Understanding: Editable Worksheet Intended Role: Instructor 1-7: Build Mathematical Literacy: Answer Key Intended Role: Instructor 1-7: Build Mathematical Literacy: Editable Worksheet Intended Role: Instructor 1-7: Enrichment: Answer Key Intended Role: Instructor 1-7: Enrichment: Editable Worksheet Intended Role: Instructor 1-7: eText del Libro del estudiante: Clave de respuestas Intended Role: Instructor 1-7: Repaso diario: Clave de respuestas Intended Role: Instructor 1-7: Práctica adicional Intended Role: Instructor 1-7: Práctica adicional: Clave de respuestas Intended Role: Instructor 1-7: Refuerzo para mejorar la comprensión: Clave de respuestas Intended Role: Instructor 1-7: Desarrollar la competencia matemática: Clave de respuestas Intended Role: Instructor 1-7: Ampliación: Clave de respuestas Intended Role: Instructor Topic 1: 3-Act Math Recording Sheets Intended Role: Instructor Teacher's Edition eText: Grade 5, Topic 1: 3-Act Math Intended Role: Instructor Topic 1: Vocabulary Review Intended Role: Instructor Topic 1: Reteaching Intended Role: Instructor Topic 1 Performance Task: Answer Key Intended Role: Instructor Topic 1 Performance Task: Editable Assessment Intended Role: Instructor Topic 1 Assessment: Answer Key Intended Role: Instructor Topic 1 Topic Assessments: Editable Assessment Intended Role: Instructor Topic 1 Online Assessment: Answer Key Intended Role: Instructor Topic 1 Online Assessment: Printable Intended Role: Instructor Tema 1: Tarea de rendimento: Clave de respuestas Intended Role: Instructor Tema 1: Evaluación: Clave de respuestas Intended Role: Instructor Topic 2: Home-School Connection Intended Role: Instructor Topic 2: Problem-Solving Reading Activity Guide Intended Role: Instructor Topic 2: Problem-Solving Leveled Reading Mat Intended Role: Instructor Topic 2: Home-School Connection(Spanish) Intended Role: Instructor Topic 2: Pick a Project (Spanish) Intended Role: Instructor Topic 2: enVision STEM Activity (Spanish) Intended Role: Instructor Teacher's Edition eText: Grade 5 Topic 2 Intended Role: Instructor Topic 2: Today's Challenge Teacher Guide Intended Role: Instructor 2-1: Lesson Plan Intended Role: Instructor Teacher's Edition eText: Grade 5 Lesson 2-1 Intended Role: Instructor 2-1: Listen & Look For Intended Role: Instructor 2-1: Daily Review: Editable Worksheet Intended Role: Instructor 2-1: Daily Review: Answer Key Intended Role: Instructor Topic 2: Today's Challenge Teacher Guide Intended Role: Instructor 2-1: Solve & Share Solution Intended Role: Instructor 2-1: Solve & Share Solution Intended Role: Instructor 2-1: Printable Additional Practice Intended Role: Instructor 2-1: Additional Practice: Editable Assessment Intended Role: Instructor 2-1: Quick Check: Answer Key Intended Role: Instructor 2-1: Printable Quick Check Intended Role: Instructor 2-1: Reteach to Build Understanding: Answer Key Intended Role: Instructor 2-1: Reteach to Build Understanding: Editable Worksheet Intended Role: Instructor 2-1: Build Mathematical Literacy: Answer Key Intended Role: Instructor 2-1: Build Mathematical Literacy: Editable Worksheet Intended Role: Instructor 2-1: Enrichment: Answer Key Intended Role: Instructor 2-1: Enrichment: Editable Worksheet Intended Role: Instructor Topic 2: Problem-Solving Leveled Reading Mat Intended Role: Instructor 2-1: eText del Libro del estudiante: Clave de respuestas Intended Role: Instructor 2-1: Repaso diario: Clave de respuestas Intended Role: Instructor 2-1: Práctica adicional Intended Role: Instructor 2-1: Práctica adicional: Clave de respuestas Intended Role: Instructor 2-1: Refuerzo para mejorar la comprensión: Clave de respuestas Intended Role: Instructor 2-1: Desarrollar la competencia matemática: Clave de respuestas Intended Role: Instructor 2-1: Ampliación: Clave de respuestas Intended Role: Instructor 2-2: Lesson Plan Intended Role: Instructor Teacher's Edition eText: Grade 5 Lesson 2-2 Intended Role: Instructor 2-2: Listen & Look For Intended Role: Instructor 2-2: Daily Review: Editable Worksheet Intended Role: Instructor 2-2: Daily Review: Answer Key Intended Role: Instructor Topic 2: Today's Challenge Teacher Guide Intended Role: Instructor 2-2: Solve & Share Solution Intended Role: Instructor 2-2: Solve & Share Solution Intended Role: Instructor 2-2: Printable Additional Practice Intended Role: Instructor 2-2: Additional Practice: Editable Assessment Intended Role: Instructor 2-2: Quick Check: Answer Key Intended Role: Instructor 2-2: Printable Quick Check Intended Role: Instructor 2-2: Reteach to Build Understanding: Answer Key Intended Role: Instructor 2-2: Reteach to Build Understanding: Editable Worksheet Intended Role: Instructor 2-2: Build Mathematical Literacy: Answer Key Intended Role: Instructor 2-2: Build Mathematical Literacy: Editable Worksheet Intended Role: Instructor 2-2: Enrichment: Answer Key Intended Role: Instructor 2-2: Enrichment: Editable Worksheet Intended Role: Instructor 2-2: eText del Libro del estudiante: Clave de respuestas Intended Role: Instructor 2-2: Repaso diario: Clave de respuestas Intended Role: Instructor 2-2: Práctica adicional Intended Role: Instructor 2-2: Práctica adicional: Clave de respuestas Intended Role: Instructor 2-2: Refuerzo para mejorar la comprensión: Clave de respuestas Intended Role: Instructor 2-2: Desarrollar la competencia matemática: Clave de respuestas Intended Role: Instructor 2-2: Ampliación: Clave de respuestas Intended Role: Instructor 2-3: Lesson Plan Intended Role: Instructor Teacher's Edition eText: Grade 5 Lesson 2-3 Intended Role: Instructor 2-3: Daily Review: Editable Worksheet Intended Role: Instructor 2-3: Daily Review: Answer Key Intended Role: Instructor Topic 2: Today's Challenge Teacher Guide Intended Role: Instructor 2-3: Solve & Share Solution Intended Role: Instructor 2-3: Solve & Share Solution Intended Role: Instructor 2-3: Printable Additional Practice Intended Role: Instructor 2-3: Additional Practice: Editable Assessment Intended Role: Instructor 2-3: Quick Check: Answer Key Intended Role: Instructor 2-3: Printable Quick Check Intended Role: Instructor 2-3: Reteach to Build Understanding: Answer Key Intended Role: Instructor 2-3: Reteach to Build Understanding: Editable Worksheet Intended Role: Instructor 2-3: Build Mathematical Literacy: Answer Key Intended Role: Instructor 2-3: Build Mathematical Literacy: Editable Worksheet Intended Role: Instructor 2-3: Enrichment: Answer Key Intended Role: Instructor 2-3: Enrichment: Editable Worksheet Intended Role: Instructor 2-3: eText del Libro del estudiante: Clave de respuestas Intended Role: Instructor 2-3: Repaso diario: Clave de respuestas Intended Role: Instructor 2-3: Práctica adicional Intended Role: Instructor 2-3: Práctica adicional: Clave de respuestas Intended Role: Instructor 2-3: Refuerzo para mejorar la comprensión: Clave de respuestas Intended Role: Instructor 2-3: Desarrollar la competencia matemática: Clave de respuestas Intended Role: Instructor 2-3: Ampliación: Clave de respuestas Intended Role: Instructor 2-4: Lesson Plan Intended Role: Instructor Teacher's Edition eText: Grade 5 Lesson 2-4 Intended Role: Instructor 2-4: Daily Review: Editable Worksheet Intended Role: Instructor 2-4: Daily Review: Answer Key Intended Role: Instructor Topic 2: Today's Challenge Teacher Guide Intended Role: Instructor 2-4: Solve & Share Solution Intended Role: Instructor 2-4: Solve & Share Solution Intended Role: Instructor 2-4: Printable Additional Practice Intended Role: Instructor 2-4: Additional Practice: Editable Assessment Intended Role: Instructor 2-4: Quick Check: Answer Key Intended Role: Instructor 2-4: Printable Quick Check Intended Role: Instructor 2-4: Reteach to Build Understanding: Answer Key Intended Role: Instructor 2-4: Reteach to Build Understanding: Editable Worksheet Intended Role: Instructor 2-4: Build Mathematical Literacy: Answer Key Intended Role: Instructor 2-4: Build Mathematical Literacy: Editable Worksheet Intended Role: Instructor 2-4: Enrichment: Answer Key Intended Role: Instructor 2-4: Enrichment: Editable Worksheet Intended Role: Instructor 2-4: eText del Libro del estudiante: Clave de respuestas Intended Role: Instructor 2-4: Repaso diario: Clave de respuestas Intended Role: Instructor 2-4: Práctica adicional Intended Role: Instructor 2-4: Práctica adicional: Clave de respuestas Intended Role: Instructor 2-4: Refuerzo para mejorar la comprensión: Clave de respuestas Intended Role: Instructor 2-4: Desarrollar la competencia matemática: Clave de respuestas Intended Role: Instructor 2-4: Ampliación: Clave de respuestas Intended Role: Instructor 2-5: Lesson Plan Intended Role: Instructor Teacher's Edition eText: Grade 5 Lesson 2-5 Intended Role: Instructor 2-5: Daily Review: Editable Worksheet Intended Role: Instructor 2-5: Daily Review: Answer Key Intended Role: Instructor Topic 2: Today's Challenge Teacher Guide Intended Role: Instructor 2-5: Solve & Share Solution Intended Role: Instructor 2-5: Solve & Share Solution Intended Role: Instructor 2-5: Printable Additional Practice Intended Role: Instructor 2-5: Additional Practice: Editable Assessment Intended Role: Instructor 2-5: Quick Check: Answer Key Intended Role: Instructor 2-5: Printable Quick Check Intended Role: Instructor 2-5: Reteach to Build Understanding: Answer Key Intended Role: Instructor 2-5: Reteach to Build Understanding: Editable Worksheet Intended Role: Instructor 2-5: Build Mathematical Literacy: Answer Key Intended Role: Instructor 2-5: Build Mathematical Literacy: Editable Worksheet Intended Role: Instructor 2-5: Enrichment: Answer Key Intended Role: Instructor 2-5: Enrichment: Editable Worksheet Intended Role: Instructor 2-5: eText del Libro del estudiante: Clave de respuestas Intended Role: Instructor 2-5: Repaso diario: Clave de respuestas Intended Role: Instructor 2-5: Práctica adicional Intended Role: Instructor 2-5: Práctica adicional: Clave de respuestas Intended Role: Instructor 2-5: Refuerzo para mejorar la comprensión: Clave de respuestas Intended Role: Instructor 2-5: Desarrollar la competencia matemática: Clave de respuestas Intended Role: Instructor 2-5: Ampliación: Clave de respuestas Intended Role: Instructor 2-6: Lesson Plan Intended Role: Instructor Teacher's Edition eText: Grade 5 Lesson 2-6 Intended Role: Instructor 2-6: Daily Review: Editable Worksheet Intended Role: Instructor 2-6: Daily Review: Answer Key Intended Role: Instructor Topic 2: Today's Challenge Teacher Guide Intended Role: Instructor 2-6: Solve & Share Solution Intended Role: Instructor 2-6: Solve & Share Solution Intended Role: Instructor 2-6: Printable Additional Practice Intended Role: Instructor 2-6: Additional Practice: Editable Assessment Intended Role: Instructor 2-6: Quick Check: Answer Key Intended Role: Instructor 2-6: Printable Quick Check Intended Role: Instructor 2-6: Reteach to Build Understanding: Answer Key Intended Role: Instructor 2-6: Reteach to Build Understanding: Editable Worksheet Intended Role: Instructor 2-6: Build Mathematical Literacy: Answer Key Intended Role: Instructor 2-6: Build Mathematical Literacy: Editable Worksheet Intended Role: Instructor 2-6: Enrichment: Answer Key Intended Role: Instructor 2-6: Enrichment: Editable Worksheet Intended Role: Instructor Topic 2: Problem-Solving Leveled Reading Mat Intended Role: Instructor 2-6: eText del Libro del estudiante: Clave de respuestas Intended Role: Instructor 2-6: Repaso diario: Clave de respuestas Intended Role: Instructor 2-6: Práctica adicional Intended Role: Instructor 2-6: Práctica adicional: Clave de respuestas Intended Role: Instructor 2-6: Refuerzo para mejorar la comprensión: Clave de respuestas Intended Role: Instructor 2-6: Desarrollar la competencia matemática: Clave de respuestas Intended Role: Instructor 2-6: Ampliación: Clave de respuestas Intended Role: Instructor Topic 2: Vocabulary Review Intended Role: Instructor Topic 2: Reteaching Intended Role: Instructor Topic 2 Performance Task: Answer Key Intended Role: Instructor Topic 2 Performance Task: Editable Assessment Intended Role: Instructor Topic 2 Assessment: Answer Key Intended Role: Instructor Topic 2 Topic Assessments: Editable Assessment Intended Role: Instructor Topic 2 Online Assessment: Answer Key Intended Role: Instructor Topic 2 Online Assessment: Printable Intended Role: Instructor Tema 2: Tarea de rendimento: Clave de respuestas Intended Role: Instructor Tema 2: Evaluación: Clave de respuestas Intended Role: Instructor Topic 3: Home-School Connection Intended Role: Instructor Topic 3: Problem-Solving Reading Activity Guide Intended Role: Instructor Fluency Practice/Assessment Master Intended Role: Instructor Fluency Practice/Assessment Master: Answer Key Intended Role: Instructor Topic 3: Fluency/Practice Assessment (Spanish) Intended Role: Instructor Topic 3: Fluency/Practice Assessment: Answer Key (Spanish) Intended Role: Instructor Topic 3: Problem-Solving Leveled Reading Mat Intended Role: Instructor Topic 3: Home-School Connection(Spanish) Intended Role: Instructor Topic 3: Pick a Project (Spanish) Intended Role: Instructor Topic 3: enVision STEM Activity (Spanish) Intended Role: Instructor Teacher's Edition eText: Grade 5 Topic 3 Intended Role: Instructor Topic 3: Professional Development Video Intended Role: Instructor Topic 3: Today's Challenge Teacher Guide Intended Role: Instructor 3-1: Lesson Plan Intended Role: Instructor Teacher's Edition eText: Grade 5 Lesson 3-1 Intended Role: Instructor 3-1: Listen & Look For Intended Role: Instructor 3-1: Daily Review: Editable Worksheet Intended Role: Instructor 3-1: Daily Review: Answer Key Intended Role: Instructor Topic 3: Today's Challenge Teacher Guide Intended Role: Instructor 3-1: Solve & Share Solution Intended Role: Instructor 3-1: Solve & Share Solution Intended Role: Instructor 3-1: Printable Additional Practice Intended Role: Instructor 3-1: Additional Practice: Editable Assessment Intended Role: Instructor 3-1: Quick Check: Answer Key Intended Role: Instructor 3-1: Printable Quick Check Intended Role: Instructor 3-1: Reteach to Build Understanding: Answer Key Intended Role: Instructor 3-1: Reteach to Build Understanding: Editable Worksheet Intended Role: Instructor 3-1: Build Mathematical Literacy: Answer Key Intended Role: Instructor 3-1: Build Mathematical Literacy: Editable Worksheet Intended Role: Instructor 3-1: Enrichment: Answer Key Intended Role: Instructor 3-1: Enrichment: Editable Worksheet Intended Role: Instructor 3-1: eText del Libro del estudiante: Clave de respuestas Intended Role: Instructor 3-1: Repaso diario: Clave de respuestas Intended Role: Instructor 3-1: Práctica adicional Intended Role: Instructor 3-1: Práctica adicional: Clave de respuestas Intended Role: Instructor 3-1: Refuerzo para mejorar la comprensión: Clave de respuestas Intended Role: Instructor 3-1: Desarrollar la competencia matemática: Clave de respuestas Intended Role: Instructor 3-1: Ampliación: Clave de respuestas Intended Role: Instructor 3-2: Lesson Plan Intended Role: Instructor Teacher's Edition eText: Grade 5 Lesson 3-2 Intended Role: Instructor 3-2: Listen & Look For Intended Role: Instructor 3-2: Daily Review: Editable Worksheet Intended Role: Instructor 3-2: Daily Review: Answer Key Intended Role: Instructor Topic 3: Today's Challenge Teacher Guide Intended Role: Instructor 3-2: Solve & Share Solution Intended Role: Instructor 3-2: Solve & Share Solution Intended Role: Instructor 3-2: Printable Additional Practice Intended Role: Instructor 3-2: Additional Practice: Editable Assessment Intended Role: Instructor 3-2: Quick Check: Answer Key Intended Role: Instructor 3-2: Printable Quick Check Intended Role: Instructor 3-2: Reteach to Build Understanding: Answer Key Intended Role: Instructor 3-2: Reteach to Build Understanding: Editable Worksheet Intended Role: Instructor 3-2: Build Mathematical Literacy: Answer Key Intended Role: Instructor 3-2: Build Mathematical Literacy: Editable Worksheet Intended Role: Instructor 3-2: Enrichment: Answer Key Intended Role: Instructor 3-2: Enrichment: Editable Worksheet Intended Role: Instructor Topic 3: Problem-Solving Leveled Reading Mat Intended Role: Instructor 3-2: eText del Libro del estudiante: Clave de respuestas Intended Role: Instructor 3-2: Repaso diario: Clave de respuestas Intended Role: Instructor 3-2: Práctica adicional Intended Role: Instructor 3-2: Práctica adicional: Clave de respuestas Intended Role: Instructor 3-2: Refuerzo para mejorar la comprensión: Clave de respuestas Intended Role: Instructor 3-2: Desarrollar la competencia matemática: Clave de respuestas Intended Role: Instructor 3-2: Ampliación: Clave de respuestas Intended Role: Instructor 3-3: Lesson Plan Intended Role: Instructor Teacher's Edition eText: Grade 5 Lesson 3-3 Intended Role: Instructor 3-3: Listen & Look For Intended Role: Instructor 3-3: Daily Review: Editable Worksheet Intended Role: Instructor 3-3: Daily Review: Answer Key Intended Role: Instructor Topic 3: Today's Challenge Teacher Guide Intended Role: Instructor 3-3: Solve & Share Solution Intended Role: Instructor 3-3: Solve & Share Solution Intended Role: Instructor 3-3: Printable Additional Practice Intended Role: Instructor 3-3: Additional Practice: Editable Assessment Intended Role: Instructor 3-3: Quick Check: Answer Key Intended Role: Instructor 3-3: Printable Quick Check Intended Role: Instructor 3-3: Reteach to Build Understanding: Answer Key Intended Role: Instructor 3-3: Reteach to Build Understanding: Editable Worksheet Intended Role: Instructor 3-3: Build Mathematical Literacy: Answer Key Intended Role: Instructor 3-3: Build Mathematical Literacy: Editable Worksheet Intended Role: Instructor 3-3: Enrichment: Answer Key Intended Role: Instructor 3-3: Enrichment: Editable Worksheet Intended Role: Instructor 3-3: eText del Libro del estudiante: Clave de respuestas Intended Role: Instructor 3-3: Repaso diario: Clave de respuestas Intended Role: Instructor 3-3: Práctica adicional Intended Role: Instructor 3-3: Práctica adicional: Clave de respuestas Intended Role: Instructor 3-3: Refuerzo para mejorar la comprensión: Clave de respuestas Intended Role: Instructor 3-3: Desarrollar la competencia matemática: Clave de respuestas Intended Role: Instructor 3-3: Ampliación: Clave de respuestas Intended Role: Instructor 3-4: Lesson Plan Intended Role: Instructor Teacher's Edition eText: Grade 5 Lesson 3-4 Intended Role: Instructor 3-4: Listen & Look For Intended Role: Instructor 3-4: Daily Review: Editable Worksheet Intended Role: Instructor 3-4: Daily Review: Answer Key Intended Role: Instructor Topic 3: Today's Challenge Teacher Guide Intended Role: Instructor 3-4: Solve & Share Solution Intended Role: Instructor 3-4: Solve & Share Solution Intended Role: Instructor 3-4: Printable Additional Practice Intended Role: Instructor 3-4: Additional Practice: Editable Assessment Intended Role: Instructor 3-4: Quick Check: Answer Key Intended Role: Instructor 3-4: Printable Quick Check Intended Role: Instructor 3-4: Reteach to Build Understanding: Answer Key Intended Role: Instructor 3-4: Reteach to Build Understanding: Editable Worksheet Intended Role: Instructor 3-4: Build Mathematical Literacy: Answer Key Intended Role: Instructor 3-4: Build Mathematical Literacy: Editable Worksheet Intended Role: Instructor 3-4: Enrichment: Answer Key Intended Role: Instructor 3-4: Enrichment: Editable Worksheet Intended Role: Instructor 3-4: eText del Libro del estudiante: Clave de respuestas Intended Role: Instructor 3-4: Repaso diario: Clave de respuestas Intended Role: Instructor 3-4: Práctica adicional Intended Role: Instructor 3-4: Práctica adicional: Clave de respuestas Intended Role: Instructor 3-4: Refuerzo para mejorar la comprensión: Clave de respuestas Intended Role: Instructor 3-4: Desarrollar la competencia matemática: Clave de respuestas Intended Role: Instructor 3-4: Ampliación: Clave de respuestas Intended Role: Instructor 3-5: Lesson Plan Intended Role: Instructor Teacher's Edition eText: Grade 5 Lesson 3-5 Intended Role: Instructor 3-5: Listen & Look For Intended Role: Instructor 3-5: Daily Review: Editable Worksheet Intended Role: Instructor 3-5: Daily Review: Answer Key Intended Role: Instructor Topic 3: Today's Challenge Teacher Guide Intended Role: Instructor 3-5: Solve & Share Solution Intended Role: Instructor 3-5: Solve & Share Solution Intended Role: Instructor 3-5: Printable Additional Practice Intended Role: Instructor 3-5: Additional Practice: Editable Assessment Intended Role: Instructor 3-5: Quick Check: Answer Key Intended Role: Instructor 3-5: Printable Quick Check Intended Role: Instructor 3-5: Reteach to Build Understanding: Answer Key Intended Role: Instructor 3-5: Reteach to Build Understanding: Editable Worksheet Intended Role: Instructor 3-5: Build Mathematical Literacy: Answer Key Intended Role: Instructor 3-5: Build Mathematical Literacy: Editable Worksheet Intended Role: Instructor 3-5: Enrichment: Answer Key Intended Role: Instructor 3-5: Enrichment: Editable Worksheet Intended Role: Instructor 3-5: eText del Libro del estudiante: Clave de respuestas Intended Role: Instructor 3-5: Repaso diario: Clave de respuestas Intended Role: Instructor 3-5: Práctica adicional Intended Role: Instructor 3-5: Práctica adicional: Clave de respuestas Intended Role: Instructor 3-5: Refuerzo para mejorar la comprensión: Clave de respuestas Intended Role: Instructor 3-5: Desarrollar la competencia matemática: Clave de respuestas Intended Role: Instructor 3-5: Ampliación: Clave de respuestas Intended Role: Instructor Topic 3: 3-Act Math Recording Sheets Intended Role: Instructor Teacher's Edition eText: Grade 5, Topic 3: 3-Act Math Intended Role: Instructor 3-6: Lesson Plan Intended Role: Instructor Teacher's Edition eText: Grade 5 Lesson 3-6 Intended Role: Instructor 3-6: Listen & Look For Intended Role: Instructor 3-6: Daily Review: Editable Worksheet Intended Role: Instructor 3-6: Daily Review: Answer Key Intended Role: Instructor Topic 3: Today's Challenge Teacher Guide Intended Role: Instructor 3-6: Solve & Share Solution Intended Role: Instructor 3-6: Solve & Share Solution Intended Role: Instructor 3-6: Printable Additional Practice Intended Role: Instructor 3-6: Additional Practice: Editable Assessment Intended Role: Instructor 3-6: Quick Check: Answer Key Intended Role: Instructor 3-6: Printable Quick Check Intended Role: Instructor 3-6: Reteach to Build Understanding: Answer Key Intended Role: Instructor 3-6: Reteach to Build Understanding: Editable Worksheet Intended Role: Instructor 3-6: Build Mathematical Literacy: Answer Key Intended Role: Instructor 3-6: Build Mathematical Literacy: Editable Worksheet Intended Role: Instructor 3-6: Enrichment: Answer Key Intended Role: Instructor 3-6: Enrichment: Editable Worksheet Intended Role: Instructor Topic 3: Problem-Solving Leveled Reading Mat Intended Role: Instructor 3-6: eText del Libro del estudiante: Clave de respuestas Intended Role: Instructor 3-6: Repaso diario: Clave de respuestas Intended Role: Instructor 3-6: Práctica adicional Intended Role: Instructor 3-6: Práctica adicional: Clave de respuestas Intended Role: Instructor 3-6: Refuerzo para mejorar la comprensión: Clave de respuestas Intended Role: Instructor 3-6: Desarrollar la competencia matemática: Clave de respuestas Intended Role: Instructor 3-6: Ampliación: Clave de respuestas Intended Role: Instructor 3-7: Lesson Plan Intended Role: Instructor Teacher's Edition eText: Grade 5 Lesson 3-7 Intended Role: Instructor 3-7: Listen & Look For Intended Role: Instructor 3-7: Daily Review: Editable Worksheet Intended Role: Instructor 3-7: Daily Review: Answer Key Intended Role: Instructor Topic 3: Today's Challenge Teacher Guide Intended Role: Instructor 3-7: Solve & Share Solution Intended Role: Instructor 3-7: Solve & Share Solution Intended Role: Instructor 3-7: Printable Additional Practice Intended Role: Instructor 3-7: Additional Practice: Editable Assessment Intended Role: Instructor 3-7: Quick Check: Answer Key Intended Role: Instructor 3-7: Printable Quick Check Intended Role: Instructor 3-7: Reteach to Build Understanding: Answer Key Intended Role: Instructor 3-7: Reteach to Build Understanding: Editable Worksheet Intended Role: Instructor 3-7: Build Mathematical Literacy: Answer Key Intended Role: Instructor 3-7: Build Mathematical Literacy: Editable Worksheet Intended Role: Instructor 3-7: Enrichment: Answer Key Intended Role: Instructor 3-7: Enrichment: Editable Worksheet Intended Role: Instructor 3-7: eText del Libro del estudiante: Clave de respuestas Intended Role: Instructor 3-7: Repaso diario: Clave de respuestas Intended Role: Instructor 3-7: Práctica adicional Intended Role: Instructor 3-7: Práctica adicional: Clave de respuestas Intended Role: Instructor 3-7: Refuerzo para mejorar la comprensión: Clave de respuestas Intended Role: Instructor 3-7: Desarrollar la competencia matemática: Clave de respuestas Intended Role: Instructor 3-7: Ampliación: Clave de respuestas Intended Role: Instructor 3-8: Lesson Plan Intended Role: Instructor Teacher's Edition eText: Grade 5 Lesson 3-8 Intended Role: Instructor 3-8: Listen & Look For Intended Role: Instructor 3-8: Daily Review: Editable Worksheet Intended Role: Instructor 3-8: Daily Review: Answer Key Intended Role: Instructor Topic 3: Today's Challenge Teacher Guide Intended Role: Instructor 3-8: Solve & Share Solution Intended Role: Instructor 3-8: Solve & Share Solution Intended Role: Instructor 3-8: Printable Additional Practice Intended Role: Instructor 3-8: Additional Practice: Editable Assessment Intended Role: Instructor 3-8: Quick Check: Answer Key Intended Role: Instructor 3-8: Printable Quick Check Intended Role: Instructor 3-8: Reteach to Build Understanding: Answer Key Intended Role: Instructor 3-8: Reteach to Build Understanding: Editable Worksheet Intended Role: Instructor 3-8: Build Mathematical Literacy: Answer Key Intended Role: Instructor 3-8: Build Mathematical Literacy: Editable Worksheet Intended Role: Instructor 3-8: Enrichment: Answer Key Intended Role: Instructor 3-8: Enrichment: Editable Worksheet Intended Role: Instructor 3-8: eText del Libro del estudiante: Clave de respuestas Intended Role: Instructor 3-8: Repaso diario: Clave de respuestas Intended Role: Instructor 3-8: Práctica adicional Intended Role: Instructor 3-8: Práctica adicional: Clave de respuestas Intended Role: Instructor 3-8: Refuerzo para mejorar la comprensión: Clave de respuestas Intended Role: Instructor 3-8: Desarrollar la competencia matemática: Clave de respuestas Intended Role: Instructor 3-8: Ampliación: Clave de respuestas Intended Role: Instructor 3-9: Lesson Plan Intended Role: Instructor Teacher's Edition eText: Grade 5 Lesson 3-9 Intended Role: Instructor 3-9: Listen & Look For Intended Role: Instructor 3-9: Daily Review: Editable Worksheet Intended Role: Instructor 3-9: Daily Review: Answer Key Intended Role: Instructor Topic 3: Today's Challenge Teacher Guide Intended Role: Instructor 3-9: Solve & Share Solution Intended Role: Instructor 3-9: Solve & Share Solution Intended Role: Instructor 3-9: Printable Additional Practice Intended Role: Instructor 3-9: Additional Practice: Editable Assessment Intended Role: Instructor 3-9: Quick Check: Answer Key Intended Role: Instructor 3-9: Printable Quick Check Intended Role: Instructor 3-9: Reteach to Build Understanding: Answer Key Intended Role: Instructor 3-9: Reteach to Build Understanding: Editable Worksheet Intended Role: Instructor 3-9: Build Mathematical Literacy: Answer Key Intended Role: Instructor 3-9: Build Mathematical Literacy: Editable Worksheet Intended Role: Instructor 3-9: Enrichment: Answer Key Intended Role: Instructor 3-9: Enrichment: Editable Worksheet Intended Role: Instructor 3-9: eText del Libro del estudiante: Clave de respuestas Intended Role: Instructor 3-9: Repaso diario: Clave de respuestas Intended Role: Instructor 3-9: Práctica adicional Intended Role: Instructor 3-9: Práctica adicional: Clave de respuestas Intended Role: Instructor 3-9: Refuerzo para mejorar la comprensión: Clave de respuestas Intended Role: Instructor 3-9: Desarrollar la competencia matemática: Clave de respuestas Intended Role: Instructor 3-9: Ampliación: Clave de respuestas Intended Role: Instructor Topic 3: Vocabulary Review Intended Role: Instructor Topic 3: Reteaching Intended Role: Instructor Topic 3 Performance Task: Answer Key Intended Role: Instructor Topic 3 Performance Task: Editable Assessment Intended Role: Instructor Topic 3 Assessment: Answer Key Intended Role: Instructor Topic 3 Topic Assessments: Editable Assessment Intended Role: Instructor Topic 3 Online Assessment: Answer Key Intended Role: Instructor Topic 3 Online Assessment: Printable Intended Role: Instructor Tema 3: Tarea de rendimento: Clave de respuestas Intended Role: Instructor Tema 3: Evaluación: Clave de respuestas Intended Role: Instructor Topic 4: Home-School Connection Intended Role: Instructor Topic 4: Problem-Solving Reading Activity Guide Intended Role: Instructor Topic 4: Problem-Solving Leveled Reading Mat Intended Role: Instructor Topic 4: Home-School Connection(Spanish) Intended Role: Instructor Topic 4: Pick a Project (Spanish) Intended Role: Instructor Topic 4: enVision STEM Activity (Spanish) Intended Role: Instructor Teacher's Edition eText: Grade 5 Topic 4 Intended Role: Instructor Topic 4: Today's Challenge Teacher Guide Intended Role: Instructor 4-1: Lesson Plan Intended Role: Instructor Teacher's Edition eText: Grade 5 Lesson 4-1 Intended Role: Instructor 4-1: Listen & Look For Intended Role: Instructor 4-1: Daily Review: Editable Worksheet Intended Role: Instructor 4-1: Daily Review: Answer Key Intended Role: Instructor Topic 4: Today's Challenge Teacher Guide Intended Role: Instructor 4-1: Solve & Share Solution Intended Role: Instructor 4-1: Solve & Share Solution Intended Role: Instructor 4-1: Printable Additional Practice Intended Role: Instructor 4-1: Additional Practice: Editable Assessment Intended Role: Instructor 4-1: Quick Check: Answer Key Intended Role: Instructor 4-1: Printable Quick Check Intended Role: Instructor 4-1: Reteach to Build Understanding: Answer Key Intended Role: Instructor 4-1: Reteach to Build Understanding: Editable Worksheet Intended Role: Instructor 4-1: Build Mathematical Literacy: Answer Key Intended Role: Instructor 4-1: Build Mathematical Literacy: Editable Worksheet Intended Role: Instructor 4-1: Enrichment: Answer Key Intended Role: Instructor 4-1: Enrichment: Editable Worksheet Intended Role: Instructor 4-1: eText del Libro del estudiante: Clave de respuestas Intended Role: Instructor 4-1: Repaso diario: Clave de respuestas Intended Role: Instructor 4-1: Práctica adicional Intended Role: Instructor 4-1: Práctica adicional: Clave de respuestas Intended Role: Instructor 4-1: Refuerzo para mejorar la comprensión: Clave de respuestas Intended Role: Instructor 4-1: Desarrollar la competencia matemática: Clave de respuestas Intended Role: Instructor 4-1: Ampliación: Clave de respuestas Intended Role: Instructor 4-2: Lesson Plan Intended Role: Instructor Teacher's Edition eText: Grade 5 Lesson 4-2 Intended Role: Instructor 4-2: Listen & Look For Intended Role: Instructor 4-2: Daily Review: Editable Worksheet Intended Role: Instructor 4-2: Daily Review: Answer Key Intended Role: Instructor Topic 4: Today's Challenge Teacher Guide Intended Role: Instructor 4-2: Solve & Share Solution Intended Role: Instructor 4-2: Solve & Share Solution Intended Role: Instructor 4-2: Printable Additional Practice Intended Role: Instructor 4-2: Additional Practice: Editable Assessment Intended Role: Instructor 4-2: Quick Check: Answer Key Intended Role: Instructor 4-2: Printable Quick Check Intended Role: Instructor 4-2: Reteach to Build Understanding: Answer Key Intended Role: Instructor 4-2: Reteach to Build Understanding: Editable Worksheet Intended Role: Instructor 4-2: Build Mathematical Literacy: Answer Key Intended Role: Instructor 4-2: Build Mathematical Literacy: Editable Worksheet Intended Role: Instructor 4-2: Enrichment: Answer Key Intended Role: Instructor 4-2: Enrichment: Editable Worksheet Intended Role: Instructor 4-2: eText del Libro del estudiante: Clave de respuestas Intended Role: Instructor 4-2: Repaso diario: Clave de respuestas Intended Role: Instructor 4-2: Práctica adicional Intended Role: Instructor 4-2: Práctica adicional: Clave de respuestas Intended Role: Instructor 4-2: Refuerzo para mejorar la comprensión: Clave de respuestas Intended Role: Instructor 4-2: Desarrollar la competencia matemática: Clave de respuestas Intended Role: Instructor 4-2: Ampliación: Clave de respuestas Intended Role: Instructor 4-3: Lesson Plan Intended Role: Instructor Teacher's Edition eText: Grade 5 Lesson 4-3 Intended Role: Instructor 4-3: Daily Review: Editable Worksheet Intended Role: Instructor 4-3: Daily Review: Answer Key Intended Role: Instructor Topic 4: Today's Challenge Teacher Guide Intended Role: Instructor 4-3: Solve & Share Solution Intended Role: Instructor 4-3: Solve & Share Solution Intended Role: Instructor 4-3: Printable Additional Practice Intended Role: Instructor 4-3: Additional Practice: Editable Assessment Intended Role: Instructor 4-3: Quick Check: Answer Key Intended Role: Instructor 4-3: Printable Quick Check Intended Role: Instructor 4-3: Reteach to Build Understanding: Answer Key Intended Role: Instructor 4-3: Reteach to Build Understanding: Editable Worksheet Intended Role: Instructor 4-3: Build Mathematical Literacy: Answer Key Intended Role: Instructor 4-3: Build Mathematical Literacy: Editable Worksheet Intended Role: Instructor 4-3: Enrichment: Answer Key Intended Role: Instructor 4-3: Enrichment: Editable Worksheet Intended Role: Instructor Topic 4: Problem-Solving Leveled Reading Mat Intended Role: Instructor 4-3: eText del Libro del estudiante: Clave de respuestas Intended Role: Instructor 4-3: Repaso diario: Clave de respuestas Intended Role: Instructor 4-3: Práctica adicional Intended Role: Instructor 4-3: Práctica adicional: Clave de respuestas Intended Role: Instructor 4-3: Refuerzo para mejorar la comprensión: Clave de respuestas Intended Role: Instructor 4-3: Desarrollar la competencia matemática: Clave de respuestas Intended Role: Instructor 4-3: Ampliación: Clave de respuestas Intended Role: Instructor 4-4: Lesson Plan Intended Role: Instructor Teacher's Edition eText: Grade 5 Lesson 4-4 Intended Role: Instructor 4-4: Listen & Look For Intended Role: Instructor 4-4: Daily Review: Editable Worksheet Intended Role: Instructor 4-4: Daily Review: Answer Key Intended Role: Instructor Topic 4: Today's Challenge Teacher Guide Intended Role: Instructor 4-4: Solve & Share Solution Intended Role: Instructor 4-4: Solve & Share Solution Intended Role: Instructor 4-4: Printable Additional Practice Intended Role: Instructor 4-4: Additional Practice: Editable Assessment Intended Role: Instructor 4-4: Quick Check: Answer Key Intended Role: Instructor 4-4: Printable Quick Check Intended Role: Instructor 4-4: Reteach to Build Understanding: Answer Key Intended Role: Instructor 4-4: Reteach to Build Understanding: Editable Worksheet Intended Role: Instructor 4-4: Build Mathematical Literacy: Answer Key Intended Role: Instructor 4-4: Build Mathematical Literacy: Editable Worksheet Intended Role: Instructor 4-4: Enrichment: Answer Key Intended Role: Instructor 4-4: Enrichment: Editable Worksheet Intended Role: Instructor 4-4: eText del Libro del estudiante: Clave de respuestas Intended Role: Instructor 4-4: Repaso diario: Clave de respuestas Intended Role: Instructor 4-4: Práctica adicional Intended Role: Instructor 4-4: Práctica adicional: Clave de respuestas Intended Role: Instructor 4-4: Refuerzo para mejorar la comprensión: Clave de respuestas Intended Role: Instructor 4-4: Desarrollar la competencia matemática: Clave de respuestas Intended Role: Instructor 4-4: Ampliación: Clave de respuestas Intended Role: Instructor 4-5: Lesson Plan Intended Role: Instructor Teacher's Edition eText: Grade 5 Lesson 4-5 Intended Role: Instructor 4-5: Listen & Look For Intended Role: Instructor 4-5: Daily Review: Editable Worksheet Intended Role: Instructor 4-5: Daily Review: Answer Key Intended Role: Instructor Topic 4: Today's Challenge Teacher Guide Intended Role: Instructor 4-5: Solve & Share Solution Intended Role: Instructor 4-5: Solve & Share Solution Intended Role: Instructor 4-5: Printable Additional Practice Intended Role: Instructor 4-5: Additional Practice: Editable Assessment Intended Role: Instructor 4-5: Quick Check: Answer Key Intended Role: Instructor 4-5: Printable Quick Check Intended Role: Instructor 4-5: Reteach to Build Understanding: Answer Key Intended Role: Instructor 4-5: Reteach to Build Understanding: Editable Worksheet Intended Role: Instructor 4-5: Build Mathematical Literacy: Answer Key Intended Role: Instructor 4-5: Build Mathematical Literacy: Editable Worksheet Intended Role: Instructor 4-5: Enrichment: Answer Key Intended Role: Instructor 4-5: Enrichment: Editable Worksheet Intended Role: Instructor 4-5: eText del Libro del estudiante: Clave de respuestas Intended Role: Instructor 4-5: Repaso diario: Clave de respuestas Intended Role: Instructor 4-5: Práctica adicional Intended Role: Instructor 4-5: Práctica adicional: Clave de respuestas Intended Role: Instructor 4-5: Refuerzo para mejorar la comprensión: Clave de respuestas Intended Role: Instructor 4-5: Desarrollar la competencia matemática: Clave de respuestas Intended Role: Instructor 4-5: Ampliación: Clave de respuestas Intended Role: Instructor 4-6: Lesson Plan Intended Role: Instructor Teacher's Edition eText: Grade 5 Lesson 4-6 Intended Role: Instructor 4-6: Listen & Look For Intended Role: Instructor 4-6: Daily Review: Editable Worksheet Intended Role: Instructor 4-6: Daily Review: Answer Key Intended Role: Instructor Topic 4: Today's Challenge Teacher Guide Intended Role: Instructor 4-6: Solve & Share Solution Intended Role: Instructor 4-6: Solve & Share Solution Intended Role: Instructor 4-6: Printable Additional Practice Intended Role: Instructor 4-6: Additional Practice: Editable Assessment Intended Role: Instructor 4-6: Quick Check: Answer Key Intended Role: Instructor 4-6: Printable Quick Check Intended Role: Instructor 4-6: Reteach to Build Understanding: Answer Key Intended Role: Instructor 4-6: Reteach to Build Understanding: Editable Worksheet Intended Role: Instructor 4-6: Build Mathematical Literacy: Answer Key Intended Role: Instructor 4-6: Build Mathematical Literacy: Editable Worksheet Intended Role: Instructor 4-6: Enrichment: Answer Key Intended Role: Instructor 4-6: Enrichment: Editable Worksheet Intended Role: Instructor 4-6: eText del Libro del estudiante: Clave de respuestas Intended Role: Instructor 4-6: Repaso diario: Clave de respuestas Intended Role: Instructor 4-6: Práctica adicional Intended Role: Instructor 4-6: Práctica adicional: Clave de respuestas Intended Role: Instructor 4-6: Refuerzo para mejorar la comprensión: Clave de respuestas Intended Role: Instructor 4-6: Desarrollar la competencia matemática: Clave de respuestas Intended Role: Instructor 4-6: Ampliación: Clave de respuestas Intended Role: Instructor 4-7: Lesson Plan Intended Role: Instructor Teacher's Edition eText: Grade 5 Lesson 4-7 Intended Role: Instructor 4-7: Daily Review: Editable Worksheet Intended Role: Instructor 4-7: Daily Review: Answer Key Intended Role: Instructor Topic 4: Today's Challenge Teacher Guide Intended Role: Instructor 4-7: Solve & Share Solution Intended Role: Instructor 4-7: Solve & Share Solution Intended Role: Instructor 4-7: Printable Additional Practice Intended Role: Instructor 4-7: Additional Practice: Editable Assessment Intended Role: Instructor 4-7: Quick Check: Answer Key Intended Role: Instructor 4-7: Printable Quick Check Intended Role: Instructor 4-7: Reteach to Build Understanding: Answer Key Intended Role: Instructor 4-7: Reteach to Build Understanding: Editable Worksheet Intended Role: Instructor 4-7: Build Mathematical Literacy: Answer Key Intended Role: Instructor 4-7: Build Mathematical Literacy: Editable Worksheet Intended Role: Instructor 4-7: Enrichment: Answer Key Intended Role: Instructor 4-7: Enrichment: Editable Worksheet Intended Role: Instructor 4-7: eText del Libro del estudiante: Clave de respuestas Intended Role: Instructor 4-7: Repaso diario: Clave de respuestas Intended Role: Instructor 4-7: Práctica adicional Intended Role: Instructor 4-7: Práctica adicional: Clave de respuestas Intended Role: Instructor 4-7: Refuerzo para mejorar la comprensión: Clave de respuestas Intended Role: Instructor 4-7: Desarrollar la competencia matemática: Clave de respuestas Intended Role: Instructor 4-7: Ampliación: Clave de respuestas Intended Role: Instructor 4-8: Lesson Plan Intended Role: Instructor Teacher's Edition eText: Grade 5 Lesson 4-8 Intended Role: Instructor 4-8: Listen & Look For Intended Role: Instructor 4-8: Daily Review: Editable Worksheet Intended Role: Instructor 4-8: Daily Review: Answer Key Intended Role: Instructor Topic 4: Today's Challenge Teacher Guide Intended Role: Instructor 4-8: Solve & Share Solution Intended Role: Instructor 4-8: Solve & Share Solution Intended Role: Instructor 4-8: Printable Additional Practice Intended Role: Instructor 4-8: Additional Practice: Editable Assessment Intended Role: Instructor 4-8: Quick Check: Answer Key Intended Role: Instructor 4-8: Printable Quick Check Intended Role: Instructor 4-8: Reteach to Build Understanding: Answer Key Intended Role: Instructor 4-8: Reteach to Build Understanding: Editable Worksheet Intended Role: Instructor 4-8: Build Mathematical Literacy: Answer Key Intended Role: Instructor 4-8: Build Mathematical Literacy: Editable Worksheet Intended Role: Instructor 4-8: Enrichment: Answer Key Intended Role: Instructor 4-8: Enrichment: Editable Worksheet Intended Role: Instructor Topic 4: Problem-Solving Leveled Reading Mat Intended Role: Instructor 4-8: eText del Libro del estudiante: Clave de respuestas Intended Role: Instructor 4-8: Repaso diario: Clave de respuestas Intended Role: Instructor 4-8: Práctica adicional Intended Role: Instructor 4-8: Práctica adicional: Clave de respuestas Intended Role: Instructor 4-8: Refuerzo para mejorar la comprensión: Clave de respuestas Intended Role: Instructor 4-8: Desarrollar la competencia matemática: Clave de respuestas Intended Role: Instructor 4-8: Ampliación: Clave de respuestas Intended Role: Instructor 4-9: Lesson Plan Intended Role: Instructor Teacher's Edition eText: Grade 5 Lesson 4-9 Intended Role: Instructor 4-9: Daily Review: Editable Worksheet Intended Role: Instructor 4-9: Daily Review: Answer Key Intended Role: Instructor Topic 4: Today's Challenge Teacher Guide Intended Role: Instructor 4-9: Solve & Share Solution Intended Role: Instructor 4-9: Solve & Share Solution Intended Role: Instructor 4-9: Printable Additional Practice Intended Role: Instructor 4-9: Additional Practice: Editable Assessment Intended Role: Instructor 4-9: Quick Check: Answer Key Intended Role: Instructor 4-9: Printable Quick Check Intended Role: Instructor 4-9: Reteach to Build Understanding: Answer Key Intended Role: Instructor 4-9: Reteach to Build Understanding: Editable Worksheet Intended Role: Instructor 4-9: Build Mathematical Literacy: Answer Key Intended Role: Instructor 4-9: Build Mathematical Literacy: Editable Worksheet Intended Role: Instructor 4-9: Enrichment: Answer Key Intended Role: Instructor 4-9: Enrichment: Editable Worksheet Intended Role: Instructor 4-9: eText del Libro del estudiante: Clave de respuestas Intended Role: Instructor 4-9: Repaso diario: Clave de respuestas Intended Role: Instructor 4-9: Práctica adicional Intended Role: Instructor 4-9: Práctica adicional: Clave de respuestas Intended Role: Instructor 4-9: Refuerzo para mejorar la comprensión: Clave de respuestas Intended Role: Instructor 4-9: Desarrollar la competencia matemática: Clave de respuestas Intended Role: Instructor 4-9: Ampliación: Clave de respuestas Intended Role: Instructor Topic 4: Vocabulary Review Intended Role: Instructor Topic 4: Reteaching Intended Role: Instructor Topic 4 Performance Task: Answer Key Intended Role: Instructor Topic 4 Performance Task: Editable Assessment Intended Role: Instructor Topic 4 Assessment: Answer Key Intended Role: Instructor Topic 4 Topic Assessments: Editable Assessment Intended Role: Instructor Topic 4 Online Assessment: Answer Key Intended Role: Instructor Topic 4 Online Assessment: Printable Intended Role: Instructor Tema 4: Tarea de rendimento: Clave de respuestas Intended Role: Instructor Tema 4: Evaluación: Clave de respuestas Intended Role: Instructor Topics 1–4: Cumulative/Benchmark Assessment: Answer Key Intended Role: Instructor Topics 1–4: Online Cumulative/Benchmark Assessment: Answer Key Intended Role: Instructor Topics 1–4: Printable Online Cumulative/Benchmark Assessment Intended Role: Instructor Topic 5: Home-School Connection Intended Role: Instructor Topic 5: Problem-Solving Reading Activity Guide Intended Role: Instructor Topic 5: Problem-Solving Leveled Reading Mat Intended Role: Instructor Topic 5: Home-School Connection(Spanish) Intended Role: Instructor Topic 5: Pick a Project (Spanish) Intended Role: Instructor Topic 5: enVision STEM Activity (Spanish) Intended Role: Instructor Teacher's Edition eText: Grade 5 Topic 5 Intended Role: Instructor Topic 5: Professional Development Video Intended Role: Instructor Topic 5: Today's Challenge Teacher Guide Intended Role: Instructor 5-1: Lesson Plan Intended Role: Instructor Teacher's Edition eText: Grade 5 Lesson 5-1 Intended Role: Instructor 5-1: Listen & Look For Intended Role: Instructor 5-1: Daily Review: Editable Worksheet Intended Role: Instructor 5-1: Daily Review: Answer Key Intended Role: Instructor Topic 5: Today's Challenge Teacher Guide Intended Role: Instructor 5-1: Solve & Share Solution Intended Role: Instructor 5-1: Solve & Share Solution Intended Role: Instructor 5-1: Printable Additional Practice Intended Role: Instructor 5-1: Additional Practice: Editable Assessment Intended Role: Instructor 5-1: Quick Check: Answer Key Intended Role: Instructor 5-1: Printable Quick Check Intended Role: Instructor 5-1: Reteach to Build Understanding: Answer Key Intended Role: Instructor 5-1: Reteach to Build Understanding: Editable Worksheet Intended Role: Instructor 5-1: Build Mathematical Literacy: Answer Key Intended Role: Instructor 5-1: Build Mathematical Literacy: Editable Worksheet Intended Role: Instructor 5-1: Enrichment: Answer Key Intended Role: Instructor 5-1: Enrichment: Editable Worksheet Intended Role: Instructor 5-1: eText del Libro del estudiante: Clave de respuestas Intended Role: Instructor 5-1: Repaso diario: Clave de respuestas Intended Role: Instructor 5-1: Práctica adicional Intended Role: Instructor 5-1: Práctica adicional: Clave de respuestas Intended Role: Instructor 5-1: Refuerzo para mejorar la comprensión: Clave de respuestas Intended Role: Instructor 5-1: Desarrollar la competencia matemática: Clave de respuestas Intended Role: Instructor 5-1: Ampliación: Clave de respuestas Intended Role: Instructor 5-2: Lesson Plan Intended Role: Instructor Teacher's Edition eText: Grade 5 Lesson 5-2 Intended Role: Instructor 5-2: Daily Review: Editable Worksheet Intended Role: Instructor 5-2: Daily Review: Answer Key Intended Role: Instructor Topic 5: Today's Challenge Teacher Guide Intended Role: Instructor 5-2: Solve & Share Solution Intended Role: Instructor 5-2: Solve & Share Solution Intended Role: Instructor 5-2: Printable Additional Practice Intended Role: Instructor 5-2: Additional Practice: Editable Assessment Intended Role: Instructor 5-2: Quick Check: Answer Key Intended Role: Instructor 5-2: Printable Quick Check Intended Role: Instructor 5-2: Reteach to Build Understanding: Answer Key Intended Role: Instructor 5-2: Reteach to Build Understanding: Editable Worksheet Intended Role: Instructor 5-2: Build Mathematical Literacy: Answer Key Intended Role: Instructor 5-2: Build Mathematical Literacy: Editable Worksheet Intended Role: Instructor 5-2: Enrichment: Answer Key Intended Role: Instructor 5-2: Enrichment: Editable Worksheet Intended Role: Instructor Topic 5: Problem-Solving Leveled Reading Mat Intended Role: Instructor 5-2: eText del Libro del estudiante: Clave de respuestas Intended Role: Instructor 5-2: Repaso diario: Clave de respuestas Intended Role: Instructor 5-2: Práctica adicional Intended Role: Instructor 5-2: Práctica adicional: Clave de respuestas Intended Role: Instructor 5-2: Refuerzo para mejorar la comprensión: Clave de respuestas Intended Role: Instructor 5-2: Desarrollar la competencia matemática: Clave de respuestas Intended Role: Instructor 5-2: Ampliación: Clave de respuestas Intended Role: Instructor 5-3: Lesson Plan Intended Role: Instructor Teacher's Edition eText: Grade 5 Lesson 5-3 Intended Role: Instructor 5-3: Listen & Look For Intended Role: Instructor 5-3: Daily Review: Editable Worksheet Intended Role: Instructor 5-3: Daily Review: Answer Key Intended Role: Instructor Topic 5: Today's Challenge Teacher Guide Intended Role: Instructor 5-3: Solve & Share Solution Intended Role: Instructor 5-3: Solve & Share Solution Intended Role: Instructor 5-3: Printable Additional Practice Intended Role: Instructor 5-3: Additional Practice: Editable Assessment Intended Role: Instructor 5-3: Quick Check: Answer Key Intended Role: Instructor 5-3: Printable Quick Check Intended Role: Instructor 5-3: Reteach to Build Understanding: Answer Key Intended Role: Instructor 5-3: Reteach to Build Understanding: Editable Worksheet Intended Role: Instructor 5-3: Build Mathematical Literacy: Answer Key Intended Role: Instructor 5-3: Build Mathematical Literacy: Editable Worksheet Intended Role: Instructor 5-3: Enrichment: Answer Key Intended Role: Instructor 5-3: Enrichment: Editable Worksheet Intended Role: Instructor Topic 5: Problem-Solving Leveled Reading Mat Intended Role: Instructor 5-3: eText del Libro del estudiante: Clave de respuestas Intended Role: Instructor 5-3: Repaso diario: Clave de respuestas Intended Role: Instructor 5-3: Práctica adicional Intended Role: Instructor 5-3: Práctica adicional: Clave de respuestas Intended Role: Instructor 5-3: Refuerzo para mejorar la comprensión: Clave de respuestas Intended Role: Instructor 5-3: Desarrollar la competencia matemática: Clave de respuestas Intended Role: Instructor 5-3: Ampliación: Clave de respuestas Intended Role: Instructor 5-4: Lesson Plan Intended Role: Instructor Teacher's Edition eText: Grade 5 Lesson 5-4 Intended Role: Instructor 5-4: Listen & Look For Intended Role: Instructor 5-4: Daily Review: Editable Worksheet Intended Role: Instructor 5-4: Daily Review: Answer Key Intended Role: Instructor Topic 5: Today's Challenge Teacher Guide Intended Role: Instructor 5-4: Solve & Share Solution Intended Role: Instructor 5-4: Solve & Share Solution Intended Role: Instructor 5-4: Printable Additional Practice Intended Role: Instructor 5-4: Additional Practice: Editable Assessment Intended Role: Instructor 5-4: Quick Check: Answer Key Intended Role: Instructor 5-4: Printable Quick Check Intended Role: Instructor 5-4: Reteach to Build Understanding: Answer Key Intended Role: Instructor 5-4: Reteach to Build Understanding: Editable Worksheet Intended Role: Instructor 5-4: Build Mathematical Literacy: Answer Key Intended Role: Instructor 5-4: Build Mathematical Literacy: Editable Worksheet Intended Role: Instructor 5-4: Enrichment: Answer Key Intended Role: Instructor 5-4: Enrichment: Editable Worksheet Intended Role: Instructor 5-4: eText del Libro del estudiante: Clave de respuestas Intended Role: Instructor 5-4: Repaso diario: Clave de respuestas Intended Role: Instructor 5-4: Práctica adicional Intended Role: Instructor 5-4: Práctica adicional: Clave de respuestas Intended Role: Instructor 5-4: Refuerzo para mejorar la comprensión: Clave de respuestas Intended Role: Instructor 5-4: Desarrollar la competencia matemática: Clave de respuestas Intended Role: Instructor 5-4: Ampliación: Clave de respuestas Intended Role: Instructor 5-5: Lesson Plan Intended Role: Instructor Teacher's Edition eText: Grade 5 Lesson 5-5 Intended Role: Instructor 5-5: Daily Review: Editable Worksheet Intended Role: Instructor 5-5: Daily Review: Answer Key Intended Role: Instructor Topic 5: Today's Challenge Teacher Guide Intended Role: Instructor 5-5: Solve & Share Solution Intended Role: Instructor 5-5: Solve & Share Solution Intended Role: Instructor 5-5: Printable Additional Practice Intended Role: Instructor 5-5: Additional Practice: Editable Assessment Intended Role: Instructor 5-5: Quick Check: Answer Key Intended Role: Instructor 5-5: Printable Quick Check Intended Role: Instructor 5-5: Reteach to Build Understanding: Answer Key Intended Role: Instructor 5-5: Reteach to Build Understanding: Editable Worksheet Intended Role: Instructor 5-5: Build Mathematical Literacy: Answer Key Intended Role: Instructor 5-5: Build Mathematical Literacy: Editable Worksheet Intended Role: Instructor 5-5: Enrichment: Answer Key Intended Role: Instructor 5-5: Enrichment: Editable Worksheet Intended Role: Instructor 5-5: eText del Libro del estudiante: Clave de respuestas Intended Role: Instructor 5-5: Repaso diario: Clave de respuestas Intended Role: Instructor 5-5: Práctica adicional Intended Role: Instructor 5-5: Práctica adicional: Clave de respuestas Intended Role: Instructor 5-5: Refuerzo para mejorar la comprensión: Clave de respuestas Intended Role: Instructor 5-5: Desarrollar la competencia matemática: Clave de respuestas Intended Role: Instructor 5-5: Ampliación: Clave de respuestas Intended Role: Instructor Topic 5: 3-Act Math Recording Sheets Intended Role: Instructor Teacher's Edition eText: Grade 5, Topic 5: 3-Act Math Intended Role: Instructor 5-6: Lesson Plan Intended Role: Instructor Teacher's Edition eText: Grade 5 Lesson 5-6 Intended Role: Instructor 5-6: Daily Review: Editable Worksheet Intended Role: Instructor 5-6: Daily Review: Answer Key Intended Role: Instructor Topic 5: Today's Challenge Teacher Guide Intended Role: Instructor 5-6: Solve & Share Solution Intended Role: Instructor 5-6: Solve & Share Solution Intended Role: Instructor 5-6: Printable Additional Practice Intended Role: Instructor 5-6: Additional Practice: Editable Assessment Intended Role: Instructor 5-6: Quick Check: Answer Key Intended Role: Instructor 5-6: Printable Quick Check Intended Role: Instructor 5-6: Reteach to Build Understanding: Answer Key Intended Role: Instructor 5-6: Reteach to Build Understanding: Editable Worksheet Intended Role: Instructor 5-6: Build Mathematical Literacy: Answer Key Intended Role: Instructor 5-6: Build Mathematical Literacy: Editable Worksheet Intended Role: Instructor 5-6: Enrichment: Answer Key Intended Role: Instructor 5-6: Enrichment: Editable Worksheet Intended Role: Instructor 5-6: eText del Libro del estudiante: Clave de respuestas Intended Role: Instructor 5-6: Repaso diario: Clave de respuestas Intended Role: Instructor 5-6: Práctica adicional Intended Role: Instructor 5-6: Práctica adicional: Clave de respuestas Intended Role: Instructor 5-6: Refuerzo para mejorar la comprensión: Clave de respuestas Intended Role: Instructor 5-6: Desarrollar la competencia matemática: Clave de respuestas Intended Role: Instructor 5-6: Ampliación: Clave de respuestas Intended Role: Instructor 5-7: Lesson Plan Intended Role: Instructor Teacher's Edition eText: Grade 5 Lesson 5-7 Intended Role: Instructor 5-7: Daily Review: Editable Worksheet Intended Role: Instructor 5-7: Daily Review: Answer Key Intended Role: Instructor Topic 5: Today's Challenge Teacher Guide Intended Role: Instructor 5-7: Solve & Share Solution Intended Role: Instructor 5-7: Solve & Share Solution Intended Role: Instructor 5-7: Printable Additional Practice Intended Role: Instructor 5-7: Additional Practice: Editable Assessment Intended Role: Instructor 5-7: Quick Check: Answer Key Intended Role: Instructor 5-7: Printable Quick Check Intended Role: Instructor 5-7: Reteach to Build Understanding: Answer Key Intended Role: Instructor 5-7: Reteach to Build Understanding: Editable Worksheet Intended Role: Instructor 5-7: Build Mathematical Literacy: Answer Key Intended Role: Instructor 5-7: Build Mathematical Literacy: Editable Worksheet Intended Role: Instructor 5-7: Enrichment: Answer Key Intended Role: Instructor 5-7: Enrichment: Editable Worksheet Intended Role: Instructor 5-7: eText del Libro del estudiante: Clave de respuestas Intended Role: Instructor 5-7: Repaso diario: Clave de respuestas Intended Role: Instructor 5-7: Práctica adicional Intended Role: Instructor 5-7: Práctica adicional: Clave de respuestas Intended Role: Instructor 5-7: Refuerzo para mejorar la comprensión: Clave de respuestas Intended Role: Instructor 5-7: Desarrollar la competencia matemática: Clave de respuestas Intended Role: Instructor 5-7: Ampliación: Clave de respuestas Intended Role: Instructor 5-8: Lesson Plan Intended Role: Instructor Teacher's Edition eText: Grade 5 Lesson 5-8 Intended Role: Instructor 5-8: Daily Review: Editable Worksheet Intended Role: Instructor 5-8: Daily Review: Answer Key Intended Role: Instructor Topic 5: Today's Challenge Teacher Guide Intended Role: Instructor 5-8: Solve & Share Solution Intended Role: Instructor 5-8: Solve & Share Solution Intended Role: Instructor 5-8: Printable Additional Practice Intended Role: Instructor 5-8: Additional Practice: Editable Assessment Intended Role: Instructor 5-8: Quick Check: Answer Key Intended Role: Instructor 5-8: Printable Quick Check Intended Role: Instructor 5-8: Reteach to Build Understanding: Answer Key Intended Role: Instructor 5-8: Reteach to Build Understanding: Editable Worksheet Intended Role: Instructor 5-8: Build Mathematical Literacy: Answer Key Intended Role: Instructor 5-8: Build Mathematical Literacy: Editable Worksheet Intended Role: Instructor 5-8: Enrichment: Answer Key Intended Role: Instructor 5-8: Enrichment: Editable Worksheet Intended Role: Instructor 5-8: eText del Libro del estudiante: Clave de respuestas Intended Role: Instructor 5-8: Repaso diario: Clave de respuestas Intended Role: Instructor 5-8: Práctica adicional Intended Role: Instructor 5-8: Práctica adicional: Clave de respuestas Intended Role: Instructor 5-8: Refuerzo para mejorar la comprensión: Clave de respuestas Intended Role: Instructor 5-8: Desarrollar la competencia matemática: Clave de respuestas Intended Role: Instructor 5-8: Ampliación: Clave de respuestas Intended Role: Instructor Topic 5: Vocabulary Review Intended Role: Instructor Topic 5: Reteaching Intended Role: Instructor Topic 5 Performance Task: Answer Key Intended Role: Instructor Topic 5 Performance Task: Editable Assessment Intended Role: Instructor Topic 5 Assessment: Answer Key Intended Role: Instructor Topic 5 Topic Assessments: Editable Assessment Intended Role: Instructor Topic 5 Online Assessment: Answer Key Intended Role: Instructor Topic 5 Online Assessment: Printable Intended Role: Instructor Tema 5: Tarea de rendimento: Clave de respuestas Intended Role: Instructor Tema 5: Evaluación: Clave de respuestas Intended Role: Instructor Topic 6: Home-School Connection Intended Role: Instructor Topic 6: Problem-Solving Reading Activity Guide Intended Role: Instructor Topic 6: Problem-Solving Leveled Reading Mat Intended Role: Instructor Topic 6: Home-School Connection(Spanish) Intended Role: Instructor Topic 6: Pick a Project (Spanish) Intended Role: Instructor Topic 6: enVision STEM Activity (Spanish) Intended Role: Instructor Teacher's Edition eText: Grade 5 Topic 6 Intended Role: Instructor Topic 6: Today's Challenge Teacher Guide Intended Role: Instructor 6-1: Lesson Plan Intended Role: Instructor Teacher's Edition eText: Grade 5 Lesson 6-1 Intended Role: Instructor 6-1: Listen & Look For Intended Role: Instructor 6-1: Daily Review: Editable Worksheet Intended Role: Instructor 6-1: Daily Review: Answer Key Intended Role: Instructor Topic 6: Today's Challenge Teacher Guide Intended Role: Instructor 6-1: Solve & Share Solution Intended Role: Instructor 6-1: Solve & Share Solution Intended Role: Instructor 6-1: Printable Additional Practice Intended Role: Instructor 6-1: Additional Practice: Editable Assessment Intended Role: Instructor 6-1: Quick Check: Answer Key Intended Role: Instructor 6-1: Printable Quick Check Intended Role: Instructor 6-1: Reteach to Build Understanding: Answer Key Intended Role: Instructor 6-1: Reteach to Build Understanding: Editable Worksheet Intended Role: Instructor 6-1: Build Mathematical Literacy: Answer Key Intended Role: Instructor 6-1: Build Mathematical Literacy: Editable Worksheet Intended Role: Instructor 6-1: Enrichment: Answer Key Intended Role: Instructor 6-1: Enrichment: Editable Worksheet Intended Role: Instructor Topic 6: Problem-Solving Leveled Reading Mat Intended Role: Instructor 6-1: eText del Libro del estudiante: Clave de respuestas Intended Role: Instructor 6-1: Repaso diario: Clave de respuestas Intended Role: Instructor 6-1: Práctica adicional Intended Role: Instructor 6-1: Práctica adicional: Clave de respuestas Intended Role: Instructor 6-1: Refuerzo para mejorar la comprensión: Clave de respuestas Intended Role: Instructor 6-1: Desarrollar la competencia matemática: Clave de respuestas Intended Role: Instructor 6-1: Ampliación: Clave de respuestas Intended Role: Instructor 6-2: Lesson Plan Intended Role: Instructor Teacher's Edition eText: Grade 5 Lesson 6-2 Intended Role: Instructor 6-2: Listen & Look For Intended Role: Instructor 6-2: Daily Review: Editable Worksheet Intended Role: Instructor 6-2: Daily Review: Answer Key Intended Role: Instructor Topic 6: Today's Challenge Teacher Guide Intended Role: Instructor 6-2: Solve & Share Solution Intended Role: Instructor 6-2: Solve & Share Solution Intended Role: Instructor 6-2: Printable Additional Practice Intended Role: Instructor 6-2: Additional Practice: Editable Assessment Intended Role: Instructor 6-2: Quick Check: Answer Key Intended Role: Instructor 6-2: Printable Quick Check Intended Role: Instructor 6-2: Reteach to Build Understanding: Answer Key Intended Role: Instructor 6-2: Reteach to Build Understanding: Editable Worksheet Intended Role: Instructor 6-2: Build Mathematical Literacy: Answer Key Intended Role: Instructor 6-2: Build Mathematical Literacy: Editable Worksheet Intended Role: Instructor 6-2: Enrichment: Answer Key Intended Role: Instructor 6-2: Enrichment: Editable Worksheet Intended Role: Instructor 6-2: eText del Libro del estudiante: Clave de respuestas Intended Role: Instructor 6-2: Repaso diario: Clave de respuestas Intended Role: Instructor 6-2: Práctica adicional Intended Role: Instructor 6-2: Práctica adicional: Clave de respuestas Intended Role: Instructor 6-2: Refuerzo para mejorar la comprensión: Clave de respuestas Intended Role: Instructor 6-2: Desarrollar la competencia matemática: Clave de respuestas Intended Role: Instructor 6-2: Ampliación: Clave de respuestas Intended Role: Instructor 6-3: Lesson Plan Intended Role: Instructor Teacher's Edition eText: Grade 5 Lesson 6-3 Intended Role: Instructor 6-3: Daily Review: Editable Worksheet Intended Role: Instructor 6-3: Daily Review: Answer Key Intended Role: Instructor Topic 6: Today's Challenge Teacher Guide Intended Role: Instructor 6-3: Solve & Share Solution Intended Role: Instructor 6-3: Solve & Share Solution Intended Role: Instructor 6-3: Printable Additional Practice Intended Role: Instructor 6-3: Additional Practice: Editable Assessment Intended Role: Instructor 6-3: Quick Check: Answer Key Intended Role: Instructor 6-3: Printable Quick Check Intended Role: Instructor 6-3: Reteach to Build Understanding: Answer Key Intended Role: Instructor 6-3: Reteach to Build Understanding: Editable Worksheet Intended Role: Instructor 6-3: Build Mathematical Literacy: Answer Key Intended Role: Instructor 6-3: Build Mathematical Literacy: Editable Worksheet Intended Role: Instructor 6-3: Enrichment: Answer Key Intended Role: Instructor 6-3: Enrichment: Editable Worksheet Intended Role: Instructor 6-3: eText del Libro del estudiante: Clave de respuestas Intended Role: Instructor 6-3: Repaso diario: Clave de respuestas Intended Role: Instructor 6-3: Práctica adicional Intended Role: Instructor 6-3: Práctica adicional: Clave de respuestas Intended Role: Instructor 6-3: Refuerzo para mejorar la comprensión: Clave de respuestas Intended Role: Instructor 6-3: Desarrollar la competencia matemática: Clave de respuestas Intended Role: Instructor 6-3: Ampliación: Clave de respuestas Intended Role: Instructor 6-4: Lesson Plan Intended Role: Instructor Teacher's Edition eText: Grade 5 Lesson 6-4 Intended Role: Instructor 6-4: Daily Review: Editable Worksheet Intended Role: Instructor 6-4: Daily Review: Answer Key Intended Role: Instructor Topic 6: Today's Challenge Teacher Guide Intended Role: Instructor 6-4: Solve & Share Solution Intended Role: Instructor 6-4: Solve & Share Solution Intended Role: Instructor 6-4: Printable Additional Practice Intended Role: Instructor 6-4: Additional Practice: Editable Assessment Intended Role: Instructor 6-4: Quick Check: Answer Key Intended Role: Instructor 6-4: Printable Quick Check Intended Role: Instructor 6-4: Reteach to Build Understanding: Answer Key Intended Role: Instructor 6-4: Reteach to Build Understanding: Editable Worksheet Intended Role: Instructor 6-4: Build Mathematical Literacy: Answer Key Intended Role: Instructor 6-4: Build Mathematical Literacy: Editable Worksheet Intended Role: Instructor 6-4: Enrichment: Answer Key Intended Role: Instructor 6-4: Enrichment: Editable Worksheet Intended Role: Instructor 6-4: eText del Libro del estudiante: Clave de respuestas Intended Role: Instructor 6-4: Repaso diario: Clave de respuestas Intended Role: Instructor 6-4: Práctica adicional Intended Role: Instructor 6-4: Práctica adicional: Clave de respuestas Intended Role: Instructor 6-4: Refuerzo para mejorar la comprensión: Clave de respuestas Intended Role: Instructor 6-4: Desarrollar la competencia matemática: Clave de respuestas Intended Role: Instructor 6-4: Ampliación: Clave de respuestas Intended Role: Instructor 6-5: Lesson Plan Intended Role: Instructor Teacher's Edition eText: Grade 5 Lesson 6-5 Intended Role: Instructor 6-5: Daily Review: Editable Worksheet Intended Role: Instructor 6-5: Daily Review: Answer Key Intended Role: Instructor Topic 6: Today's Challenge Teacher Guide Intended Role: Instructor 6-5: Solve & Share Solution Intended Role: Instructor 6-5: Solve & Share Solution Intended Role: Instructor 6-5: Printable Additional Practice Intended Role: Instructor 6-5: Additional Practice: Editable Assessment Intended Role: Instructor 6-5: Quick Check: Answer Key Intended Role: Instructor 6-5: Printable Quick Check Intended Role: Instructor 6-5: Reteach to Build Understanding: Answer Key Intended Role: Instructor 6-5: Reteach to Build Understanding: Editable Worksheet Intended Role: Instructor 6-5: Build Mathematical Literacy: Answer Key Intended Role: Instructor 6-5: Build Mathematical Literacy: Editable Worksheet Intended Role: Instructor 6-5: Enrichment: Answer Key Intended Role: Instructor 6-5: Enrichment: Editable Worksheet Intended Role: Instructor Topic 6: Problem-Solving Leveled Reading Mat Intended Role: Instructor 6-5: eText del Libro del estudiante: Clave de respuestas Intended Role: Instructor 6-5: Repaso diario: Clave de respuestas Intended Role: Instructor 6-5: Práctica adicional Intended Role: Instructor 6-5: Práctica adicional: Clave de respuestas Intended Role: Instructor 6-5: Refuerzo para mejorar la comprensión: Clave de respuestas Intended Role: Instructor 6-5: Desarrollar la competencia matemática: Clave de respuestas Intended Role: Instructor 6-5: Ampliación: Clave de respuestas Intended Role: Instructor 6-6: Lesson Plan Intended Role: Instructor Teacher's Edition eText: Grade 5 Lesson 6-6 Intended Role: Instructor 6-6: Listen & Look For Intended Role: Instructor 6-6: Daily Review: Editable Worksheet Intended Role: Instructor 6-6: Daily Review: Answer Key Intended Role: Instructor Topic 6: Today's Challenge Teacher Guide Intended Role: Instructor 6-6: Solve & Share Solution Intended Role: Instructor 6-6: Solve & Share Solution Intended Role: Instructor 6-6: Printable Additional Practice Intended Role: Instructor 6-6: Additional Practice: Editable Assessment Intended Role: Instructor 6-6: Quick Check: Answer Key Intended Role: Instructor 6-6: Printable Quick Check Intended Role: Instructor 6-6: Reteach to Build Understanding: Answer Key Intended Role: Instructor 6-6: Reteach to Build Understanding: Editable Worksheet Intended Role: Instructor 6-6: Build Mathematical Literacy: Answer Key Intended Role: Instructor 6-6: Build Mathematical Literacy: Editable Worksheet Intended Role: Instructor 6-6: Enrichment: Answer Key Intended Role: Instructor 6-6: Enrichment: Editable Worksheet Intended Role: Instructor 6-6: eText del Libro del estudiante: Clave de respuestas Intended Role: Instructor 6-6: Repaso diario: Clave de respuestas Intended Role: Instructor 6-6: Práctica adicional Intended Role: Instructor 6-6: Práctica adicional: Clave de respuestas Intended Role: Instructor 6-6: Refuerzo para mejorar la comprensión: Clave de respuestas Intended Role: Instructor 6-6: Desarrollar la competencia matemática: Clave de respuestas Intended Role: Instructor 6-6: Ampliación: Clave de respuestas Intended Role: Instructor Topic 6: Vocabulary Review Intended Role: Instructor Topic 6: Reteaching Intended Role: Instructor Topic 6 Performance Task: Answer Key Intended Role: Instructor Topic 6 Performance Task: Editable Assessment Intended Role: Instructor Topic 6 Assessment: Answer Key Intended Role: Instructor Topic 6 Topic Assessments: Editable Assessment Intended Role: Instructor Topic 6 Online Assessment: Answer Key Intended Role: Instructor Topic 6 Online Assessment: Printable Intended Role: Instructor Tema 6: Tarea de rendimento: Clave de respuestas Intended Role: Instructor Tema 6: Evaluación: Clave de respuestas Intended Role: Instructor Topic 7: Home-School Connection Intended Role: Instructor Topic 7: Problem-Solving Leveled Reading Mat Intended Role: Instructor Topic 7: Problem-Solving Reading Activity Guide Intended Role: Instructor Topic 7: Home-School Connection(Spanish) Intended Role: Instructor Topic 7: Pick a Project (Spanish) Intended Role: Instructor Topic 7: enVision STEM Activity (Spanish) Intended Role: Instructor Teacher's Edition eText: Grade 5 Topic 7 Intended Role: Instructor Topic 7: Professional Development Video Intended Role: Instructor Topic 7: Today's Challenge Teacher Guide Intended Role: Instructor 7-1: Lesson Plan Intended Role: Instructor Teacher's Edition eText: Grade 5 Lesson 7-1 Intended Role: Instructor 7-1: Listen & Look For Intended Role: Instructor 7-1: Daily Review: Editable Worksheet Intended Role: Instructor 7-1: Daily Review: Answer Key Intended Role: Instructor Topic 7: Today's Challenge Teacher Guide Intended Role: Instructor 7-1: Solve & Share Solution Intended Role: Instructor 7-1: Solve & Share Solution Intended Role: Instructor 7-1: Printable Additional Practice Intended Role: Instructor 7-1: Additional Practice: Editable Assessment Intended Role: Instructor 7-1: Quick Check: Answer Key Intended Role: Instructor 7-1: Printable Quick Check Intended Role: Instructor 7-1: Reteach to Build Understanding: Answer Key Intended Role: Instructor 7-1: Reteach to Build Understanding: Editable Worksheet Intended Role: Instructor 7-1: Build Mathematical Literacy: Answer Key Intended Role: Instructor 7-1: Build Mathematical Literacy: Editable Worksheet Intended Role: Instructor 7-1: Enrichment: Answer Key Intended Role: Instructor 7-1: Enrichment: Editable Worksheet Intended Role: Instructor 7-1: eText del Libro del estudiante: Clave de respuestas Intended Role: Instructor 7-1: Repaso diario: Clave de respuestas Intended Role: Instructor 7-1: Práctica adicional Intended Role: Instructor 7-1: Práctica adicional: Clave de respuestas Intended Role: Instructor 7-1: Refuerzo para mejorar la comprensión: Clave de respuestas Intended Role: Instructor 7-1: Desarrollar la competencia matemática: Clave de respuestas Intended Role: Instructor 7-1: Ampliación: Clave de respuestas Intended Role: Instructor 7-2: Lesson Plan Intended Role: Instructor Teacher's Edition eText: Grade 5 Lesson 7-2 Intended Role: Instructor 7-2: Listen & Look For Intended Role: Instructor 7-2: Daily Review: Editable Worksheet Intended Role: Instructor 7-2: Daily Review: Answer Key Intended Role: Instructor Topic 7: Today's Challenge Teacher Guide Intended Role: Instructor 7-2: Solve & Share Solution Intended Role: Instructor 7-2: Solve & Share Solution Intended Role: Instructor 7-2: Printable Additional Practice Intended Role: Instructor 7-2: Additional Practice: Editable Assessment Intended Role: Instructor 7-2: Quick Check: Answer Key Intended Role: Instructor 7-2: Printable Quick Check Intended Role: Instructor 7-2: Reteach to Build Understanding: Answer Key Intended Role: Instructor 7-2: Reteach to Build Understanding: Editable Worksheet Intended Role: Instructor 7-2: Build Mathematical Literacy: Answer Key Intended Role: Instructor 7-2: Build Mathematical Literacy: Editable Worksheet Intended Role: Instructor 7-2: Enrichment: Answer Key Intended Role: Instructor 7-2: Enrichment: Editable Worksheet Intended Role: Instructor 7-2: eText del Libro del estudiante: Clave de respuestas Intended Role: Instructor 7-2: Repaso diario: Clave de respuestas Intended Role: Instructor 7-2: Práctica adicional Intended Role: Instructor 7-2: Práctica adicional: Clave de respuestas Intended Role: Instructor 7-2: Refuerzo para mejorar la comprensión: Clave de respuestas Intended Role: Instructor 7-2: Desarrollar la competencia matemática: Clave de respuestas Intended Role: Instructor 7-2: Ampliación: Clave de respuestas Intended Role: Instructor 7-3: Lesson Plan Intended Role: Instructor Teacher's Edition eText: Grade 5 Lesson 7-3 Intended Role: Instructor 7-3: Listen & Look For Intended Role: Instructor 7-3: Daily Review: Editable Worksheet Intended Role: Instructor 7-3: Daily Review: Answer Key Intended Role: Instructor Topic 7: Today's Challenge Teacher Guide Intended Role: Instructor 7-3: Solve & Share Solution Intended Role: Instructor 7-3: Solve & Share Solution Intended Role: Instructor 7-3: Printable Additional Practice Intended Role: Instructor 7-3: Additional Practice: Editable Assessment Intended Role: Instructor 7-3: Quick Check: Answer Key Intended Role: Instructor 7-3: Printable Quick Check Intended Role: Instructor 7-3: Reteach to Build Understanding: Answer Key Intended Role: Instructor 7-3: Reteach to Build Understanding: Editable Worksheet Intended Role: Instructor 7-3: Build Mathematical Literacy: Answer Key Intended Role: Instructor 7-3: Build Mathematical Literacy: Editable Worksheet Intended Role: Instructor 7-3: Enrichment: Answer Key Intended Role: Instructor 7-3: Enrichment: Editable Worksheet Intended Role: Instructor 7-3: eText del Libro del estudiante: Clave de respuestas Intended Role: Instructor 7-3: Repaso diario: Clave de respuestas Intended Role: Instructor 7-3: Práctica adicional Intended Role: Instructor 7-3: Práctica adicional: Clave de respuestas Intended Role: Instructor 7-3: Refuerzo para mejorar la comprensión: Clave de respuestas Intended Role: Instructor 7-3: Desarrollar la competencia matemática: Clave de respuestas Intended Role: Instructor 7-3: Ampliación: Clave de respuestas Intended Role: Instructor 7-4: Lesson Plan Intended Role: Instructor Teacher's Edition eText: Grade 5 Lesson 7-4 Intended Role: Instructor 7-4: Listen & Look For Intended Role: Instructor 7-4: Daily Review: Editable Worksheet Intended Role: Instructor 7-4: Daily Review: Answer Key Intended Role: Instructor Topic 7: Today's Challenge Teacher Guide Intended Role: Instructor 7-4: Solve & Share Solution Intended Role: Instructor 7-4: Solve & Share Solution Intended Role: Instructor 7-4: Printable Additional Practice Intended Role: Instructor 7-4: Additional Practice: Editable Assessment Intended Role: Instructor 7-4: Quick Check: Answer Key Intended Role: Instructor 7-4: Printable Quick Check Intended Role: Instructor 7-4: Reteach to Build Understanding: Answer Key Intended Role: Instructor 7-4: Reteach to Build Understanding: Editable Worksheet Intended Role: Instructor 7-4: Build Mathematical Literacy: Answer Key Intended Role: Instructor 7-4: Build Mathematical Literacy: Editable Worksheet Intended Role: Instructor 7-4: Enrichment: Answer Key Intended Role: Instructor 7-4: Enrichment: Editable Worksheet Intended Role: Instructor 7-4: eText del Libro del estudiante: Clave de respuestas Intended Role: Instructor 7-4: Repaso diario: Clave de respuestas Intended Role: Instructor 7-4: Práctica adicional Intended Role: Instructor 7-4: Práctica adicional: Clave de respuestas Intended Role: Instructor 7-4: Refuerzo para mejorar la comprensión: Clave de respuestas Intended Role: Instructor 7-4: Desarrollar la competencia matemática: Clave de respuestas Intended Role: Instructor 7-4: Ampliación: Clave de respuestas Intended Role: Instructor 7-5: Lesson Plan Intended Role: Instructor Teacher's Edition eText: Grade 5 Lesson 7-5 Intended Role: Instructor 7-5: Listen & Look For Intended Role: Instructor 7-5: Daily Review: Editable Worksheet Intended Role: Instructor 7-5: Daily Review: Answer Key Intended Role: Instructor Topic 7: Today's Challenge Teacher Guide Intended Role: Instructor 7-5: Solve & Share Solution Intended Role: Instructor 7-5: Solve & Share Solution Intended Role: Instructor 7-5: Printable Additional Practice Intended Role: Instructor 7-5: Additional Practice: Editable Assessment Intended Role: Instructor 7-5: Quick Check: Answer Key Intended Role: Instructor 7-5: Printable Quick Check Intended Role: Instructor 7-5: Reteach to Build Understanding: Answer Key Intended Role: Instructor 7-5: Reteach to Build Understanding: Editable Worksheet Intended Role: Instructor 7-5: Build Mathematical Literacy: Answer Key Intended Role: Instructor 7-5: Build Mathematical Literacy: Editable Worksheet Intended Role: Instructor 7-5: Enrichment: Answer Key Intended Role: Instructor 7-5: Enrichment: Editable Worksheet Intended Role: Instructor Topic 7: Problem-Solving Leveled Reading Mat Intended Role: Instructor 7-5: eText del Libro del estudiante: Clave de respuestas Intended Role: Instructor 7-5: Repaso diario: Clave de respuestas Intended Role: Instructor 7-5: Práctica adicional Intended Role: Instructor 7-5: Práctica adicional: Clave de respuestas Intended Role: Instructor 7-5: Refuerzo para mejorar la comprensión: Clave de respuestas Intended Role: Instructor 7-5: Desarrollar la competencia matemática: Clave de respuestas Intended Role: Instructor 7-5: Ampliación: Clave de respuestas Intended Role: Instructor 7-6: Lesson Plan Intended Role: Instructor Teacher's Edition eText: Grade 5 Lesson 7-6 Intended Role: Instructor 7-6: Listen & Look For Intended Role: Instructor 7-6: Daily Review: Editable Worksheet Intended Role: Instructor 7-6: Daily Review: Answer Key Intended Role: Instructor Topic 7: Today's Challenge Teacher Guide Intended Role: Instructor 7-6: Solve & Share Solution Intended Role: Instructor 7-6: Solve & Share Solution Intended Role: Instructor 7-6: Printable Additional Practice Intended Role: Instructor 7-6: Additional Practice: Editable Assessment Intended Role: Instructor 7-6: Quick Check: Answer Key Intended Role: Instructor 7-6: Printable Quick Check Intended Role: Instructor 7-6: Reteach to Build Understanding: Answer Key Intended Role: Instructor 7-6: Reteach to Build Understanding: Editable Worksheet Intended Role: Instructor 7-6: Build Mathematical Literacy: Answer Key Intended Role: Instructor 7-6: Build Mathematical Literacy: Editable Worksheet Intended Role: Instructor 7-6: Enrichment: Answer Key Intended Role: Instructor 7-6: Enrichment: Editable Worksheet Intended Role: Instructor 7-6: eText del Libro del estudiante: Clave de respuestas Intended Role: Instructor 7-6: Repaso diario: Clave de respuestas Intended Role: Instructor 7-6: Práctica adicional Intended Role: Instructor 7-6: Práctica adicional: Clave de respuestas Intended Role: Instructor 7-6: Refuerzo para mejorar la comprensión: Clave de respuestas Intended Role: Instructor 7-6: Desarrollar la competencia matemática: Clave de respuestas Intended Role: Instructor 7-6: Ampliación: Clave de respuestas Intended Role: Instructor 7-7: Lesson Plan Intended Role: Instructor Teacher's Edition eText: Grade 5 Lesson 7-7 Intended Role: Instructor 7-7: Listen & Look For Intended Role: Instructor 7-7: Daily Review: Editable Worksheet Intended Role: Instructor 7-7: Daily Review: Answer Key Intended Role: Instructor Topic 7: Today's Challenge Teacher Guide Intended Role: Instructor 7-7: Solve & Share Solution Intended Role: Instructor 7-7: Solve & Share Solution Intended Role: Instructor 7-7: Printable Additional Practice Intended Role: Instructor 7-7: Additional Practice: Editable Assessment Intended Role: Instructor 7-7: Quick Check: Answer Key Intended Role: Instructor 7-7: Printable Quick Check Intended Role: Instructor 7-7: Reteach to Build Understanding: Answer Key Intended Role: Instructor 7-7: Reteach to Build Understanding: Editable Worksheet Intended Role: Instructor 7-7: Build Mathematical Literacy: Answer Key Intended Role: Instructor 7-7: Build Mathematical Literacy: Editable Worksheet Intended Role: Instructor 7-7: Enrichment: Answer Key Intended Role: Instructor 7-7: Enrichment: Editable Worksheet Intended Role: Instructor 7-7: eText del Libro del estudiante: Clave de respuestas Intended Role: Instructor 7-7: Repaso diario: Clave de respuestas Intended Role: Instructor 7-7: Práctica adicional Intended Role: Instructor 7-7: Práctica adicional: Clave de respuestas Intended Role: Instructor 7-7: Refuerzo para mejorar la comprensión: Clave de respuestas Intended Role: Instructor 7-7: Desarrollar la competencia matemática: Clave de respuestas Intended Role: Instructor 7-7: Ampliación: Clave de respuestas Intended Role: Instructor 7-8: Lesson Plan Intended Role: Instructor Teacher's Edition eText: Grade 5 Lesson 7-8 Intended Role: Instructor 7-8: Listen & Look For Intended Role: Instructor 7-8: Daily Review: Editable Worksheet Intended Role: Instructor 7-8: Daily Review: Answer Key Intended Role: Instructor Topic 7: Today's Challenge Teacher Guide Intended Role: Instructor 7-8: Solve & Share Solution Intended Role: Instructor 7-8: Solve & Share Solution Intended Role: Instructor 7-8: Printable Additional Practice Intended Role: Instructor 7-8: Additional Practice: Editable Assessment Intended Role: Instructor 7-8: Quick Check: Answer Key Intended Role: Instructor 7-8: Printable Quick Check Intended Role: Instructor 7-8: Reteach to Build Understanding: Answer Key Intended Role: Instructor 7-8: Reteach to Build Understanding: Editable Worksheet Intended Role: Instructor 7-8: Build Mathematical Literacy: Answer Key Intended Role: Instructor 7-8: Build Mathematical Literacy: Editable Worksheet Intended Role: Instructor 7-8: Enrichment: Answer Key Intended Role: Instructor 7-8: Enrichment: Editable Worksheet Intended Role: Instructor 7-8: eText del Libro del estudiante: Clave de respuestas Intended Role: Instructor 7-8: Repaso diario: Clave de respuestas Intended Role: Instructor 7-8: Práctica adicional Intended Role: Instructor 7-8: Práctica adicional: Clave de respuestas Intended Role: Instructor 7-8: Refuerzo para mejorar la comprensión: Clave de respuestas Intended Role: Instructor 7-8: Desarrollar la competencia matemática: Clave de respuestas Intended Role: Instructor 7-8: Ampliación: Clave de respuestas Intended Role: Instructor 7-9: Lesson Plan Intended Role: Instructor Teacher's Edition eText: Grade 5 Lesson 7-9 Intended Role: Instructor 7-9: Listen & Look For Intended Role: Instructor 7-9: Daily Review: Editable Worksheet Intended Role: Instructor 7-9: Daily Review: Answer Key Intended Role: Instructor Topic 7: Today's Challenge Teacher Guide Intended Role: Instructor 7-9: Solve & Share Solution Intended Role: Instructor 7-9: Solve & Share Solution Intended Role: Instructor 7-9: Printable Additional Practice Intended Role: Instructor 7-9: Additional Practice: Editable Assessment Intended Role: Instructor 7-9: Quick Check: Answer Key Intended Role: Instructor 7-9: Printable Quick Check Intended Role: Instructor 7-9: Reteach to Build Understanding: Answer Key Intended Role: Instructor 7-9: Reteach to Build Understanding: Editable Worksheet Intended Role: Instructor 7-9: Build Mathematical Literacy: Answer Key Intended Role: Instructor 7-9: Build Mathematical Literacy: Editable Worksheet Intended Role: Instructor 7-9: Enrichment: Answer Key Intended Role: Instructor 7-9: Enrichment: Editable Worksheet Intended Role: Instructor 7-9: eText del Libro del estudiante: Clave de respuestas Intended Role: Instructor 7-9: Repaso diario: Clave de respuestas Intended Role: Instructor 7-9: Práctica adicional Intended Role: Instructor 7-9: Práctica adicional: Clave de respuestas Intended Role: Instructor 7-9: Refuerzo para mejorar la comprensión: Clave de respuestas Intended Role: Instructor 7-9: Desarrollar la competencia matemática: Clave de respuestas Intended Role: Instructor 7-9: Ampliación: Clave de respuestas Intended Role: Instructor 7-10: Lesson Plan Intended Role: Instructor Teacher's Edition eText: Grade 5 Lesson 7-10 Intended Role: Instructor 7-10: Listen & Look For Intended Role: Instructor 7-10: Daily Review: Editable Worksheet Intended Role: Instructor 7-10: Daily Review: Answer Key Intended Role: Instructor Topic 7: Today's Challenge Teacher Guide Intended Role: Instructor 7-10: Solve & Share Solution Intended Role: Instructor 7-10: Solve & Share Solution Intended Role: Instructor 7-10: Printable Additional Practice Intended Role: Instructor 7-10: Additional Practice: Editable Assessment Intended Role: Instructor 7-10: Quick Check: Answer Key Intended Role: Instructor 7-10: Printable Quick Check Intended Role: Instructor 7-10: Reteach to Build Understanding: Answer Key Intended Role: Instructor 7-10: Reteach to Build Understanding: Editable Worksheet Intended Role: Instructor 7-10: Build Mathematical Literacy: Answer Key Intended Role: Instructor 7-10: Build Mathematical Literacy: Editable Worksheet Intended Role: Instructor 7-10: Enrichment: Answer Key Intended Role: Instructor 7-10: Enrichment: Editable Worksheet Intended Role: Instructor 7-10: eText del Libro del estudiante: Clave de respuestas Intended Role: Instructor 7-10: Repaso diario: Clave de respuestas Intended Role: Instructor 7-10: Práctica adicional Intended Role: Instructor 7-10: Práctica adicional: Clave de respuestas Intended Role: Instructor 7-10: Refuerzo para mejorar la comprensión: Clave de respuestas Intended Role: Instructor 7-10: Desarrollar la competencia matemática: Clave de respuestas Intended Role: Instructor 7-10: Ampliación: Clave de respuestas Intended Role: Instructor 7-11: Lesson Plan Intended Role: Instructor Teacher's Edition eText: Grade 5 Lesson 7-11 Intended Role: Instructor 7-11: Listen & Look For Intended Role: Instructor 7-11: Daily Review: Editable Worksheet Intended Role: Instructor 7-11: Daily Review: Answer Key Intended Role: Instructor Topic 7: Today's Challenge Teacher Guide Intended Role: Instructor 7-11: Solve & Share Solution Intended Role: Instructor 7-11: Solve & Share Solution Intended Role: Instructor 7-11: Printable Additional Practice Intended Role: Instructor 7-11: Additional Practice: Editable Assessment Intended Role: Instructor 7-11: Quick Check: Answer Key Intended Role: Instructor 7-11: Printable Quick Check Intended Role: Instructor 7-11: Reteach to Build Understanding: Answer Key Intended Role: Instructor 7-11: Reteach to Build Understanding: Editable Worksheet Intended Role: Instructor 7-11: Build Mathematical Literacy: Answer Key Intended Role: Instructor 7-11: Build Mathematical Literacy: Editable Worksheet Intended Role: Instructor 7-11: Enrichment: Answer Key Intended Role: Instructor 7-11: Enrichment: Editable Worksheet Intended Role: Instructor Topic 7: Problem-Solving Leveled Reading Mat Intended Role: Instructor 7-11: eText del Libro del estudiante: Clave de respuestas Intended Role: Instructor 7-11: Repaso diario: Clave de respuestas Intended Role: Instructor 7-11: Práctica adicional Intended Role: Instructor 7-11: Práctica adicional: Clave de respuestas Intended Role: Instructor 7-11: Refuerzo para mejorar la comprensión: Clave de respuestas Intended Role: Instructor 7-11: Desarrollar la competencia matemática: Clave de respuestas Intended Role: Instructor 7-11: Ampliación: Clave de respuestas Intended Role: Instructor Topic 7: 3-Act Math Recording Sheets Intended Role: Instructor Teacher's Edition eText: Grade 5, Topic 7: 3-Act Math Intended Role: Instructor 7-12: Lesson Plan Intended Role: Instructor Teacher's Edition eText: Grade 5 Lesson 7-12 Intended Role: Instructor 7-12: Listen & Look For Intended Role: Instructor 7-12: Daily Review: Editable Worksheet Intended Role: Instructor 7-12: Daily Review: Answer Key Intended Role: Instructor Topic 7: Today's Challenge Teacher Guide Intended Role: Instructor 7-12: Solve & Share Solution Intended Role: Instructor 7-12: Solve & Share Solution Intended Role: Instructor 7-12: Printable Additional Practice Intended Role: Instructor 7-12: Additional Practice: Editable Assessment Intended Role: Instructor 7-12: Quick Check: Answer Key Intended Role: Instructor 7-12: Printable Quick Check Intended Role: Instructor 7-12: Reteach to Build Understanding: Answer Key Intended Role: Instructor 7-12: Reteach to Build Understanding: Editable Worksheet Intended Role: Instructor 7-12: Build Mathematical Literacy: Answer Key Intended Role: Instructor 7-12: Build Mathematical Literacy: Editable Worksheet Intended Role: Instructor 7-12: Enrichment: Answer Key Intended Role: Instructor 7-12: Enrichment: Editable Worksheet Intended Role: Instructor 7-12: eText del Libro del estudiante: Clave de respuestas Intended Role: Instructor 7-12: Repaso diario: Clave de respuestas Intended Role: Instructor 7-12: Práctica adicional Intended Role: Instructor 7-12: Práctica adicional: Clave de respuestas Intended Role: Instructor 7-12: Refuerzo para mejorar la comprensión: Clave de respuestas Intended Role: Instructor 7-12: Desarrollar la competencia matemática: Clave de respuestas Intended Role: Instructor 7-12: Ampliación: Clave de respuestas Intended Role: Instructor Topic 7: Vocabulary Review Intended Role: Instructor Topic 7: Reteaching Intended Role: Instructor Topic 7 Performance Task: Answer Key Intended Role: Instructor Topic 7 Performance Task: Editable Assessment Intended Role: Instructor Topic 7 Assessment: Answer Key Intended Role: Instructor Topic 7 Topic Assessments: Editable Assessment Intended Role: Instructor Topic 7 Online Assessment: Answer Key Intended Role: Instructor Topic 7 Online Assessment: Printable Intended Role: Instructor Tema 7: Tarea de rendimento: Clave de respuestas Intended Role: Instructor Tema 7: Evaluación: Clave de respuestas Intended Role: Instructor Topic 8: Home-School Connection Intended Role: Instructor Topic 8: Problem-Solving Leveled Reading Mat Intended Role: Instructor Topic 8: Problem-Solving Reading Activity Guide Intended Role: Instructor Topic 8: Home-School Connection(Spanish) Intended Role: Instructor Topic 8: Pick a Project (Spanish) Intended Role: Instructor Topic 8: enVision STEM Activity (Spanish) Intended Role: Instructor Teacher's Edition eText: Grade 5 Topic 8 Intended Role: Instructor Topic 8: Professional Development Video Intended Role: Instructor Topic 8: Today's Challenge Teacher Guide Intended Role: Instructor 8-1: Lesson Plan Intended Role: Instructor Teacher's Edition eText: Grade 5 Lesson 8-1 Intended Role: Instructor 8-1: Daily Review: Editable Worksheet Intended Role: Instructor 8-1: Daily Review: Answer Key Intended Role: Instructor Topic 8: Today's Challenge Teacher Guide Intended Role: Instructor 8-1: Solve & Share Solution Intended Role: Instructor 8-1: Solve & Share Solution Intended Role: Instructor 8-1: Printable Additional Practice Intended Role: Instructor 8-1: Additional Practice: Editable Assessment Intended Role: Instructor 8-1: Quick Check: Answer Key Intended Role: Instructor 8-1: Printable Quick Check Intended Role: Instructor 8-1: Reteach to Build Understanding: Answer Key Intended Role: Instructor 8-1: Reteach to Build Understanding: Editable Worksheet Intended Role: Instructor 8-1: Build Mathematical Literacy: Answer Key Intended Role: Instructor 8-1: Build Mathematical Literacy: Editable Worksheet Intended Role: Instructor 8-1: Enrichment: Answer Key Intended Role: Instructor 8-1: Enrichment: Editable Worksheet Intended Role: Instructor 8-1: eText del Libro del estudiante: Clave de respuestas Intended Role: Instructor 8-1: Repaso diario: Clave de respuestas Intended Role: Instructor 8-1: Práctica adicional Intended Role: Instructor 8-1: Práctica adicional: Clave de respuestas Intended Role: Instructor 8-1: Refuerzo para mejorar la comprensión: Clave de respuestas Intended Role: Instructor 8-1: Desarrollar la competencia matemática: Clave de respuestas Intended Role: Instructor 8-1: Ampliación: Clave de respuestas Intended Role: Instructor 8-2: Lesson Plan Intended Role: Instructor Teacher's Edition eText: Grade 5 Lesson 8-2 Intended Role: Instructor 8-2: Daily Review: Editable Worksheet Intended Role: Instructor 8-2: Daily Review: Answer Key Intended Role: Instructor Topic 8: Today's Challenge Teacher Guide Intended Role: Instructor 8-2: Solve & Share Solution Intended Role: Instructor 8-2: Solve & Share Solution Intended Role: Instructor 8-2: Printable Additional Practice Intended Role: Instructor 8-2: Additional Practice: Editable Assessment Intended Role: Instructor 8-2: Quick Check: Answer Key Intended Role: Instructor 8-2: Printable Quick Check Intended Role: Instructor 8-2: Reteach to Build Understanding: Answer Key Intended Role: Instructor 8-2: Reteach to Build Understanding: Editable Worksheet Intended Role: Instructor 8-2: Build Mathematical Literacy: Answer Key Intended Role: Instructor 8-2: Build Mathematical Literacy: Editable Worksheet Intended Role: Instructor 8-2: Enrichment: Answer Key Intended Role: Instructor 8-2: Enrichment: Editable Worksheet Intended Role: Instructor Topic 8: Problem-Solving Leveled Reading Mat Intended Role: Instructor 8-2: eText del Libro del estudiante: Clave de respuestas Intended Role: Instructor 8-2: Repaso diario: Clave de respuestas Intended Role: Instructor 8-2: Práctica adicional Intended Role: Instructor 8-2: Práctica adicional: Clave de respuestas Intended Role: Instructor 8-2: Refuerzo para mejorar la comprensión: Clave de respuestas Intended Role: Instructor 8-2: Desarrollar la competencia matemática: Clave de respuestas Intended Role: Instructor 8-2: Ampliación: Clave de respuestas Intended Role: Instructor 8-3: Lesson Plan Intended Role: Instructor Teacher's Edition eText: Grade 5 Lesson 8-3 Intended Role: Instructor 8-3: Daily Review: Editable Worksheet Intended Role: Instructor 8-3: Daily Review: Answer Key Intended Role: Instructor Topic 8: Today's Challenge Teacher Guide Intended Role: Instructor 8-3: Solve & Share Solution Intended Role: Instructor 8-3: Solve & Share Solution Intended Role: Instructor 8-3: Printable Additional Practice Intended Role: Instructor 8-3: Additional Practice: Editable Assessment Intended Role: Instructor 8-3: Quick Check: Answer Key Intended Role: Instructor 8-3: Printable Quick Check Intended Role: Instructor 8-3: Reteach to Build Understanding: Answer Key Intended Role: Instructor 8-3: Reteach to Build Understanding: Editable Worksheet Intended Role: Instructor 8-3: Build Mathematical Literacy: Answer Key Intended Role: Instructor 8-3: Build Mathematical Literacy: Editable Worksheet Intended Role: Instructor 8-3: Enrichment: Answer Key Intended Role: Instructor 8-3: Enrichment: Editable Worksheet Intended Role: Instructor 8-3: eText del Libro del estudiante: Clave de respuestas Intended Role: Instructor 8-3: Repaso diario: Clave de respuestas Intended Role: Instructor 8-3: Práctica adicional Intended Role: Instructor 8-3: Práctica adicional: Clave de respuestas Intended Role: Instructor 8-3: Refuerzo para mejorar la comprensión: Clave de respuestas Intended Role: Instructor 8-3: Desarrollar la competencia matemática: Clave de respuestas Intended Role: Instructor 8-3: Ampliación: Clave de respuestas Intended Role: Instructor 8-4: Lesson Plan Intended Role: Instructor Teacher's Edition eText: Grade 5 Lesson 8-4 Intended Role: Instructor 8-4: Listen & Look For Intended Role: Instructor 8-4: Daily Review: Editable Worksheet Intended Role: Instructor 8-4: Daily Review: Answer Key Intended Role: Instructor Topic 8: Today's Challenge Teacher Guide Intended Role: Instructor 8-4: Solve & Share Solution Intended Role: Instructor 8-4: Solve & Share Solution Intended Role: Instructor 8-4: Printable Additional Practice Intended Role: Instructor 8-4: Additional Practice: Editable Assessment Intended Role: Instructor 8-4: Quick Check: Answer Key Intended Role: Instructor 8-4: Printable Quick Check Intended Role: Instructor 8-4: Reteach to Build Understanding: Answer Key Intended Role: Instructor 8-4: Reteach to Build Understanding: Editable Worksheet Intended Role: Instructor 8-4: Build Mathematical Literacy: Answer Key Intended Role: Instructor 8-4: Build Mathematical Literacy: Editable Worksheet Intended Role: Instructor 8-4: Enrichment: Answer Key Intended Role: Instructor 8-4: Enrichment: Editable Worksheet Intended Role: Instructor 8-4: eText del Libro del estudiante: Clave de respuestas Intended Role: Instructor 8-4: Repaso diario: Clave de respuestas Intended Role: Instructor 8-4: Práctica adicional Intended Role: Instructor 8-4: Práctica adicional: Clave de respuestas Intended Role: Instructor 8-4: Refuerzo para mejorar la comprensión: Clave de respuestas Intended Role: Instructor 8-4: Desarrollar la competencia matemática: Clave de respuestas Intended Role: Instructor 8-4: Ampliación: Clave de respuestas Intended Role: Instructor 8-5: Lesson Plan Intended Role: Instructor Teacher's Edition eText: Grade 5 Lesson 8-5 Intended Role: Instructor 8-5: Daily Review: Editable Worksheet Intended Role: Instructor 8-5: Daily Review: Answer Key Intended Role: Instructor Topic 8: Today's Challenge Teacher Guide Intended Role: Instructor 8-5: Solve & Share Solution Intended Role: Instructor 8-5: Solve & Share Solution Intended Role: Instructor 8-5: Printable Additional Practice Intended Role: Instructor 8-5: Additional Practice: Editable Assessment Intended Role: Instructor 8-5: Quick Check: Answer Key Intended Role: Instructor 8-5: Printable Quick Check Intended Role: Instructor 8-5: Reteach to Build Understanding: Answer Key Intended Role: Instructor 8-5: Reteach to Build Understanding: Editable Worksheet Intended Role: Instructor 8-5: Build Mathematical Literacy: Answer Key Intended Role: Instructor 8-5: Build Mathematical Literacy: Editable Worksheet Intended Role: Instructor 8-5: Enrichment: Answer Key Intended Role: Instructor 8-5: Enrichment: Editable Worksheet Intended Role: Instructor Topic 8: Problem-Solving Leveled Reading Mat Intended Role: Instructor 8-5: eText del Libro del estudiante: Clave de respuestas Intended Role: Instructor 8-5: Repaso diario: Clave de respuestas Intended Role: Instructor 8-5: Práctica adicional Intended Role: Instructor 8-5: Práctica adicional: Clave de respuestas Intended Role: Instructor 8-5: Refuerzo para mejorar la comprensión: Clave de respuestas Intended Role: Instructor 8-5: Desarrollar la competencia matemática: Clave de respuestas Intended Role: Instructor 8-5: Ampliación: Clave de respuestas Intended Role: Instructor 8-6: Lesson Plan Intended Role: Instructor Teacher's Edition eText: Grade 5 Lesson 8-6 Intended Role: Instructor 8-6: Listen & Look For Intended Role: Instructor 8-6: Daily Review: Editable Worksheet Intended Role: Instructor 8-6: Daily Review: Answer Key Intended Role: Instructor Topic 8: Today's Challenge Teacher Guide Intended Role: Instructor 8-6: Solve & Share Solution Intended Role: Instructor 8-6: Solve & Share Solution Intended Role: Instructor 8-6: Printable Additional Practice Intended Role: Instructor 8-6: Additional Practice: Editable Assessment Intended Role: Instructor 8-6: Quick Check: Answer Key Intended Role: Instructor 8-6: Printable Quick Check Intended Role: Instructor 8-6: Reteach to Build Understanding: Answer Key Intended Role: Instructor 8-6: Reteach to Build Understanding: Editable Worksheet Intended Role: Instructor 8-6: Build Mathematical Literacy: Answer Key Intended Role: Instructor 8-6: Build Mathematical Literacy: Editable Worksheet Intended Role: Instructor 8-6: Enrichment: Answer Key Intended Role: Instructor 8-6: Enrichment: Editable Worksheet Intended Role: Instructor 8-6: eText del Libro del estudiante: Clave de respuestas Intended Role: Instructor 8-6: Repaso diario: Clave de respuestas Intended Role: Instructor 8-6: Práctica adicional Intended Role: Instructor 8-6: Práctica adicional: Clave de respuestas Intended Role: Instructor 8-6: Refuerzo para mejorar la comprensión: Clave de respuestas Intended Role: Instructor 8-6: Desarrollar la competencia matemática: Clave de respuestas Intended Role: Instructor 8-6: Ampliación: Clave de respuestas Intended Role: Instructor 8-7: Lesson Plan Intended Role: Instructor Teacher's Edition eText: Grade 5 Lesson 8-7 Intended Role: Instructor 8-7: Listen & Look For Intended Role: Instructor 8-7: Daily Review: Editable Worksheet Intended Role: Instructor 8-7: Daily Review: Answer Key Intended Role: Instructor Topic 8: Today's Challenge Teacher Guide Intended Role: Instructor 8-7: Solve & Share Solution Intended Role: Instructor 8-7: Solve & Share Solution Intended Role: Instructor 8-7: Printable Additional Practice Intended Role: Instructor 8-7: Additional Practice: Editable Assessment Intended Role: Instructor 8-7: Quick Check: Answer Key Intended Role: Instructor 8-7: Printable Quick Check Intended Role: Instructor 8-7: Reteach to Build Understanding: Answer Key Intended Role: Instructor 8-7: Reteach to Build Understanding: Editable Worksheet Intended Role: Instructor 8-7: Build Mathematical Literacy: Answer Key Intended Role: Instructor 8-7: Build Mathematical Literacy: Editable Worksheet Intended Role: Instructor 8-7: Enrichment: Answer Key Intended Role: Instructor 8-7: Enrichment: Editable Worksheet Intended Role: Instructor 8-7: eText del Libro del estudiante: Clave de respuestas Intended Role: Instructor 8-7: Repaso diario: Clave de respuestas Intended Role: Instructor 8-7: Práctica adicional Intended Role: Instructor 8-7: Práctica adicional: Clave de respuestas Intended Role: Instructor 8-7: Refuerzo para mejorar la comprensión: Clave de respuestas Intended Role: Instructor 8-7: Desarrollar la competencia matemática: Clave de respuestas Intended Role: Instructor 8-7: Ampliación: Clave de respuestas Intended Role: Instructor 8-8: Lesson Plan Intended Role: Instructor Teacher's Edition eText: Grade 5 Lesson 8-8 Intended Role: Instructor 8-8: Listen & Look For Intended Role: Instructor 8-8: Daily Review: Editable Worksheet Intended Role: Instructor 8-8: Daily Review: Answer Key Intended Role: Instructor Topic 8: Today's Challenge Teacher Guide Intended Role: Instructor 8-8: Solve & Share Solution Intended Role: Instructor 8-8: Solve & Share Solution Intended Role: Instructor 8-8: Printable Additional Practice Intended Role: Instructor 8-8: Additional Practice: Editable Assessment Intended Role: Instructor 8-8: Quick Check: Answer Key Intended Role: Instructor 8-8: Printable Quick Check Intended Role: Instructor 8-8: Reteach to Build Understanding: Answer Key Intended Role: Instructor 8-8: Reteach to Build Understanding: Editable Worksheet Intended Role: Instructor 8-8: Build Mathematical Literacy: Answer Key Intended Role: Instructor 8-8: Build Mathematical Literacy: Editable Worksheet Intended Role: Instructor 8-8: Enrichment: Answer Key Intended Role: Instructor 8-8: Enrichment: Editable Worksheet Intended Role: Instructor 8-8: eText del Libro del estudiante: Clave de respuestas Intended Role: Instructor 8-8: Repaso diario: Clave de respuestas Intended Role: Instructor 8-8: Práctica adicional Intended Role: Instructor 8-8: Práctica adicional: Clave de respuestas Intended Role: Instructor 8-8: Refuerzo para mejorar la comprensión: Clave de respuestas Intended Role: Instructor 8-8: Desarrollar la competencia matemática: Clave de respuestas Intended Role: Instructor 8-8: Ampliación: Clave de respuestas Intended Role: Instructor 8-9: Lesson Plan Intended Role: Instructor Teacher's Edition eText: Grade 5 Lesson 8-9 Intended Role: Instructor 8-9: Listen & Look For Intended Role: Instructor 8-9: Daily Review: Editable Worksheet Intended Role: Instructor 8-9: Daily Review: Answer Key Intended Role: Instructor Topic 8: Today's Challenge Teacher Guide Intended Role: Instructor 8-9: Solve & Share Solution Intended Role: Instructor 8-9: Solve & Share Solution Intended Role: Instructor 8-9: Printable Additional Practice Intended Role: Instructor 8-9: Additional Practice: Editable Assessment Intended Role: Instructor 8-9: Quick Check: Answer Key Intended Role: Instructor 8-9: Printable Quick Check Intended Role: Instructor 8-9: Reteach to Build Understanding: Answer Key Intended Role: Instructor 8-9: Reteach to Build Understanding: Editable Worksheet Intended Role: Instructor 8-9: Build Mathematical Literacy: Answer Key Intended Role: Instructor 8-9: Build Mathematical Literacy: Editable Worksheet Intended Role: Instructor 8-9: Enrichment: Answer Key Intended Role: Instructor 8-9: Enrichment: Editable Worksheet Intended Role: Instructor 8-9: eText del Libro del estudiante: Clave de respuestas Intended Role: Instructor 8-9: Repaso diario: Clave de respuestas Intended Role: Instructor 8-9: Práctica adicional Intended Role: Instructor 8-9: Práctica adicional: Clave de respuestas Intended Role: Instructor 8-9: Refuerzo para mejorar la comprensión: Clave de respuestas Intended Role: Instructor 8-9: Desarrollar la competencia matemática: Clave de respuestas Intended Role: Instructor 8-9: Ampliación: Clave de respuestas Intended Role: Instructor Topic 8: Vocabulary Review Intended Role: Instructor Topic 8: Reteaching Intended Role: Instructor Topic 8 Performance Task: Answer Key Intended Role: Instructor Topic 8 Performance Task: Editable Assessment Intended Role: Instructor Topic 8 Assessment: Answer Key Intended Role: Instructor Topic 8 Topic Assessments: Editable Assessment Intended Role: Instructor Topic 8 Online Assessment: Answer Key Intended Role: Instructor Topic 8 Online Assessment: Printable Intended Role: Instructor Tema 8: Tarea de rendimento: Clave de respuestas Intended Role: Instructor Tema 8: Evaluación: Clave de respuestas Intended Role: Instructor Topics 1–8: Cumulative/Benchmark Assessment: Answer Key Intended Role: Instructor Topics 1–8: Cumulative/Benchmark Assessment: Editable Assessment Intended Role: Instructor Topics 1–8: Online Cumulative/Benchmark Assessment: Answer Key Intended Role: Instructor Topics 1–8: Printable Online Cumulative/Benchmark Assessment Intended Role: Instructor Topic 9: Home-School Connection Intended Role: Instructor Topic 9: Problem-Solving Reading Activity Guide Intended Role: Instructor Topic 9: Problem-Solving Leveled Reading Mat Intended Role: Instructor Topic 9: Home-School Connection(Spanish) Intended Role: Instructor Topic 9: Pick a Project (Spanish) Intended Role: Instructor Topic 9: enVision STEM Activity (Spanish) Intended Role: Instructor Teacher's Edition eText: Grade 5 Topic 9 Intended Role: Instructor Topic 9: Professional Development Video Intended Role: Instructor Topic 9: Today's Challenge Teacher Guide Intended Role: Instructor 9-1: Lesson Plan Intended Role: Instructor Teacher's Edition eText: Grade 5 Lesson 9-1 Intended Role: Instructor 9-1: Listen & Look For Intended Role: Instructor 9-1: Daily Review: Editable Worksheet Intended Role: Instructor 9-1: Daily Review: Answer Key Intended Role: Instructor Topic 9: Today's Challenge Teacher Guide Intended Role: Instructor 9-1: Solve & Share Solution Intended Role: Instructor 9-1: Solve & Share Solution Intended Role: Instructor 9-1: Printable Additional Practice Intended Role: Instructor 9-1: Additional Practice: Editable Assessment Intended Role: Instructor 9-1: Quick Check: Answer Key Intended Role: Instructor 9-1: Printable Quick Check Intended Role: Instructor 9-1: Reteach to Build Understanding: Answer Key Intended Role: Instructor 9-1: Reteach to Build Understanding: Editable Worksheet Intended Role: Instructor 9-1: Build Mathematical Literacy: Answer Key Intended Role: Instructor 9-1: Build Mathematical Literacy: Editable Worksheet Intended Role: Instructor 9-1: Enrichment: Answer Key Intended Role: Instructor 9-1: Enrichment: Editable Worksheet Intended Role: Instructor 9-1: eText del Libro del estudiante: Clave de respuestas Intended Role: Instructor 9-1: Repaso diario: Clave de respuestas Intended Role: Instructor 9-1: Práctica adicional Intended Role: Instructor 9-1: Práctica adicional: Clave de respuestas Intended Role: Instructor 9-1: Refuerzo para mejorar la comprensión: Clave de respuestas Intended Role: Instructor 9-1: Desarrollar la competencia matemática: Clave de respuestas Intended Role: Instructor 9-1: Ampliación: Clave de respuestas Intended Role: Instructor 9-2: Lesson Plan Intended Role: Instructor Teacher's Edition eText: Grade 5 Lesson 9-2 Intended Role: Instructor 9-2: Listen & Look For Intended Role: Instructor 9-2: Daily Review: Editable Worksheet Intended Role: Instructor 9-2: Daily Review: Answer Key Intended Role: Instructor Topic 9: Today's Challenge Teacher Guide Intended Role: Instructor 9-2: Solve & Share Solution Intended Role: Instructor 9-2: Solve & Share Solution Intended Role: Instructor 9-2: Printable Additional Practice Intended Role: Instructor 9-2: Additional Practice: Editable Assessment Intended Role: Instructor 9-2: Quick Check: Answer Key Intended Role: Instructor 9-2: Printable Quick Check Intended Role: Instructor 9-2: Reteach to Build Understanding: Answer Key Intended Role: Instructor 9-2: Reteach to Build Understanding: Editable Worksheet Intended Role: Instructor 9-2: Build Mathematical Literacy: Answer Key Intended Role: Instructor 9-2: Build Mathematical Literacy: Editable Worksheet Intended Role: Instructor 9-2: Enrichment: Answer Key Intended Role: Instructor 9-2: Enrichment: Editable Worksheet Intended Role: Instructor 9-2: eText del Libro del estudiante: Clave de respuestas Intended Role: Instructor 9-2: Repaso diario: Clave de respuestas Intended Role: Instructor 9-2: Práctica adicional Intended Role: Instructor 9-2: Práctica adicional: Clave de respuestas Intended Role: Instructor 9-2: Refuerzo para mejorar la comprensión: Clave de respuestas Intended Role: Instructor 9-2: Desarrollar la competencia matemática: Clave de respuestas Intended Role: Instructor 9-2: Ampliación: Clave de respuestas Intended Role: Instructor 9-3: Lesson Plan Intended Role: Instructor Teacher's Edition eText: Grade 5 Lesson 9-3 Intended Role: Instructor 9-3: Listen & Look For Intended Role: Instructor 9-3: Daily Review: Editable Worksheet Intended Role: Instructor 9-3: Daily Review: Answer Key Intended Role: Instructor Topic 9: Today's Challenge Teacher Guide Intended Role: Instructor 9-3: Solve & Share Solution Intended Role: Instructor 9-3: Solve & Share Solution Intended Role: Instructor 9-3: Printable Additional Practice Intended Role: Instructor 9-3: Additional Practice: Editable Assessment Intended Role: Instructor 9-3: Quick Check: Answer Key Intended Role: Instructor 9-3: Printable Quick Check Intended Role: Instructor 9-3: Reteach to Build Understanding: Answer Key Intended Role: Instructor 9-3: Reteach to Build Understanding: Editable Worksheet Intended Role: Instructor 9-3: Build Mathematical Literacy: Answer Key Intended Role: Instructor 9-3: Build Mathematical Literacy: Editable Worksheet Intended Role: Instructor 9-3: Enrichment: Answer Key Intended Role: Instructor 9-3: Enrichment: Editable Worksheet Intended Role: Instructor 9-3: eText del Libro del estudiante: Clave de respuestas Intended Role: Instructor 9-3: Repaso diario: Clave de respuestas Intended Role: Instructor 9-3: Práctica adicional Intended Role: Instructor 9-3: Práctica adicional: Clave de respuestas Intended Role: Instructor 9-3: Refuerzo para mejorar la comprensión: Clave de respuestas Intended Role: Instructor 9-3: Desarrollar la competencia matemática: Clave de respuestas Intended Role: Instructor 9-3: Ampliación: Clave de respuestas Intended Role: Instructor 9-4: Lesson Plan Intended Role: Instructor Teacher's Edition eText: Grade 5 Lesson 9-4 Intended Role: Instructor 9-4: Listen & Look For Intended Role: Instructor 9-4: Daily Review: Editable Worksheet Intended Role: Instructor 9-4: Daily Review: Answer Key Intended Role: Instructor Topic 9: Today's Challenge Teacher Guide Intended Role: Instructor 9-4: Solve & Share Solution Intended Role: Instructor 9-4: Solve & Share Solution Intended Role: Instructor 9-4: Printable Additional Practice Intended Role: Instructor 9-4: Additional Practice: Editable Assessment Intended Role: Instructor 9-4: Quick Check: Answer Key Intended Role: Instructor 9-4: Printable Quick Check Intended Role: Instructor 9-4: Reteach to Build Understanding: Answer Key Intended Role: Instructor 9-4: Reteach to Build Understanding: Editable Worksheet Intended Role: Instructor 9-4: Build Mathematical Literacy: Answer Key Intended Role: Instructor 9-4: Build Mathematical Literacy: Editable Worksheet Intended Role: Instructor 9-4: Enrichment: Answer Key Intended Role: Instructor 9-4: Enrichment: Editable Worksheet Intended Role: Instructor 9-4: eText del Libro del estudiante: Clave de respuestas Intended Role: Instructor 9-4: Repaso diario: Clave de respuestas Intended Role: Instructor 9-4: Práctica adicional Intended Role: Instructor 9-4: Práctica adicional: Clave de respuestas Intended Role: Instructor 9-4: Refuerzo para mejorar la comprensión: Clave de respuestas Intended Role: Instructor 9-4: Desarrollar la competencia matemática: Clave de respuestas Intended Role: Instructor 9-4: Ampliación: Clave de respuestas Intended Role: Instructor 9-5: Lesson Plan Intended Role: Instructor Teacher's Edition eText: Grade 5 Lesson 9-5 Intended Role: Instructor 9-5: Listen & Look For Intended Role: Instructor 9-5: Daily Review: Editable Worksheet Intended Role: Instructor 9-5: Daily Review: Answer Key Intended Role: Instructor Topic 9: Today's Challenge Teacher Guide Intended Role: Instructor 9-5: Solve & Share Solution Intended Role: Instructor 9-5: Solve & Share Solution Intended Role: Instructor 9-5: Printable Additional Practice Intended Role: Instructor 9-5: Additional Practice: Editable Assessment Intended Role: Instructor 9-5: Quick Check: Answer Key Intended Role: Instructor 9-5: Printable Quick Check Intended Role: Instructor 9-5: Reteach to Build Understanding: Answer Key Intended Role: Instructor 9-5: Reteach to Build Understanding: Editable Worksheet Intended Role: Instructor 9-5: Build Mathematical Literacy: Answer Key Intended Role: Instructor 9-5: Build Mathematical Literacy: Editable Worksheet Intended Role: Instructor 9-5: Enrichment: Answer Key Intended Role: Instructor 9-5: Enrichment: Editable Worksheet Intended Role: Instructor 9-5: eText del Libro del estudiante: Clave de respuestas Intended Role: Instructor 9-5: Repaso diario: Clave de respuestas Intended Role: Instructor 9-5: Práctica adicional Intended Role: Instructor 9-5: Práctica adicional: Clave de respuestas Intended Role: Instructor 9-5: Refuerzo para mejorar la comprensión: Clave de respuestas Intended Role: Instructor 9-5: Desarrollar la competencia matemática: Clave de respuestas Intended Role: Instructor 9-5: Ampliación: Clave de respuestas Intended Role: Instructor 9-6: Lesson Plan Intended Role: Instructor Teacher's Edition eText: Grade 5 Lesson 9-6 Intended Role: Instructor 9-6: Listen & Look For Intended Role: Instructor 9-6: Daily Review: Editable Worksheet Intended Role: Instructor 9-6: Daily Review: Answer Key Intended Role: Instructor Topic 9: Today's Challenge Teacher Guide Intended Role: Instructor 9-6: Solve & Share Solution Intended Role: Instructor 9-6: Solve & Share Solution Intended Role: Instructor 9-6: Printable Additional Practice Intended Role: Instructor 9-6: Additional Practice: Editable Assessment Intended Role: Instructor 9-6: Quick Check: Answer Key Intended Role: Instructor 9-6: Printable Quick Check Intended Role: Instructor 9-6: Reteach to Build Understanding: Answer Key Intended Role: Instructor 9-6: Reteach to Build Understanding: Editable Worksheet Intended Role: Instructor 9-6: Build Mathematical Literacy: Answer Key Intended Role: Instructor 9-6: Build Mathematical Literacy: Editable Worksheet Intended Role: Instructor 9-6: Enrichment: Answer Key Intended Role: Instructor 9-6: Enrichment: Editable Worksheet Intended Role: Instructor Topic 9: Problem-Solving Leveled Reading Mat Intended Role: Instructor 9-6: eText del Libro del estudiante: Clave de respuestas Intended Role: Instructor 9-6: Repaso diario: Clave de respuestas Intended Role: Instructor 9-6: Práctica adicional Intended Role: Instructor 9-6: Práctica adicional: Clave de respuestas Intended Role: Instructor 9-6: Refuerzo para mejorar la comprensión: Clave de respuestas Intended Role: Instructor 9-6: Desarrollar la competencia matemática: Clave de respuestas Intended Role: Instructor 9-6: Ampliación: Clave de respuestas Intended Role: Instructor 9-7: Lesson Plan Intended Role: Instructor Teacher's Edition eText: Grade 5 Lesson 9-7 Intended Role: Instructor 9-7: Listen & Look For Intended Role: Instructor 9-7: Daily Review: Editable Worksheet Intended Role: Instructor 9-7: Daily Review: Answer Key Intended Role: Instructor Topic 9: Today's Challenge Teacher Guide Intended Role: Instructor 9-7: Solve & Share Solution Intended Role: Instructor 9-7: Printable Additional Practice Intended Role: Instructor 9-7: Additional Practice: Editable Assessment Intended Role: Instructor 9-7: Quick Check: Answer Key Intended Role: Instructor 9-7: Printable Quick Check Intended Role: Instructor 9-7: Reteach to Build Understanding: Answer Key Intended Role: Instructor 9-7: Reteach to Build Understanding: Editable Worksheet Intended Role: Instructor 9-7: Build Mathematical Literacy: Answer Key Intended Role: Instructor 9-7: Build Mathematical Literacy: Editable Worksheet Intended Role: Instructor 9-7: Enrichment: Answer Key Intended Role: Instructor 9-7: Enrichment: Editable Worksheet Intended Role: Instructor 9-7: eText del Libro del estudiante: Clave de respuestas Intended Role: Instructor 9-7: Repaso diario: Clave de respuestas Intended Role: Instructor 9-7: Práctica adicional Intended Role: Instructor 9-7: Práctica adicional: Clave de respuestas Intended Role: Instructor 9-7: Refuerzo para mejorar la comprensión: Clave de respuestas Intended Role: Instructor 9-7: Desarrollar la competencia matemática: Clave de respuestas Intended Role: Instructor 9-7: Ampliación: Clave de respuestas Intended Role: Instructor Topic 9: 3-Act Math Recording Sheets Intended Role: Instructor Teacher's Edition eText: Grade 5, Topic 9: 3-Act Math Intended Role: Instructor 9-8: Lesson Plan Intended Role: Instructor Teacher's Edition eText: Grade 5 Lesson 9-8 Intended Role: Instructor 9-8: Listen & Look For Intended Role: Instructor 9-8: Daily Review: Editable Worksheet Intended Role: Instructor 9-8: Daily Review: Answer Key Intended Role: Instructor Topic 9: Today's Challenge Teacher Guide Intended Role: Instructor 9-8: Solve & Share Solution Intended Role: Instructor 9-8: Solve & Share Solution Intended Role: Instructor 9-8: Printable Additional Practice Intended Role: Instructor 9-8: Additional Practice: Editable Assessment Intended Role: Instructor 9-8: Quick Check: Answer Key Intended Role: Instructor 9-8: Printable Quick Check Intended Role: Instructor 9-8: Reteach to Build Understanding: Answer Key Intended Role: Instructor 9-8: Reteach to Build Understanding: Editable Worksheet Intended Role: Instructor 9-8: Build Mathematical Literacy: Answer Key Intended Role: Instructor 9-8: Build Mathematical Literacy: Editable Worksheet Intended Role: Instructor 9-8: Enrichment: Answer Key Intended Role: Instructor 9-8: Enrichment: Editable Worksheet Intended Role: Instructor Topic 9: Problem-Solving Leveled Reading Mat Intended Role: Instructor 9-8: eText del Libro del estudiante: Clave de respuestas Intended Role: Instructor 9-8: Repaso diario: Clave de respuestas Intended Role: Instructor 9-8: Práctica adicional Intended Role: Instructor 9-8: Práctica adicional: Clave de respuestas Intended Role: Instructor 9-8: Refuerzo para mejorar la comprensión: Clave de respuestas Intended Role: Instructor 9-8: Desarrollar la competencia matemática: Clave de respuestas Intended Role: Instructor 9-8: Ampliación: Clave de respuestas Intended Role: Instructor Topic 9: Vocabulary Review Intended Role: Instructor Topic 9: Reteaching Intended Role: Instructor Topic 9 Performance Task: Answer Key Intended Role: Instructor Topic 9 Performance Task: Editable Assessment Intended Role: Instructor Topic 9 Assessment: Answer Key Intended Role: Instructor Topic 9 Topic Assessments: Editable Assessment Intended Role: Instructor Topic 9 Online Assessment: Answer Key Intended Role: Instructor Topic 9 Online Assessment: Printable Intended Role: Instructor Tema 9: Tarea de rendimento: Clave de respuestas Intended Role: Instructor Tema 9: Evaluación: Clave de respuestas Intended Role: Instructor Topic 10: Home-School Connection Intended Role: Instructor Topic 10: Problem-Solving Reading Activity Guide Intended Role: Instructor Topic 10: Problem-Solving Leveled Reading Mat Intended Role: Instructor Topic 10: Home-School Connection(Spanish) Intended Role: Instructor Topic 10: Pick a Project (Spanish) Intended Role: Instructor Topic 10: enVision STEM Activity (Spanish) Intended Role: Instructor Teacher's Edition eText: Grade 5 Topic 10 Intended Role: Instructor Topic 10: Professional Development Video Intended Role: Instructor Topic 10: Today's Challenge Teacher Guide Intended Role: Instructor 10-1: Lesson Plan Intended Role: Instructor Teacher's Edition eText: Grade 5 Lesson 10-1 Intended Role: Instructor 10-1: Listen & Look For Intended Role: Instructor 10-1: Daily Review: Editable Worksheet Intended Role: Instructor 10-1: Daily Review: Answer Key Intended Role: Instructor Topic 10: Today's Challenge Teacher Guide Intended Role: Instructor 10-1: Solve & Share Solution Intended Role: Instructor 10-1: Solve & Share Solution Intended Role: Instructor 10-1: Printable Additional Practice Intended Role: Instructor 10-1: Additional Practice: Editable Assessment Intended Role: Instructor 10-1: Quick Check: Answer Key Intended Role: Instructor 10-1: Printable Quick Check Intended Role: Instructor 10-1: Reteach to Build Understanding: Answer Key Intended Role: Instructor 10-1: Reteach to Build Understanding: Editable Worksheet Intended Role: Instructor 10-1: Build Mathematical Literacy: Answer Key Intended Role: Instructor 10-1: Build Mathematical Literacy: Editable Worksheet Intended Role: Instructor 10-1: Enrichment: Answer Key Intended Role: Instructor 10-1: Enrichment: Editable Worksheet Intended Role: Instructor 10-1: eText del Libro del estudiante: Clave de respuestas Intended Role: Instructor 10-1: Repaso diario: Clave de respuestas Intended Role: Instructor 10-1: Práctica adicional Intended Role: Instructor 10-1: Práctica adicional: Clave de respuestas Intended Role: Instructor 10-1: Refuerzo para mejorar la comprensión: Clave de respuestas Intended Role: Instructor 10-1: Desarrollar la competencia matemática: Clave de respuestas Intended Role: Instructor 10-1: Ampliación: Clave de respuestas Intended Role: Instructor 10-2: Lesson Plan Intended Role: Instructor Teacher's Edition eText: Grade 5 Lesson 10-2 Intended Role: Instructor 10-2: Listen & Look For Intended Role: Instructor 10-2: Daily Review: Editable Worksheet Intended Role: Instructor 10-2: Daily Review: Answer Key Intended Role: Instructor Topic 10: Today's Challenge Teacher Guide Intended Role: Instructor 10-2: Solve & Share Solution Intended Role: Instructor 10-2: Solve & Share Solution Intended Role: Instructor 10-2: Printable Additional Practice Intended Role: Instructor 10-2: Additional Practice: Editable Assessment Intended Role: Instructor 10-2: Quick Check: Answer Key Intended Role: Instructor 10-2: Printable Quick Check Intended Role: Instructor 10-2: Reteach to Build Understanding: Answer Key Intended Role: Instructor 10-2: Reteach to Build Understanding: Editable Worksheet Intended Role: Instructor 10-2: Build Mathematical Literacy: Answer Key Intended Role: Instructor 10-2: Build Mathematical Literacy: Editable Worksheet Intended Role: Instructor 10-2: Enrichment: Answer Key Intended Role: Instructor 10-2: Enrichment: Editable Worksheet Intended Role: Instructor Topic 10: Problem-Solving Leveled Reading Mat Intended Role: Instructor 10-2: eText del Libro del estudiante: Clave de respuestas Intended Role: Instructor 10-2: Repaso diario: Clave de respuestas Intended Role: Instructor 10-2: Práctica adicional Intended Role: Instructor 10-2: Práctica adicional: Clave de respuestas Intended Role: Instructor 10-2: Refuerzo para mejorar la comprensión: Clave de respuestas Intended Role: Instructor 10-2: Desarrollar la competencia matemática: Clave de respuestas Intended Role: Instructor 10-2: Ampliación: Clave de respuestas Intended Role: Instructor 10-3: Lesson Plan Intended Role: Instructor Teacher's Edition eText: Grade 5 Lesson 10-3 Intended Role: Instructor 10-3: Listen & Look For Intended Role: Instructor 10-3: Daily Review: Editable Worksheet Intended Role: Instructor 10-3: Daily Review: Answer Key Intended Role: Instructor Topic 10: Today's Challenge Teacher Guide Intended Role: Instructor 10-3: Solve & Share Solution Intended Role: Instructor 10-3: Solve & Share Solution Intended Role: Instructor 10-3: Printable Additional Practice Intended Role: Instructor 10-3: Additional Practice: Editable Assessment Intended Role: Instructor 10-3: Quick Check: Answer Key Intended Role: Instructor 10-3: Printable Quick Check Intended Role: Instructor 10-3: Reteach to Build Understanding: Answer Key Intended Role: Instructor 10-3: Reteach to Build Understanding: Editable Worksheet Intended Role: Instructor 10-3: Build Mathematical Literacy: Answer Key Intended Role: Instructor 10-3: Build Mathematical Literacy: Editable Worksheet Intended Role: Instructor 10-3: Enrichment: Answer Key Intended Role: Instructor 10-3: Enrichment: Editable Worksheet Intended Role: Instructor Topic 10: Problem-Solving Leveled Reading Mat Intended Role: Instructor 10-3: eText del Libro del estudiante: Clave de respuestas Intended Role: Instructor 10-3: Repaso diario: Clave de respuestas Intended Role: Instructor 10-3: Práctica adicional Intended Role: Instructor 10-3: Práctica adicional: Clave de respuestas Intended Role: Instructor 10-3: Refuerzo para mejorar la comprensión: Clave de respuestas Intended Role: Instructor 10-3: Desarrollar la competencia matemática: Clave de respuestas Intended Role: Instructor 10-3: Ampliación: Clave de respuestas Intended Role: Instructor 10-4: Lesson Plan Intended Role: Instructor Teacher's Edition eText: Grade 5 Lesson 10-4 Intended Role: Instructor 10-4: Listen & Look For Intended Role: Instructor 10-4: Daily Review: Editable Worksheet Intended Role: Instructor 10-4: Daily Review: Answer Key Intended Role: Instructor Topic 10: Today's Challenge Teacher Guide Intended Role: Instructor 10-4: Solve & Share Solution Intended Role: Instructor 10-4: Solve & Share Solution Intended Role: Instructor 10-4: Printable Additional Practice Intended Role: Instructor 10-4: Additional Practice: Editable Assessment Intended Role: Instructor 10-4: Quick Check: Answer Key Intended Role: Instructor 10-4: Printable Quick Check Intended Role: Instructor 10-4: Reteach to Build Understanding: Answer Key Intended Role: Instructor 10-4: Reteach to Build Understanding: Editable Worksheet Intended Role: Instructor 10-4: Build Mathematical Literacy: Answer Key Intended Role: Instructor 10-4: Build Mathematical Literacy: Editable Worksheet Intended Role: Instructor 10-4: Enrichment: Answer Key Intended Role: Instructor 10-4: Enrichment: Editable Worksheet Intended Role: Instructor 10-4: eText del Libro del estudiante: Clave de respuestas Intended Role: Instructor 10-4: Repaso diario: Clave de respuestas Intended Role: Instructor 10-4: Práctica adicional Intended Role: Instructor 10-4: Práctica adicional: Clave de respuestas Intended Role: Instructor 10-4: Refuerzo para mejorar la comprensión: Clave de respuestas Intended Role: Instructor 10-4: Desarrollar la competencia matemática: Clave de respuestas Intended Role: Instructor 10-4: Ampliación: Clave de respuestas Intended Role: Instructor Topic 10: Vocabulary Review Intended Role: Instructor Topic 10: Reteaching Intended Role: Instructor Topic 10 Performance Task: Answer Key Intended Role: Instructor Topic 10 Performance Task: Editable Assessment Intended Role: Instructor Topic 10 Assessment: Answer Key Intended Role: Instructor Topic 10 Topic Assessments: Editable Assessment Intended Role: Instructor Topic 10 Online Assessment: Answer Key Intended Role: Instructor Topic 10 Online Assessment: Printable Intended Role: Instructor Tema 10: Tarea de rendimento: Clave de respuestas Intended Role: Instructor Tema 10: Evaluación: Clave de respuestas Intended Role: Instructor Topic 11: Home-School Connection Intended Role: Instructor Topic 11: Problem-Solving Reading Activity Guide Intended Role: Instructor Topic 11: Problem-Solving Leveled Reading Mat Intended Role: Instructor Topic 11: Home-School Connection(Spanish) Intended Role: Instructor Topic 11: Pick a Project (Spanish) Intended Role: Instructor Topic 11: enVision STEM Activity (Spanish) Intended Role: Instructor Teacher's Edition eText: Grade 5 Topic 11 Intended Role: Instructor Topic 11: Professional Development Video Intended Role: Instructor Topic 11: Today's Challenge Teacher Guide Intended Role: Instructor 11-1: Lesson Plan Intended Role: Instructor Teacher's Edition eText: Grade 5 Lesson 11-1 Intended Role: Instructor 11-1: Listen & Look For Intended Role: Instructor 11-1: Daily Review: Editable Worksheet Intended Role: Instructor 11-1: Daily Review: Answer Key Intended Role: Instructor Topic 11: Today's Challenge Teacher Guide Intended Role: Instructor 11-1: Solve & Share Solution Intended Role: Instructor 11-1: Solve & Share Solution Intended Role: Instructor 11-1: Printable Additional Practice Intended Role: Instructor 11-1: Additional Practice: Editable Assessment Intended Role: Instructor 11-1: Quick Check: Answer Key Intended Role: Instructor 11-1: Printable Quick Check Intended Role: Instructor 11-1: Reteach to Build Understanding: Answer Key Intended Role: Instructor 11-1: Reteach to Build Understanding: Editable Worksheet Intended Role: Instructor 11-1: Build Mathematical Literacy: Answer Key Intended Role: Instructor 11-1: Build Mathematical Literacy: Editable Worksheet Intended Role: Instructor 11-1: Enrichment: Answer Key Intended Role: Instructor 11-1: Enrichment: Editable Worksheet Intended Role: Instructor Topic 11: Problem-Solving Leveled Reading Mat Intended Role: Instructor 11-1: eText del Libro del estudiante: Clave de respuestas Intended Role: Instructor 11-1: Repaso diario: Clave de respuestas Intended Role: Instructor 11-1: Práctica adicional Intended Role: Instructor 11-1: Práctica adicional: Clave de respuestas Intended Role: Instructor 11-1: Refuerzo para mejorar la comprensión: Clave de respuestas Intended Role: Instructor 11-1: Desarrollar la competencia matemática: Clave de respuestas Intended Role: Instructor 11-1: Ampliación: Clave de respuestas Intended Role: Instructor 11-2: Lesson Plan Intended Role: Instructor Teacher's Edition eText: Grade 5 Lesson 11-2 Intended Role: Instructor 11-2: Listen & Look For Intended Role: Instructor 11-2: Daily Review: Editable Worksheet Intended Role: Instructor 11-2: Daily Review: Answer Key Intended Role: Instructor Topic 11: Today's Challenge Teacher Guide Intended Role: Instructor 11-2: Solve & Share Solution Intended Role: Instructor 11-2: Solve & Share Solution Intended Role: Instructor 11-2: Printable Additional Practice Intended Role: Instructor 11-2: Additional Practice: Editable Assessment Intended Role: Instructor 11-2: Quick Check: Answer Key Intended Role: Instructor 11-2: Printable Quick Check Intended Role: Instructor 11-2: Reteach to Build Understanding: Answer Key Intended Role: Instructor 11-2: Reteach to Build Understanding: Editable Worksheet Intended Role: Instructor 11-2: Build Mathematical Literacy: Answer Key Intended Role: Instructor 11-2: Build Mathematical Literacy: Editable Worksheet Intended Role: Instructor 11-2: Enrichment: Answer Key Intended Role: Instructor 11-2: Enrichment: Editable Worksheet Intended Role: Instructor 11-2: eText del Libro del estudiante: Clave de respuestas Intended Role: Instructor 11-2: Repaso diario: Clave de respuestas Intended Role: Instructor 11-2: Práctica adicional Intended Role: Instructor 11-2: Práctica adicional: Clave de respuestas Intended Role: Instructor 11-2: Refuerzo para mejorar la comprensión: Clave de respuestas Intended Role: Instructor 11-2: Desarrollar la competencia matemática: Clave de respuestas Intended Role: Instructor 11-2: Ampliación: Clave de respuestas Intended Role: Instructor Topic 11: 3-Act Math Recording Sheets Intended Role: Instructor Teacher's Edition eText: Grade 5, Topic 11: 3-Act Math Intended Role: Instructor 11-3: Lesson Plan Intended Role: Instructor Teacher's Edition eText: Grade 5 Lesson 11-3 Intended Role: Instructor 11-3: Listen & Look For Intended Role: Instructor 11-3: Daily Review: Editable Worksheet Intended Role: Instructor 11-3: Daily Review: Answer Key Intended Role: Instructor Topic 11: Today's Challenge Teacher Guide Intended Role: Instructor 11-3: Solve & Share Solution Intended Role: Instructor 11-3: Solve & Share Solution Intended Role: Instructor 11-3: Printable Additional Practice Intended Role: Instructor 11-3: Additional Practice: Editable Assessment Intended Role: Instructor 11-3: Quick Check: Answer Key Intended Role: Instructor 11-3: Printable Quick Check Intended Role: Instructor 11-3: Reteach to Build Understanding: Answer Key Intended Role: Instructor 11-3: Reteach to Build Understanding: Editable Worksheet Intended Role: Instructor 11-3: Build Mathematical Literacy: Answer Key Intended Role: Instructor 11-3: Build Mathematical Literacy: Editable Worksheet Intended Role: Instructor 11-3: Enrichment: Answer Key Intended Role: Instructor 11-3: Enrichment: Editable Worksheet Intended Role: Instructor 11-3: eText del Libro del estudiante: Clave de respuestas Intended Role: Instructor 11-3: Repaso diario: Clave de respuestas Intended Role: Instructor 11-3: Práctica adicional Intended Role: Instructor 11-3: Práctica adicional: Clave de respuestas Intended Role: Instructor 11-3: Refuerzo para mejorar la comprensión: Clave de respuestas Intended Role: Instructor 11-3: Desarrollar la competencia matemática: Clave de respuestas Intended Role: Instructor 11-3: Ampliación: Clave de respuestas Intended Role: Instructor 11-4: Lesson Plan Intended Role: Instructor Teacher's Edition eText: Grade 5 Lesson 11-4 Intended Role: Instructor 11-4: Daily Review: Editable Worksheet Intended Role: Instructor 11-4: Daily Review: Answer Key Intended Role: Instructor Topic 11: Today's Challenge Teacher Guide Intended Role: Instructor 11-4: Solve & Share Solution Intended Role: Instructor 11-4: Solve & Share Solution Intended Role: Instructor 11-4: Printable Additional Practice Intended Role: Instructor 11-4: Additional Practice: Editable Assessment Intended Role: Instructor 11-4: Quick Check: Answer Key Intended Role: Instructor 11-4: Printable Quick Check Intended Role: Instructor 11-4: Reteach to Build Understanding: Answer Key Intended Role: Instructor 11-4: Reteach to Build Understanding: Editable Worksheet Intended Role: Instructor 11-4: Build Mathematical Literacy: Answer Key Intended Role: Instructor 11-4: Build Mathematical Literacy: Editable Worksheet Intended Role: Instructor 11-4: Enrichment: Answer Key Intended Role: Instructor 11-4: Enrichment: Editable Worksheet Intended Role: Instructor 11-4: eText del Libro del estudiante: Clave de respuestas Intended Role: Instructor 11-4: Repaso diario: Clave de respuestas Intended Role: Instructor 11-4: Práctica adicional Intended Role: Instructor 11-4: Práctica adicional: Clave de respuestas Intended Role: Instructor 11-4: Refuerzo para mejorar la comprensión: Clave de respuestas Intended Role: Instructor 11-4: Desarrollar la competencia matemática: Clave de respuestas Intended Role: Instructor 11-4: Ampliación: Clave de respuestas Intended Role: Instructor 11-5: Lesson Plan Intended Role: Instructor Teacher's Edition eText: Grade 5 Lesson 11-5 Intended Role: Instructor 11-5: Listen & Look For Intended Role: Instructor 11-5: Daily Review: Editable Worksheet Intended Role: Instructor 11-5: Daily Review: Answer Key Intended Role: Instructor Topic 11: Today's Challenge Teacher Guide Intended Role: Instructor 11-5: Solve & Share Solution Intended Role: Instructor 11-5: Solve & Share Solution Intended Role: Instructor 11-5: Printable Additional Practice Intended Role: Instructor 11-5: Additional Practice: Editable Assessment Intended Role: Instructor 11-5: Quick Check: Answer Key Intended Role: Instructor 11-5: Printable Quick Check Intended Role: Instructor 11-5: Reteach to Build Understanding: Answer Key Intended Role: Instructor 11-5: Reteach to Build Understanding: Editable Worksheet Intended Role: Instructor 11-5: Build Mathematical Literacy: Answer Key Intended Role: Instructor 11-5: Build Mathematical Literacy: Editable Worksheet Intended Role: Instructor 11-5: Enrichment: Answer Key Intended Role: Instructor 11-5: Enrichment: Editable Worksheet Intended Role: Instructor Topic 11: Problem-Solving Leveled Reading Mat Intended Role: Instructor 11-5: eText del Libro del estudiante: Clave de respuestas Intended Role: Instructor 11-5: Repaso diario: Clave de respuestas Intended Role: Instructor 11-5: Práctica adicional Intended Role: Instructor 11-5: Práctica adicional: Clave de respuestas Intended Role: Instructor 11-5: Refuerzo para mejorar la comprensión: Clave de respuestas Intended Role: Instructor 11-5: Desarrollar la competencia matemática: Clave de respuestas Intended Role: Instructor 11-5: Ampliación: Clave de respuestas Intended Role: Instructor Topic 11: Vocabulary Review Intended Role: Instructor Topic 11: Reteaching Intended Role: Instructor Topic 11 Performance Task: Answer Key Intended Role: Instructor Topic 11 Performance Task: Editable Assessment Intended Role: Instructor Topic 11 Assessment: Answer Key Intended Role: Instructor Topic 11 Topic Assessments: Editable Assessment Intended Role: Instructor Topic 11 Online Assessment: Answer Key Intended Role: Instructor Topic 11 Online Assessment: Printable Intended Role: Instructor Tema 11: Tarea de rendimento: Clave de respuestas Intended Role: Instructor Tema 11: Evaluación: Clave de respuestas Intended Role: Instructor Topic 12: Home-School Connection Intended Role: Instructor Topic 12: Problem-Solving Reading Activity Guide Intended Role: Instructor Topic 12: Problem-Solving Leveled Reading Mat Intended Role: Instructor Topic 12: Home-School Connection(Spanish) Intended Role: Instructor Topic 12: Pick a Project (Spanish) Intended Role: Instructor Topic 12: enVision STEM Activity (Spanish) Intended Role: Instructor Teacher's Edition eText: Grade 5 Topic 12 Intended Role: Instructor Topic 12: Professional Development Video Intended Role: Instructor Topic 12: Today's Challenge Teacher Guide Intended Role: Instructor 12-1: Lesson Plan Intended Role: Instructor Teacher's Edition eText: Grade 5 Lesson 12-1 Intended Role: Instructor 12-1: Listen & Look For Intended Role: Instructor 12-1: Daily Review: Editable Worksheet Intended Role: Instructor 12-1: Daily Review: Answer Key Intended Role: Instructor Topic 12: Today's Challenge Teacher Guide Intended Role: Instructor 12-1: Solve & Share Solution Intended Role: Instructor 12-1: Solve & Share Solution Intended Role: Instructor 12-1: Printable Additional Practice Intended Role: Instructor 12-1: Additional Practice: Editable Assessment Intended Role: Instructor 12-1: Quick Check: Answer Key Intended Role: Instructor 12-1: Printable Quick Check Intended Role: Instructor 12-1: Reteach to Build Understanding: Answer Key Intended Role: Instructor 12-1: Reteach to Build Understanding: Editable Worksheet Intended Role: Instructor 12-1: Build Mathematical Literacy: Answer Key Intended Role: Instructor 12-1: Build Mathematical Literacy: Editable Worksheet Intended Role: Instructor 12-1: Enrichment: Answer Key Intended Role: Instructor 12-1: Enrichment: Editable Worksheet Intended Role: Instructor 12-1: eText del Libro del estudiante: Clave de respuestas Intended Role: Instructor 12-1: Repaso diario: Clave de respuestas Intended Role: Instructor 12-1: Práctica adicional Intended Role: Instructor 12-1: Práctica adicional: Clave de respuestas Intended Role: Instructor 12-1: Refuerzo para mejorar la comprensión: Clave de respuestas Intended Role: Instructor 12-1: Desarrollar la competencia matemática: Clave de respuestas Intended Role: Instructor 12-1: Ampliación: Clave de respuestas Intended Role: Instructor 12-2: Lesson Plan Intended Role: Instructor Teacher's Edition eText: Grade 5 Lesson 12-2 Intended Role: Instructor 12-2: Listen & Look For Intended Role: Instructor 12-2: Daily Review: Editable Worksheet Intended Role: Instructor 12-2: Daily Review: Answer Key Intended Role: Instructor Topic 12: Today's Challenge Teacher Guide Intended Role: Instructor 12-2: Solve & Share Solution Intended Role: Instructor 12-2: Solve & Share Solution Intended Role: Instructor 12-2: Printable Additional Practice Intended Role: Instructor 12-2: Additional Practice: Editable Assessment Intended Role: Instructor 12-2: Quick Check: Answer Key Intended Role: Instructor 12-2: Printable Quick Check Intended Role: Instructor 12-2: Reteach to Build Understanding: Answer Key Intended Role: Instructor 12-2: Reteach to Build Understanding: Editable Worksheet Intended Role: Instructor 12-2: Build Mathematical Literacy: Answer Key Intended Role: Instructor 12-2: Build Mathematical Literacy: Editable Worksheet Intended Role: Instructor 12-2: Enrichment: Answer Key Intended Role: Instructor 12-2: Enrichment: Editable Worksheet Intended Role: Instructor 12-2: eText del Libro del estudiante: Clave de respuestas Intended Role: Instructor 12-2: Repaso diario: Clave de respuestas Intended Role: Instructor 12-2: Práctica adicional Intended Role: Instructor 12-2: Práctica adicional: Clave de respuestas Intended Role: Instructor 12-2: Refuerzo para mejorar la comprensión: Clave de respuestas Intended Role: Instructor 12-2: Desarrollar la competencia matemática: Clave de respuestas Intended Role: Instructor 12-2: Ampliación: Clave de respuestas Intended Role: Instructor 12-3: Lesson Plan Intended Role: Instructor Teacher's Edition eText: Grade 5 Lesson 12-3 Intended Role: Instructor 12-3: Listen & Look For Intended Role: Instructor 12-3: Daily Review: Editable Worksheet Intended Role: Instructor 12-3: Daily Review: Answer Key Intended Role: Instructor Topic 12: Today's Challenge Teacher Guide Intended Role: Instructor 12-3: Solve & Share Solution Intended Role: Instructor 12-3: Solve & Share Solution Intended Role: Instructor 12-3: Printable Additional Practice Intended Role: Instructor 12-3: Additional Practice: Editable Assessment Intended Role: Instructor 12-3: Quick Check: Answer Key Intended Role: Instructor 12-3: Printable Quick Check Intended Role: Instructor 12-3: Reteach to Build Understanding: Answer Key Intended Role: Instructor 12-3: Reteach to Build Understanding: Editable Worksheet Intended Role: Instructor 12-3: Build Mathematical Literacy: Answer Key Intended Role: Instructor 12-3: Build Mathematical Literacy: Editable Worksheet Intended Role: Instructor 12-3: Enrichment: Answer Key Intended Role: Instructor 12-3: Enrichment: Editable Worksheet Intended Role: Instructor 12-3: eText del Libro del estudiante: Clave de respuestas Intended Role: Instructor 12-3: Repaso diario: Clave de respuestas Intended Role: Instructor 12-3: Práctica adicional Intended Role: Instructor 12-3: Práctica adicional: Clave de respuestas Intended Role: Instructor 12-3: Refuerzo para mejorar la comprensión: Clave de respuestas Intended Role: Instructor 12-3: Desarrollar la competencia matemática: Clave de respuestas Intended Role: Instructor 12-3: Ampliación: Clave de respuestas Intended Role: Instructor 12-4: Lesson Plan Intended Role: Instructor Teacher's Edition eText: Grade 5 Lesson 12-4 Intended Role: Instructor 12-4: Listen & Look For Intended Role: Instructor 12-4: Daily Review: Editable Worksheet Intended Role: Instructor 12-4: Daily Review: Answer Key Intended Role: Instructor Topic 12: Today's Challenge Teacher Guide Intended Role: Instructor 12-4: Solve & Share Solution Intended Role: Instructor 12-4: Solve & Share Solution Intended Role: Instructor 12-4: Printable Additional Practice Intended Role: Instructor 12-4: Additional Practice: Editable Assessment Intended Role: Instructor 12-4: Quick Check: Answer Key Intended Role: Instructor 12-4: Printable Quick Check Intended Role: Instructor 12-4: Reteach to Build Understanding: Answer Key Intended Role: Instructor 12-4: Reteach to Build Understanding: Editable Worksheet Intended Role: Instructor 12-4: Build Mathematical Literacy: Answer Key Intended Role: Instructor 12-4: Build Mathematical Literacy: Editable Worksheet Intended Role: Instructor 12-4: Enrichment: Answer Key Intended Role: Instructor 12-4: Enrichment: Editable Worksheet Intended Role: Instructor Topic 12: Problem-Solving Leveled Reading Mat Intended Role: Instructor 12-4: eText del Libro del estudiante: Clave de respuestas Intended Role: Instructor 12-4: Repaso diario: Clave de respuestas Intended Role: Instructor 12-4: Práctica adicional Intended Role: Instructor 12-4: Práctica adicional: Clave de respuestas Intended Role: Instructor 12-4: Refuerzo para mejorar la comprensión: Clave de respuestas Intended Role: Instructor 12-4: Desarrollar la competencia matemática: Clave de respuestas Intended Role: Instructor 12-4: Ampliación: Clave de respuestas Intended Role: Instructor 12-5: Lesson Plan Intended Role: Instructor Teacher's Edition eText: Grade 5 Lesson 12-5 Intended Role: Instructor 12-5: Listen & Look For Intended Role: Instructor 12-5: Daily Review: Editable Worksheet Intended Role: Instructor 12-5: Daily Review: Answer Key Intended Role: Instructor Topic 12: Today's Challenge Teacher Guide Intended Role: Instructor 12-5: Solve & Share Solution Intended Role: Instructor 12-5: Solve & Share Solution Intended Role: Instructor 12-5: Printable Additional Practice Intended Role: Instructor 12-5: Additional Practice: Editable Assessment Intended Role: Instructor 12-5: Quick Check: Answer Key Intended Role: Instructor 12-5: Printable Quick Check Intended Role: Instructor 12-5: Reteach to Build Understanding: Answer Key Intended Role: Instructor 12-5: Reteach to Build Understanding: Editable Worksheet Intended Role: Instructor 12-5: Build Mathematical Literacy: Answer Key Intended Role: Instructor 12-5: Build Mathematical Literacy: Editable Worksheet Intended Role: Instructor 12-5: Enrichment: Answer Key Intended Role: Instructor 12-5: Enrichment: Editable Worksheet Intended Role: Instructor 12-5: eText del Libro del estudiante: Clave de respuestas Intended Role: Instructor 12-5: Repaso diario: Clave de respuestas Intended Role: Instructor 12-5: Práctica adicional Intended Role: Instructor 12-5: Práctica adicional: Clave de respuestas Intended Role: Instructor 12-5: Refuerzo para mejorar la comprensión: Clave de respuestas Intended Role: Instructor 12-5: Desarrollar la competencia matemática: Clave de respuestas Intended Role: Instructor 12-5: Ampliación: Clave de respuestas Intended Role: Instructor 12-6: Lesson Plan Intended Role: Instructor Teacher's Edition eText: Grade 5 Lesson 12-6 Intended Role: Instructor 12-6: Listen & Look For Intended Role: Instructor 12-6: Daily Review: Editable Worksheet Intended Role: Instructor 12-6: Daily Review: Answer Key Intended Role: Instructor Topic 12: Today's Challenge Teacher Guide Intended Role: Instructor 12-6: Solve & Share Solution Intended Role: Instructor 12-6: Solve & Share Solution Intended Role: Instructor 12-6: Printable Additional Practice Intended Role: Instructor 12-6: Additional Practice: Editable Assessment Intended Role: Instructor 12-6: Quick Check: Answer Key Intended Role: Instructor 12-6: Printable Quick Check Intended Role: Instructor 12-6: Reteach to Build Understanding: Answer Key Intended Role: Instructor 12-6: Reteach to Build Understanding: Editable Worksheet Intended Role: Instructor 12-6: Build Mathematical Literacy: Answer Key Intended Role: Instructor 12-6: Build Mathematical Literacy: Editable Worksheet Intended Role: Instructor 12-6: Enrichment: Answer Key Intended Role: Instructor 12-6: Enrichment: Editable Worksheet Intended Role: Instructor 12-6: eText del Libro del estudiante: Clave de respuestas Intended Role: Instructor 12-6: Repaso diario: Clave de respuestas Intended Role: Instructor 12-6: Práctica adicional Intended Role: Instructor 12-6: Práctica adicional: Clave de respuestas Intended Role: Instructor 12-6: Refuerzo para mejorar la comprensión: Clave de respuestas Intended Role: Instructor 12-6: Desarrollar la competencia matemática: Clave de respuestas Intended Role: Instructor 12-6: Ampliación: Clave de respuestas Intended Role: Instructor 12-7: Lesson Plan Intended Role: Instructor Teacher's Edition eText: Grade 5 Lesson 12-7 Intended Role: Instructor 12-7: Listen & Look For Intended Role: Instructor 12-7: Daily Review: Editable Worksheet Intended Role: Instructor 12-7: Daily Review: Answer Key Intended Role: Instructor Topic 12: Today's Challenge Teacher Guide Intended Role: Instructor 12-7: Solve & Share Solution Intended Role: Instructor 12-7: Solve & Share Solution Intended Role: Instructor 12-7: Printable Additional Practice Intended Role: Instructor 12-7: Additional Practice: Editable Assessment Intended Role: Instructor 12-7: Quick Check: Answer Key Intended Role: Instructor 12-7: Printable Quick Check Intended Role: Instructor 12-7: Reteach to Build Understanding: Answer Key Intended Role: Instructor 12-7: Reteach to Build Understanding: Editable Worksheet Intended Role: Instructor 12-7: Build Mathematical Literacy: Answer Key Intended Role: Instructor 12-7: Build Mathematical Literacy: Editable Worksheet Intended Role: Instructor 12-7: Enrichment: Answer Key Intended Role: Instructor 12-7: Enrichment: Editable Worksheet Intended Role: Instructor 12-7: eText del Libro del estudiante: Clave de respuestas Intended Role: Instructor 12-7: Repaso diario: Clave de respuestas Intended Role: Instructor 12-7: Práctica adicional Intended Role: Instructor 12-7: Práctica adicional: Clave de respuestas Intended Role: Instructor 12-7: Refuerzo para mejorar la comprensión: Clave de respuestas Intended Role: Instructor 12-7: Desarrollar la competencia matemática: Clave de respuestas Intended Role: Instructor 12-7: Ampliación: Clave de respuestas Intended Role: Instructor 12-8: Lesson Plan Intended Role: Instructor Teacher's Edition eText: Grade 5 Lesson 12-8 Intended Role: Instructor 12-8: Listen & Look For Intended Role: Instructor 12-8: Daily Review: Editable Worksheet Intended Role: Instructor 12-8: Daily Review: Answer Key Intended Role: Instructor Topic 12: Today's Challenge Teacher Guide Intended Role: Instructor 12-8: Solve & Share Solution Intended Role: Instructor 12-8: Solve & Share Solution Intended Role: Instructor 12-8: Printable Additional Practice Intended Role: Instructor 12-8: Additional Practice: Editable Assessment Intended Role: Instructor 12-8: Quick Check: Answer Key Intended Role: Instructor 12-8: Printable Quick Check Intended Role: Instructor 12-8: Reteach to Build Understanding: Answer Key Intended Role: Instructor 12-8: Reteach to Build Understanding: Editable Worksheet Intended Role: Instructor 12-8: Build Mathematical Literacy: Answer Key Intended Role: Instructor 12-8: Build Mathematical Literacy: Editable Worksheet Intended Role: Instructor 12-8: Enrichment: Answer Key Intended Role: Instructor 12-8: Enrichment: Editable Worksheet Intended Role: Instructor Topic 12: Problem-Solving Leveled Reading Mat Intended Role: Instructor 12-8: eText del Libro del estudiante: Clave de respuestas Intended Role: Instructor 12-8: Repaso diario: Clave de respuestas Intended Role: Instructor 12-8: Práctica adicional Intended Role: Instructor 12-8: Práctica adicional: Clave de respuestas Intended Role: Instructor 12-8: Refuerzo para mejorar la comprensión: Clave de respuestas Intended Role: Instructor 12-8: Desarrollar la competencia matemática: Clave de respuestas Intended Role: Instructor 12-8: Ampliación: Clave de respuestas Intended Role: Instructor 12-9: Lesson Plan Intended Role: Instructor Teacher's Edition eText: Grade 5 Lesson 12-9 Intended Role: Instructor 12-9: Listen & Look For Intended Role: Instructor 12-9: Daily Review: Editable Worksheet Intended Role: Instructor 12-9: Daily Review: Answer Key Intended Role: Instructor Topic 12: Today's Challenge Teacher Guide Intended Role: Instructor 12-9: Solve & Share Solution Intended Role: Instructor 12-9: Solve & Share Solution Intended Role: Instructor 12-9: Printable Additional Practice Intended Role: Instructor 12-9: Additional Practice: Editable Assessment Intended Role: Instructor 12-9: Quick Check: Answer Key Intended Role: Instructor 12-9: Printable Quick Check Intended Role: Instructor 12-9: Reteach to Build Understanding: Answer Key Intended Role: Instructor 12-9: Reteach to Build Understanding: Editable Worksheet Intended Role: Instructor 12-9: Build Mathematical Literacy: Answer Key Intended Role: Instructor 12-9: Build Mathematical Literacy: Editable Worksheet Intended Role: Instructor 12-9: Enrichment: Answer Key Intended Role: Instructor 12-9: Enrichment: Editable Worksheet Intended Role: Instructor 12-9: eText del Libro del estudiante: Clave de respuestas Intended Role: Instructor 12-9: Repaso diario: Clave de respuestas Intended Role: Instructor 12-9: Práctica adicional Intended Role: Instructor 12-9: Práctica adicional: Clave de respuestas Intended Role: Instructor 12-9: Refuerzo para mejorar la comprensión: Clave de respuestas Intended Role: Instructor 12-9: Desarrollar la competencia matemática: Clave de respuestas Intended Role: Instructor 12-9: Ampliación: Clave de respuestas Intended Role: Instructor Topic 12: Vocabulary Review Intended Role: Instructor Topic 12: Reteaching Intended Role: Instructor Topic 12 Performance Task: Answer Key Intended Role: Instructor Topic 12 Performance Task: Editable Assessment Intended Role: Instructor Topic 12 Assessment: Answer Key Intended Role: Instructor Topic 12 Topic Assessments: Editable Assessment Intended Role: Instructor Topic 12 Online Assessment: Answer Key Intended Role: Instructor Topic 12 Online Assessment: Printable Intended Role: Instructor Tema 12: Tarea de rendimento: Clave de respuestas Intended Role: Instructor Tema 12: Evaluación: Clave de respuestas Intended Role: Instructor Topics 1–12: Cumulative/Benchmark Assessment: Answer Key Intended Role: Instructor Topics 1–12: Cumulative/Benchmark Assessment: Editable Assessment Intended Role: Instructor Topics 1–12: Online Cumulative/Benchmark Assessment: Answer Key Intended Role: Instructor Topics 1–12: Printable Online Cumulative/Benchmark Assessment Intended Role: Instructor Topic 13: Home-School Connection Intended Role: Instructor Topic 13: Problem-Solving Leveled Reading Mat Intended Role: Instructor Topic 13: Problem-Solving Reading Activity Guide Intended Role: Instructor Topic 13: Home-School Connection(Spanish) Intended Role: Instructor Topic 13: Pick a Project (Spanish) Intended Role: Instructor Topic 13: enVision STEM Activity (Spanish) Intended Role: Instructor Teacher's Edition eText: Grade 5 Topic 13 Intended Role: Instructor Topic 13: Professional Development Video Intended Role: Instructor Topic 13: Today's Challenge Teacher Guide Intended Role: Instructor 13-1: Lesson Plan Intended Role: Instructor Teacher's Edition eText: Grade 5 Lesson 13-1 Intended Role: Instructor 13-1: Listen & Look For Intended Role: Instructor 13-1: Daily Review: Editable Worksheet Intended Role: Instructor 13-1: Daily Review: Answer Key Intended Role: Instructor Topic 13: Today's Challenge Teacher Guide Intended Role: Instructor 13-1: Solve & Share Solution Intended Role: Instructor 13-1: Solve & Share Solution Intended Role: Instructor 13-1: Printable Additional Practice Intended Role: Instructor 13-1: Additional Practice: Editable Assessment Intended Role: Instructor 13-1: Quick Check: Answer Key Intended Role: Instructor 13-1: Printable Quick Check Intended Role: Instructor 13-1: Reteach to Build Understanding: Answer Key Intended Role: Instructor 13-1: Reteach to Build Understanding: Editable Worksheet Intended Role: Instructor 13-1: Build Mathematical Literacy: Answer Key Intended Role: Instructor 13-1: Build Mathematical Literacy: Editable Worksheet Intended Role: Instructor 13-1: Enrichment: Answer Key Intended Role: Instructor 13-1: Enrichment: Editable Worksheet Intended Role: Instructor 13-1: eText del Libro del estudiante: Clave de respuestas Intended Role: Instructor 13-1: Repaso diario: Clave de respuestas Intended Role: Instructor 13-1: Práctica adicional Intended Role: Instructor 13-1: Práctica adicional: Clave de respuestas Intended Role: Instructor 13-1: Refuerzo para mejorar la comprensión: Clave de respuestas Intended Role: Instructor 13-1: Desarrollar la competencia matemática: Clave de respuestas Intended Role: Instructor 13-1: Ampliación: Clave de respuestas Intended Role: Instructor 13-2: Lesson Plan Intended Role: Instructor Teacher's Edition eText: Grade 5 Lesson 13-2 Intended Role: Instructor 13-2: Listen & Look For Intended Role: Instructor 13-2: Daily Review: Editable Worksheet Intended Role: Instructor 13-2: Daily Review: Answer Key Intended Role: Instructor Topic 13: Today's Challenge Teacher Guide Intended Role: Instructor 13-2: Solve & Share Solution Intended Role: Instructor 13-2: Solve & Share Solution Intended Role: Instructor 13-2: Printable Additional Practice Intended Role: Instructor 13-2: Additional Practice: Editable Assessment Intended Role: Instructor 13-2: Quick Check: Answer Key Intended Role: Instructor 13-2: Printable Quick Check Intended Role: Instructor 13-2: Reteach to Build Understanding: Answer Key Intended Role: Instructor 13-2: Reteach to Build Understanding: Editable Worksheet Intended Role: Instructor 13-2: Build Mathematical Literacy: Answer Key Intended Role: Instructor 13-2: Build Mathematical Literacy: Editable Worksheet Intended Role: Instructor 13-2: Enrichment: Answer Key Intended Role: Instructor 13-2: Enrichment: Editable Worksheet Intended Role: Instructor Topic 13: Problem-Solving Leveled Reading Mat Intended Role: Instructor 13-2: eText del Libro del estudiante: Clave de respuestas Intended Role: Instructor 13-2: Repaso diario: Clave de respuestas Intended Role: Instructor 13-2: Práctica adicional Intended Role: Instructor 13-2: Práctica adicional: Clave de respuestas Intended Role: Instructor 13-2: Refuerzo para mejorar la comprensión: Clave de respuestas Intended Role: Instructor 13-2: Desarrollar la competencia matemática: Clave de respuestas Intended Role: Instructor 13-2: Ampliación: Clave de respuestas Intended Role: Instructor 13-3: Lesson Plan Intended Role: Instructor Teacher's Edition eText: Grade 5 Lesson 13-3 Intended Role: Instructor 13-3: Listen & Look For Intended Role: Instructor 13-3: Daily Review: Editable Worksheet Intended Role: Instructor 13-3: Daily Review: Answer Key Intended Role: Instructor Topic 13: Today's Challenge Teacher Guide Intended Role: Instructor 13-3: Solve & Share Solution Intended Role: Instructor 13-3: Solve & Share Solution Intended Role: Instructor 13-3: Printable Additional Practice Intended Role: Instructor 13-3: Additional Practice: Editable Assessment Intended Role: Instructor 13-3: Quick Check: Answer Key Intended Role: Instructor 13-3: Printable Quick Check Intended Role: Instructor 13-3: Reteach to Build Understanding: Answer Key Intended Role: Instructor 13-3: Reteach to Build Understanding: Editable Worksheet Intended Role: Instructor 13-3: Build Mathematical Literacy: Answer Key Intended Role: Instructor 13-3: Build Mathematical Literacy: Editable Worksheet Intended Role: Instructor 13-3: Enrichment: Answer Key Intended Role: Instructor 13-3: Enrichment: Editable Worksheet Intended Role: Instructor Topic 13: Problem-Solving Leveled Reading Mat Intended Role: Instructor 13-3: eText del Libro del estudiante: Clave de respuestas Intended Role: Instructor 13-3: Repaso diario: Clave de respuestas Intended Role: Instructor 13-3: Práctica adicional Intended Role: Instructor 13-3: Práctica adicional: Clave de respuestas Intended Role: Instructor 13-3: Refuerzo para mejorar la comprensión: Clave de respuestas Intended Role: Instructor 13-3: Desarrollar la competencia matemática: Clave de respuestas Intended Role: Instructor 13-3: Ampliación: Clave de respuestas Intended Role: Instructor Topic 13: 3-Act Math Recording Sheets Intended Role: Instructor Teacher's Edition eText: Grade 5, Topic 13: 3-Act Math Intended Role: Instructor 13-4: Lesson Plan Intended Role: Instructor Teacher's Edition eText: Grade 5 Lesson 13-4 Intended Role: Instructor 13-4: Listen & Look For Intended Role: Instructor 13-4: Daily Review: Editable Worksheet Intended Role: Instructor 13-4: Daily Review: Answer Key Intended Role: Instructor Topic 13: Today's Challenge Teacher Guide Intended Role: Instructor 13-4: Solve & Share Solution Intended Role: Instructor 13-4: Solve & Share Solution Intended Role: Instructor 13-4: Printable Additional Practice Intended Role: Instructor 13-4: Additional Practice: Editable Assessment Intended Role: Instructor 13-4: Quick Check: Answer Key Intended Role: Instructor 13-4: Printable Quick Check Intended Role: Instructor 13-4: Reteach to Build Understanding: Answer Key Intended Role: Instructor 13-4: Reteach to Build Understanding: Editable Worksheet Intended Role: Instructor 13-4: Build Mathematical Literacy: Answer Key Intended Role: Instructor 13-4: Build Mathematical Literacy: Editable Worksheet Intended Role: Instructor 13-4: Enrichment: Answer Key Intended Role: Instructor 13-4: Enrichment: Editable Worksheet Intended Role: Instructor 13-4: eText del Libro del estudiante: Clave de respuestas Intended Role: Instructor 13-4: Repaso diario: Clave de respuestas Intended Role: Instructor 13-4: Práctica adicional Intended Role: Instructor 13-4: Práctica adicional: Clave de respuestas Intended Role: Instructor 13-4: Refuerzo para mejorar la comprensión: Clave de respuestas Intended Role: Instructor 13-4: Desarrollar la competencia matemática: Clave de respuestas Intended Role: Instructor 13-4: Ampliación: Clave de respuestas Intended Role: Instructor Topic 13: Vocabulary Review Intended Role: Instructor Topic 13: Reteaching Intended Role: Instructor Topic 13 Performance Task: Answer Key Intended Role: Instructor Topic 13 Performance Task: Editable Assessment Intended Role: Instructor Topic 13 Assessment: Answer Key Intended Role: Instructor Topic 13 Topic Assessments: Editable Assessment Intended Role: Instructor Topic 13 Online Assessment: Answer Key Intended Role: Instructor Topic 13 Online Assessment: Printable Intended Role: Instructor Tema 13: Tarea de rendimento: Clave de respuestas Intended Role: Instructor Tema 13: Evaluación: Clave de respuestas Intended Role: Instructor Topic 14: Home-School Connection Intended Role: Instructor Topic 14: Problem-Solving Reading Activity Guide Intended Role: Instructor Topic 14: Problem-Solving Leveled Reading Mat Intended Role: Instructor Topic 14: Home-School Connection(Spanish) Intended Role: Instructor Topic 14: Pick a Project (Spanish) Intended Role: Instructor Topic 14: enVision STEM Activity (Spanish) Intended Role: Instructor Teacher's Edition eText: Grade 5 Topic 14 Intended Role: Instructor Topic 14: Professional Development Video Intended Role: Instructor Topic 14: Today's Challenge Teacher Guide Intended Role: Instructor 14-1: Lesson Plan Intended Role: Instructor Teacher's Edition eText: Grade 5 Lesson 14-1 Intended Role: Instructor 14-1: Listen & Look For Intended Role: Instructor 14-1: Daily Review: Editable Worksheet Intended Role: Instructor 14-1: Daily Review: Answer Key Intended Role: Instructor Topic 14: Today's Challenge Teacher Guide Intended Role: Instructor 14-1: Solve & Share Solution Intended Role: Instructor 14-1: Solve & Share Solution Intended Role: Instructor 14-1: Printable Additional Practice Intended Role: Instructor 14-1: Additional Practice: Editable Assessment Intended Role: Instructor 14-1: Quick Check: Answer Key Intended Role: Instructor 14-1: Printable Quick Check Intended Role: Instructor 14-1: Reteach to Build Understanding: Answer Key Intended Role: Instructor 14-1: Reteach to Build Understanding: Editable Worksheet Intended Role: Instructor 14-1: Build Mathematical Literacy: Answer Key Intended Role: Instructor 14-1: Build Mathematical Literacy: Editable Worksheet Intended Role: Instructor 14-1: Enrichment: Answer Key Intended Role: Instructor 14-1: Enrichment: Editable Worksheet Intended Role: Instructor 14-1: eText del Libro del estudiante: Clave de respuestas Intended Role: Instructor 14-1: Repaso diario: Clave de respuestas Intended Role: Instructor 14-1: Práctica adicional Intended Role: Instructor 14-1: Práctica adicional: Clave de respuestas Intended Role: Instructor 14-1: Refuerzo para mejorar la comprensión: Clave de respuestas Intended Role: Instructor 14-1: Desarrollar la competencia matemática: Clave de respuestas Intended Role: Instructor 14-1: Ampliación: Clave de respuestas Intended Role: Instructor 14-2: Lesson Plan Intended Role: Instructor Teacher's Edition eText: Grade 5 Lesson 14-2 Intended Role: Instructor 14-2: Listen & Look For Intended Role: Instructor 14-2: Daily Review: Editable Worksheet Intended Role: Instructor 14-2: Daily Review: Answer Key Intended Role: Instructor Topic 14: Today's Challenge Teacher Guide Intended Role: Instructor 14-2: Solve & Share Solution Intended Role: Instructor 14-2: Solve & Share Solution Intended Role: Instructor 14-2: Printable Additional Practice Intended Role: Instructor 14-2: Additional Practice: Editable Assessment Intended Role: Instructor 14-2: Quick Check: Answer Key Intended Role: Instructor 14-2: Printable Quick Check Intended Role: Instructor 14-2: Reteach to Build Understanding: Answer Key Intended Role: Instructor 14-2: Reteach to Build Understanding: Editable Worksheet Intended Role: Instructor 14-2: Build Mathematical Literacy: Answer Key Intended Role: Instructor 14-2: Build Mathematical Literacy: Editable Worksheet Intended Role: Instructor 14-2: Enrichment: Answer Key Intended Role: Instructor 14-2: Enrichment: Editable Worksheet Intended Role: Instructor Topic 14: Problem-Solving Leveled Reading Mat Intended Role: Instructor 14-2: eText del Libro del estudiante: Clave de respuestas Intended Role: Instructor 14-2: Repaso diario: Clave de respuestas Intended Role: Instructor 14-2: Práctica adicional Intended Role: Instructor 14-2: Práctica adicional: Clave de respuestas Intended Role: Instructor 14-2: Refuerzo para mejorar la comprensión: Clave de respuestas Intended Role: Instructor 14-2: Desarrollar la competencia matemática: Clave de respuestas Intended Role: Instructor 14-2: Ampliación: Clave de respuestas Intended Role: Instructor 14-3: Lesson Plan Intended Role: Instructor Teacher's Edition eText: Grade 5 Lesson 14-3 Intended Role: Instructor 14-3: Listen & Look For Intended Role: Instructor 14-3: Daily Review: Editable Worksheet Intended Role: Instructor 14-3: Daily Review: Answer Key Intended Role: Instructor Topic 14: Today's Challenge Teacher Guide Intended Role: Instructor 14-3: Solve & Share Solution Intended Role: Instructor 14-3: Solve & Share Solution Intended Role: Instructor 14-3: Printable Additional Practice Intended Role: Instructor 14-3: Additional Practice: Editable Assessment Intended Role: Instructor 14-3: Quick Check: Answer Key Intended Role: Instructor 14-3: Printable Quick Check Intended Role: Instructor 14-3: Reteach to Build Understanding: Answer Key Intended Role: Instructor 14-3: Reteach to Build Understanding: Editable Worksheet Intended Role: Instructor 14-3: Build Mathematical Literacy: Answer Key Intended Role: Instructor 14-3: Build Mathematical Literacy: Editable Worksheet Intended Role: Instructor 14-3: Enrichment: Answer Key Intended Role: Instructor 14-3: Enrichment: Editable Worksheet Intended Role: Instructor Topic 14: Problem-Solving Leveled Reading Mat Intended Role: Instructor 14-3: eText del Libro del estudiante: Clave de respuestas Intended Role: Instructor 14-3: Repaso diario: Clave de respuestas Intended Role: Instructor 14-3: Práctica adicional Intended Role: Instructor 14-3: Práctica adicional: Clave de respuestas Intended Role: Instructor 14-3: Refuerzo para mejorar la comprensión: Clave de respuestas Intended Role: Instructor 14-3: Desarrollar la competencia matemática: Clave de respuestas Intended Role: Instructor 14-3: Ampliación: Clave de respuestas Intended Role: Instructor 14-4: Lesson Plan Intended Role: Instructor Teacher's Edition eText: Grade 5 Lesson 14-4 Intended Role: Instructor 14-4: Listen & Look For Intended Role: Instructor 14-4: Daily Review: Editable Worksheet Intended Role: Instructor 14-4: Daily Review: Answer Key Intended Role: Instructor Topic 14: Today's Challenge Teacher Guide Intended Role: Instructor 14-4: Solve & Share Solution Intended Role: Instructor 14-4: Solve & Share Solution Intended Role: Instructor 14-4: Printable Additional Practice Intended Role: Instructor 14-4: Additional Practice: Editable Assessment Intended Role: Instructor 14-4: Quick Check: Answer Key Intended Role: Instructor 14-4: Printable Quick Check Intended Role: Instructor 14-4: Reteach to Build Understanding: Answer Key Intended Role: Instructor 14-4: Reteach to Build Understanding: Editable Worksheet Intended Role: Instructor 14-4: Build Mathematical Literacy: Answer Key Intended Role: Instructor 14-4: Build Mathematical Literacy: Editable Worksheet Intended Role: Instructor 14-4: Enrichment: Answer Key Intended Role: Instructor 14-4: Enrichment: Editable Worksheet Intended Role: Instructor 14-4: eText del Libro del estudiante: Clave de respuestas Intended Role: Instructor 14-4: Repaso diario: Clave de respuestas Intended Role: Instructor 14-4: Práctica adicional Intended Role: Instructor 14-4: Práctica adicional: Clave de respuestas Intended Role: Instructor 14-4: Refuerzo para mejorar la comprensión: Clave de respuestas Intended Role: Instructor 14-4: Desarrollar la competencia matemática: Clave de respuestas Intended Role: Instructor 14-4: Ampliación: Clave de respuestas Intended Role: Instructor Topic 14: Vocabulary Review Intended Role: Instructor Topic 14: Reteaching Intended Role: Instructor Topic 14 Performance Task: Answer Key Intended Role: Instructor Topic 14 Performance Task: Editable Assessment Intended Role: Instructor Topic 14 Assessment: Answer Key Intended Role: Instructor Topic 14 Topic Assessments: Editable Assessment Intended Role: Instructor Topic 14 Online Assessment: Answer Key Intended Role: Instructor Topic 14 Online Assessment: Printable Intended Role: Instructor Tema 14: Tarea de rendimento: Clave de respuestas Intended Role: Instructor Tema 14: Evaluación: Clave de respuestas Intended Role: Instructor Topic 15: Home-School Connection Intended Role: Instructor Topic 15: Problem-Solving Reading Activity Guide Intended Role: Instructor Topic 15: Problem-Solving Leveled Reading Mat Intended Role: Instructor Topic 15: Home-School Connection(Spanish) Intended Role: Instructor Topic 15: Pick a Project (Spanish) Intended Role: Instructor Topic 15: enVision STEM Activity (Spanish) Intended Role: Instructor Teacher's Edition eText: Grade 5 Topic 15 Intended Role: Instructor Topic 15: Professional Development Video Intended Role: Instructor Topic 15: Today's Challenge Teacher Guide Intended Role: Instructor 15-1: Lesson Plan Intended Role: Instructor Teacher's Edition eText: Grade 5 Lesson 15-1 Intended Role: Instructor 15-1: Listen & Look For Intended Role: Instructor 15-1: Daily Review: Editable Worksheet Intended Role: Instructor 15-1: Daily Review: Answer Key Intended Role: Instructor Topic 15: Today's Challenge Teacher Guide Intended Role: Instructor 15-1: Solve & Share Solution Intended Role: Instructor 15-1: Solve & Share Solution Intended Role: Instructor 15-1: Printable Additional Practice Intended Role: Instructor 15-1: Additional Practice: Editable Assessment Intended Role: Instructor 15-1: Quick Check: Answer Key Intended Role: Instructor 15-1: Printable Quick Check Intended Role: Instructor 15-1: Reteach to Build Understanding: Answer Key Intended Role: Instructor 15-1: Reteach to Build Understanding: Editable Worksheet Intended Role: Instructor 15-1: Build Mathematical Literacy: Answer Key Intended Role: Instructor 15-1: Build Mathematical Literacy: Editable Worksheet Intended Role: Instructor 15-1: Enrichment: Answer Key Intended Role: Instructor 15-1: Enrichment: Editable Worksheet Intended Role: Instructor 15-1: eText del Libro del estudiante: Clave de respuestas Intended Role: Instructor 15-1: Repaso diario: Clave de respuestas Intended Role: Instructor 15-1: Práctica adicional Intended Role: Instructor 15-1: Práctica adicional: Clave de respuestas Intended Role: Instructor 15-1: Refuerzo para mejorar la comprensión: Clave de respuestas Intended Role: Instructor 15-1: Desarrollar la competencia matemática: Clave de respuestas Intended Role: Instructor 15-1: Ampliación: Clave de respuestas Intended Role: Instructor 15-2: Lesson Plan Intended Role: Instructor Teacher's Edition eText: Grade 5 Lesson 15-2 Intended Role: Instructor 15-2: Listen & Look For Intended Role: Instructor 15-2: Daily Review: Editable Worksheet Intended Role: Instructor 15-2: Daily Review: Answer Key Intended Role: Instructor Topic 15: Today's Challenge Teacher Guide Intended Role: Instructor 15-2: Solve & Share Solution Intended Role: Instructor 15-2: Solve & Share Solution Intended Role: Instructor 15-2: Printable Additional Practice Intended Role: Instructor 15-2: Additional Practice: Editable Assessment Intended Role: Instructor 15-2: Quick Check: Answer Key Intended Role: Instructor 15-2: Printable Quick Check Intended Role: Instructor 15-2: Reteach to Build Understanding: Answer Key Intended Role: Instructor 15-2: Reteach to Build Understanding: Editable Worksheet Intended Role: Instructor 15-2: Build Mathematical Literacy: Answer Key Intended Role: Instructor 15-2: Build Mathematical Literacy: Editable Worksheet Intended Role: Instructor 15-2: Enrichment: Answer Key Intended Role: Instructor 15-2: Enrichment: Editable Worksheet Intended Role: Instructor Topic 15: Problem-Solving Leveled Reading Mat Intended Role: Instructor 15-2: eText del Libro del estudiante: Clave de respuestas Intended Role: Instructor 15-2: Repaso diario: Clave de respuestas Intended Role: Instructor 15-2: Práctica adicional Intended Role: Instructor 15-2: Práctica adicional: Clave de respuestas Intended Role: Instructor 15-2: Refuerzo para mejorar la comprensión: Clave de respuestas Intended Role: Instructor 15-2: Desarrollar la competencia matemática: Clave de respuestas Intended Role: Instructor 15-2: Ampliación: Clave de respuestas Intended Role: Instructor 15-3: Lesson Plan Intended Role: Instructor Teacher's Edition eText: Grade 5 Lesson 15-3 Intended Role: Instructor 15-3: Listen & Look For Intended Role: Instructor 15-3: Daily Review: Editable Worksheet Intended Role: Instructor 15-3: Daily Review: Answer Key Intended Role: Instructor Topic 15: Today's Challenge Teacher Guide Intended Role: Instructor 15-3: Solve & Share Solution Intended Role: Instructor 15-3: Solve & Share Solution Intended Role: Instructor 15-3: Printable Additional Practice Intended Role: Instructor 15-3: Additional Practice: Editable Assessment Intended Role: Instructor 15-3: Quick Check: Answer Key Intended Role: Instructor 15-3: Printable Quick Check Intended Role: Instructor 15-3: Reteach to Build Understanding: Answer Key Intended Role: Instructor 15-3: Reteach to Build Understanding: Editable Worksheet Intended Role: Instructor 15-3: Build Mathematical Literacy: Answer Key Intended Role: Instructor 15-3: Build Mathematical Literacy: Editable Worksheet Intended Role: Instructor 15-3: Enrichment: Answer Key Intended Role: Instructor 15-3: Enrichment: Editable Worksheet Intended Role: Instructor Topic 15: Problem-Solving Leveled Reading Mat Intended Role: Instructor 15-3: eText del Libro del estudiante: Clave de respuestas Intended Role: Instructor 15-3: Repaso diario: Clave de respuestas Intended Role: Instructor 15-3: Práctica adicional Intended Role: Instructor 15-3: Práctica adicional: Clave de respuestas Intended Role: Instructor 15-3: Refuerzo para mejorar la comprensión: Clave de respuestas Intended Role: Instructor 15-3: Desarrollar la competencia matemática: Clave de respuestas Intended Role: Instructor 15-3: Ampliación: Clave de respuestas Intended Role: Instructor Topic 15: 3-Act Math Recording Sheets Intended Role: Instructor Teacher's Edition eText: Grade 5, Topic 15: 3-Act Math Intended Role: Instructor 15-4: Lesson Plan Intended Role: Instructor Teacher's Edition eText: Grade 5 Lesson 15-4 Intended Role: Instructor 15-4: Listen & Look For Intended Role: Instructor 15-4: Daily Review: Editable Worksheet Intended Role: Instructor 15-4: Daily Review: Answer Key Intended Role: Instructor Topic 15: Today's Challenge Teacher Guide Intended Role: Instructor 15-4: Solve & Share Solution Intended Role: Instructor 15-4: Solve & Share Solution Intended Role: Instructor 15-4: Printable Additional Practice Intended Role: Instructor 15-4: Additional Practice: Editable Assessment Intended Role: Instructor 15-4: Quick Check: Answer Key Intended Role: Instructor 15-4: Printable Quick Check Intended Role: Instructor 15-4: Reteach to Build Understanding: Answer Key Intended Role: Instructor 15-4: Reteach to Build Understanding: Editable Worksheet Intended Role: Instructor 15-4: Build Mathematical Literacy: Answer Key Intended Role: Instructor 15-4: Build Mathematical Literacy: Editable Worksheet Intended Role: Instructor 15-4: Enrichment: Answer Key Intended Role: Instructor 15-4: Enrichment: Editable Worksheet Intended Role: Instructor 15-4: eText del Libro del estudiante: Clave de respuestas Intended Role: Instructor 15-4: Repaso diario: Clave de respuestas Intended Role: Instructor 15-4: Práctica adicional Intended Role: Instructor 15-4: Práctica adicional: Clave de respuestas Intended Role: Instructor 15-4: Refuerzo para mejorar la comprensión: Clave de respuestas Intended Role: Instructor 15-4: Desarrollar la competencia matemática: Clave de respuestas Intended Role: Instructor 15-4: Ampliación: Clave de respuestas Intended Role: Instructor Topic 15: Vocabulary Review Intended Role: Instructor Topic 15: Reteaching Intended Role: Instructor Topic 15 Performance Task: Answer Key Intended Role: Instructor Topic 15 Performance Task: Editable Assessment Intended Role: Instructor Topic 15 Assessment: Answer Key Intended Role: Instructor Topic 15 Topic Assessments: Editable Assessment Intended Role: Instructor Topic 15 Online Assessment: Answer Key Intended Role: Instructor Topic 15 Online Assessment: Printable Intended Role: Instructor Tema 15: Tarea de rendimento: Clave de respuestas Intended Role: Instructor Tema 15: Evaluación: Clave de respuestas Intended Role: Instructor Topic 16: Home-School Connection Intended Role: Instructor Topic 16: Problem-Solving Reading Activity Guide Intended Role: Instructor Topic 16: Problem-Solving Leveled Reading Mat Intended Role: Instructor Topic 16: Home-School Connection(Spanish) Intended Role: Instructor Topic 16: Pick a Project (Spanish) Intended Role: Instructor Topic 16: enVision STEM Activity (Spanish) Intended Role: Instructor Teacher's Edition eText: Grade 5 Topic 16 Intended Role: Instructor Topic 16: Today's Challenge Teacher Guide Intended Role: Instructor 16-1: Lesson Plan Intended Role: Instructor Teacher's Edition eText: Grade 5 Lesson 16-1 Intended Role: Instructor 16-1: Listen & Look For Intended Role: Instructor 16-1: Daily Review: Editable Worksheet Intended Role: Instructor 16-1: Daily Review: Answer Key Intended Role: Instructor Topic 16: Today's Challenge Teacher Guide Intended Role: Instructor 16-1: Solve & Share Solution Intended Role: Instructor 16-1: Solve & Share Solution Intended Role: Instructor 16-1: Printable Additional Practice Intended Role: Instructor 16-1: Additional Practice: Editable Assessment Intended Role: Instructor 16-1: Quick Check: Answer Key Intended Role: Instructor 16-1: Printable Quick Check Intended Role: Instructor 16-1: Reteach to Build Understanding: Answer Key Intended Role: Instructor 16-1: Reteach to Build Understanding: Editable Worksheet Intended Role: Instructor 16-1: Build Mathematical Literacy: Answer Key Intended Role: Instructor 16-1: Build Mathematical Literacy: Editable Worksheet Intended Role: Instructor 16-1: Enrichment: Answer Key Intended Role: Instructor 16-1: Enrichment: Editable Worksheet Intended Role: Instructor Topic 16: Problem-Solving Leveled Reading Mat Intended Role: Instructor 16-1: eText del Libro del estudiante: Clave de respuestas Intended Role: Instructor 16-1: Repaso diario: Clave de respuestas Intended Role: Instructor 16-1: Práctica adicional Intended Role: Instructor 16-1: Práctica adicional: Clave de respuestas Intended Role: Instructor 16-1: Refuerzo para mejorar la comprensión: Clave de respuestas Intended Role: Instructor 16-1: Desarrollar la competencia matemática: Clave de respuestas Intended Role: Instructor 16-1: Ampliación: Clave de respuestas Intended Role: Instructor 16-2: Lesson Plan Intended Role: Instructor Teacher's Edition eText: Grade 5 Lesson 16-2 Intended Role: Instructor 16-2: Listen & Look For Intended Role: Instructor 16-2: Daily Review: Editable Worksheet Intended Role: Instructor 16-2: Daily Review: Answer Key Intended Role: Instructor Topic 16: Today's Challenge Teacher Guide Intended Role: Instructor 16-2: Solve & Share Solution Intended Role: Instructor 16-2: Solve & Share Solution Intended Role: Instructor 16-2: Printable Additional Practice Intended Role: Instructor 16-2: Additional Practice: Editable Assessment Intended Role: Instructor 16-2: Quick Check: Answer Key Intended Role: Instructor 16-2: Printable Quick Check Intended Role: Instructor 16-2: Reteach to Build Understanding: Answer Key Intended Role: Instructor 16-2: Reteach to Build Understanding: Editable Worksheet Intended Role: Instructor 16-2: Build Mathematical Literacy: Answer Key Intended Role: Instructor 16-2: Build Mathematical Literacy: Editable Worksheet Intended Role: Instructor 16-2: Enrichment: Answer Key Intended Role: Instructor 16-2: Enrichment: Editable Worksheet Intended Role: Instructor 16-2: eText del Libro del estudiante: Clave de respuestas Intended Role: Instructor 16-2: Repaso diario: Clave de respuestas Intended Role: Instructor 16-2: Práctica adicional Intended Role: Instructor 16-2: Práctica adicional: Clave de respuestas Intended Role: Instructor 16-2: Refuerzo para mejorar la comprensión: Clave de respuestas Intended Role: Instructor 16-2: Desarrollar la competencia matemática: Clave de respuestas Intended Role: Instructor 16-2: Ampliación: Clave de respuestas Intended Role: Instructor 16-3: Lesson Plan Intended Role: Instructor Teacher's Edition eText: Grade 5 Lesson 16-3 Intended Role: Instructor 16-3: Listen & Look For Intended Role: Instructor 16-3: Daily Review: Editable Worksheet Intended Role: Instructor 16-3: Daily Review: Answer Key Intended Role: Instructor Topic 16: Today's Challenge Teacher Guide Intended Role: Instructor 16-3: Solve & Share Solution Intended Role: Instructor 16-3: Solve & Share Solution Intended Role: Instructor 16-3: Printable Additional Practice Intended Role: Instructor 16-3: Additional Practice: Editable Assessment Intended Role: Instructor 16-3: Quick Check: Answer Key Intended Role: Instructor 16-3: Printable Quick Check Intended Role: Instructor 16-3: Reteach to Build Understanding: Answer Key Intended Role: Instructor 16-3: Reteach to Build Understanding: Editable Worksheet Intended Role: Instructor 16-3: Build Mathematical Literacy: Answer Key Intended Role: Instructor 16-3: Build Mathematical Literacy: Editable Worksheet Intended Role: Instructor 16-3: Enrichment: Answer Key Intended Role: Instructor 16-3: Enrichment: Editable Worksheet Intended Role: Instructor Topic 16: Problem-Solving Leveled Reading Mat Intended Role: Instructor 16-3: eText del Libro del estudiante: Clave de respuestas Intended Role: Instructor 16-3: Repaso diario: Clave de respuestas Intended Role: Instructor 16-3: Práctica adicional Intended Role: Instructor 16-3: Práctica adicional: Clave de respuestas Intended Role: Instructor 16-3: Refuerzo para mejorar la comprensión: Clave de respuestas Intended Role: Instructor 16-3: Desarrollar la competencia matemática: Clave de respuestas Intended Role: Instructor 16-3: Ampliación: Clave de respuestas Intended Role: Instructor 16-4: Lesson Plan Intended Role: Instructor Teacher's Edition eText: Grade 5 Lesson 16-4 Intended Role: Instructor 16-4: Listen & Look For Intended Role: Instructor 16-4: Solve & Share Solution Intended Role: Instructor 16-4: Solve & Share Solution Intended Role: Instructor 16-4: Daily Review: Editable Worksheet Intended Role: Instructor 16-4: Daily Review: Answer Key Intended Role: Instructor Topic 16: Today's Challenge Teacher Guide Intended Role: Instructor 16-4: Printable Additional Practice Intended Role: Instructor 16-4: Additional Practice: Editable Assessment Intended Role: Instructor 16-4: Quick Check: Answer Key Intended Role: Instructor 16-4: Printable Quick Check Intended Role: Instructor 16-4: Reteach to Build Understanding: Answer Key Intended Role: Instructor 16-4: Reteach to Build Understanding: Editable Worksheet Intended Role: Instructor 16-4: Build Mathematical Literacy: Answer Key Intended Role: Instructor 16-4: Build Mathematical Literacy: Editable Worksheet Intended Role: Instructor 16-4: Enrichment: Answer Key Intended Role: Instructor 16-4: Enrichment: Editable Worksheet Intended Role: Instructor 16-4: eText del Libro del estudiante: Clave de respuestas Intended Role: Instructor 16-4: Repaso diario: Clave de respuestas Intended Role: Instructor 16-4: Práctica adicional Intended Role: Instructor 16-4: Práctica adicional: Clave de respuestas Intended Role: Instructor 16-4: Refuerzo para mejorar la comprensión: Clave de respuestas Intended Role: Instructor 16-4: Desarrollar la competencia matemática: Clave de respuestas Intended Role: Instructor 16-4: Ampliación: Clave de respuestas Intended Role: Instructor Topic 16: Vocabulary Review Intended Role: Instructor Topic 16: Reteaching Intended Role: Instructor Topic 16 Performance Task: Answer Key Intended Role: Instructor Topic 16 Performance Task: Editable Assessment Intended Role: Instructor Topic 16 Assessment: Answer Key Intended Role: Instructor Topic 16 Topic Assessments: Editable Assessment Intended Role: Instructor Topic 16 Online Assessment: Answer Key Intended Role: Instructor Topic 16 Online Assessment: Printable Intended Role: Instructor Tema 16: Tarea de rendimento: Clave de respuestas Intended Role: Instructor Tema 16: Evaluación: Clave de respuestas Intended Role: Instructor Topics 1–16: Cumulative/Benchmark Assessment: Answer Key Intended Role: Instructor Topics 1–16: Cumulative/Benchmark Assessment: Editable Assessment Intended Role: Instructor Topics 1–16: Online Cumulative/Benchmark Assessment: Answer Key Intended Role: Instructor Topics 1–16: Printable Online Cumulative/Benchmark Assessment Intended Role: Instructor Grade 5 Progress Monitoring Assessment: Form A: Answer Key Intended Role: Instructor Grade 5 Progress Monitoring Assessment: Form A: Editable Assessment Intended Role: Instructor Grade 5 Online Progress Monitoring: Form A: Answer Key Intended Role: Instructor Grade 5 Printable Online Progress Monitoring: Form A Intended Role: Instructor Grade 5 Progress Monitoring Assessment: Form B: Answer Key Intended Role: Instructor Grade 5 Progress Monitoring Assessment: Form B: Editable Assessment Intended Role: Instructor Grade 5 Online Progress Monitoring: Form B: Answer Key Intended Role: Instructor Grade 5 Printable Online Progress Monitoring: Form B Intended Role: Instructor Grade 5 Progress Monitoring Assessment: Form C: Answer Key Intended Role: Instructor Grade 5 Progress Monitoring Assessment: Form C: Editable Assessment Intended Role: Instructor Grade 5 Printable Online Progress Monitoring: Form C Intended Role: Instructor Teacher's Edition: Grade 5 Lesson 17-1 Intended Role: Instructor 17-1: Explore It! Solution Intended Role: Instructor 17-1: Explore It! Solution Intended Role: Instructor Teacher's Edition: Grade 5 Lesson 17-2 Intended Role: Instructor 17-2: Explain It! Solution Intended Role: Instructor 17-2: Explain It! Solution Intended Role: Instructor Teacher's Edition: Grade 5 Lesson 17-3 Intended Role: Instructor 17-3: Solve & Discuss It! Solution Intended Role: Instructor 17-3: Solve & Discuss It! Solution Intended Role: Instructor Teacher's Edition: Grade 5 Lesson 17-4 Intended Role: Instructor 17-4: Solve & Discuss It! Solution Intended Role: Instructor 17-4: Solve & Discuss It! Solution Intended Role: Instructor Teacher's Edition: Grade 5 Lesson 17-5 Intended Role: Instructor 17-5: Solve & Discuss It! Solution Intended Role: Instructor 17-5: Solve & Discuss It! Solution Intended Role: Instructor Teacher's Edition: Grade 5 Lesson 17-6 Intended Role: Instructor 17-6: Explore It! Solution Intended Role: Instructor 17-6: Explore It! Solution Intended Role: Instructor Teacher's Edition: Grade 5 Lesson 17-7 Intended Role: Instructor 17-7: Solve & Discuss It! Solution Intended Role: Instructor 17-7: Solve & Discuss It! Solution Intended Role: Instructor Teacher's Edition: Grade 5 Lesson 17-8 Intended Role: Instructor 17-8: Explain It! Solution Intended Role: Instructor 17-8: Explain It! Solution Intended Role: Instructor Teacher's Edition: Grade 5 Lesson 17-9 Intended Role: Instructor 17-9: Solve & Discuss It! Solution Intended Role: Instructor 17-9: Solve & Discuss It! Solution Intended Role: Instructor Teacher's Edition: Grade 5 Lesson 17-10 Intended Role: Instructor 17-10: Solve & Discuss It! Solution Intended Role: Instructor 17-10: Solve & Discuss It! Solution Intended Role: Instructor Booklet A: Numbers, Place Value, Money, and Patterns in Grades K-3 Intended Role: Instructor Booklet B: Basic Facts in Grades K-3 Intended Role: Instructor Booklet C: Computation with Whole numbers in Grades K-3 Intended Role: Instructor Booklet D: Measurement, Geometry, Data, and Probability in Grades K-3 Intended Role: Instructor Booklet E: Problem Solving in Grades K-3 Intended Role: Instructor Teacher's Guide, Grades K-3 Intended Role: Instructor Diagnostic Tests and Answer Keys, Grades K-3 Intended Role: Instructor Booklet F: Numeration, Patterns, and Relationships in Grades 4-6 Intended Role: Instructor Booklet G: Operations with Whole Numbers in Grades 4-6 Intended Role: Instructor Booklet H: Fractions, Decimals, and Percents in Grades 4-6 Intended Role: Instructor Booklet I: Measurement, Geometry, Data, and Probability in Grades 4-6 Intended Role: Instructor Booklet J: Problem Solving in Grades 4-6 Intended Role: Instructor Teacher's Guide, Grades 4-6 Intended Role: Instructor Diagnostic Tests and Answer Keys, Grades 4-6 Intended Role: Instructor Evaluación de conocimientos para el Grado 5: Clave de respuestas Intended Role: Instructor Temas 1 a 4 Evaluación acumulativa/de referencia: Clave de respuestas Intended Role: Instructor Temas 1 a 8: Evaluación acumulativa/de referencia: Clave de respuestas Intended Role: Instructor Temas 1 a 12: Evaluación acumulativa/de referencia: Clave de respuestas Intended Role: Instructor Temas 1 a 16: Evaluación acumulativa/de referencia: Clave de respuestas Intended Role: Instructor Evaluación para observar el progreso, Forma A: Clave de respuestas Intended Role: Instructor Evaluación para observar el progreso, Forma B: Clave de respuestas Intended Role: Instructor Evaluación para observar el progreso, Forma C: Clave de respuestas Intended Role: Instructor Minnesota Grade 5 Standards Tabs Intended Role: Instructor Minnesota-Specific Teaching Tools Intended Role: Instructor MN-1: Find 0.1, 0.01, or 0.001 More or Less Than a Number: Teacher's Guide Intended Role: Instructor MN-2: Fractions, Mixed Numbers, and Decimals: Teacher's Guide Intended Role: Instructor MN-3: Display and Interpret Data: Double Bar Graphs: Teacher's Guide Intended Role: Instructor MN-4: Understand Mean: Teacher's Guide Intended Role: Instructor MN-5: Median, Mode, and Range: Teacher's Guide Intended Role: Instructor MN-6: Describe and Classify 3-D Figures: Teacher's Guide Intended Role: Instructor MN-7: Solid Figures and Nets: Teacher's Guide Intended Role: Instructor MN-8: Variables and Expressions: Teacher's Guide Intended Role: Instructor MN-9: Variables, Expressions, and Equations: Teacher's Guide Intended Role: Instructor MN-10: Understand Equations and Solutions: Teacher's Guide Intended Role: Instructor MN-11: Understand Inequalities with Variables: Teacher's Guide Intended Role: Instructor MN-12: Display and Interpret Data: Double Line Graphs: Teacher's Guide Intended Role: Instructor MN-13: Areas of Parallelograms: Teacher's Guide Intended Role: Instructor MN-13: Areas of Parallelograms Intended Role: Instructor MN-14: Areas of Triangles: Teacher's Guide Intended Role: Instructor Credits, enVision Mathematics 2020 Grade 5 Intended Role: Instructor Teacher's Edition: Grade 5 Intended Role: Instructor Teacher's Edition: Grade 5 Intended Role: Instructor eText Container Student Edition: Grade 5 Student Edition: Grade 5 Interactive Additional Practice: Grade 5 Interactive Additional Practice: Grade 5 Interactive Student Edition: Grade 5 Interactive Student Edition: Grade 5 eText del Libro del estudiante: Grado 5 eText del Libro del estudiante: Grado 5 enVision Matemáticas 2020, Grado 5: Práctica adicional interactiva enVision Matemáticas 2020, Grado 5: Práctica adicional interactiva Tools Math Tool-Place-Value Blocks: Place-Value Chips Math Tool - Geometry: Exploring Solids Math Tool - Money Math Tool - Data and Graphs: Create Plots Math Tool - Money Math Tool - Fractions: Array Math Tool - Geometry: Shapes Math Tool - Place Value Blocks: Place-Value Blocks Math Tool - Place Value Blocks: Place-Value Blocks Math Tool - Bar Diagrams: Select Equal Groups: Multiplication and Division Math Tool - Place Value Blocks: Place-Value Chips Math Tool - I/O Machine: Explore Math Tool - Fractions: Modeling Fractions Math Tool - Fractions: Pieces Math Tool - Place Value Blocks: Place-Value Blocks Math Tool - Bar diagram: Compare: Multiplication and Division Math Tool - Number Line: Add & Subtract Fractions Math Tool - Bar Diagrams: Select Equal Groups: Multiplication and Division Math Tool - Number Line: Numbers Math Tool - Place Value Blocks: Place-Value Blocks Math Tool - Place Value Blocks: Place-Value Blocks Math Tool - Fractions: Pieces Math Tool - Geometry: Exploring Solids Math Tool - Data and Graphs: Plot Data Math Tool - Number Line: Add & Subtract Fractions Math Tool - Number Line: Add & Subtract Fractions Math Tool - Place-Value Blocks: Place-Value Blocks Math Tool - Data and Graphs: Graph Coordinates and Equations Math Tool - Number Line: Add & Subtract Fractions Math Tool - Place Value Blocks: Arrays Math Tool - Data and Graphs: Create Plots Math Tool - Fractions: Array Math Tool - I/O Machine: Explore Grado 5: Centro de juegos Math Tool - Place Value Blocks: Place-Value Blocks Math Tool - Fractions: Pieces Math Tool - I/O Machine: Explore Math Tool - Number Line: Numbers Math Tool - Number Charts: Multiplication Chart Math Tool - Bar Diagrams: Create a Bar Diagram Math Tool - I/O Machine: Explore Math Tool - Fractions: Denominators Math Tool - Place Value Blocks: Place-Value Blocks Math Tool - Fractions: Array Math Tool - Fractions: Pieces Data and Graphs: Plot Points and Write Coordinates Math Tool - Fractions: Pieces Math Tool - Place Value Blocks: Place-Value Blocks Math Tool - Number Charts: Multiplication Chart Math Tool-Place-Value Blocks: Array Grade 5: Glossary Math Tool - I/O Machine: Explore Math Tool - Geometry: Exploring Solids Math Tool - Geometry: Shapes Math Tools Grade 5: Game Center Math Tool - Place Value Blocks: Arrays