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GRADE Mathematics Curriculum GRADE MODULE Table of Contents GRADE MODULE Fraction Equivalence, Ordering, and Operations Module Overview... i Topic A: Decomposition and Fraction Equivalence....A. Topic B: Fraction Equivalence Using Multiplication and Division....B. Topic C: Fraction Comparison....C. Topic D: Fraction Addition and Subtraction....D. Topic E: Extending Fraction Equivalence to Fractions Greater Than....E. Topic F: Addition and Subtraction of Fractions by Decomposition....F. Topic G: Repeated Addition of Fractions as Multiplication...G. Topic H: Exploring a Fraction Pattern....H. Module Assessments....S. Module : Fraction Equivalence, Ordering, and Operations i
Lesson Homework Name Date. Draw a number bond and write the number sentence to match each tape diagram. The first one is done for you. = + c. d. e. f. g. h. Lesson : Decompose fractions as a sum of unit fractions using tape diagrams.
Lesson Homework. Draw and label tape diagrams to match each number sentence. 8 = 8 + 8 + 8 8 = 6 8 + 8 + 8 c. 0 = 0 + 0 + 0 d. = 7 + + e. = + f. 7 = + 7 Lesson : Decompose fractions as a sum of unit fractions using tape diagrams.
Lesson Homework Name Date. Step : Draw and shade a tape diagram of the given fraction. Step : Record the decomposition as a sum of unit fractions. Step : Record the decomposition of the fraction two more ways. (The first one has been done for you.) 6 6 = 6 + 6 + 6 + 6 + 6 6 = 6 + 6 + 6 6 = 6 + 6 6 8 c. 7 0 Lesson : Decompose fractions as a sum of unit fractions using tape diagrams. 7
Lesson Homework. Step : Draw and shade a tape diagram of the given fraction. Step : Record the decomposition of the fraction in three different ways using number sentences. 0 c. 6 d. Lesson : Decompose fractions as a sum of unit fractions using tape diagrams. 8
Lesson Homework Name Date. Decompose each fraction modeled by a tape diagram as a sum of unit fractions. Write the equivalent multiplication sentence. The first one has been done for you. = + = c. d. Lesson : Decompose non-unit fractions and represent them as a whole number times a unit fraction using tape diagrams.
Lesson Homework. Write the following fractions greater than as the sum of two products.. Draw a tape diagram and record the given fraction s decomposition into unit fractions as a multiplication sentence. 8 c. d. 8 e. Lesson : Decompose non-unit fractions and represent them as a whole number times a unit fraction using tape diagrams.
Lesson Homework Name Date. The total length of each tape diagram represents. Decompose the shaded unit fractions as the sum of smaller unit fractions in at least two different ways. The first one has been done for you. = 6 + 6 + 6 = 0 + 0 + 0 + 0 + 0. The total length of each tape diagram represents. Decompose the shaded fractions as the sum of smaller unit fractions in at least two different ways. c. Lesson : Decompose fractions into sums of smaller unit fractions using tape diagrams.
Lesson Homework. Draw tape diagrams to prove the following statements. The first one has been done for you. = 0 6 = 6 c. = 6 6 8 d. = 6. Show that is equivalent to 6 using a tape diagram and a number sentence.. Show that is equivalent to 8 using a tape diagram and a number sentence. 6. Show that is equivalent to using a tape diagram and a number sentence. Lesson : Decompose fractions into sums of smaller unit fractions using tape diagrams. 6
Lesson Homework Name Date. Draw horizontal lines to decompose each rectangle into the number of rows as indicated. Use the model to give the shaded area as both a sum of unit fractions and as a multiplication sentence. rows = = 6 + + = 6 = = 6 rows c. rows Lesson : Decompose unit fractions using area models to show equivalence. 9
Lesson Homework. Draw area models to show the decompositions represented by the number sentences below. Represent the decomposition as a sum of unit fractions and as a multiplication sentence. = 6 = 9 c. = d. = e. = 0 f. =. Explain why + + + is the same as. Lesson : Decompose unit fractions using area models to show equivalence. 0
Lesson 6 Homework Name Date. Each rectangle represents. Draw horizontal lines to decompose each rectangle into the fractional units as indicated. Use the model to give the shaded area as a sum and as a product of unit fractions. Use parentheses to show the relationship between the number sentences. The first one has been partially done for you. Tenths = + = 0 + 0 + 0 + 0 = 0 + 0 + 0 + = + = 0 0 = = Eighths c. Fifteenths Lesson 6: Decompose fractions using area models to show equivalence.
Lesson 6 Homework. Draw area models to show the decompositions represented by the number sentences below. Express each as a sum and product of unit fractions. Use parentheses to show the relationship between the number sentences. = 6 = 8 0. Step : Draw an area model for a fraction with units of thirds, fourths, or fifths. Step : Shade in more than one fractional unit. Step : Partition the area model again to find an equivalent fraction. Step : Write the equivalent fractions as a number sentence. (If you have written a number sentence like this one already in this homework, start over.) Lesson 6: Decompose fractions using area models to show equivalence.
Lesson 7 Homework Name Each rectangle represents. Date. The shaded unit fractions have been decomposed into smaller units. Express the equivalent fractions in a number sentence using multiplication. The first one has been done for you. = = c. d.. Decompose the shaded fractions into smaller units using the area models. Express the equivalent fractions in a number sentence using multiplication. c. d. d. Lesson 7: Use the area model and multiplication to show the equivalence of two fractions. 7
Lesson 7 Homework. Draw three different area models to represent fourth by shading. Decompose the shaded fraction into (a) eighths, (b) twelfths, and (c) sixteenths. Use multiplication to show how each fraction is equivalent to fourth. c. Lesson 7: Use the area model and multiplication to show the equivalence of two fractions. 8
Lesson 8 Homework Name Each rectangle represents. Date. The shaded fractions have been decomposed into smaller units. Express the equivalent fractions in a number sentence using multiplication. The first one has been done for you. = = 6 c. d.. Decompose both shaded fractions into twelfths. Express the equivalent fractions in a number sentence using multiplication. Lesson 8: Use the area model and multiplication to show the equivalence of two fractions.
Lesson 8 Homework. Draw area models to prove that the following number sentences are true. = 6 = 0 c. = 0 7 d. = 6 8. Use multiplication to create an equivalent fraction for each fraction below. 6 c. 6 d. 0 8. Determine which of the following are true number sentences. Correct those that are false by changing the right-hand side of the number sentence. = = 0 6 c. = 6 d. 7 = Lesson 8: Use the area model and multiplication to show the equivalence of two fractions.
Lesson 9 Homework Name Each rectangle represents. Date. Compose the shaded fractions into larger fractional units. Express the equivalent fractions in a number sentence using division. The first one has been done for you. = = c. d.. Compose the shaded fractions into larger fractional units. Express the equivalent fractions in a number sentence using division. c. d. Lesson 9: Use the area model and division to show the equivalence of two fractions.
Lesson 9 Homework e. What happened to the size of the fractional units when you composed the fraction? f. What happened to the total number of units in the whole when you composed the fraction?. In the first area model, show eighths. In the second area model, show 6 twelfths. Show how both fractions can be composed, or renamed, as the same unit fraction. Express the equivalent fractions in a number sentence using division.. In the first area model, show eighths. In the second area model, show 8 sixteenths. Show how both fractions can be composed, or renamed, as the same unit fraction. Express the equivalent fractions in a number sentence using division. Lesson 9: Use the area model and division to show the equivalence of two fractions. 6
Lesson 0 Homework Name Each rectangle represents. Date. Compose the shaded fraction into larger fractional units. Express the equivalent fractions in a number sentence using division. The first one has been done for you. 6 = 6 = c. d.. Compose the shaded fractions into larger fractional units. Express the equivalent fractions in a number sentence using division. Lesson 0: Use the area model and division to show the equivalence of two fractions. 9
Lesson 0 Homework. Draw an area model to represent each number sentence below. 6 = 6 = 6 = 6 = 8 8 6. Use division to rename each fraction given below. Draw a model if that helps you. See if you can use the largest common factor. 8 0 9 c. 8 d. 8 Lesson 0: Use the area model and division to show the equivalence of two fractions. 0
Lesson Homework Name Date. Label each number line with the fractions shown on the tape diagram. Circle the fraction that labels the point on the number line that also names the selected part of the tape diagram. c.. Write number sentences using multiplication to show: The fraction represented in (a) is equivalent to the fraction represented in (b). The fraction represented in (a) is equivalent to the fraction represented in (c). Lesson : Explain fraction equivalence using a tape diagram and the number line, and relate that to the use of multiplication and division.
Lesson Homework. Use each shaded tape diagram below as a ruler to draw a number line. Mark each number line with the fractional units shown on the tape diagram, and circle the fraction that labels the point on the number line that also names the selected part of the tape diagram. c.. Write a number sentence using division to show the fraction represented in (a) is equivalent to the fraction represented in (b).. Partition a number line from 0 to into fourths. Decompose into 6 equal lengths. Write a number sentence using multiplication to show what fraction represented on the number line is equivalent to. c. Write a number sentence using division to show what fraction represented on the number line is equivalent to. Lesson : Explain fraction equivalence using a tape diagram and the number line, and relate that to the use of multiplication and division.
Lesson Homework Name Date. Plot the following points on the number line without measuring. i. ii. 6 iii. 0 0 Use the number line in Part (a) to compare the fractions. i. ii. 0 6. Plot the following points on the number line without measuring. i. ii. iii. 6 0 Select two fractions from Part (a), and use the given number line to compare them by writing. c. Explain how you plotted the points in Part (a). Lesson : Reason using benchmarks to compare two fractions on the number line. 7
Lesson Homework. Give a brief explanation for each answer referring to the benchmark of 0,, and. 6 8 c. d. 6 e. f. 8 g. 6 h. 7 8 i. 00 0 j. 8 00 Lesson : Reason using benchmarks to compare two fractions on the number line. 8
Lesson Homework Name Date. Place the following fractions on the number line given. 9 c. 0. Use the number line in Problem to compare the fractions : 6. Place the following fractions on the number line given. 9 6 c. 8. Use the number line in Problem to explain the reasoning you used when determining whether 9 was greater. or 8 Lesson : Reason using benchmarks to compare two fractions on the number line.
Lesson Homework. Give a brief explanation for each answer referring to benchmarks. 6 8 6 0 6 c. 6 7 8 d. 8 e. 6 f. 8 9 g. 7 8 0 h. i. 8 j. 9 6 6 Lesson : Reason using benchmarks to compare two fractions on the number line.
Lesson Homework Name Date. Compare the pairs of fractions by reasoning about the size of the units. Use >, <, or =. third sixth halves thirds c. fourths sixths d. eighths tenths. Compare by reasoning about the following pairs of fractions with the same or related numerators. Use >, <, or =. Explain your thinking using words, pictures, or numbers. Problem (b) has been done for you. 6 7 < 9 because = 0 tenths is less than ninths because tenths are smaller than ninths. c. d. 7 0. Draw two tape diagrams to model each pair of the following fractions with related denominators. Use >, <, or = to compare. 7 8 c. 0 Lesson : Find common units or number of units to compare two fractions. 8
Lesson Homework. Draw one number line to model each pair of fractions with related denominators. Use >, <, or = to compare. 8 c. 7 0 d. 8 9. Compare each pair of fractions using >, <, or =. Draw a model if you choose to. 7 7 7 c. 7 0 d. 9 e. 9 f. g. 9 h. 9 7 6. Simon claims is greater than. Ted thinks is less than. Who is correct? Support your answer with a 9 9 picture. Lesson : Find common units or number of units to compare two fractions. 9
Lesson Homework Name Date. Draw an area model for each pair of fractions, and use it to compare the two fractions by writing >, <, or = on the line. The first two have been partially done for you. Each rectangle represents. < = 0 = 6 0 0 < 6 0 so < c. 6 8 d. 7 e. 6 6 f. 6 Lesson : Find common units or number of units to compare two fractions. 6
Lesson Homework. Rename the fractions, as needed, using multiplication in order to compare each pair of fractions by writing >, <, or =. 7 c. 8 d. 8 8. Use any method to compare the fractions. Record your answer using >, <, or =. 8 7 c. 6 d. 7. Explain which method you prefer using to compare fractions. Provide an example using words, pictures, or numbers. Lesson : Find common units or number of units to compare two fractions. 6
Lesson 6 Homework Name Date. Solve. sixths sixths = tenths tenths = c. fourths fourths = d. thirds thirds =. Solve. 7 c. 7 d. 6 6 6 e. f. 7. Solve. Use a number bond to decompose the difference. Record your final answer as a mixed number. Problem (a) has been completed for you. 9 = 7 = 6 6 6 6 8 6 8 6 6 6 c. d. 6 e. 0 7 7 f. 0 0 Lesson 6: Use visual models to add and subtract two fractions with the same units. 66
Lesson 6 Homework. Solve. Write the sum in unit form. fifths + fifths = eighths + eighths =. Solve. + 6 0 + 6 0 6. Solve. Use a number bond to decompose the sum. Record your final answer as a mixed number. + 8 + 6 c. 8 + 7 8 d. 8 0 + 0 e. + 6 f. + 7. Solve. Use a number line to model your answer. + Lesson 6: Use visual models to add and subtract two fractions with the same units. 67
Lesson 7 Homework Name Date. Use the following three fractions to write two subtraction and two addition number sentences.,, 6 6 6,, 8. Solve. Model each subtraction problem with a number line, and solve by both counting up and subtracting. 8 c. 6 6 d. e. f. Lesson 7: Use visual models to add and subtract two fractions with the same units, including subtracting from one whole. 7
Lesson 7 Homework. Find the difference in two ways. Use number bonds to decompose the total. Part (a) has been completed for you. + = 7 7 = = + = 8 7 8 c. d. 7 7 e. 0 7 0 Lesson 7: Use visual models to add and subtract two fractions with the same units, including subtracting from one whole. 7
Lesson 8 Homework Name Date. Show one way to solve each problem. Express sums and differences as a mixed number when possible. Use number bonds when it helps you. Part (a) is partially completed. + + 8 + 8 + 8 c. 6 + 6 6 + 6 = + = + = d. e. 7 + 7 + 7 f. + 7 + 0 0 0 g. 0 0 h. i. 0 + 7 + + Lesson 8: Add and subtract more than two fractions. 7
Lesson 8 Homework. Bonnie used two different strategies to solve 0 + 0 + 0. Bonnie s First Strategy Bonnie s Second Strategy Which strategy do you like best? Why?. You gave one solution for each part of Problem. Now, for each problem indicated below, give a different solution method. (b) 8 + 8 + 8 (e) 7 + 7 + 7 (h) Lesson 8: Add and subtract more than two fractions. 76
Lesson 9 Homework Name Date Use the RDW process to solve.. Isla walked mile each way to and from school on Wednesday. How many miles did Isla walk that day?. Zach spent hour reading on Friday and hours reading on Saturday. How much more time did he read on Saturday than on Friday?. Mrs. Cashmore bought a large melon. She cut a piece that weighed pounds and gave it to her 8 neighbor. The remaining piece of melon weighed 6 pound. How much did the whole melon weigh? 8 Lesson 9: Solve word problems involving addition and subtraction of fractions. 79
Lesson 9 Homework. Ally s little sister wanted to help her make some oatmeal cookies. First, she put cup of oatmeal in the 8 bowl. Next, she added another cup of oatmeal. Finally, she added another cup of oatmeal. How 8 8 much oatmeal did she put in the bowl?. Marcia baked pans of brownies. Her family ate pans. What fraction of a pan of brownies was left? 6 6. Joanie wrote a letter that was pages long. Katie wrote a letter that was page shorter than Joanie s letter. How long was Katie s letter? Lesson 9: Solve word problems involving addition and subtraction of fractions. 80
Lesson 0 Homework Name Date. Use a tape diagram to represent each addend. Decompose one of the tape diagrams to make like units. Then, write the complete number sentence. + 6 + c. + 8 d. + e. 8 + f. + 0 Lesson 0: Use visual models to add two fractions with related units using the denominators,,,, 6, 8, 0, and. 8
Lesson 0 Homework. Estimate to determine if the sum is between 0 and or and. Draw a number line to model the addition. Then, write a complete number sentence. The first one has been completed for you. + 6 + 7 0 c. + d. + 8 e. 7 8 + f. 6 +. Solve the following addition problem without drawing a model. Show your work. 6 + Lesson 0: Use visual models to add two fractions with related units using the denominators,,,, 6, 8, 0, and. 8
Lesson Homework Name Date. Draw a tape diagram to represent each addend. Decompose one of the tape diagrams to make like units. Then, write a complete number sentence. Use a number bond to write each sum as a mixed number. 7 8 + 8 + c. 6 + d. + 8 0. Draw a number line to model the addition. Then, write a complete number sentence. Use a number bond to write each sum as a mixed number. + 8 + 8 Lesson : Use visual models to add two fractions with related units using the denominators,,,, 6, 8, 0, and. 87
Lesson Homework c. 0 + d. + 6. Solve. Write the sum as a mixed number. Draw a model if needed. + 6 8 7 8 + c. 6 + d. 0 + e. + f. + 6 g. + 6 h. 7 0 + Lesson : Use visual models to add two fractions with related units using the denominators,,,, 6, 8, 0, and. 88
Lesson Homework Name Date. Draw a tape diagram to match each number sentence. Then, complete the number sentence. + = + = c. = d. =. Use the following three numbers to write two subtraction and two addition number sentences., 8, 8 7, 7, 6. Solve using a number bond. Draw a number line to represent each number sentence. The first one has been done for you. = 8 6 = Lesson : Add a fraction less than to, or subtract a fraction less than from, a whole number using decomposition and visual models. 9
Lesson Homework c. 7 = d. 0 =. Complete the subtraction sentences using number bonds. 6 = 7 0 = c. 6 = d. 6 6 8 = e. 7 8 = f. 6 7 0 = Lesson : Add a fraction less than to, or subtract a fraction less than from, a whole number using decomposition and visual models. 9
Lesson Homework Name Date. Circle any fractions that are equivalent to a whole number. Record the whole number below the fraction. Count by fourths. Start at 0 fourths. Stop at 6 fourths. 0,, 0 Count by sixths. Start at 0 sixths. Stop at sixths.. Use parentheses to show how to make ones in the following number sentence. + + + + + + + + + + + =. Multiply, as shown below. Draw a number line to support your answer. 6 6 = = 0 c. 8 Lesson : Add and multiply unit fractions to build fractions greater than using visual models. 9
Lesson Homework. Multiply, as shown below. Write the product as a mixed number. Draw a number line to support your answer. 7 copies of third 7 = + = + = 7 copies of fourth c. groups of fifth d. 7 e. 9 Lesson : Add and multiply unit fractions to build fractions greater than using visual models. 96
Lesson Homework Name Date. Rename each fraction as a mixed number by decomposing it into two parts as shown below. Model the decomposition with a number line and a number bond. = + = + = c. 6 d. e. 7 Lesson : Decompose and compose fractions greater than to express them in various forms. 99
Lesson Homework. Convert each fraction to a mixed number. Show your work as in the example. Model with a number line. = + = + = c. 8. Convert each fraction to a mixed number. = 7 = c. 7 = d. 8 6 = e. 7 = f. 7 8 = g. = h. 7 0 = i. = Lesson : Decompose and compose fractions greater than to express them in various forms. 00
Lesson Homework Name Date. Convert each mixed number to a fraction greater than. Draw a number line to model your work. = + = + = c. 8 d. 7 0 e. 6 Lesson : Decompose and compose fractions greater than to express them in various forms. 0
Lesson Homework. Convert each mixed number to a fraction greater than. Show your work as in the example. (Note: = ) = + = + = + = c. d. 7 8. Convert each mixed number to a fraction greater than. c. d. 6 e. f. g. 0 h. i. 6 j. 6 k. 7 l. 7 Lesson : Decompose and compose fractions greater than to express them in various forms. 0
Lesson 6 Homework Name Date. Plot the following points on the number line without measuring. i. 6 ii. iii. Use the number line in Problem (a) to compare the fractions. i. ii. 6. Plot the following points on the number line without measuring. i. 6 8 ii. 8 6 iii. 7 8 9 i. 8 6 6 8 ii. 6 8 c. Explain how you plotted the points in Problem (a). Lesson 6: Compare fractions greater than by reasoning using benchmark fractions. 07
Lesson 6 Homework. Com Give a brief explanation for each answer, referring to benchmark fractions. 8 c. 8 7 6 d. 0 e. 6 6 f. 6 7 g. 0 0 8 h. 7 6 i. 0 00 j. 6 6 00 Lesson 6: Compare fractions greater than by reasoning using benchmark fractions. 08
Lesson 7 Homework Name Date. Draw a tape diagram to model each comparison. Use >, <, or = to compare. 7 8 0 6 0 c. 8 d.. Use an area model to make like units. Then, use >, <, or = to compare. Lesson 7: Compare fractions greater than by creating common numerators or denominators.
Lesson 7 Homework. Compare each pair of fractions using >, <, or = using any strategy. 6 6 8 7 6 7 c. 6 0 d. 8 e. 0 0 f. 0 g. 8 h. i. 0 8 7 j. 0 0 6 Lesson 7: Compare fractions greater than by creating common numerators or denominators.
Lesson 8 Homework Name Date. A group of children measured the lengths of their shoes. The measurements are shown in the table. Make a line plot to display the dat Students Length of Shoe (in inches) Collin 8 Dickon 7 Ben 7 Martha 7 Lilias 8 Susan 8 Frances 7 Mary 8. Solve each problem. Who has a shoe length inch longer than Dickon? Who has a shoe length inch shorter than Susan? Lesson 8: Solve word problems with line plots.
Lesson 8 Homework c. How many quarter inches long is Martha s shoe length? d. What is the difference, in inches, between Lilias s and Martha s shoe lengths? e. Compare the shoe length of Ben and Frances using >, <, or =. f. How many students had shoes that measured less than 8 inches? g. How many children measured the length of their shoes? h. Mr. Jones s shoe length was inches. Use >, <, or = to compare the length of Mr. Jones s shoe to the length of the longest student shoe length. Who had the longer shoe?. Using the information in the table and on the line plot, write a question you could solve by using the line plot. Solve. Lesson 8: Solve word problems with line plots. 6
Lesson 9 Homework Name Date. Estimate each sum or difference to the nearest half or whole number by rounding. Explain your estimate using words or a number line. 0 + 9 0 + c. 9 9 0 d. 9 0 e. 6 + 9 Lesson 9: Estimate sums and differences using benchmark numbers. 9
Lesson 9 Homework. Estimate each sum or difference to the nearest half or whole number by rounding. Explain your estimate using words or a number line. 6 + 7 8 7 c. 7 8 + 6 8. Gina s estimate for 7 was. Dominick s estimate was. Whose estimate do you think is closer to 8 the actual difference? Explain.. Use benchmark numbers or mental math to estimate the sum or difference. 0 + 7 0 + 8 c. 9 8 d. 6 7 8 Lesson 9: Estimate sums and differences using benchmark numbers. 0
Lesson 0 Homework Name Date. Solve. + + c. 6 + 6 d. 8 + 7 8. Complete the number sentences. 6 + = 7 + = 6 c. = 8 + d. = +. Draw a number bond and the arrow way to show how to make one. Solve. + + c. 6 + 6 Lesson 0: Add a mixed number and a fraction.
Lesson 0 Homework. Solve. + 6 8 + 8 c. 6 + 6 d. 7 + 6 6 0 0 e. + 8 9 0 0 f. 7 8 + g. 90 00 + 8 00 h. 60 00 + 79 00. To solve 8 + 8, Carmen thought, + =, and + =. 0 0 0 0 0 0 Benny thought, 8 + = = + 0 + =." Explain why Carmen and Benny are both right. 0 0 0 0 0 0 Lesson 0: Add a mixed number and a fraction.
Lesson Homework Name Date. Solve. + = + = + c. 8 + 8. Solve. Use a number line to show your work. + = + = 6 + 6 c. 9 + 7 Lesson : Add mixed numbers. 7
Lesson Homework. Solve. Use the arrow way to show how to make one. + = + = 7 8 + 8 c. 7 9 + 9. Solve. Use whichever method you prefer. + 8 0 + 0 c. 7 + 6 7 Lesson : Add mixed numbers. 8
Lesson Homework Name. Subtract. Model with a number line or the arrow way. Date 6 7 c. 7 d. 8 8 8. Use decomposition to subtract the fractions. Model with a number line or the arrow way. c. 6 6 d. 6 6 Lesson : Subtract a fraction from a mixed number.
Lesson Homework e. 9 8 7 8 f. 7 0 6 0 g. 0 8 8 h. 9 7 i. j. 7. Decompose the total to subtract the fractions. 8 8 = 8 + 8 = 6 8 8 c. 7 8 8 d. e. 6 0 7 0 f. 8 Lesson : Subtract a fraction from a mixed number.
Lesson Homework Name Date. Write a related addition sentence. Subtract by counting on. Use a number line or the arrow way to help. The first one has been partially done for you. = + = 8 8. Subtract, as shown in Problem (a) below, by decomposing the fractional part of the number you are subtracting. Use a number line or the arrow way to help you. = = 7 7 c. 8 Lesson : Subtract a mixed number from a mixed number.
Lesson Homework. Subtract, as shown in (a) below, by decomposing to take one out. 8 7 8 = 8 7 8 = 8 8 c. 9 6 0 0. Solve using any strategy. 6 0 6 0 c. 8 7 d. 7 00 00 Lesson : Subtract a mixed number from a mixed number. 6
Lesson Homework Name Date. Subtract. 6 8 6 8 c. 7 6 6. Subtract the ones first. = = 6 6 6 Lesson : Subtract mixed numbers. 9
Lesson Homework c. 8 8 8 d. 0 8 7 0. Solve using any strategy. 7 9 6 0 8 0 c. 7 6 9 7 6 d. 00 8 00 Lesson : Subtract mixed numbers. 0
Lesson Homework Name Date. Draw and label a tape diagram to show the following are true. 8 thirds = ( thirds) = ( ) thirds eighths = ( eighths) = ( ) eighths. Write the expression in unit form to solve. 0 6 c. 9 d. 7 Lesson : Represent the multiplication of n times a/b as (n a)/b using the associative property and visual models.
Lesson Homework. Solve. 6 7 8 c. d. 8 e. 7 0 f. 7 00. Mrs. Smith bought some orange juice. Each member of her family drank cup for breakfast. There are five people in her family. How many cups of orange juice did they drink? Lesson : Represent the multiplication of n times a/b as (n a)/b using the associative property and visual models.
Lesson 6 Homework Name Date. Draw a tape diagram to represent. Draw a tape diagram to represent + + +. 7 + 7 + 7. 8 8 8 Write a multiplication expression equal to Write a multiplication expression equal to + + +. 7 + 7 + 7. 8 8 8. Rewrite each repeated addition problem as a multiplication problem and solve. Express the result as a mixed number. The first one has been completed for you. 7 + 7 + 7 + 7 = 7 = 7 = 8 = 7 0 + 7 0 + 7 0 c. + + + + + d. 8 + 8 + 8 + 8 + 8 + 8 + 8 + 8 + 8 + 8 + 8 + 8. Solve using any method. Express your answers as whole or mixed numbers. 7 Lesson 6: Represent the multiplication of n times a/b as (n a)/b using the associative property and visual models. 7
Lesson 6 Homework c. 0 6 d. 6 e. f. 8. Coleton is playing with interlocking blocks that are each inch tall. He makes a tower 7 blocks tall. How tall is his tower in inches? 6. There were players on Mr. Maiorani s softball team. They each ate of a pizz How many pizzas did 8 they eat? 7. A bricklayer places bricks along an outside wall of a shed. Each brick is foot long. How many feet long is that wall of the shed? Lesson 6: Represent the multiplication of n times a/b as (n a)/b using the associative property and visual models. 8
Lesson 7 Homework Name Date. Draw tape diagrams to show two ways to represent units of. Write a multiplication expression to match each tape diagram.. Solve the following using the distributive property. The first one has been done for you. (As soon as you are ready, you may omit the step that is in line.) 6 = 6 + 6 = ( 6) + = 8 + = 8 + = 0 c. 6 d. 7 0 Lesson 7: Find the product of a whole number and a mixed number using the distributive property.
Lesson 7 Homework e. 8 7 f. 8. Sara s street is miles long. She ran the length of the street 6 times. How far did she run? 0. Kelly s new puppy weighed 7 pounds when she brought him home. Now, he weighs six times as much. 0 How much does he weigh now? Lesson 7: Find the product of a whole number and a mixed number using the distributive property.
Lesson 8 Homework Name Date. Fill in the unknown factors. 8 7 = ( ) + ( 7 ) 9 7 7 0 = (9 ) + (9 ). Multiply. Use the distributive property. 6 8 7 7 9 c. 9 8 7 d. 7 8 Lesson 8: Find the product of a whole number and a mixed number using the distributive property.
Lesson 8 Homework e. 0 8 f. 0 00. Brandon is cutting 9 boards for a woodworking project. Each board is feet long. What is the total 8 length of the boards?. Rocky the collie ate cups of dog food each day for two weeks. How much dog food did Rocky eat in that time?. At the class party, each student will be given a container that holds 8 ounces of juice. There are 8 students in the class. If each student s container is filled, how many ounces of juice does the teacher need to buy? Lesson 8: Find the product of a whole number and a mixed number using the distributive property. 6
Lesson 9 Homework Name Date Use the RDW process to solve.. Ground turkey is sold in packages of pounds. Dawn bought eight times as much turkey that is sold in package for her son s birthday party. How many pounds of ground turkey did Dawn buy?. Trevor s stack of books is 7 7 inches tall. Rick s stack is times as tall. What is the difference in the 8 heights of their stacks of books?. It takes 8 yards of fabric to make one quilt. Gail needs three times as much fabric to make three quilts. She already has two yards of fabric. How many more yards of fabric does Gail need to buy in order to make three quilts? Lesson 9: Solve multiplicative comparison word problems involving fractions. 9
Lesson 9 Homework. Carol made punch. She used cups of juice and then added three times as much ginger ale. Then, she 8 added cup of lemonade. How many cups of punch did her recipe make?. Brandon drove 7 7 miles on Monday. He drove times as far on Tuesday. How far did he drive in the 0 two days? 6. Mrs. Reiser used 9 8 gallons of gas this week. Mr. Reiser used five times as much gas as Mrs. Reiser used 0 this week. If Mr. Reiser pays $ for each gallon of gas, how much did Mr. Reiser pay for gas this week? Lesson 9: Solve multiplicative comparison word problems involving fractions. 60
Lesson 0 Homework Name Date The chart to the right shows the total monthly rainfall for a city.. Use the data to create a line plot at the bottom of this page and to answer the following questions. Month Rainfall (in inches) January 8 February 8 March 8 April 8 May June July 7 8 August September 8 October 8 November December 8 Lesson 0: Solve word problems involving the multiplication of a whole number and a fraction including those involving line plots. 6
Lesson 0 Homework. What is the difference in rainfall from the wettest and driest months?. How much more rain fell in May than in April?. What is the combined rainfall amount for the summer months of June, July, and August?. How much more rain fell in the summer months than the combined rainfall for the last months of the year? 6. In which months did it rain twice as much as it rained in December? 7. Each inch of rain can produce ten times that many inches of snow. If all of the rainfall in January was in the form of snow, how many inches of snow fell in January? Lesson 0: Solve word problems involving the multiplication of a whole number and a fraction including those involving line plots. 6
Lesson Homework Name Date. Find the sums. 0 + + + + + 0 6 + 6 + 6 + 6 + 6 + 6 + 6 6 c. 0 7 + 7 + 7 + 7 + 7 + 7 + 6 7 + 7 7 d. 0 8 + 8 + 8 + 8 + 8 + 8 + 6 8 + 7 8 + 8 8 e. 0 9 + 9 + 9 + 9 + 9 + 9 + 6 9 + 7 9 + 8 9 + 9 9 f. 0 + + + + + + 6 + 7 + 8 + 9 + 0 0 0 0 0 0 0 0 0 0 0 0. Describe a pattern you notice when adding the sums of fractions with even denominators as opposed to those with odd denominators.. How would the sums change if the addition started with the unit fraction rather than with 0? Lesson : Find and use a pattern to calculate the sum of all fractional parts between 0 and. Share and critique peer strategies. 67
Lesson Homework. Find the sums. 0 + + +... 0 0 0 0 0 0 + + +... c. 0 + + +... + 6 6 6 6 6 d. 0 + + +... 7 7 7 7 7 e. 0 + + +... 00 00 00 00 00 f. 0 + + +... 99 99 99 99 99. How can you apply this strategy to find the sum of all the whole numbers from 0 to 0? To 99? Lesson : Find and use a pattern to calculate the sum of all fractional parts between 0 and. Share and critique peer strategies. 68
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