G5 U6 Constructed Response
Name: ________________________________________ Date:_______________
Grade 5 Unit 6 Constructed Response Multiplying Fractions TASK 1: Fractions as Division; Multiplying Fractions by One (CCSS 5.NF.3, 5.NF.5a, b, 5.NF.6; SMP 1, 2, 4, 7, 8)
1. Ricky picked 12 pounds of apples from his apple orchard. He wants to give apples to eight of his friends. How many pounds of apples can he give to each of his friends if he wants to share the apples equally? a. Write two equations that represent how the apples will be divided. Answer: ___________________ ___________________ b. Using an area model, find how many pounds of apples Ricky will give each of his friends. Area Model:
Answer: ________________
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Grade 5 Unit 6 Constructed Response Multiplying Fractions c. After solving the problem, describe the relationship between division and fractions. Use the problem and your work to justify your reasoning.
2. Billy and his family moved into a new home. His room has a width of 16 feet and a length of 26 feet. His parents’ room has a width of 16 feet and a length of 52 feet. a. How does the area of Billy’s room compare to the area of his parents’ room? In the table below, show your work in detailed and organized steps. Give your answer in a complete sentence. Process:
Answer:
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Grade 5 Unit 6 Constructed Response Multiplying Fractions b. Create an illustration that represents your answer from question 2a. Illustration:
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Grade 5 Unit 6 Constructed Response Multiplying Fractions 3. Gale has 8 spools of yarn left over from different knitting projects. Each spool 3 has 1 yards of yarn. Will the total length of the yarn Gale has left be less 4 than or greater than 8 yards? a. In the table below, find your answer using an area model. Give your answer in a complete sentence. Area Model:
Answer:
b. Write an explanation in which you discuss the meaning of your answer. What properties could you use to explain the accuracy of your answer?
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Grade 5 Unit 6 Constructed Response Multiplying Fractions TASK 2: Reasoning About Multiplying Fractions by Fractions, and Multiplying Fractions Using an Area Model (CCSS: 5.NF.4b, 5.NF.5b; SMP: 1, 3, 4, 6, 7, 8)
4. Lily takes a gallon of ice cream to a birthday party. After the party is over she 5 1 5 has of the gallon of ice cream left. Later that week she uses of the of 8 3 8 the gallon to make root beer floats for her niece and nephew. 1
a. Will the remaining amount of ice cream be greater than or less than of 3 the gallon? In the table below show your work using a diagram. Diagram:
Answer: 5
b. Will the remaining amount of ice cream be greater than or less than of 8 the gallon? In the table below show your work using a diagram. Diagram:
Answer: Copyright © Swun Math Grade 5 Unit 6 Constructed Response, Page 5
Grade 5 Unit 6 Constructed Response Multiplying Fractions c. After finding your solution, write a discussion explaining how you know your answers from questions 4a and 4b are reasonable.
5. Analyze the expression below: 3 ×
3 7
a. In the table below, find the product of the expression using an area model. Show your work in detailed and organized steps. Area Model:
Answer: __________________
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Grade 5 Unit 6 Constructed Response Multiplying Fractions b. Explain how creating an area model helps you make sense of the problem. How does this illustration help you visualize what is happening as you solve the problem?
6. Gianna encounters the problem below on a test. She gets the following answer: 6 4 24 2 × 3 =6 7 9 63 a. After analyzing Gianna’s answer, determine if her answer is correct or incorrect. Explain how you know. If Gianna is incorrect, identify her error(s) and correct them.
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Grade 5 Unit 6 Constructed Response Multiplying Fractions b. If Gianna is incorrect, find the correct product using an algorithm. Show your work in detailed and organized steps. Algorithm:
Answer: __________________
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Grade 5 Unit 6 Constructed Response Multiplying Fractions TASK 3: Word Problems with Fractions (CCSS: 5.NF.4a, 5.NF.6; SMP: 1, 2, 7, 8)
7. Maggie buys a 3-pound bag of soil for her plants at a local gardening store. 5 She places of the soil in a pot holding a large plant. What fraction of the soil 6 did she place in the pot? a. Write an expression that can be used to find the fraction of soil Maggie placed in the pot. Answer: _____________________ b. Find the quantity of soil she placed in the pot. In the table below show how to find the solution using both an area model and an algorithm. Give your answer as a mixed number and in simplest form. Area Model:
Algorithm:
Answer: Copyright © Swun Math Grade 5 Unit 6 Constructed Response, Page 9
Grade 5 Unit 6 Constructed Response Multiplying Fractions c. Maggie later places the remaining soil in a flowerpot. How much soil did Maggie place in this pot? Give your answer in simplest form.
Answer: _______________________ 8. Paula and her three friends are participating in a bike race in town. Each person’s time is listed in the table below. Racer:
Time:
Paula
18 2 minutes
Carly
1 3 times Paula’s time
Julian
1 5 times Paula’s time
Robby
1
2 1
15 16
times Paula’s time
a. Using Paula’s time, find the race time for each of her friends. In the table below write the expression necessary to find the race time for each person and give your answer in simplest form. Carly
Answer: Copyright © Swun Math Grade 5 Unit 6 Constructed Response, Page 10
Grade 5 Unit 6 Constructed Response Multiplying Fractions Julian
Answer: Robby
Answer: b. Based on your answers, identify the order in which Paula and her friends finished the race. Who was the winner of the race?
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Grade 5 Unit 6 Constructed Response Multiplying Fractions 9. Pete and Molly work at an animal shelter during the summer. Pete works 1 every Tuesday and Thursday for of the day. Molly works every Monday and 1
4
Wednesday for of the day. In four weeks, how many hours do Pete and 3 Molly each work? Who works the most hours at the animal shelter? a. Before you begin solving the problem, write a discussion in which you explain the meaning of the problem and describe a possible starting point for solving the problem.
b. In the table below, find the number of hours Pete and Molly each work, and determine who works the most hours. Show your work in detailed and organized steps. Give your answer in a complete sentence. Strategy:
Answer:
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Grade 5 Unit 6 Constructed Response Multiplying Fractions
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Grade 5 Unit 6 Constructed Response Multiplying Fractions TASK 1: Fractions as Division; Multiplying Fractions by One (CCSS 5.NF.3, 5.NF.5a, b, 5.NF.6; SMP 1, 2, 4, 7, 8)
1. Ricky picked 12 pounds of apples from his apple orchard. He wants to give apples to eight of his friends. How many pounds of apples can he give to each of his friends if he wants to share the apples equally? a. Write two equations that represent how the apples will be divided. Answer: ___________________ ___________________ b. Using an area model, find how many pounds of apples Ricky will give each of his friends. Area Model:
Answer: ________________
Copyright © Swun Math Grade 5 Unit 6 Constructed Response, Page 1
Grade 5 Unit 6 Constructed Response Multiplying Fractions c. After solving the problem, describe the relationship between division and fractions. Use the problem and your work to justify your reasoning.
2. Billy and his family moved into a new home. His room has a width of 16 feet and a length of 26 feet. His parents’ room has a width of 16 feet and a length of 52 feet. a. How does the area of Billy’s room compare to the area of his parents’ room? In the table below, show your work in detailed and organized steps. Give your answer in a complete sentence. Process:
Answer:
Copyright © Swun Math Grade 5 Unit 6 Constructed Response, Page 2
Grade 5 Unit 6 Constructed Response Multiplying Fractions b. Create an illustration that represents your answer from question 2a. Illustration:
Copyright © Swun Math Grade 5 Unit 6 Constructed Response, Page 3
Grade 5 Unit 6 Constructed Response Multiplying Fractions 3. Gale has 8 spools of yarn left over from different knitting projects. Each spool 3 has 1 yards of yarn. Will the total length of the yarn Gale has left be less 4 than or greater than 8 yards? a. In the table below, find your answer using an area model. Give your answer in a complete sentence. Area Model:
Answer:
b. Write an explanation in which you discuss the meaning of your answer. What properties could you use to explain the accuracy of your answer?
Copyright © Swun Math Grade 5 Unit 6 Constructed Response, Page 4
Grade 5 Unit 6 Constructed Response Multiplying Fractions TASK 2: Reasoning About Multiplying Fractions by Fractions, and Multiplying Fractions Using an Area Model (CCSS: 5.NF.4b, 5.NF.5b; SMP: 1, 3, 4, 6, 7, 8)
4. Lily takes a gallon of ice cream to a birthday party. After the party is over she 5 1 5 has of the gallon of ice cream left. Later that week she uses of the of 8 3 8 the gallon to make root beer floats for her niece and nephew. 1
a. Will the remaining amount of ice cream be greater than or less than of 3 the gallon? In the table below show your work using a diagram. Diagram:
Answer: 5
b. Will the remaining amount of ice cream be greater than or less than of 8 the gallon? In the table below show your work using a diagram. Diagram:
Answer: Copyright © Swun Math Grade 5 Unit 6 Constructed Response, Page 5
Grade 5 Unit 6 Constructed Response Multiplying Fractions c. After finding your solution, write a discussion explaining how you know your answers from questions 4a and 4b are reasonable.
5. Analyze the expression below: 3 ×
3 7
a. In the table below, find the product of the expression using an area model. Show your work in detailed and organized steps. Area Model:
Answer: __________________
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Grade 5 Unit 6 Constructed Response Multiplying Fractions b. Explain how creating an area model helps you make sense of the problem. How does this illustration help you visualize what is happening as you solve the problem?
6. Gianna encounters the problem below on a test. She gets the following answer: 6 4 24 2 × 3 =6 7 9 63 a. After analyzing Gianna’s answer, determine if her answer is correct or incorrect. Explain how you know. If Gianna is incorrect, identify her error(s) and correct them.
Copyright © Swun Math Grade 5 Unit 6 Constructed Response, Page 7
Grade 5 Unit 6 Constructed Response Multiplying Fractions b. If Gianna is incorrect, find the correct product using an algorithm. Show your work in detailed and organized steps. Algorithm:
Answer: __________________
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Grade 5 Unit 6 Constructed Response Multiplying Fractions TASK 3: Word Problems with Fractions (CCSS: 5.NF.4a, 5.NF.6; SMP: 1, 2, 7, 8)
7. Maggie buys a 3-pound bag of soil for her plants at a local gardening store. 5 She places of the soil in a pot holding a large plant. What fraction of the soil 6 did she place in the pot? a. Write an expression that can be used to find the fraction of soil Maggie placed in the pot. Answer: _____________________ b. Find the quantity of soil she placed in the pot. In the table below show how to find the solution using both an area model and an algorithm. Give your answer as a mixed number and in simplest form. Area Model:
Algorithm:
Answer: Copyright © Swun Math Grade 5 Unit 6 Constructed Response, Page 9
Grade 5 Unit 6 Constructed Response Multiplying Fractions c. Maggie later places the remaining soil in a flowerpot. How much soil did Maggie place in this pot? Give your answer in simplest form.
Answer: _______________________ 8. Paula and her three friends are participating in a bike race in town. Each person’s time is listed in the table below. Racer:
Time:
Paula
18 2 minutes
Carly
1 3 times Paula’s time
Julian
1 5 times Paula’s time
Robby
1
2 1
15 16
times Paula’s time
a. Using Paula’s time, find the race time for each of her friends. In the table below write the expression necessary to find the race time for each person and give your answer in simplest form. Carly
Answer: Copyright © Swun Math Grade 5 Unit 6 Constructed Response, Page 10
Grade 5 Unit 6 Constructed Response Multiplying Fractions Julian
Answer: Robby
Answer: b. Based on your answers, identify the order in which Paula and her friends finished the race. Who was the winner of the race?
Copyright © Swun Math Grade 5 Unit 6 Constructed Response, Page 11
Grade 5 Unit 6 Constructed Response Multiplying Fractions 9. Pete and Molly work at an animal shelter during the summer. Pete works 1 every Tuesday and Thursday for of the day. Molly works every Monday and 1
4
Wednesday for of the day. In four weeks, how many hours do Pete and 3 Molly each work? Who works the most hours at the animal shelter? a. Before you begin solving the problem, write a discussion in which you explain the meaning of the problem and describe a possible starting point for solving the problem.
b. In the table below, find the number of hours Pete and Molly each work, and determine who works the most hours. Show your work in detailed and organized steps. Give your answer in a complete sentence. Strategy:
Answer:
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Grade 5 Unit 6 Constructed Response Multiplying Fractions
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