G4 U6 Constructed Response
Name: ________________________________________ Date:_______________
Grade 4 Unit 6 Constructed Response Multiplying Fractions TASK 1: Decomposing Fractions (CCSS 4.NF.4 a; SMP 1, 2, 4, 6, 7, 8) 5
1. Decompose the fraction as a whole number multiplied by a unit fraction. 8
a. In the table below, use a number line to find your answer. Number Line:
Answer: ________________ b. Explain how the number line helped you solve the problem. What steps did you take to decompose the fraction?
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Grade 4 Unit 6 Constructed Response Multiplying Fractions 2. Decompose the fraction
7 10
as a whole number multiplied by a unit fraction.
a. In the table below, find your answer using an area model. Area Model:
Answer: ________________ b. Explain how using an area model helped you solve the problem. What steps did you take to decompose the fraction?
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Grade 4 Unit 6 Constructed Response Multiplying Fractions 1
1
3. a. In the table below show that 3 can also be written as 16 × using a 5 5 visual model. Area Model:
b. Write an explanation in which you discuss how your visual model shows 1 1 that 3 can also be written as 16 × . 5
5
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Grade 4 Unit 6 Constructed Response Multiplying Fractions
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Grade 4 Unit 6 Constructed Response Multiplying Fractions TASK 2: Multiplying Fractions (CCSS: 4.NF.4b; SMP: 1, 2, 3, 5, 7)
4. Lewis encounters the problem below on a test. He does the following work 5 to find his solution: 3 × 8
0
𝟓 𝟖
1
𝟏𝟑 𝟖
2
𝟐𝟏 𝟖
a. After analyzing Lewis’ work, determine if his work and his answer are correct. Explain how you know whether his work and answer are correct or incorrect. If Lewis is incorrect, identify his error(s) and correct them.
b. If Lewis is incorrect, find the correct product of the problem he solved using a number line. Show your work in detailed and organized steps. Number Line:
Answer: __________________ Copyright © Swun Math Grade 4 Unit 6 Constructed Response, Page 5
Grade 4 Unit 6 Constructed Response Multiplying Fractions 5. Analyze the expression below: 5 ×
4 9
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: __________________ 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?
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Grade 4 Unit 6 Constructed Response Multiplying Fractions 6. Analyze the expression below: 7 ×
3 10
a. In the table below, find the product of the expression using an area model or a number line. Show your work in detailed and organized steps. Area Model or Number Line:
Answer: __________________ b. Analyze the strategies you used in questions 4, 5, and 6. Explain how using repeated addition helped in multiplying fractions by a whole number. How does repeated addition and multiplication relate?
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Grade 4 Unit 6 Constructed Response Multiplying Fractions TASK 3: Word Problems with Fractions (CCSS: 4.NF.4 b, c; SMP: 1, 2, 3, 5, 8)
7. Chestnut Ridge Camp has 84 kids registered in their summer session. During 1 3 the first week of camp, of the campers participated in archery lessons, and 3 7 of the campers participated in rowing class. How many campers participated in archery lessons? How many campers participated in rowing class? a. Write two expressions that can be used to find the number of camper’s participating in archery class, and the number of campers participating in rowing class. Answer: Archery Class: _____________________ Rowing Class: _____________________ b. Using the expressions you wrote above, find the number of campers that participated in archery class and rowing class. In the table below show your work by using a number line, an area model, or properties of operations. Give your answer as a mixed number. Strategy:
Answer: Archery Class: __________________ Rowing Class: __________________
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Grade 4 Unit 6 Constructed Response Multiplying Fractions 8. Samantha prepared goodie bags for her little sister’s birthday party. She planned on a total of 7 kids at the birthday party, including Samantha’s little 1 sister. Samantha bought a bag of candy and each child will get of this candy 7 in their goodie bag. She also bought 21 toys to put in the bags so each child will get the same number of toys. On the day of the party, one child did not show up, so Samantha’s sister got two goodie bags. How many toys did each child get in his or her goodie bag? How many toys did Samantha’s little sister get? a. Before finding your solutions, describe a strategy you could use to find your solution with the information given.
b. Write a numerical expression you can use to find how many toys each child got in their goodie bag.
Answer:__________________ Copyright © Swun Math Grade 4 Unit 6 Constructed Response, Page 9
Grade 4 Unit 6 Constructed Response Multiplying Fractions c. Find how many toys were in each child’s goodie bag, and how many toys Samantha’s little sister got at the birthday party. In the table below show your work in detailed and organized steps. Strategy:
Answer: Number of toys: __________________ Number of toys: _________________ (Samantha’s little sister)
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Grade 4 Unit 6 Constructed Response Multiplying Fractions 9. Brandi takes two flavors of cookies to a tea party. She takes 12 White 1 Chocolate Macadamia cookies and of them are eaten. She also takes 15 1
2
Peanut Butter Cookies and of them are eaten at the tea party. Read each of 3 the statements in the table below. Determine which of the statements are true or false. Statement: a. The same number of White Chocolate Macadamia and Peanut Butter Cookies were eaten. b. 6 White Chocolate Macadamia Cookies and 5 Peanut Butter Cookies were eaten. c. 5 White Chocolate Macadamia Cookies and 6 Peanut Butter Cookies were eaten. d. Brandi had 6 White Chocolate Macadamia Cookies and 10 Peanut Butter Cookies left over.
True/ False
e. In the table below create a model to prove your answers are correct. Model:
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Grade 4 Unit 6 Constructed Response Multiplying Fractions TASK 1: Decomposing Fractions (CCSS 4.NF.4 a; SMP 1, 2, 4, 6, 7, 8) 5
1. Decompose the fraction as a whole number multiplied by a unit fraction. 8
a. In the table below, use a number line to find your answer. Number Line:
Answer: ________________ b. Explain how the number line helped you solve the problem. What steps did you take to decompose the fraction?
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Grade 4 Unit 6 Constructed Response Multiplying Fractions 2. Decompose the fraction
7 10
as a whole number multiplied by a unit fraction.
a. In the table below, find your answer using an area model. Area Model:
Answer: ________________ b. Explain how using an area model helped you solve the problem. What steps did you take to decompose the fraction?
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Grade 4 Unit 6 Constructed Response Multiplying Fractions 1
1
3. a. In the table below show that 3 can also be written as 16 × using a 5 5 visual model. Area Model:
b. Write an explanation in which you discuss how your visual model shows 1 1 that 3 can also be written as 16 × . 5
5
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Grade 4 Unit 6 Constructed Response Multiplying Fractions
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Grade 4 Unit 6 Constructed Response Multiplying Fractions TASK 2: Multiplying Fractions (CCSS: 4.NF.4b; SMP: 1, 2, 3, 5, 7)
4. Lewis encounters the problem below on a test. He does the following work 5 to find his solution: 3 × 8
0
𝟓 𝟖
1
𝟏𝟑 𝟖
2
𝟐𝟏 𝟖
a. After analyzing Lewis’ work, determine if his work and his answer are correct. Explain how you know whether his work and answer are correct or incorrect. If Lewis is incorrect, identify his error(s) and correct them.
b. If Lewis is incorrect, find the correct product of the problem he solved using a number line. Show your work in detailed and organized steps. Number Line:
Answer: __________________ Copyright © Swun Math Grade 4 Unit 6 Constructed Response, Page 5
Grade 4 Unit 6 Constructed Response Multiplying Fractions 5. Analyze the expression below: 5 ×
4 9
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: __________________ 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?
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Grade 4 Unit 6 Constructed Response Multiplying Fractions 6. Analyze the expression below: 7 ×
3 10
a. In the table below, find the product of the expression using an area model or a number line. Show your work in detailed and organized steps. Area Model or Number Line:
Answer: __________________ b. Analyze the strategies you used in questions 4, 5, and 6. Explain how using repeated addition helped in multiplying fractions by a whole number. How does repeated addition and multiplication relate?
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Grade 4 Unit 6 Constructed Response Multiplying Fractions TASK 3: Word Problems with Fractions (CCSS: 4.NF.4 b, c; SMP: 1, 2, 3, 5, 8)
7. Chestnut Ridge Camp has 84 kids registered in their summer session. During 1 3 the first week of camp, of the campers participated in archery lessons, and 3 7 of the campers participated in rowing class. How many campers participated in archery lessons? How many campers participated in rowing class? a. Write two expressions that can be used to find the number of camper’s participating in archery class, and the number of campers participating in rowing class. Answer: Archery Class: _____________________ Rowing Class: _____________________ b. Using the expressions you wrote above, find the number of campers that participated in archery class and rowing class. In the table below show your work by using a number line, an area model, or properties of operations. Give your answer as a mixed number. Strategy:
Answer: Archery Class: __________________ Rowing Class: __________________
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Grade 4 Unit 6 Constructed Response Multiplying Fractions 8. Samantha prepared goodie bags for her little sister’s birthday party. She planned on a total of 7 kids at the birthday party, including Samantha’s little 1 sister. Samantha bought a bag of candy and each child will get of this candy 7 in their goodie bag. She also bought 21 toys to put in the bags so each child will get the same number of toys. On the day of the party, one child did not show up, so Samantha’s sister got two goodie bags. How many toys did each child get in his or her goodie bag? How many toys did Samantha’s little sister get? a. Before finding your solutions, describe a strategy you could use to find your solution with the information given.
b. Write a numerical expression you can use to find how many toys each child got in their goodie bag.
Answer:__________________ Copyright © Swun Math Grade 4 Unit 6 Constructed Response, Page 9
Grade 4 Unit 6 Constructed Response Multiplying Fractions c. Find how many toys were in each child’s goodie bag, and how many toys Samantha’s little sister got at the birthday party. In the table below show your work in detailed and organized steps. Strategy:
Answer: Number of toys: __________________ Number of toys: _________________ (Samantha’s little sister)
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Grade 4 Unit 6 Constructed Response Multiplying Fractions 9. Brandi takes two flavors of cookies to a tea party. She takes 12 White 1 Chocolate Macadamia cookies and of them are eaten. She also takes 15 1
2
Peanut Butter Cookies and of them are eaten at the tea party. Read each of 3 the statements in the table below. Determine which of the statements are true or false. Statement: a. The same number of White Chocolate Macadamia and Peanut Butter Cookies were eaten. b. 6 White Chocolate Macadamia Cookies and 5 Peanut Butter Cookies were eaten. c. 5 White Chocolate Macadamia Cookies and 6 Peanut Butter Cookies were eaten. d. Brandi had 6 White Chocolate Macadamia Cookies and 10 Peanut Butter Cookies left over.
True/ False
e. In the table below create a model to prove your answers are correct. Model:
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