G4 U5 Constructed Response
Name: ________________________________________ Date:_______________
Grade 4 Unit 5 Constructed Response Add and Subtract Fractions TASK 1: Decompose Fractions, Add Fractions by Joining Parts, Subtract Fractions by Separating Parts (CCSS 4.NF.3 a,b; SMP 1, 2, 4, 5, 6, 7, 8) 11
1. In the table below, decompose the fraction in two ways. Create a model to 15 show the decomposition of the fraction and write a fraction sentence to represent it. Model: a.
Answer: ________________________________ b.
Answer: ________________________________
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Grade 4 Unit 5 Constructed Response Add and Subtract Fractions 2. After a family get together, Brad had 2 plates of leftover pie and he wanted 1 to combine them. On one plate he had of the pie left and on the other he 8
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had of the pie left over. 8
a. Write a fraction sentence that can be used to find the total quantity of pie he had left over. Answer: ____________________ b. Using the fraction sentence you wrote, find the total quantity of pie he had left over. Show your work by creating a visual model in the table below. Model:
Answer: _______________
c. Write an explanation in which you discuss why you decided to use this type of model to represent your work.
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Grade 4 Unit 5 Constructed Response Add and Subtract Fractions 3. Tiffany and Courtney bought some ribbon to make decorative bows for their 7 3 house. They used of the ribbon to make the first bow, and of the ribbon 15 15 to make the second bow. How much ribbon do they have leftover after making the bows? a. Before solving the problem, write an explanation in which you describe a starting point for finding the solution. What mathematical operation is necessary to find the solution?
b. In the table below, solve the problem using a number line and the mathematical operation you identified. Number Line:
Answer: ______________________
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Grade 4 Unit 5 Constructed Response Add and Subtract Fractions TASK 2: Addition and Subtraction of Mixed Numbers: Equivalent Fractions and Properties of Operations (CCSS: 4.NF.3c; SMP: 1, 2, 4, 5, 6, 7, 8)
4. Analyze the expression: 2 5 2 +1 8 8 a. In the table below, add the mixed numbers by using equivalent fractions on a number line. Show your work in detailed and organized steps. Number Line:
Answer: __________________ b. Write an explanation in which you discuss how using a number line helped you to visualize the location of each equivalent fraction. How did this help you find your answer?
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Grade 4 Unit 5 Constructed Response Add and Subtract Fractions 5. Analyze the expression: 3 1 4 −2 5 5 a. In the table below, subtract the mixed numbers using the Properties of Operations and an illustration. Show your work in detailed and organized steps. Illustration:
Answer: __________________ b. Explain how creating an illustration helps you to 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 5 Constructed Response Add and Subtract Fractions
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Grade 4 Unit 5 Constructed Response Add and Subtract Fractions TASK 3: Addition and Subtraction Word Problems (CCSS: 4.NF.3 c, d; SMP: 1, 2, 4, 5, 6, 7, 8)
6. Alice is training for a race. At the end of her second week of training she ran a 5 1 total of 7 miles. This distance was 2 miles more than the distance she ran 7 7 during her first week of training. How many miles did she run during the first week of her training? a. Before finding your solution, explain the meaning of the information you are given in the problem. How is this information helpful in developing a strategy to find your solution?
b. Write an expression with the mixed numbers that you can use to find the solution for this problem.
Answer: _____________________ Copyright © Swun Math Grade 4 Unit 5 Constructed Response, Page 7
Grade 4 Unit 5 Constructed Response Add and Subtract Fractions c. Find the total miles Alice ran during her first week of training. 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: __________________
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Grade 4 Unit 5 Constructed Response Add and Subtract Fractions 7. Tammy and her family run a local ice cream shop in their beachside town. 5 During the first two weeks of June, they made 20 gallons of ice cream. 6
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During the last two weeks of the month they made an additional 8 gallons of 6 ice cream. At the end of the month they checked their inventory and they had 1 5 gallons of ice cream left. How many gallons of ice cream did they sell 6 during the month of June? a. Before finding your solution, describe a strategy you could use to find your solution with the information given. What mathematical operations are important for finding your solution?
b. Write an expression with the mixed numbers that you can use to find the solution for this problem.
Answer:__________________ Copyright © Swun Math Grade 4 Unit 5 Constructed Response, Page 9
Grade 4 Unit 5 Constructed Response Add and Subtract Fractions c. Find how many gallons of ice cream they sold during the month of June. 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: __________________
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Grade 4 Unit 5 Constructed Response Add and Subtract Fractions 8. Denise and Johanna are in the final round of a discus throwing competition. The winner of the competition will be the person who has the highest combined distance after the three rounds. Johanna has thrown three times already, and it is now Denise’s turn to throw. Competitor Johanna Denise
1st Throw 1 12 3 84 12 90
2nd Throw 5 12 11 89 12 83
3rd Throw 2 95 12 ?
a. What is the total distance Johanna has thrown the discus? 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: __________________
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Grade 4 Unit 5 Constructed Response Add and Subtract Fractions b. How far does Denise need to throw the discus during her third throw in order to get a tie? 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: __________________
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Grade 4 Unit 5 Constructed Response Add and Subtract Fractions TASK 1: Decompose Fractions, Add Fractions by Joining Parts, Subtract Fractions by Separating Parts (CCSS 4.NF.3 a,b; SMP 1, 2, 4, 5, 6, 7, 8) 11
1. In the table below, decompose the fraction in two ways. Create a model to 15 show the decomposition of the fraction and write a fraction sentence to represent it. Model: a.
Answer: ________________________________ b.
Answer: ________________________________
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Grade 4 Unit 5 Constructed Response Add and Subtract Fractions 2. After a family get together, Brad had 2 plates of leftover pie and he wanted 1 to combine them. On one plate he had of the pie left and on the other he 8
5
had of the pie left over. 8
a. Write a fraction sentence that can be used to find the total quantity of pie he had left over. Answer: ____________________ b. Using the fraction sentence you wrote, find the total quantity of pie he had left over. Show your work by creating a visual model in the table below. Model:
Answer: _______________
c. Write an explanation in which you discuss why you decided to use this type of model to represent your work.
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Grade 4 Unit 5 Constructed Response Add and Subtract Fractions 3. Tiffany and Courtney bought some ribbon to make decorative bows for their 7 3 house. They used of the ribbon to make the first bow, and of the ribbon 15 15 to make the second bow. How much ribbon do they have leftover after making the bows? a. Before solving the problem, write an explanation in which you describe a starting point for finding the solution. What mathematical operation is necessary to find the solution?
b. In the table below, solve the problem using a number line and the mathematical operation you identified. Number Line:
Answer: ______________________
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Grade 4 Unit 5 Constructed Response Add and Subtract Fractions TASK 2: Addition and Subtraction of Mixed Numbers: Equivalent Fractions and Properties of Operations (CCSS: 4.NF.3c; SMP: 1, 2, 4, 5, 6, 7, 8)
4. Analyze the expression: 2 5 2 +1 8 8 a. In the table below, add the mixed numbers by using equivalent fractions on a number line. Show your work in detailed and organized steps. Number Line:
Answer: __________________ b. Write an explanation in which you discuss how using a number line helped you to visualize the location of each equivalent fraction. How did this help you find your answer?
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Grade 4 Unit 5 Constructed Response Add and Subtract Fractions 5. Analyze the expression: 3 1 4 −2 5 5 a. In the table below, subtract the mixed numbers using the Properties of Operations and an illustration. Show your work in detailed and organized steps. Illustration:
Answer: __________________ b. Explain how creating an illustration helps you to 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 5 Constructed Response Add and Subtract Fractions
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Grade 4 Unit 5 Constructed Response Add and Subtract Fractions TASK 3: Addition and Subtraction Word Problems (CCSS: 4.NF.3 c, d; SMP: 1, 2, 4, 5, 6, 7, 8)
6. Alice is training for a race. At the end of her second week of training she ran a 5 1 total of 7 miles. This distance was 2 miles more than the distance she ran 7 7 during her first week of training. How many miles did she run during the first week of her training? a. Before finding your solution, explain the meaning of the information you are given in the problem. How is this information helpful in developing a strategy to find your solution?
b. Write an expression with the mixed numbers that you can use to find the solution for this problem.
Answer: _____________________ Copyright © Swun Math Grade 4 Unit 5 Constructed Response, Page 7
Grade 4 Unit 5 Constructed Response Add and Subtract Fractions c. Find the total miles Alice ran during her first week of training. 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: __________________
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Grade 4 Unit 5 Constructed Response Add and Subtract Fractions 7. Tammy and her family run a local ice cream shop in their beachside town. 5 During the first two weeks of June, they made 20 gallons of ice cream. 6
3
During the last two weeks of the month they made an additional 8 gallons of 6 ice cream. At the end of the month they checked their inventory and they had 1 5 gallons of ice cream left. How many gallons of ice cream did they sell 6 during the month of June? a. Before finding your solution, describe a strategy you could use to find your solution with the information given. What mathematical operations are important for finding your solution?
b. Write an expression with the mixed numbers that you can use to find the solution for this problem.
Answer:__________________ Copyright © Swun Math Grade 4 Unit 5 Constructed Response, Page 9
Grade 4 Unit 5 Constructed Response Add and Subtract Fractions c. Find how many gallons of ice cream they sold during the month of June. 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: __________________
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Grade 4 Unit 5 Constructed Response Add and Subtract Fractions 8. Denise and Johanna are in the final round of a discus throwing competition. The winner of the competition will be the person who has the highest combined distance after the three rounds. Johanna has thrown three times already, and it is now Denise’s turn to throw. Competitor Johanna Denise
1st Throw 1 12 3 84 12 90
2nd Throw 5 12 11 89 12 83
3rd Throw 2 95 12 ?
a. What is the total distance Johanna has thrown the discus? 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: __________________
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Grade 4 Unit 5 Constructed Response Add and Subtract Fractions b. How far does Denise need to throw the discus during her third throw in order to get a tie? 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: __________________
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