G5 U5 Constructed Response
Name: ________________________________________ Date:_______________
Grade 5 Unit 5 Constructed Response Subtracting Fractions TASK 1: Subtracting Fractions with Unlike Denominators Using Models and the Area Model (No Regrouping) (CCSS 5.NF.1, 5.NF.2; SMP 1, 2, 4, 5, 6, 8) 8
1. Stanley made chocolate chip cookies with his mom. They had pound of 9 chocolate chips available to make the cookies. When they finished making 1 the cookie batter they had pound of chocolate chips left. What is the 3 amount of chocolate chips they used to make the cookie batter? a. Write an equation that best represents the word problem. Answer: _______________________ b. Using the equation you wrote above, estimate and then find the amount of chocolate chips Stanley and his mom used. In the table, show your work by creating an illustration or number line and label your estimate. Strategy:
Answer: ________________________________
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Grade 5 Unit 5 Constructed Response Subtracting Fractions
2. Madeline and Christine go for a bike ride along the beach every week. The 5 first week they travelled 3 miles on their bike ride. The second week they 1
8
travelled 2 miles. How much further did they travel the first week than the 6 second week? a. Write an equation that best represents the word problem.
Answer: ____________________
b. Using the equation you wrote in 2a, estimate and then find how much further they travelled the first week. In the table, show your work by using an area model.
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Grade 5 Unit 5 Constructed Response Subtracting Fractions Area Model:
Answer: _______________ c. After finding your solution, write an explanation in which you discuss how using an area model helped 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 5 Unit 5 Constructed Response Subtracting Fractions 3. a. Analyze the equation below. Use the values in the number bank to make the equation true. Number bank: 8
7
5
−6
1
10
4
=4 8
b. Write a discussion in which you explain how you made the equation true using the number bank.
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Grade 5 Unit 5 Constructed Response Subtracting Fractions TASK 2: Subtracting Fractions with Unlike Denominators Using a Number Line and an Algorithm (CCSS: 5.NF.1, 5.NF.2; SMP: 1, 2, 3, 4, 6, 7, 8)
4. Analyze the expression below: 2 3 − 3 5 a. In the table below, subtract the fractions by using a number line. Show your work in detailed and organized steps. Number Line:
Answer: __________________ b. Explain how you were able to find your answer using a number line. How did this strategy help create a common denominator in the fraction?
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Grade 5 Unit 5 Constructed Response Subtracting Fractions 5. Stella and Joel work at a day camp for kids. At the beginning of the month 7 they had 7 pounds of pretzels to distribute as snacks. The table below 9 shows how many pounds of pretzels they distributed per week. Quantity (pounds) 3
Week 1
3
Week 2
2
4
They want to find how many pounds of pretzels they have left after week 2, so they do the following work: 7 3 4 7 −3 −2=2 9 4 5 a. After analyzing the data and their work, determine if Stella and Joel found the correct number of pounds they had left after week 2. If they are incorrect, identify and correct any flaws in their work.
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Grade 5 Unit 5 Constructed Response Subtracting Fractions b. If Stella and Joel were incorrect, show the correct process for finding the total pounds they have left by using the standard algorithm strategy. In the table below show your work and give your answer in its simplest form. Standard Algorithm:
Answer: ____________________
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Grade 5 Unit 5 Constructed Response Subtracting Fractions 6. Samantha, Jerry, and Ted participated in a bike race in their town. Samantha 1 was the second place finisher and crossed the finish line 1 minutes after 12 the winner who was Jerry. Ted was the third place winner and he crossed the 1 2 finish line 1 minutes behind Samantha. Ted took 21 minutes to complete 2 3 the race. a. Using the information given in the problem, find how long it took for Samantha to complete the race and for Jerry to complete the race. In the table below show your work by using a number line or a standard algorithm. Strategy:
Answer: Samantha’s time: ____________ Jerry’s time: ____________ Copyright © Swun Math Grade 5 Unit 5 Constructed Response, Page 8
Grade 5 Unit 5 Constructed Response Subtracting Fractions b. After finding the solutions, write a discussion in which you explain how you determined the process necessary to find your answer. What parts of the information given to you were important in helping you find the solutions?
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Grade 5 Unit 5 Constructed Response Subtracting Fractions TASK 3: Subtracting Fractions with Unlike Denominators Using an Area Model and an Algorithm (With Regrouping) (CCSS: 5.NF.1, 5.NF.2; SMP: 1, 2, 4, 6, 7, 8) 2
7. Suzanne and her mom purchased 4 pounds of strawberries. They decided to 3
3
make a pie with some of the strawberries and used 1 pounds. How many 4 pounds of strawberries do they have left? a. Write an expression with the mixed numbers that you can use to find the solution for this problem. Answer: _____________________________ b. In the table below, find how many pounds of strawberries they have left using an area model. Area Model:
Answer: __________________
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Grade 5 Unit 5 Constructed Response Subtracting Fractions 2
8. Evan had about 3 feet of rope to use on a camping trip with his dad. Before 5
5
leaving they bought an additional 2 feet of rope. When they came back from 8
6
their trip they had 2 feet of rope left. How many feet of rope did Evan and 15 his dad use while on their trip? 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 equation that you can use to find the solution for this problem.
Answer: _________________________
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Grade 5 Unit 5 Constructed Response Subtracting Fractions c. Find how many feet of rope they used while on their camping trip. In the table below show your work by using a standard algorithm. Strategy:
Answer: __________________ 5
9. Henry has 30 minutes to complete a 5-problem quiz. He spends 8 minutes 3
6
on question #1 and 7 minutes on question #2. Henry then finishes question 4 #3 in 4 minutes. How much time does he have left for questions #4 and #5?
a. How much time did Henry spend working on question #1, #2, and #3? Show your work in detailed and organized steps.
Answer: _________________ Copyright © Swun Math Grade 5 Unit 5 Constructed Response, Page 12
Grade 5 Unit 5 Constructed Response Subtracting Fractions b. Find how much time Henry has left for question #4 and #5. In the table show your work by using an area model or a standard algorithm. Strategy:
Answer: _______________
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Grade 5 Unit 5 Constructed Response Subtracting Fractions TASK 1: Subtracting Fractions with Unlike Denominators Using Models and the Area Model (No Regrouping) (CCSS 5.NF.1, 5.NF.2; SMP 1, 2, 4, 5, 6, 8) 8
1. Stanley made chocolate chip cookies with his mom. They had pound of 9 chocolate chips available to make the cookies. When they finished making 1 the cookie batter they had pound of chocolate chips left. What is the 3 amount of chocolate chips they used to make the cookie batter? a. Write an equation that best represents the word problem. Answer: _______________________ b. Using the equation you wrote above, estimate and then find the amount of chocolate chips Stanley and his mom used. In the table, show your work by creating an illustration or number line and label your estimate. Strategy:
Answer: ________________________________
Copyright © Swun Math Grade 5 Unit 5 Constructed Response, Page 1
Grade 5 Unit 5 Constructed Response Subtracting Fractions
2. Madeline and Christine go for a bike ride along the beach every week. The 5 first week they travelled 3 miles on their bike ride. The second week they 1
8
travelled 2 miles. How much further did they travel the first week than the 6 second week? a. Write an equation that best represents the word problem.
Answer: ____________________
b. Using the equation you wrote in 2a, estimate and then find how much further they travelled the first week. In the table, show your work by using an area model.
Copyright © Swun Math Grade 5 Unit 5 Constructed Response, Page 2
Grade 5 Unit 5 Constructed Response Subtracting Fractions Area Model:
Answer: _______________ c. After finding your solution, write an explanation in which you discuss how using an area model helped you make sense of the problem. How does this illustration help you visualize what is happening as you solve the problem?
Copyright © Swun Math Grade 5 Unit 5 Constructed Response, Page 3
Grade 5 Unit 5 Constructed Response Subtracting Fractions 3. a. Analyze the equation below. Use the values in the number bank to make the equation true. Number bank: 8
7
5
−6
1
10
4
=4 8
b. Write a discussion in which you explain how you made the equation true using the number bank.
Copyright © Swun Math Grade 5 Unit 5 Constructed Response, Page 4
Grade 5 Unit 5 Constructed Response Subtracting Fractions TASK 2: Subtracting Fractions with Unlike Denominators Using a Number Line and an Algorithm (CCSS: 5.NF.1, 5.NF.2; SMP: 1, 2, 3, 4, 6, 7, 8)
4. Analyze the expression below: 2 3 − 3 5 a. In the table below, subtract the fractions by using a number line. Show your work in detailed and organized steps. Number Line:
Answer: __________________ b. Explain how you were able to find your answer using a number line. How did this strategy help create a common denominator in the fraction?
Copyright © Swun Math Grade 5 Unit 5 Constructed Response, Page 5
Grade 5 Unit 5 Constructed Response Subtracting Fractions 5. Stella and Joel work at a day camp for kids. At the beginning of the month 7 they had 7 pounds of pretzels to distribute as snacks. The table below 9 shows how many pounds of pretzels they distributed per week. Quantity (pounds) 3
Week 1
3
Week 2
2
4
They want to find how many pounds of pretzels they have left after week 2, so they do the following work: 7 3 4 7 −3 −2=2 9 4 5 a. After analyzing the data and their work, determine if Stella and Joel found the correct number of pounds they had left after week 2. If they are incorrect, identify and correct any flaws in their work.
Copyright © Swun Math Grade 5 Unit 5 Constructed Response, Page 6
Grade 5 Unit 5 Constructed Response Subtracting Fractions b. If Stella and Joel were incorrect, show the correct process for finding the total pounds they have left by using the standard algorithm strategy. In the table below show your work and give your answer in its simplest form. Standard Algorithm:
Answer: ____________________
Copyright © Swun Math Grade 5 Unit 5 Constructed Response, Page 7
Grade 5 Unit 5 Constructed Response Subtracting Fractions 6. Samantha, Jerry, and Ted participated in a bike race in their town. Samantha 1 was the second place finisher and crossed the finish line 1 minutes after 12 the winner who was Jerry. Ted was the third place winner and he crossed the 1 2 finish line 1 minutes behind Samantha. Ted took 21 minutes to complete 2 3 the race. a. Using the information given in the problem, find how long it took for Samantha to complete the race and for Jerry to complete the race. In the table below show your work by using a number line or a standard algorithm. Strategy:
Answer: Samantha’s time: ____________ Jerry’s time: ____________ Copyright © Swun Math Grade 5 Unit 5 Constructed Response, Page 8
Grade 5 Unit 5 Constructed Response Subtracting Fractions b. After finding the solutions, write a discussion in which you explain how you determined the process necessary to find your answer. What parts of the information given to you were important in helping you find the solutions?
Copyright © Swun Math Grade 5 Unit 5 Constructed Response, Page 9
Grade 5 Unit 5 Constructed Response Subtracting Fractions TASK 3: Subtracting Fractions with Unlike Denominators Using an Area Model and an Algorithm (With Regrouping) (CCSS: 5.NF.1, 5.NF.2; SMP: 1, 2, 4, 6, 7, 8) 2
7. Suzanne and her mom purchased 4 pounds of strawberries. They decided to 3
3
make a pie with some of the strawberries and used 1 pounds. How many 4 pounds of strawberries do they have left? a. Write an expression with the mixed numbers that you can use to find the solution for this problem. Answer: _____________________________ b. In the table below, find how many pounds of strawberries they have left using an area model. Area Model:
Answer: __________________
Copyright © Swun Math Grade 5 Unit 5 Constructed Response, Page 10
Grade 5 Unit 5 Constructed Response Subtracting Fractions 2
8. Evan had about 3 feet of rope to use on a camping trip with his dad. Before 5
5
leaving they bought an additional 2 feet of rope. When they came back from 8
6
their trip they had 2 feet of rope left. How many feet of rope did Evan and 15 his dad use while on their trip? 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 equation that you can use to find the solution for this problem.
Answer: _________________________
Copyright © Swun Math Grade 5 Unit 5 Constructed Response, Page 11
Grade 5 Unit 5 Constructed Response Subtracting Fractions c. Find how many feet of rope they used while on their camping trip. In the table below show your work by using a standard algorithm. Strategy:
Answer: __________________ 5
9. Henry has 30 minutes to complete a 5-problem quiz. He spends 8 minutes 3
6
on question #1 and 7 minutes on question #2. Henry then finishes question 4 #3 in 4 minutes. How much time does he have left for questions #4 and #5?
a. How much time did Henry spend working on question #1, #2, and #3? Show your work in detailed and organized steps.
Answer: _________________ Copyright © Swun Math Grade 5 Unit 5 Constructed Response, Page 12
Grade 5 Unit 5 Constructed Response Subtracting Fractions b. Find how much time Henry has left for question #4 and #5. In the table show your work by using an area model or a standard algorithm. Strategy:
Answer: _______________
Copyright © Swun Math Grade 5 Unit 5 Constructed Response, Page 13
