G5 U4 Constructed Response
Name: ________________________________________ Date:_______________
Grade 5 Unit 4 Constructed Response Adding Fractions TASK 1: Simplifying Fractions, Estimating Reasonable Fractions: Sums and Differences (CCSS 5.NF.1, 5.NF.2; SMP 1, 4, 5, 6, 7, 8)
1. Simplify the fraction using an area model. a. In the table below show your process and give the simplified fraction. 18 24 Steps:
Answer: _________________
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Grade 5 Unit 4 Constructed Response Adding Fractions b. Explain how the area models of the fractions helped you understand the simplified form.
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Grade 5 Unit 4 Constructed Response Adding Fractions 2. Lily planted flowers in her garden. When they finally bloomed, she saw that 35 of the 55 flowers were yellow. Express the fraction of yellow flowers in simplest form. a. In the table below find the simplified fraction using only numbers. Steps:
Answer: _________________ b. Compare the ways you simplified fractions in problems 1 and 2. How are the strategies similar and different? Which strategy is the most efficient way to simplify a fraction?
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Grade 5 Unit 4 Constructed Response Adding Fractions 3
3. Max bought 4 pounds of tomatoes and made some spaghetti sauce. He had 1
4
2 pounds of tomatoes left over. How many pounds of tomatoes did Max use 3 to make the spaghetti sauce? a. Represent the word problem as an equation.
Equation: _____________________ b. Make a reasonable estimate of the number of pounds of tomatoes Max used to make the sauce and then solve the problem. Show your work in detailed and complete steps. Give your answer in simplest form.
Estimate: ______________________
Answer: ______________________ Copyright © Swun Math Grade 5 Unit 4 Constructed Response, Page 4
Grade 5 Unit 4 Constructed Response Adding Fractions c. After solving the problem, explain how the estimate was useful to check the accuracy or reasonableness of your answer. Was your estimate similar to your actual answer?
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Grade 5 Unit 4 Constructed Response Adding Fractions TASK 2: Adding Fractions with Unlike Denominators (CCSS: 5.NF.1, 5.NF.2; SMP: 1, 2, 4, 5, 6, 7)
4. Analyze the expression: 3 1 +2 8 4 a. Estimate your answer and then solve the expression using the area model. Reduce your answer to its simplest form.
Estimate: ______________________ Area Model:
Answer: _____________________
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Grade 5 Unit 4 Constructed Response Adding Fractions b. Explain how you were able to find your answer using the area model. How did this strategy help you create the numerator in the fraction? How did this strategy help create a common denominator in the fraction?
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Grade 5 Unit 4 Constructed Response Adding Fractions 5. Analyze the expression: 4 1 + 5 2 a. Estimate your answer and then solve the expression using a number line. Reduce your answer to its simplest form. Estimate: ______________________ Number Line:
Answer: _____________________
b. Analyze the two strategies you worked with in question 4a and 5a. Write an explanation in which you describe how the process for finding the common denominator using these two strategies is similar.
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Grade 5 Unit 4 Constructed Response Adding Fractions 6. Jeremiah and his dad painted their house. Two cans of the same size had 5 2 some paint left over. One can was full and the other can was full. They 7 3 want to combine the leftover paint into one can to use for their next project. Will their leftover paint fit in one can or will they need more cans? a. Before solving the problem, describe a strategy you could use to determine if the paint will fit into one can.
b. In the table below, use an area model or number line to find the total amount of leftover paint. Reduce the fraction to its simplest form. Strategy:
Answer: _____________________ Copyright © Swun Math Grade 5 Unit 4 Constructed Response, Page 9
Grade 5 Unit 4 Constructed Response Adding Fractions c. Based on your answer from above, determine how many paint cans they need to store their leftover paint. Explain how this paint will be distributed in the cans.
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Grade 5 Unit 4 Constructed Response Adding Fractions TASK 3: Adding Fractions Using an Algorithm (CCSS: 5.NF.1, 5.NF.2 ; SMP: 1, 2, 3, 6, 7, 8 )
7. Analyze the expression: 1
3 1 + 4 5
a. Solve the expression using an algorithm. Reduce your answer to its simplest form. Algorithm:
Answer: _____________________ b. Prove your answer is correct by using an area model to show the combined shaded pieces from your model.
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Grade 5 Unit 4 Constructed Response Adding Fractions 8. Tristan and George went kayaking three times in one week. The table below shows how far they traveled each day. Day
Distance (miles)
Monday
1
1
Wednesday
2
2
Friday
1
1
4 5 8
They want to find how many total miles they kayaked during the week so they did the following work: 1 2 1 4 1 +2 +1 =3 4 5 8 17 a. After analyzing the data and their work, determine whether Tristan and George found the correct number of miles they kayaked during the week. If they are incorrect, identify and correct any flaws in their work.
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Grade 5 Unit 4 Constructed Response Adding Fractions b. If Tristan and George were incorrect, show the correct process for finding the total miles they traveled using the standard algorithm. 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 4 Constructed Response Adding Fractions 9. Katrina and Joel want to grow carrots in their garden. On the first day, they 2 1 plant seeds in 2 rows, and on their second day they plant seeds in 3 rows. 5 6 a. How many rows of carrot seeds did they plant altogether? Show your work in detailed and organized steps.
Answer: _________________ 3
b. Katrina and Joel also planted 2 rows of tomatoes. Using your answer 5 from question 9a, write an equation they could use to find how many rows of vegetables they have planted altogether.
Equation: ___________________ c. Using your equation from above, find thetotal number of rows of vegetables they have planted altogether.
Answer: ___________________
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Grade 5 Unit 4 Constructed Response Adding Fractions TASK 1: Simplifying Fractions, Estimating Reasonable Fractions: Sums and Differences (CCSS 5.NF.1, 5.NF.2; SMP 1, 4, 5, 6, 7, 8)
1. Simplify the fraction using an area model. a. In the table below show your process and give the simplified fraction. 18 24 Steps:
Answer: _________________
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Grade 5 Unit 4 Constructed Response Adding Fractions b. Explain how the area models of the fractions helped you understand the simplified form.
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Grade 5 Unit 4 Constructed Response Adding Fractions 2. Lily planted flowers in her garden. When they finally bloomed, she saw that 35 of the 55 flowers were yellow. Express the fraction of yellow flowers in simplest form. a. In the table below find the simplified fraction using only numbers. Steps:
Answer: _________________ b. Compare the ways you simplified fractions in problems 1 and 2. How are the strategies similar and different? Which strategy is the most efficient way to simplify a fraction?
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Grade 5 Unit 4 Constructed Response Adding Fractions 3
3. Max bought 4 pounds of tomatoes and made some spaghetti sauce. He had 1
4
2 pounds of tomatoes left over. How many pounds of tomatoes did Max use 3 to make the spaghetti sauce? a. Represent the word problem as an equation.
Equation: _____________________ b. Make a reasonable estimate of the number of pounds of tomatoes Max used to make the sauce and then solve the problem. Show your work in detailed and complete steps. Give your answer in simplest form.
Estimate: ______________________
Answer: ______________________ Copyright © Swun Math Grade 5 Unit 4 Constructed Response, Page 4
Grade 5 Unit 4 Constructed Response Adding Fractions c. After solving the problem, explain how the estimate was useful to check the accuracy or reasonableness of your answer. Was your estimate similar to your actual answer?
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Grade 5 Unit 4 Constructed Response Adding Fractions TASK 2: Adding Fractions with Unlike Denominators (CCSS: 5.NF.1, 5.NF.2; SMP: 1, 2, 4, 5, 6, 7)
4. Analyze the expression: 3 1 +2 8 4 a. Estimate your answer and then solve the expression using the area model. Reduce your answer to its simplest form.
Estimate: ______________________ Area Model:
Answer: _____________________
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Grade 5 Unit 4 Constructed Response Adding Fractions b. Explain how you were able to find your answer using the area model. How did this strategy help you create the numerator in the fraction? How did this strategy help create a common denominator in the fraction?
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Grade 5 Unit 4 Constructed Response Adding Fractions 5. Analyze the expression: 4 1 + 5 2 a. Estimate your answer and then solve the expression using a number line. Reduce your answer to its simplest form. Estimate: ______________________ Number Line:
Answer: _____________________
b. Analyze the two strategies you worked with in question 4a and 5a. Write an explanation in which you describe how the process for finding the common denominator using these two strategies is similar.
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Grade 5 Unit 4 Constructed Response Adding Fractions 6. Jeremiah and his dad painted their house. Two cans of the same size had 5 2 some paint left over. One can was full and the other can was full. They 7 3 want to combine the leftover paint into one can to use for their next project. Will their leftover paint fit in one can or will they need more cans? a. Before solving the problem, describe a strategy you could use to determine if the paint will fit into one can.
b. In the table below, use an area model or number line to find the total amount of leftover paint. Reduce the fraction to its simplest form. Strategy:
Answer: _____________________ Copyright © Swun Math Grade 5 Unit 4 Constructed Response, Page 9
Grade 5 Unit 4 Constructed Response Adding Fractions c. Based on your answer from above, determine how many paint cans they need to store their leftover paint. Explain how this paint will be distributed in the cans.
Copyright © Swun Math Grade 5 Unit 4 Constructed Response, Page 10
Grade 5 Unit 4 Constructed Response Adding Fractions TASK 3: Adding Fractions Using an Algorithm (CCSS: 5.NF.1, 5.NF.2 ; SMP: 1, 2, 3, 6, 7, 8 )
7. Analyze the expression: 1
3 1 + 4 5
a. Solve the expression using an algorithm. Reduce your answer to its simplest form. Algorithm:
Answer: _____________________ b. Prove your answer is correct by using an area model to show the combined shaded pieces from your model.
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Grade 5 Unit 4 Constructed Response Adding Fractions 8. Tristan and George went kayaking three times in one week. The table below shows how far they traveled each day. Day
Distance (miles)
Monday
1
1
Wednesday
2
2
Friday
1
1
4 5 8
They want to find how many total miles they kayaked during the week so they did the following work: 1 2 1 4 1 +2 +1 =3 4 5 8 17 a. After analyzing the data and their work, determine whether Tristan and George found the correct number of miles they kayaked during the week. If they are incorrect, identify and correct any flaws in their work.
Copyright © Swun Math Grade 5 Unit 4 Constructed Response, Page 12
Grade 5 Unit 4 Constructed Response Adding Fractions b. If Tristan and George were incorrect, show the correct process for finding the total miles they traveled using the standard algorithm. 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 4 Constructed Response Adding Fractions 9. Katrina and Joel want to grow carrots in their garden. On the first day, they 2 1 plant seeds in 2 rows, and on their second day they plant seeds in 3 rows. 5 6 a. How many rows of carrot seeds did they plant altogether? Show your work in detailed and organized steps.
Answer: _________________ 3
b. Katrina and Joel also planted 2 rows of tomatoes. Using your answer 5 from question 9a, write an equation they could use to find how many rows of vegetables they have planted altogether.
Equation: ___________________ c. Using your equation from above, find thetotal number of rows of vegetables they have planted altogether.
Answer: ___________________
Copyright © Swun Math Grade 5 Unit 4 Constructed Response, Page 14
