G7 U4 Constructed Response
Name: ________________________________________ Date:_______________
Grade 7 Unit 4 Constructed Response Multiplying Fractions TASK 1: Adding, Subtracting, Multiplying, and Dividing Fractions and Mixed Numbers (CCSS 7.NS.3; SMP 1, 2, 4, 6, 7)
1. As part of her marathon training, Teresa runs every Monday, Wednesday, and 1 Friday. This week she wants to run at least 18 miles. How many miles 2 would she need to run each day to meet this goal? a. Write an expression that could be used to find the number of miles she needs to run each day. Answer: ______________________ b. In the table below, find the number of miles she needs to run per day using an area model. Show your work in detailed and organized steps.
Answer: ________________
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Grade 7 Unit 4 Constructed Response Multiplying Fractions 2. Christie bought a 1-pound bag of candy from a candy store. Some friends 1 came over to hang out and ate of the bag. Later that week she took the bag 4
5
of candy to work and her coworkers ate of the bag. What fraction of the 8 bag of candy did Christie have left? a. Write two expressions that can be used to find the fraction of the bag of candy Christie had left over. Expressions: ___________________________ ___________________________ b. In the table below, create a number line or an area model to find your answer. Area Model:
Answer: ________________ Copyright © Swun Math Grade 7 Unit 4 Constructed Response, Page 2
Grade 7 Unit 4 Constructed Response Multiplying Fractions c. What important information did you use to write the expressions to find this solution?
3. Stella, Mary, and Sheryl sold cookies to help pay for a camping trip. At the end of two months they raised $600 in cookie sales. Stella sold 75 boxes of cookies, Mary sold 60 boxes of cookies, and Sheryl sold 65 boxes of cookies. What fraction of the cookies did each of the girls sell? How much money did each girl raise? a. Before solving the problem, describe a possible strategy for solving the problem. What important information is helpful to develop this strategy?
Copyright © Swun Math Grade 7 Unit 4 Constructed Response, Page 3
Grade 7 Unit 4 Constructed Response Multiplying Fractions b. Find the fraction of the cookies each girl sold and the money each girl raised. Show your work in detailed and organized steps.
Answer: Stella
Mary
Fraction $ Raised
Copyright © Swun Math Grade 7 Unit 4 Constructed Response, Page 4
Sheryl
Grade 7 Unit 4 Constructed Response Multiplying Fractions TASK 2: Simplifying Complex Fractions, and Terminating and Repeating Decimals (CCSS: 7.NS.4; SMP: 1, 2, 3, 4, 5, 6, 7)
4. Blaine encountered the problem below on a test. He did the following work to find his solution: 2 3 4 ÷ 1 = 5
22 5
×
8 5
=
5
176 25
or 7
1 25
a. After analyzing Blaine’s work, decide whether his work and his answer are correct. Explain how you know. If Blaine is incorrect, identify the error(s) and correct them.
b. If Blaine’s answer is incorrect, find the correct answer. Show your work in detailed and organized steps. Give your answer in simplest form.
Answer: __________________
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Grade 7 Unit 4 Constructed Response Multiplying Fractions 1
5. Lily and her sister picked 16 pounds of oranges from their orange trees to 2 take to a family reunion. They want to place the oranges into baskets that 1 can hold up to 5 pounds each. How many baskets will they fill with 4 oranges? a. Write two expressions that can be used to find the number of baskets they will fill with oranges. Answer: ________________ ________________
b. In the table below, find the number of baskets of oranges they will fill. Show your work in detailed and organized steps. Area Model:
Answer: __________________
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Grade 7 Unit 4 Constructed Response Multiplying Fractions 6. When written as a decimal, will
9 16
repeat or terminate?
a. Find your answer using prime factors. Show your work in detailed and organized steps.
Answer: __________________ b. In the table below write the fraction as a decimal using long division. Show your work in detailed and organized steps.
Answer: __________________
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Grade 7 Unit 4 Constructed Response Multiplying Fractions c. After finding your answers for questions 6a and 6b, can you conclude your answers make sense? Explain your reasoning by referencing your work.
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Grade 7 Unit 4 Constructed Response Multiplying Fractions TASK 3: Approximating Square Roots (CCSS: 7.NS.5; SMP: 1, 2, 3, 4, 6)
7. Analyze the square root below: √74 a. In the table below, find the approximate value of √74 using a number line. Show your work in detailed and organized steps. Number Line:
Answer: _________________ c. How could you check that the value you found is a reasonable answer?
d. Using the strategy you explained, check the reasonableness of your answer.
Copyright © Swun Math Grade 7 Unit 4 Constructed Response, Page 9
Grade 7 Unit 4 Constructed Response Multiplying Fractions 8. Johanna has four pieces of lumber that measure 12.5 feet, √141 feet, 13 feet, and √150 feet. Place the measurement of each piece of lumber in order from least to greatest. a. Before finding your solution, describe a strategy you could use to find your solution with the information given.
b. Using the strategy you explained place the measurements in order from least to greatest. In the table below show your work in detailed and organized steps. Strategy:
Answer: __________________________________________________ Copyright © Swun Math Grade 7 Unit 4 Constructed Response, Page 10
Grade 7 Unit 4 Constructed Response Multiplying Fractions 9. a. What two perfect squares is √250 between? Write an inequality that represents this relationship. Answer: _______________ b. How did you determine the inequality? Explain your reasoning in complete sentences using your knowledge of square roots.
c. In the table below approximate the value of √250 to two decimal places, using successive approximations. Revise your approximations as needed.
Answer: __________________
Copyright © Swun Math Grade 7 Unit 4 Constructed Response, Page 11
Grade 7 Unit 4 Constructed Response Multiplying Fractions TASK 1: Adding, Subtracting, Multiplying, and Dividing Fractions and Mixed Numbers (CCSS 7.NS.3; SMP 1, 2, 4, 6, 7)
1. As part of her marathon training, Teresa runs every Monday, Wednesday, and 1 Friday. This week she wants to run at least 18 miles. How many miles 2 would she need to run each day to meet this goal? a. Write an expression that could be used to find the number of miles she needs to run each day. Answer: ______________________ b. In the table below, find the number of miles she needs to run per day using an area model. Show your work in detailed and organized steps.
Answer: ________________
Copyright © Swun Math Grade 7 Unit 4 Constructed Response, Page 1
Grade 7 Unit 4 Constructed Response Multiplying Fractions 2. Christie bought a 1-pound bag of candy from a candy store. Some friends 1 came over to hang out and ate of the bag. Later that week she took the bag 4
5
of candy to work and her coworkers ate of the bag. What fraction of the 8 bag of candy did Christie have left? a. Write two expressions that can be used to find the fraction of the bag of candy Christie had left over. Expressions: ___________________________ ___________________________ b. In the table below, create a number line or an area model to find your answer. Area Model:
Answer: ________________ Copyright © Swun Math Grade 7 Unit 4 Constructed Response, Page 2
Grade 7 Unit 4 Constructed Response Multiplying Fractions c. What important information did you use to write the expressions to find this solution?
3. Stella, Mary, and Sheryl sold cookies to help pay for a camping trip. At the end of two months they raised $600 in cookie sales. Stella sold 75 boxes of cookies, Mary sold 60 boxes of cookies, and Sheryl sold 65 boxes of cookies. What fraction of the cookies did each of the girls sell? How much money did each girl raise? a. Before solving the problem, describe a possible strategy for solving the problem. What important information is helpful to develop this strategy?
Copyright © Swun Math Grade 7 Unit 4 Constructed Response, Page 3
Grade 7 Unit 4 Constructed Response Multiplying Fractions b. Find the fraction of the cookies each girl sold and the money each girl raised. Show your work in detailed and organized steps.
Answer: Stella
Mary
Fraction $ Raised
Copyright © Swun Math Grade 7 Unit 4 Constructed Response, Page 4
Sheryl
Grade 7 Unit 4 Constructed Response Multiplying Fractions TASK 2: Simplifying Complex Fractions, and Terminating and Repeating Decimals (CCSS: 7.NS.4; SMP: 1, 2, 3, 4, 5, 6, 7)
4. Blaine encountered the problem below on a test. He did the following work to find his solution: 2 3 4 ÷ 1 = 5
22 5
×
8 5
=
5
176 25
or 7
1 25
a. After analyzing Blaine’s work, decide whether his work and his answer are correct. Explain how you know. If Blaine is incorrect, identify the error(s) and correct them.
b. If Blaine’s answer is incorrect, find the correct answer. Show your work in detailed and organized steps. Give your answer in simplest form.
Answer: __________________
Copyright © Swun Math Grade 7 Unit 4 Constructed Response, Page 5
Grade 7 Unit 4 Constructed Response Multiplying Fractions 1
5. Lily and her sister picked 16 pounds of oranges from their orange trees to 2 take to a family reunion. They want to place the oranges into baskets that 1 can hold up to 5 pounds each. How many baskets will they fill with 4 oranges? a. Write two expressions that can be used to find the number of baskets they will fill with oranges. Answer: ________________ ________________
b. In the table below, find the number of baskets of oranges they will fill. Show your work in detailed and organized steps. Area Model:
Answer: __________________
Copyright © Swun Math Grade 7 Unit 4 Constructed Response, Page 6
Grade 7 Unit 4 Constructed Response Multiplying Fractions 6. When written as a decimal, will
9 16
repeat or terminate?
a. Find your answer using prime factors. Show your work in detailed and organized steps.
Answer: __________________ b. In the table below write the fraction as a decimal using long division. Show your work in detailed and organized steps.
Answer: __________________
Copyright © Swun Math Grade 7 Unit 4 Constructed Response, Page 7
Grade 7 Unit 4 Constructed Response Multiplying Fractions c. After finding your answers for questions 6a and 6b, can you conclude your answers make sense? Explain your reasoning by referencing your work.
Copyright © Swun Math Grade 7 Unit 4 Constructed Response, Page 8
Grade 7 Unit 4 Constructed Response Multiplying Fractions TASK 3: Approximating Square Roots (CCSS: 7.NS.5; SMP: 1, 2, 3, 4, 6)
7. Analyze the square root below: √74 a. In the table below, find the approximate value of √74 using a number line. Show your work in detailed and organized steps. Number Line:
Answer: _________________ c. How could you check that the value you found is a reasonable answer?
d. Using the strategy you explained, check the reasonableness of your answer.
Copyright © Swun Math Grade 7 Unit 4 Constructed Response, Page 9
Grade 7 Unit 4 Constructed Response Multiplying Fractions 8. Johanna has four pieces of lumber that measure 12.5 feet, √141 feet, 13 feet, and √150 feet. Place the measurement of each piece of lumber in order from least to greatest. a. Before finding your solution, describe a strategy you could use to find your solution with the information given.
b. Using the strategy you explained place the measurements in order from least to greatest. In the table below show your work in detailed and organized steps. Strategy:
Answer: __________________________________________________ Copyright © Swun Math Grade 7 Unit 4 Constructed Response, Page 10
Grade 7 Unit 4 Constructed Response Multiplying Fractions 9. a. What two perfect squares is √250 between? Write an inequality that represents this relationship. Answer: _______________ b. How did you determine the inequality? Explain your reasoning in complete sentences using your knowledge of square roots.
c. In the table below approximate the value of √250 to two decimal places, using successive approximations. Revise your approximations as needed.
Answer: __________________
Copyright © Swun Math Grade 7 Unit 4 Constructed Response, Page 11
