G7 U1 Constructed Response
Name: ________________________________________ Date:_______________
Grade 7 Unit 1 Constructed Response Analyzing Proportional Relationships TASK 1: Ratios, Proportions, and Strategies for Testing Proportional Relationships (CCSS:7.RP.1 [m], 7.RP.2a [m]; SMP: 1, 2, 3, 4, 5)
1. Neil works at two different jobs during his summer vacation. The following table shows his earnings and hours worked at the two jobs. Job Bakery Pet Groomers
Money Earned $135 $120
Hours Worked 9 6
a. After analyzing the problem scenario and the information given, write an explanation of the meaning of the data. (What do the numbers represent? What units are used and how should they be classified? What is the unit rate?)
b. At which job did Neil get paid the most per hour? How much did he make per hour at that job? Show your work.
Answer: Job: _______________ Rate: ______________ c. In complete sentences, explain how you can prove that your answer is correct.
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Grade 7 Unit 1 Constructed Response Analyzing Proportional Relationships 2. The table below shows number of laps Misty was able to swim in a certain amount of time each day. Day Tuesday Wednesday Thursday
Number of Laps 8 16 12
Time (mins) 14 28 21
a. Is the number of laps she swims proportional to how long it took her to complete the laps? In the table below, show and explain the process necessary to find your solution, and give a written explanation of your answer in complete sentences. Mathematical Process
Explanation of Steps
Answer:
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Grade 7 Unit 1 Constructed Response Analyzing Proportional Relationships b. Explain how your answer from above would be different if her swimming rate on Tuesday was 12 laps in 14 minutes.
3. The table below shows the mean kicking distance and kicking speed of five soccer players. Use this information to answer the following questions. Kicker 1 2 3 4 5
Distance (meters) 35 45 68 60 64
Speed (meters per second) 15 19 26 18 22
a. After analyzing the data in the table, identify a mathematical tool you could use to determine if there is a proportional relationship between the data. Explain how this tool would be helpful to use in this situation.
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Grade 7 Unit 1 Constructed Response Analyzing Proportional Relationships b. Using the math tool you identified above, determine if the five soccer players’ kicking distances are proportional to their kicking speed. Show your work and explain your answer in complete sentences. Support your explanation with evidence.
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Grade 7 Unit 1 Constructed Response Analyzing Proportional Relationships TASK 2: Constant of Proportionality and Proportional Relationships as Equations (CCSS: 7.RP.2b [m], 7.RP.2c [m]; SMP: 1, 3, 4, 5, 6, 8)
4. Analyze the information in the diagram below: $10.50 $7.00 $3.50
4 lbs.
8 lbs.
12 lbs.
a. Place the information from the diagram in an organized data table and determine whether the relationship is proportional.
b. Prove that your answer is correct by visually representing the data on another type of display that you have learned.
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Grade 7 Unit 1 Constructed Response Analyzing Proportional Relationships c. Based on your answer from part A, determine if there is a constant of proportionality. If so, identify it.
Answer: _______________________ 5. Stella works as a pet sitter during her summer vacation. Her pay is proportional to the number of hours she works for at a constant rate. a. Write an equation that best represents the relationship between her pay and the total number of hours she works. Choose variables to represent each component of your equation and explain what they represent.
b. What predictions can you make based on the relationship between her pay and the total number of hours she works?
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Grade 7 Unit 1 Constructed Response Analyzing Proportional Relationships 6. Use the equation you wrote in question 5a for the following questions. a. Assume that Stella charges $4.75 per hour for pet sitting. Create a table in which you show the total pay she will receive if she works for 3 hours, 5 hours, and 7 hours. Show your work.
b. After creating your table, write an explanation in which you discuss whether the predictions you made in question 5b were true. Support your discussion with evidence from the table you created.
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Grade 7 Unit 1 Constructed Response Analyzing Proportional Relationships TASK 3: Interpreting Graphs and Applications of Proportional Relationships (CCSS: 7.RP.2d [m], 7.RP.3 [m]; SMP: 1, 3, 6, 8)
7. Mitch took two days to drive to his Grandmother’s house. The graphs below show the miles and the time Mitch spent driving during those two days.
a. Interpret what each point (x, y) represents on each graph.
b. Interpret the origin (0, 0). What does this point represent in terms of the scenario given in the problem? Explain your reasoning.
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Grade 7 Unit 1 Constructed Response Analyzing Proportional Relationships c. Determine the unit rate r for each graph. Show your work.
Answer: Day 1: _____________________ Day 2: _____________________ d. Interpret the point (1, r) for each graph based on your answer from question 5c. Explain how you know this answer is reasonable based on your unit rate.
e. On which day did Mitch drive the most miles? Explain your answer with evidence from your answers above.
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Grade 7 Unit 1 Constructed Response Analyzing Proportional Relationships 8. Angela wants to purchase a sweater. The same style of sweater is available at two different stores on sale. Use the information in the table below to answer the following questions. Price
Discount (%)
Store 1
$22.50
15%
Store 2
$23.25
20%
a. Which of the two stores has the best price on the sweater after the discount? What is the new price of the sweater at this store? Show your work and round to the nearest hundredth if necessary.
Answer: Store: _______________________ Price: _______________________ b. Explain how you were able to determine your answer in question 8a. What steps were important in helping you find your answer?
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Grade 7 Unit 1 Constructed Response Analyzing Proportional Relationships c. Angela purchases the sweater from the store you identified above. Her total came out to $19.97 after tax. With this information and your answer from question 8a, find the percent of tax she was charged on the sweater. Show your work and round to the nearest hundredth if necessary.
Answer: ____________________ 9. a. Henry deposits $275 in an account that earns 6% interest every month. How much is in his account after 3 months? Show your work and round to the nearest hundredth if necessary.
Answer: _________________________ b. After the 3 months, Henry withdrawals 30% of his money to buy equipment for an upcoming camping trip. What is the new balance in his account after the withdrawal? Show your work and round to the nearest hundredth if necessary.
Answer: _________________________ Copyright © Swun Math Grade 7 Unit 1 Constructed Response, Page 11
Grade 7 Unit 1 Constructed Response Analyzing Proportional Relationships c. Using evidence from your work in questions 9b, explain and show how you know your answer is correct.
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Grade 7 Unit 1 Constructed Response Analyzing Proportional Relationships TASK 1: Ratios, Proportions, and Strategies for Testing Proportional Relationships (CCSS:7.RP.1 [m], 7.RP.2a [m]; SMP: 1, 2, 3, 4, 5)
1. Neil works at two different jobs during his summer vacation. The following table shows his earnings and hours worked at the two jobs. Job Bakery Pet Groomers
Money Earned $135 $120
Hours Worked 9 6
a. After analyzing the problem scenario and the information given, write an explanation of the meaning of the data. (What do the numbers represent? What units are used and how should they be classified? What is the unit rate?)
b. At which job did Neil get paid the most per hour? How much did he make per hour at that job? Show your work.
Answer: Job: _______________ Rate: ______________ c. In complete sentences, explain how you can prove that your answer is correct.
Copyright © Swun Math Grade 7 Unit 1 Constructed Response, Page 1
Grade 7 Unit 1 Constructed Response Analyzing Proportional Relationships 2. The table below shows number of laps Misty was able to swim in a certain amount of time each day. Day Tuesday Wednesday Thursday
Number of Laps 8 16 12
Time (mins) 14 28 21
a. Is the number of laps she swims proportional to how long it took her to complete the laps? In the table below, show and explain the process necessary to find your solution, and give a written explanation of your answer in complete sentences. Mathematical Process
Explanation of Steps
Answer:
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Grade 7 Unit 1 Constructed Response Analyzing Proportional Relationships b. Explain how your answer from above would be different if her swimming rate on Tuesday was 12 laps in 14 minutes.
3. The table below shows the mean kicking distance and kicking speed of five soccer players. Use this information to answer the following questions. Kicker 1 2 3 4 5
Distance (meters) 35 45 68 60 64
Speed (meters per second) 15 19 26 18 22
a. After analyzing the data in the table, identify a mathematical tool you could use to determine if there is a proportional relationship between the data. Explain how this tool would be helpful to use in this situation.
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Grade 7 Unit 1 Constructed Response Analyzing Proportional Relationships b. Using the math tool you identified above, determine if the five soccer players’ kicking distances are proportional to their kicking speed. Show your work and explain your answer in complete sentences. Support your explanation with evidence.
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Grade 7 Unit 1 Constructed Response Analyzing Proportional Relationships TASK 2: Constant of Proportionality and Proportional Relationships as Equations (CCSS: 7.RP.2b [m], 7.RP.2c [m]; SMP: 1, 3, 4, 5, 6, 8)
4. Analyze the information in the diagram below: $10.50 $7.00 $3.50
4 lbs.
8 lbs.
12 lbs.
a. Place the information from the diagram in an organized data table and determine whether the relationship is proportional.
b. Prove that your answer is correct by visually representing the data on another type of display that you have learned.
Copyright © Swun Math Grade 7 Unit 1 Constructed Response, Page 5
Grade 7 Unit 1 Constructed Response Analyzing Proportional Relationships c. Based on your answer from part A, determine if there is a constant of proportionality. If so, identify it.
Answer: _______________________ 5. Stella works as a pet sitter during her summer vacation. Her pay is proportional to the number of hours she works for at a constant rate. a. Write an equation that best represents the relationship between her pay and the total number of hours she works. Choose variables to represent each component of your equation and explain what they represent.
b. What predictions can you make based on the relationship between her pay and the total number of hours she works?
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Grade 7 Unit 1 Constructed Response Analyzing Proportional Relationships 6. Use the equation you wrote in question 5a for the following questions. a. Assume that Stella charges $4.75 per hour for pet sitting. Create a table in which you show the total pay she will receive if she works for 3 hours, 5 hours, and 7 hours. Show your work.
b. After creating your table, write an explanation in which you discuss whether the predictions you made in question 5b were true. Support your discussion with evidence from the table you created.
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Grade 7 Unit 1 Constructed Response Analyzing Proportional Relationships TASK 3: Interpreting Graphs and Applications of Proportional Relationships (CCSS: 7.RP.2d [m], 7.RP.3 [m]; SMP: 1, 3, 6, 8)
7. Mitch took two days to drive to his Grandmother’s house. The graphs below show the miles and the time Mitch spent driving during those two days.
a. Interpret what each point (x, y) represents on each graph.
b. Interpret the origin (0, 0). What does this point represent in terms of the scenario given in the problem? Explain your reasoning.
Copyright © Swun Math Grade 7 Unit 1 Constructed Response, Page 8
Grade 7 Unit 1 Constructed Response Analyzing Proportional Relationships c. Determine the unit rate r for each graph. Show your work.
Answer: Day 1: _____________________ Day 2: _____________________ d. Interpret the point (1, r) for each graph based on your answer from question 5c. Explain how you know this answer is reasonable based on your unit rate.
e. On which day did Mitch drive the most miles? Explain your answer with evidence from your answers above.
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Grade 7 Unit 1 Constructed Response Analyzing Proportional Relationships 8. Angela wants to purchase a sweater. The same style of sweater is available at two different stores on sale. Use the information in the table below to answer the following questions. Price
Discount (%)
Store 1
$22.50
15%
Store 2
$23.25
20%
a. Which of the two stores has the best price on the sweater after the discount? What is the new price of the sweater at this store? Show your work and round to the nearest hundredth if necessary.
Answer: Store: _______________________ Price: _______________________ b. Explain how you were able to determine your answer in question 8a. What steps were important in helping you find your answer?
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Grade 7 Unit 1 Constructed Response Analyzing Proportional Relationships c. Angela purchases the sweater from the store you identified above. Her total came out to $19.97 after tax. With this information and your answer from question 8a, find the percent of tax she was charged on the sweater. Show your work and round to the nearest hundredth if necessary.
Answer: ____________________ 9. a. Henry deposits $275 in an account that earns 6% interest every month. How much is in his account after 3 months? Show your work and round to the nearest hundredth if necessary.
Answer: _________________________ b. After the 3 months, Henry withdrawals 30% of his money to buy equipment for an upcoming camping trip. What is the new balance in his account after the withdrawal? Show your work and round to the nearest hundredth if necessary.
Answer: _________________________ Copyright © Swun Math Grade 7 Unit 1 Constructed Response, Page 11
Grade 7 Unit 1 Constructed Response Analyzing Proportional Relationships c. Using evidence from your work in questions 9b, explain and show how you know your answer is correct.
Copyright © Swun Math Grade 7 Unit 1 Constructed Response, Page 12
