G7 U2 Constructed Response
Name: ________________________________________ Date:_______________
Grade 7 Unit 2 Constructed Response Adding and Subtracting Rational Numbers TASK 1: Addition and Subtraction of Signed Rational Numbers (CCSS: 7.NS.1 c, d [m]; SMP: 1, 2, 3, 4, 5)
1. Christine is flying her kite at the beach. When she releases the kite it reaches a height of 65 ft. The wind begins to die down and the kite drops 15 feet in height. After a few minutes, the wind picks up again and the kite rises 30 feet. a. After reading the problem, write an equation that represents the situation described in the problem.
Answer: ________________________ b. Describe how each value and mathematical symbol in your equation relates to the situation described in the problem.
c. Using the expression you wrote above, find the final height of the kite. Show your work.
Answer: ____________________
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Grade 7 Unit 2 Constructed Response Adding and Subtracting Rational Numbers 2. The lowest point in the state of California is the Badwater Basin in Death Valley at −86.0 meters below sea level. The highest point in California is Mt. Whitney at 4,421.0 meters. a. After analyzing the information given, write an expression that can be used to find the distance between the highest and lowest points in California.
Answer: ___________________ b. Use this expression to find the distance between Mt. Whitney and the Badwater Basin. Show your work in detailed and organized steps.
Answer: ________________________ c. Using the data given and your answer form part b, create a diagram to demonstrate your understanding of this problem.
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Grade 7 Unit 2 Constructed Response Adding and Subtracting Rational Numbers d. Analyze your answer from above. Would it make sense for the distance between the two points to be negative? Explain your reasoning.
3. a. Solve the two expressions below. Show your work.
Answer:
Expression 1
Expression 2
12 + (−6)
12 − (−6)
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Grade 7 Unit 2 Constructed Response Adding and Subtracting Rational Numbers b. Read the scenarios below and determine which of the two expressions you solved for above matches each scenario. Write a brief explanation in which you justify your selections. Scenario A. The temperature in Juneau, Alaska at midnight was −6⁰F. By 10 am the next morning, the temperature was 12⁰F. What was the change in temperature? Matching Expression (circle one): Expression 1 / Expression 2 Explanation:
Scenario B. The temperature in Juneau, Alaska at noon was 12 ⁰F. The temperature fell 6⁰F by 6pm that same day. What was the final temperature? Matching Expression (circle one): Expression 1 / Expression 2 Explanation:
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Grade 7 Unit 2 Constructed Response Adding and Subtracting Rational Numbers TASK 2: Combining Opposite Quantities to Make Zero (CCSS: 7.NS.1a [m]; SMP: 1, 3, 4, 6, 8)
4. Use the number line below to answer the following questions.
t
0
s
a. If the point s and point t represent numbers that are the same distance from 0, what is the expression s + t equal to? Explain your reasoning.
b. Prove that your answer from part A is correct by plugging in two different sets of numerical values for s and t in the expression. Show your work for both examples. Example 1
Example 2
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Grade 7 Unit 2 Constructed Response Adding and Subtracting Rational Numbers 5. Bernard and his sister are going indoor rock climbing. After gearing up they climb 15 feet and stop for a break. They then go up another 17 feet before stopping again. They climb another 8 feet and make it to the top of the wall. They must now go back down. a. How many feet do they have to travel back down the wall to get to the floor? Show your work in detailed and organized steps.
Answer: ____________________ b. Create an illustration to show what is happening in this problem. Be sure to label each point Bernard and his sister stopped along the wall and the total distance they traveled both ways.
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Grade 7 Unit 2 Constructed Response Adding and Subtracting Rational Numbers 6. Pam deposits $125 to spend on supplies for her sister’s birthday party. The table below shows the party supplies she buys and how much she paid for them. Use this information to answer the following questions. Item Invitations Food and Drinks Balloons Cake
Cost $15.10 $85.95 $18.26 $45.12
a. What is the balance in Pam’s account after purchasing all the party supplies? Show your work.
Answer: ___________________ b. Create a number line to show what is happening in Pam’s account as she is purchasing the party supplies.
c. How much money does Pam need to deposit back into her account in order to have the same balance she had before the purchases were made? Explain your reasoning in complete sentences.
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Grade 7 Unit 2 Constructed Response Adding and Subtracting Rational Numbers TASK 3: Absolute Value and Distances (CCSS: 7.NS.1b [m]; SMP: 1, 3, 4, 6, 8)
7. Marlene encounters the following problem on a test: 25 + (−35) = −10. How far away is −10 from 25? Explain how you found your answer. Marlene’s answer: The distance between −10 and 25 is −35. To find my answer I had to add −35 to 25, which meant I had to move 35 spaces to the left on the number line. This left me at −10. a. After analyzing her answer, write a critique in which you identify and explain any errors in her answer and reasoning. Correct any errors in her reasoning.
b. What is the correct answer to the problem Marlene encountered on her test? Show your work in detailed and organized steps.
Answer: __________________
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Grade 7 Unit 2 Constructed Response Adding and Subtracting Rational Numbers 8. Examine the two expressions below: Expression 1 |−12 − |−12|| =
Expression 2 |−12 − |12|| =
a. Without solving the expressions, predict whether the solutions will be similar or different. Use your knowledge of absolute value to justify your predictions.
b. Solve each expression and determine if your prediction was true.
Answer: Expression 1: _____________ Expression 1: _____________
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Grade 7 Unit 2 Constructed Response Adding and Subtracting Rational Numbers 9. Kristi and her sister live north of their school. If they want to know how many feet they travel between the two locations, should they start measuring the distance from a.) their home to the school or b.) from their school to their home? Will the direction matter in their measurement? Explain your reasoning
Answer: _________________________ b. Create an illustration of the scenario to demonstrate that your answer from above is correct.
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Grade 7 Unit 2 Constructed Response Adding and Subtracting Rational Numbers TASK 1: Addition and Subtraction of Signed Rational Numbers (CCSS: 7.NS.1 c, d [m]; SMP: 1, 2, 3, 4, 5)
1. Christine is flying her kite at the beach. When she releases the kite it reaches a height of 65 ft. The wind begins to die down and the kite drops 15 feet in height. After a few minutes, the wind picks up again and the kite rises 30 feet. a. After reading the problem, write an equation that represents the situation described in the problem.
Answer: ________________________ b. Describe how each value and mathematical symbol in your equation relates to the situation described in the problem.
c. Using the expression you wrote above, find the final height of the kite. Show your work.
Answer: ____________________
Copyright © Swun Math Grade 7 Unit 2 Constructed Response, Page 1
Grade 7 Unit 2 Constructed Response Adding and Subtracting Rational Numbers 2. The lowest point in the state of California is the Badwater Basin in Death Valley at −86.0 meters below sea level. The highest point in California is Mt. Whitney at 4,421.0 meters. a. After analyzing the information given, write an expression that can be used to find the distance between the highest and lowest points in California.
Answer: ___________________ b. Use this expression to find the distance between Mt. Whitney and the Badwater Basin. Show your work in detailed and organized steps.
Answer: ________________________ c. Using the data given and your answer form part b, create a diagram to demonstrate your understanding of this problem.
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Grade 7 Unit 2 Constructed Response Adding and Subtracting Rational Numbers d. Analyze your answer from above. Would it make sense for the distance between the two points to be negative? Explain your reasoning.
3. a. Solve the two expressions below. Show your work.
Answer:
Expression 1
Expression 2
12 + (−6)
12 − (−6)
Answer: Copyright © Swun Math Grade 7 Unit 2 Constructed Response, Page 3
Grade 7 Unit 2 Constructed Response Adding and Subtracting Rational Numbers b. Read the scenarios below and determine which of the two expressions you solved for above matches each scenario. Write a brief explanation in which you justify your selections. Scenario A. The temperature in Juneau, Alaska at midnight was −6⁰F. By 10 am the next morning, the temperature was 12⁰F. What was the change in temperature? Matching Expression (circle one): Expression 1 / Expression 2 Explanation:
Scenario B. The temperature in Juneau, Alaska at noon was 12 ⁰F. The temperature fell 6⁰F by 6pm that same day. What was the final temperature? Matching Expression (circle one): Expression 1 / Expression 2 Explanation:
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Grade 7 Unit 2 Constructed Response Adding and Subtracting Rational Numbers TASK 2: Combining Opposite Quantities to Make Zero (CCSS: 7.NS.1a [m]; SMP: 1, 3, 4, 6, 8)
4. Use the number line below to answer the following questions.
t
0
s
a. If the point s and point t represent numbers that are the same distance from 0, what is the expression s + t equal to? Explain your reasoning.
b. Prove that your answer from part A is correct by plugging in two different sets of numerical values for s and t in the expression. Show your work for both examples. Example 1
Example 2
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Grade 7 Unit 2 Constructed Response Adding and Subtracting Rational Numbers 5. Bernard and his sister are going indoor rock climbing. After gearing up they climb 15 feet and stop for a break. They then go up another 17 feet before stopping again. They climb another 8 feet and make it to the top of the wall. They must now go back down. a. How many feet do they have to travel back down the wall to get to the floor? Show your work in detailed and organized steps.
Answer: ____________________ b. Create an illustration to show what is happening in this problem. Be sure to label each point Bernard and his sister stopped along the wall and the total distance they traveled both ways.
Copyright © Swun Math Grade 7 Unit 2 Constructed Response, Page 6
Grade 7 Unit 2 Constructed Response Adding and Subtracting Rational Numbers 6. Pam deposits $125 to spend on supplies for her sister’s birthday party. The table below shows the party supplies she buys and how much she paid for them. Use this information to answer the following questions. Item Invitations Food and Drinks Balloons Cake
Cost $15.10 $85.95 $18.26 $45.12
a. What is the balance in Pam’s account after purchasing all the party supplies? Show your work.
Answer: ___________________ b. Create a number line to show what is happening in Pam’s account as she is purchasing the party supplies.
c. How much money does Pam need to deposit back into her account in order to have the same balance she had before the purchases were made? Explain your reasoning in complete sentences.
Copyright © Swun Math Grade 7 Unit 2 Constructed Response, Page 7
Grade 7 Unit 2 Constructed Response Adding and Subtracting Rational Numbers TASK 3: Absolute Value and Distances (CCSS: 7.NS.1b [m]; SMP: 1, 3, 4, 6, 8)
7. Marlene encounters the following problem on a test: 25 + (−35) = −10. How far away is −10 from 25? Explain how you found your answer. Marlene’s answer: The distance between −10 and 25 is −35. To find my answer I had to add −35 to 25, which meant I had to move 35 spaces to the left on the number line. This left me at −10. a. After analyzing her answer, write a critique in which you identify and explain any errors in her answer and reasoning. Correct any errors in her reasoning.
b. What is the correct answer to the problem Marlene encountered on her test? Show your work in detailed and organized steps.
Answer: __________________
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Grade 7 Unit 2 Constructed Response Adding and Subtracting Rational Numbers 8. Examine the two expressions below: Expression 1 |−12 − |−12|| =
Expression 2 |−12 − |12|| =
a. Without solving the expressions, predict whether the solutions will be similar or different. Use your knowledge of absolute value to justify your predictions.
b. Solve each expression and determine if your prediction was true.
Answer: Expression 1: _____________ Expression 1: _____________
Copyright © Swun Math Grade 7 Unit 2 Constructed Response, Page 9
Grade 7 Unit 2 Constructed Response Adding and Subtracting Rational Numbers 9. Kristi and her sister live north of their school. If they want to know how many feet they travel between the two locations, should they start measuring the distance from a.) their home to the school or b.) from their school to their home? Will the direction matter in their measurement? Explain your reasoning
Answer: _________________________ b. Create an illustration of the scenario to demonstrate that your answer from above is correct.
Copyright © Swun Math Grade 7 Unit 2 Constructed Response, Page 10
