G7 U3 Constructed Response
Name: ________________________________________ Date:_______________
Grade 7 Unit 3 Constructed Response Multiplying and Dividing Rational Numbers TASK 1: Multiplication of Signed Rational Numbers (CCSS: 7. NS.2 a, c [m]; SMP: 1, 2, 4)
1. Analyze the two expressions below: Expression A: −9 • 4 Expression B: −9 • −4 a. Without solving each expression, write an explanation in which you compare and contrast the possible answer for each expression. How will the answers be the same? How will they be different?
b. Solve each expression from above using a number line. Show your work by creating a number line for each expression.
Answer: Expression A: ________________________
Answer: Expression B: ________________________ Copyright © Swun Math Grade 7 Unit 3 Constructed Response, Page 1
Grade 7 Unit 3 Constructed Response Multiplying and Dividing Rational Numbers 2. During her summer vacation, Cassidy works two small jobs in her neighborhood to earn extra money in addition to her weekly allowance. She works a paper route on Tuesdays where she earns $30, walks her neighbor’s dog three days a week where she earns $15, and gets her weekly allowance of $20 on Sundays. Each week she spends $10 of her earnings on activities with her friends. After 8 weeks how much money has Casey saved up? a. After reading and analyzing the information given, write an explanation of the meaning of the problem and describe a starting point for solving the problem.
b. Write the expression which best represents what the problem is asking you to find.
Answer: ________________________ c. Solve the expression you wrote above. Show your work in organized and detailed steps.
Answer: ________________________ Copyright © Swun Math Grade 7 Unit 3 Constructed Response, Page 2
Grade 7 Unit 3 Constructed Response Multiplying and Dividing Rational Numbers d. After finding the solution to the problem, identify the property you used to find this solution. Explain how you used this property by referencing your work and solutions from above.
3. Walter and his brother are helping plant young orange trees on their grandfather’s farm. They plant 12 orange trees in an hour and a half on the first day. During that hour and a half, they took a ten minute water break. Their grandfather decides to pay them $7 for every tree they plant. If they work at this same rate for 4 days, how much money will the boys earn? a. Analyze the information given in the problem. Identify any pieces of information that are important in finding the solution and explain how you were able to determine the importance of this information. Is there any extra information that is not useful in this situation?
Copyright © Swun Math Grade 7 Unit 3 Constructed Response, Page 3
Grade 7 Unit 3 Constructed Response Multiplying and Dividing Rational Numbers b. Write the expression that can be used to find the solution to this problem.
Answer: ____________________ c. Find the solution to this problem using your expression from above. Show your work in detailed and organized steps.
Answer: ____________________ d. Identify the mathematical operation that was important when finding the solution. Explain how you knew this operation would be the most effective in this situation.
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Grade 7 Unit 3 Constructed Response Multiplying and Dividing Rational Numbers TASK 2: Division of Signed Rational Numbers (CCSS: 7.NS.2b [m], 7.NS.2c [m]; SMP: 1, 2, 3, 4, 7, 8 )
4. Analyze the expression below: −
3 45 ÷ 5 70
a. Before solving the expression, explain the strategy you will use to solve this problem.
b. Using the strategy you described above, solve the expression. Show your work in detailed and organized steps.
Answer: __________________________ c. Explain how you could prove that your answer is correct. Is there a mathematical operation that would be important in this process?
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Grade 7 Unit 3 Constructed Response Multiplying and Dividing Rational Numbers d. Using your strategy show that your answer is correct. Show your work in detailed and organized steps.
1
5. Camilla’s current running pace is 8 minutes per mile, and today she wants 2 to run for 50 minutes. Before she heads out for her run she wants to calculate how many miles she will be running in those 50 minutes. She is unsure of the process to do this, so she sets up the following expressions: 1
Expression 1:
8
Expression 2:
50 ÷ 8
2
÷ 50 1 2
a. After analyzing the information given, determine which of the two expressions is correct for her to use in this situation. Justify your answer, and explain why the other expression would not be correct for her to use in this situation.
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Grade 7 Unit 3 Constructed Response Multiplying and Dividing Rational Numbers b. Using the expression you selected as correct from above, find the total number of miles Camilla will run in 50 minutes. Show your work in detailed and organized steps. Give your answer in fractional form if necessary.
Answer: ______________________ 6. a. Solve the expression below. Show your work in detailed and organized steps. (−
220 4 80 ) ÷ (12 ) ÷ (− ) 440 10 310
Answer: ______________________ Copyright © Swun Math Grade 7 Unit 3 Constructed Response, Page 7
Grade 7 Unit 3 Constructed Response Multiplying and Dividing Rational Numbers b. After solving the problem, compare and contrast this expression to the one you encountered in Question 4. How was the process to solve each expression different? How was the process similar?
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Grade 7 Unit 3 Constructed Response Multiplying and Dividing Rational Numbers TASK 3: Converting Rational Numbers to Decimals (CCSS: 7.NS.2d [m]; SMP: 1, 2, 4, 6, 7)
7. Analyze each fraction below. Find the decimal form of each fraction to five decimal places, and identify the decimal as irrational, repeating, or terminating. Justify your answers using your knowledge about these types of numbers. Show your work in detailed and organized steps. a.
35 68
Answer: ____________________ Circle One: Irrational / Repeating / Terminating Explanation:
b.
11 33
Answer: ____________________ Circle One: Irrational / Repeating / Terminating Copyright © Swun Math Grade 7 Unit 3 Constructed Response, Page 9
Grade 7 Unit 3 Constructed Response Multiplying and Dividing Rational Numbers Explanation:
c. 2
45 60
Answer: ____________________ Circle One: Irrational / Repeating / Terminating Explanation:
8. Analyze the equation below: 2 17 9 8 2 + ÷( • ) 8 8 15 12 a. Rewrite the equation with each rational number expressed in decimal form. If needed, calculate to three decimal places. Show your work in detailed and organized steps.
Answer: ___________________ Copyright © Swun Math Grade 7 Unit 3 Constructed Response, Page 10
Grade 7 Unit 3 Constructed Response Multiplying and Dividing Rational Numbers b. Solve the equation you wrote above and give your answer to two decimal places.
Answer: ___________________ c. After solving the equation, identify and explain any rules or properties that were important in finding the correct solution to the problem.
d. Would converting rational numbers to decimals be practical when solving everyday problems involving fractions? Why or why not?
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Grade 7 Unit 3 Constructed Response Multiplying and Dividing Rational Numbers 9. Samantha and Christopher buy an ice cream cake for their sister’s birthday 2 party. After serving everyone at the party, about of the cake is eaten. Some 5
guests come back for seconds, and they eat about
3
10
more of the cake.
a. Using the information above, develop a strategy to find how much of the ice cream cake was eaten at the party. Show your work in detailed and organized steps. Give your answer in both fractional and decimal form.
Answer: Fraction: ______________ Decimal: ______________ b. Write an explanation in which you describe the strategy you used to find your solution. Would a different strategy have been more effective in finding the solution? Justify your reasoning by referencing your own work and solutions.
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Grade 7 Unit 3 Constructed Response Multiplying and Dividing Rational Numbers TASK 1: Multiplication of Signed Rational Numbers (CCSS: 7. NS.2 a, c [m]; SMP: 1, 2, 4)
1. Analyze the two expressions below: Expression A: −9 • 4 Expression B: −9 • −4 a. Without solving each expression, write an explanation in which you compare and contrast the possible answer for each expression. How will the answers be the same? How will they be different?
b. Solve each expression from above using a number line. Show your work by creating a number line for each expression.
Answer: Expression A: ________________________
Answer: Expression B: ________________________ Copyright © Swun Math Grade 7 Unit 3 Constructed Response, Page 1
Grade 7 Unit 3 Constructed Response Multiplying and Dividing Rational Numbers 2. During her summer vacation, Cassidy works two small jobs in her neighborhood to earn extra money in addition to her weekly allowance. She works a paper route on Tuesdays where she earns $30, walks her neighbor’s dog three days a week where she earns $15, and gets her weekly allowance of $20 on Sundays. Each week she spends $10 of her earnings on activities with her friends. After 8 weeks how much money has Casey saved up? a. After reading and analyzing the information given, write an explanation of the meaning of the problem and describe a starting point for solving the problem.
b. Write the expression which best represents what the problem is asking you to find.
Answer: ________________________ c. Solve the expression you wrote above. Show your work in organized and detailed steps.
Answer: ________________________ Copyright © Swun Math Grade 7 Unit 3 Constructed Response, Page 2
Grade 7 Unit 3 Constructed Response Multiplying and Dividing Rational Numbers d. After finding the solution to the problem, identify the property you used to find this solution. Explain how you used this property by referencing your work and solutions from above.
3. Walter and his brother are helping plant young orange trees on their grandfather’s farm. They plant 12 orange trees in an hour and a half on the first day. During that hour and a half, they took a ten minute water break. Their grandfather decides to pay them $7 for every tree they plant. If they work at this same rate for 4 days, how much money will the boys earn? a. Analyze the information given in the problem. Identify any pieces of information that are important in finding the solution and explain how you were able to determine the importance of this information. Is there any extra information that is not useful in this situation?
Copyright © Swun Math Grade 7 Unit 3 Constructed Response, Page 3
Grade 7 Unit 3 Constructed Response Multiplying and Dividing Rational Numbers b. Write the expression that can be used to find the solution to this problem.
Answer: ____________________ c. Find the solution to this problem using your expression from above. Show your work in detailed and organized steps.
Answer: ____________________ d. Identify the mathematical operation that was important when finding the solution. Explain how you knew this operation would be the most effective in this situation.
Copyright © Swun Math Grade 7 Unit 3 Constructed Response, Page 4
Grade 7 Unit 3 Constructed Response Multiplying and Dividing Rational Numbers TASK 2: Division of Signed Rational Numbers (CCSS: 7.NS.2b [m], 7.NS.2c [m]; SMP: 1, 2, 3, 4, 7, 8 )
4. Analyze the expression below: −
3 45 ÷ 5 70
a. Before solving the expression, explain the strategy you will use to solve this problem.
b. Using the strategy you described above, solve the expression. Show your work in detailed and organized steps.
Answer: __________________________ c. Explain how you could prove that your answer is correct. Is there a mathematical operation that would be important in this process?
Copyright © Swun Math Grade 7 Unit 3 Constructed Response, Page 5
Grade 7 Unit 3 Constructed Response Multiplying and Dividing Rational Numbers d. Using your strategy show that your answer is correct. Show your work in detailed and organized steps.
1
5. Camilla’s current running pace is 8 minutes per mile, and today she wants 2 to run for 50 minutes. Before she heads out for her run she wants to calculate how many miles she will be running in those 50 minutes. She is unsure of the process to do this, so she sets up the following expressions: 1
Expression 1:
8
Expression 2:
50 ÷ 8
2
÷ 50 1 2
a. After analyzing the information given, determine which of the two expressions is correct for her to use in this situation. Justify your answer, and explain why the other expression would not be correct for her to use in this situation.
Copyright © Swun Math Grade 7 Unit 3 Constructed Response, Page 6
Grade 7 Unit 3 Constructed Response Multiplying and Dividing Rational Numbers b. Using the expression you selected as correct from above, find the total number of miles Camilla will run in 50 minutes. Show your work in detailed and organized steps. Give your answer in fractional form if necessary.
Answer: ______________________ 6. a. Solve the expression below. Show your work in detailed and organized steps. (−
220 4 80 ) ÷ (12 ) ÷ (− ) 440 10 310
Answer: ______________________ Copyright © Swun Math Grade 7 Unit 3 Constructed Response, Page 7
Grade 7 Unit 3 Constructed Response Multiplying and Dividing Rational Numbers b. After solving the problem, compare and contrast this expression to the one you encountered in Question 4. How was the process to solve each expression different? How was the process similar?
Copyright © Swun Math Grade 7 Unit 3 Constructed Response, Page 8
Grade 7 Unit 3 Constructed Response Multiplying and Dividing Rational Numbers TASK 3: Converting Rational Numbers to Decimals (CCSS: 7.NS.2d [m]; SMP: 1, 2, 4, 6, 7)
7. Analyze each fraction below. Find the decimal form of each fraction to five decimal places, and identify the decimal as irrational, repeating, or terminating. Justify your answers using your knowledge about these types of numbers. Show your work in detailed and organized steps. a.
35 68
Answer: ____________________ Circle One: Irrational / Repeating / Terminating Explanation:
b.
11 33
Answer: ____________________ Circle One: Irrational / Repeating / Terminating Copyright © Swun Math Grade 7 Unit 3 Constructed Response, Page 9
Grade 7 Unit 3 Constructed Response Multiplying and Dividing Rational Numbers Explanation:
c. 2
45 60
Answer: ____________________ Circle One: Irrational / Repeating / Terminating Explanation:
8. Analyze the equation below: 2 17 9 8 2 + ÷( • ) 8 8 15 12 a. Rewrite the equation with each rational number expressed in decimal form. If needed, calculate to three decimal places. Show your work in detailed and organized steps.
Answer: ___________________ Copyright © Swun Math Grade 7 Unit 3 Constructed Response, Page 10
Grade 7 Unit 3 Constructed Response Multiplying and Dividing Rational Numbers b. Solve the equation you wrote above and give your answer to two decimal places.
Answer: ___________________ c. After solving the equation, identify and explain any rules or properties that were important in finding the correct solution to the problem.
d. Would converting rational numbers to decimals be practical when solving everyday problems involving fractions? Why or why not?
Copyright © Swun Math Grade 7 Unit 3 Constructed Response, Page 11
Grade 7 Unit 3 Constructed Response Multiplying and Dividing Rational Numbers 9. Samantha and Christopher buy an ice cream cake for their sister’s birthday 2 party. After serving everyone at the party, about of the cake is eaten. Some 5
guests come back for seconds, and they eat about
3
10
more of the cake.
a. Using the information above, develop a strategy to find how much of the ice cream cake was eaten at the party. Show your work in detailed and organized steps. Give your answer in both fractional and decimal form.
Answer: Fraction: ______________ Decimal: ______________ b. Write an explanation in which you describe the strategy you used to find your solution. Would a different strategy have been more effective in finding the solution? Justify your reasoning by referencing your own work and solutions.
Copyright © Swun Math Grade 7 Unit 3 Constructed Response, Page 12
