G6 U5 Constructed Response
Name: ________________________________________ Date:_______________
Grade 6 Unit 5 Constructed Response Inequalities TASK 1: Writing and Solving Expressions and Equations; Independent and Dependent Variables (CCSS 6.EE.5, 6.EE.6, 6.EE.7, 6.EE.8; SMP 1, 2, 4, 6, 7, 8)
1. In the table below, create a model, a phrase and a word problem to represent the expression. 15 + 4𝑠 Representation: a. Model:
b. Phrase:
c. Word Problem:
Copyright © Swun Math Grade 6 Unit 5 Constructed Response, Page 1
Grade 6 Unit 5 Constructed Response Inequalities 2. Marshall took a summer job as a dog groomer for one week. He worked at a rate of $15 per hour and charged an additional supply fee of $10. If he made $250 that week, how many hours did he work? a. Write an equation that can be used to find the total hours Marshall worked during the week, and identify your variable and what it represents. Answers: Equation: _____________________________ Variable: _____________________________ b. Explain how you found the equation. What pieces of information in the scenario helped you to write this equation?
c. Using the equation you wrote, find how many hours Marshall worked during the week. Show your work in detailed and organized steps.
Answer: ___________________
Copyright © Swun Math Grade 6 Unit 5 Constructed Response, Page 2
Grade 6 Unit 5 Constructed Response Inequalities 3. Christina and her sister are baking and selling cookies to raise money for a trip. They need to raise $560 to help pay for the cost of the trip. They are selling their cookies in packages for a price of $8. a. Identify the independent and dependent variables, and write an equation using the variable p for profit, and c for the number of packages of cookies sold. Answers: Independent Variable: _____________________________ Dependent Variable: _____________________________ Equation: _____________________________ b. Create a table of values (t-chart) to find the profit made from 4, 8, 12, 16, 20, and 24 packages of cookies sold.
Copyright © Swun Math Grade 6 Unit 5 Constructed Response, Page 3
Grade 6 Unit 5 Constructed Response Inequalities c. Graph the equation using the ordered pairs from the table of values you created. Label the x and y-axis appropriately, and connect your points with a straight line.
d. How many packages of cookies do Christina and her sister need to sell in order to make their goal of $560?
Answer: ______________________
Copyright © Swun Math Grade 6 Unit 5 Constructed Response, Page 4
Grade 6 Unit 5 Constructed Response Inequalities TASK 2: Writing and Solving Inequalities (CCSS: 6.EE.3, 6.EE.5; SMP: 1, 2, 3, 4, 6, 7)
4. Analyze the rectangle below: L
7 ft
If the perimeter of the rectangle can be no more than 38 ft, what is the maximum length of L? a. Write the inequality that can be used to find the maximum length of L. Answer: Inequality: _____________________________ b. Explain how you found the inequality. Were there any mathematical concepts you have learned that helped you write the inequality?
Copyright © Swun Math Grade 6 Unit 5 Constructed Response, Page 5
Grade 6 Unit 5 Constructed Response Inequalities c. Using the equation you wrote, find the maximum length of L . Show your work in detailed and organized steps.
Answer: ___________________ 5. Marilyn works at her aunt’s ice cream shop in town. This month she wants to make at least $437 in order to purchase a new bike and have some money left over. If she works at an hourly rate of $9.50, what is the minimum number of hours she needs to work to reach her monthly goal? a. Write the inequality that can be used to find the minimum number of hours Marilyn needs to work during the month to reach her goal. Answer: Inequality: _____________________________
b. Using the inequality you wrote, find the minimum number of hours Marilyn needs to work in order to reach her monthly goal. Show your work in detailed and organized steps.
Answer: ___________________ Copyright © Swun Math Grade 6 Unit 5 Constructed Response, Page 6
Grade 6 Unit 5 Constructed Response Inequalities 6. Samantha is in the first month of her training for a half marathon and she is trying to run at least 4 miles a day, Monday through Saturday. She averages 31 miles a week. The table below shows how many miles she completed so far during the week: Day: Monday
Miles 4
Tuesday
6
Wednesday
5
Thursday
7
Friday
4
a. Using the information given in the problem, write an inequality that can be used to find how many more miles Samantha needs to run to exceed her weekly average.
Answer: ___________________________ b. Using the inequality, find how many more miles Samantha needs to run to exceed her weekly average.
Answer: ___________________
Copyright © Swun Math Grade 6 Unit 5 Constructed Response, Page 7
Grade 6 Unit 5 Constructed Response Inequalities c. In the table below show and explain how you can test your answer to prove it is correct. Process:
Explanation:
Copyright © Swun Math Grade 6 Unit 5 Constructed Response, Page 8
Grade 6 Unit 5 Constructed Response Inequalities TASK 3: Graphing Inequalities on a Number line (CCSS: 6.EE.8; SMP: 1, 2, 3, 4, 6, 7)
7. Cora is taking a test and one of her questions involves writing and graphing the inequality that represents the following statement: The number of swimmers in class must be at least 25 students. Cora’s Answer: s > 25 Cora’s number line: 23 24 25
26 27 28 29
a. After analyzing Cora’s work, determine if her answers are correct or incorrect. Explain how you know whether her answers are correct. If Cora is incorrect, identify her error(s) and correct any flaws in her inequality and graph.
b. If Cora was incorrect, rewrite and graph her inequality to match the statement she was given. Give your answers in the table below. Inequality: Number Line:
Copyright © Swun Math Grade 6 Unit 5 Constructed Response, Page 9
Grade 6 Unit 5 Constructed Response Inequalities 8. Adrienne wants to create a budget for her monthly expenses. For the month of June she wants to spend less than $300 on groceries, and she wants to save at least $275. a. Write an inequality that best represents the amount of money she wants to spend on groceries, and an inequality for the amount of money she wants to save. Answers: _______________________ _______________________ b. In the table below, graph each inequality you wrote. Money Spent on Groceries:
Money Saved:
Copyright © Swun Math Grade 6 Unit 5 Constructed Response, Page 10
Grade 6 Unit 5 Constructed Response Inequalities 9. Jackson and James are competing in a toy boat race with their dad. The boat needs to be built in 45 days, at the most, in order to be ready for the race. a. Write an inequality that best represents this scenario. Answer: _______________________ b. Graph the inequality you wrote on a number line.
c. After creating your number line, write a discussion in which you explain how your number line represents the scenario and the inequality you wrote.
d. Based on the information you were given in the problem and your number line, give three possible solutions for the inequality. Explain how you know your answer is correct by referencing your work.
Copyright © Swun Math Grade 6 Unit 5 Constructed Response, Page 11
Grade 6 Unit 5 Constructed Response Inequalities TASK 1: Writing and Solving Expressions and Equations; Independent and Dependent Variables (CCSS 6.EE.5, 6.EE.6, 6.EE.7, 6.EE.8; SMP 1, 2, 4, 6, 7, 8)
1. In the table below, create a model, a phrase and a word problem to represent the expression. 15 + 4𝑠 Representation: a. Model:
b. Phrase:
c. Word Problem:
Copyright © Swun Math Grade 6 Unit 5 Constructed Response, Page 1
Grade 6 Unit 5 Constructed Response Inequalities 2. Marshall took a summer job as a dog groomer for one week. He worked at a rate of $15 per hour and charged an additional supply fee of $10. If he made $250 that week, how many hours did he work? a. Write an equation that can be used to find the total hours Marshall worked during the week, and identify your variable and what it represents. Answers: Equation: _____________________________ Variable: _____________________________ b. Explain how you found the equation. What pieces of information in the scenario helped you to write this equation?
c. Using the equation you wrote, find how many hours Marshall worked during the week. Show your work in detailed and organized steps.
Answer: ___________________
Copyright © Swun Math Grade 6 Unit 5 Constructed Response, Page 2
Grade 6 Unit 5 Constructed Response Inequalities 3. Christina and her sister are baking and selling cookies to raise money for a trip. They need to raise $560 to help pay for the cost of the trip. They are selling their cookies in packages for a price of $8. a. Identify the independent and dependent variables, and write an equation using the variable p for profit, and c for the number of packages of cookies sold. Answers: Independent Variable: _____________________________ Dependent Variable: _____________________________ Equation: _____________________________ b. Create a table of values (t-chart) to find the profit made from 4, 8, 12, 16, 20, and 24 packages of cookies sold.
Copyright © Swun Math Grade 6 Unit 5 Constructed Response, Page 3
Grade 6 Unit 5 Constructed Response Inequalities c. Graph the equation using the ordered pairs from the table of values you created. Label the x and y-axis appropriately, and connect your points with a straight line.
d. How many packages of cookies do Christina and her sister need to sell in order to make their goal of $560?
Answer: ______________________
Copyright © Swun Math Grade 6 Unit 5 Constructed Response, Page 4
Grade 6 Unit 5 Constructed Response Inequalities TASK 2: Writing and Solving Inequalities (CCSS: 6.EE.3, 6.EE.5; SMP: 1, 2, 3, 4, 6, 7)
4. Analyze the rectangle below: L
7 ft
If the perimeter of the rectangle can be no more than 38 ft, what is the maximum length of L? a. Write the inequality that can be used to find the maximum length of L. Answer: Inequality: _____________________________ b. Explain how you found the inequality. Were there any mathematical concepts you have learned that helped you write the inequality?
Copyright © Swun Math Grade 6 Unit 5 Constructed Response, Page 5
Grade 6 Unit 5 Constructed Response Inequalities c. Using the equation you wrote, find the maximum length of L . Show your work in detailed and organized steps.
Answer: ___________________ 5. Marilyn works at her aunt’s ice cream shop in town. This month she wants to make at least $437 in order to purchase a new bike and have some money left over. If she works at an hourly rate of $9.50, what is the minimum number of hours she needs to work to reach her monthly goal? a. Write the inequality that can be used to find the minimum number of hours Marilyn needs to work during the month to reach her goal. Answer: Inequality: _____________________________
b. Using the inequality you wrote, find the minimum number of hours Marilyn needs to work in order to reach her monthly goal. Show your work in detailed and organized steps.
Answer: ___________________ Copyright © Swun Math Grade 6 Unit 5 Constructed Response, Page 6
Grade 6 Unit 5 Constructed Response Inequalities 6. Samantha is in the first month of her training for a half marathon and she is trying to run at least 4 miles a day, Monday through Saturday. She averages 31 miles a week. The table below shows how many miles she completed so far during the week: Day: Monday
Miles 4
Tuesday
6
Wednesday
5
Thursday
7
Friday
4
a. Using the information given in the problem, write an inequality that can be used to find how many more miles Samantha needs to run to exceed her weekly average.
Answer: ___________________________ b. Using the inequality, find how many more miles Samantha needs to run to exceed her weekly average.
Answer: ___________________
Copyright © Swun Math Grade 6 Unit 5 Constructed Response, Page 7
Grade 6 Unit 5 Constructed Response Inequalities c. In the table below show and explain how you can test your answer to prove it is correct. Process:
Explanation:
Copyright © Swun Math Grade 6 Unit 5 Constructed Response, Page 8
Grade 6 Unit 5 Constructed Response Inequalities TASK 3: Graphing Inequalities on a Number line (CCSS: 6.EE.8; SMP: 1, 2, 3, 4, 6, 7)
7. Cora is taking a test and one of her questions involves writing and graphing the inequality that represents the following statement: The number of swimmers in class must be at least 25 students. Cora’s Answer: s > 25 Cora’s number line: 23 24 25
26 27 28 29
a. After analyzing Cora’s work, determine if her answers are correct or incorrect. Explain how you know whether her answers are correct. If Cora is incorrect, identify her error(s) and correct any flaws in her inequality and graph.
b. If Cora was incorrect, rewrite and graph her inequality to match the statement she was given. Give your answers in the table below. Inequality: Number Line:
Copyright © Swun Math Grade 6 Unit 5 Constructed Response, Page 9
Grade 6 Unit 5 Constructed Response Inequalities 8. Adrienne wants to create a budget for her monthly expenses. For the month of June she wants to spend less than $300 on groceries, and she wants to save at least $275. a. Write an inequality that best represents the amount of money she wants to spend on groceries, and an inequality for the amount of money she wants to save. Answers: _______________________ _______________________ b. In the table below, graph each inequality you wrote. Money Spent on Groceries:
Money Saved:
Copyright © Swun Math Grade 6 Unit 5 Constructed Response, Page 10
Grade 6 Unit 5 Constructed Response Inequalities 9. Jackson and James are competing in a toy boat race with their dad. The boat needs to be built in 45 days, at the most, in order to be ready for the race. a. Write an inequality that best represents this scenario. Answer: _______________________ b. Graph the inequality you wrote on a number line.
c. After creating your number line, write a discussion in which you explain how your number line represents the scenario and the inequality you wrote.
d. Based on the information you were given in the problem and your number line, give three possible solutions for the inequality. Explain how you know your answer is correct by referencing your work.
Copyright © Swun Math Grade 6 Unit 5 Constructed Response, Page 11
