
	Item 14 Anchor Papers

HSA 2008 Algebra/Data Analysis Item 14

CID: CID1da71d60a1656cfaded67d132e3d594a
itemNum: 14
initialLetter
itemType: ECR
itemAnswerKey: N/A
itemMaxScorePoints: 4
origNum: 21

Jared wants to rent a carpet cleaner. The table below shows the cost of renting a carpet cleaner.

Complete the following in the Answer Book:

Complete the table to show the cost of renting a carpet cleaner for 5 and 6 hours if this pattern continues.
Write an equation to represent the relationship between the cost of renting a carpet cleaner and the number of hours that a carpet cleaner is rented.
If Jared has $60, can he rent the carpet cleaner for 9 hours? Use mathematics to explain how you determined your answer. Use words, symbols, or both in your explanation.
The store also sells the same carpet cleaner for $165, including tax. What is the maximum number of hours that the cost of renting the carpet cleaner is less than the cost of buying the carpet cleaner? Use mathematics to justify your answer.

Score Level 1 Anchor Paper
This response indicates little application of a reasonable strategy. The correct costs for 5 and 6 hours of carpet cleaner rental are given (the last two numbers for the table would be 40 and 46). The student provides no response to the second, third or fourth parts of the question. This response demonstrates a minimal understanding and analysis of the problem.
Score Level 1 Anchor Paper
This response indicates little application of a reasonable strategy. The representation in the form of an equation is correct (y=6x+10). The student provides no response to the first, third or fourth parts of the question. The response demonstrates a minimal understanding and analysis of the problem.
Score Level 2 Anchor Paper
This response indicates application of an incomplete strategy. The table is correctly completed. The representation in the form of an equation is correct (y=6x+10). The student indicates that the carpet cleaner cannot be rented for 9 hours if Jared has $60. An explanation is not given. The student provides no response to the fourth part of the question. This response demonstrates a conceptual understanding and analysis of the problem.
Score Level 2 Anchor Paper
This response indicates application of an incomplete strategy. The table is correctly completed. The student indicates that the carpet cleaner cannot be rented for 9 hours if Jared has $60. The explanation supports the solution. The student extends the tabular pattern to 9 hours then writes (because it would be $64 for 9 hours. Jared only had $60 so he can rent the carpet cleaner for 8 hours for $58 and still stay in budget). The student provides no response to the second or fourth parts of the question. This response demonstrates a conceptual understanding and analysis of the problem.
Score Level 3 Anchor Paper
This response indicates application of a reasonable strategy that leads to some correct solutions. The correct costs for 5 and 6 hours of carpet cleaner rental are given (5 hours-$40; 6 hours-$46). The representation in the form of an equation is correct (Hx6+10=C). The student indicates that the carpet cleaner cannot be rented for 9 hours if Jared has $60. The student provides a generally well developed justification, rather than an explanation (because it will cost him $64. He will be over the $60). The maximum number of hours that the cost of renting the carpet cleaner is less than the cost of buying the carpet cleaner is incorrect (15). While the justification supports the solution, the student did not use his equation correctly (I got that by doing 15x10+6=$156). This response demonstrates a clear understanding and analysis of the problem.
Score Level 3 Anchor Paper
This response indicates application of a reasonable strategy that leads to some correct solutions. The table is correctly completed. The representation in the form of an equation is correct (y=6x+10). The student indicates that the carpet cleaner cannot be rented for 9 hours if Jared has $60. The explanation supports the solution (y=6(9)+10; y=54+10; y=64). The maximum number of hours that the cost of renting the carpet cleaner is less than the cost of buying the carpet cleaner is correct (25 hours). A justification is not given. This response demonstrates a clear understanding and analysis of the problem.
Score Level 4 Anchor Paper
This response indicates application of a reasonable strategy that leads to a correct solution within the context of the problem. The table is correctly completed. The representation in the form of an equation is correct (y=6x+10). The student indicates that the carpet cleaner cannot be rented for 9 hours if Jared has $60. The explanation is clearly presented and fully developed (Frist I would fill in the x with the number of hours than solve the problem. 6·9=54+10=$64 that is to much. So he can only rent the cleaner for 8 hours). The maximum number of hours that the cost of renting the carpet cleaner is less than the cost of buying the carpet cleaner is correct (25 hours). The fully developed justification supports the solution (it would take 25 hours to cost 160 If I had it for one more hour it would be 166 and that’s more than how much it would cost to buy it. I got my answer from add 6 until I got to $160). This response demonstrates a complete understanding and analysis of the problem.
Score Level 4 Anchor Paper
This response indicates application of a reasonable strategy that leads to a correct solution within the context of the problem. The table is correctly completed. The representation in the form of an equation is correct (y=6x+10). The student indicates that the carpet cleaner cannot be rented for 9 hours if Jared has $60. The explanation is clearly presented and fully developed. The student replaces `x` in the equation with 9, solves for `y` and then writes (No, he can not he would need $4 more). The maximum number of hours that the cost of renting the carpet cleaner is less than the cost of buying the carpet cleaner is correct (25 hours or less).The fully developed symbolic justification supports the solution. The student first replaces `x` in the equation with 25, solves for `y` and then writes (under cost of buying the carpet cleaner). The student then replaces `x` in the equation with 26, solves for `y` and writes (over cost of buying the carpet cleaner). This response demonstrates a complete understanding and analysis of the problem.

Anchor Papers ~ Algebra/Data Analysis ~ Item 14

HSA 2008 Algebra/Data Analysis Item 14

CID: CID1da71d60a1656cfaded67d132e3d594a
itemNum: 14
initialLetter
itemType: ECR
itemAnswerKey: N/A
itemMaxScorePoints: 4
origNum: 21

Jared wants to rent a carpet cleaner. The table below shows the cost of renting a carpet cleaner.

Complete the following in the Answer Book:

Complete the table to show the cost of renting a carpet cleaner for 5 and 6 hours if this pattern continues.
Write an equation to represent the relationship between the cost of renting a carpet cleaner and the number of hours that a carpet cleaner is rented.
If Jared has $60, can he rent the carpet cleaner for 9 hours? Use mathematics to explain how you determined your answer. Use words, symbols, or both in your explanation.
The store also sells the same carpet cleaner for $165, including tax. What is the maximum number of hours that the cost of renting the carpet cleaner is less than the cost of buying the carpet cleaner? Use mathematics to justify your answer.

Score Level 1 Anchor Paper
This response indicates little application of a reasonable strategy. The correct costs for 5 and 6 hours of carpet cleaner rental are given (the last two numbers for the table would be 40 and 46). The student provides no response to the second, third or fourth parts of the question. This response demonstrates a minimal understanding and analysis of the problem.

Score Level 1 Anchor Paper
This response indicates little application of a reasonable strategy. The representation in the form of an equation is correct (y=6x+10). The student provides no response to the first, third or fourth parts of the question. The response demonstrates a minimal understanding and analysis of the problem.

Score Level 2 Anchor Paper

This response indicates application of an incomplete strategy. The table is correctly completed. The representation in the form of an equation is correct (y=6x+10). The student indicates that the carpet cleaner cannot be rented for 9 hours if Jared has $60. An explanation is not given. The student provides no response to the fourth part of the question. This response demonstrates a conceptual understanding and analysis of the problem.

Score Level 2 Anchor Paper

This response indicates application of an incomplete strategy. The table is correctly completed. The student indicates that the carpet cleaner cannot be rented for 9 hours if Jared has $60. The explanation supports the solution. The student extends the tabular pattern to 9 hours then writes (because it would be $64 for 9 hours. Jared only had $60 so he can rent the carpet cleaner for 8 hours for $58 and still stay in budget). The student provides no response to the second or fourth parts of the question. This response demonstrates a conceptual understanding and analysis of the problem.

Score Level 3 Anchor Paper

This response indicates application of a reasonable strategy that leads to some correct solutions. The correct costs for 5 and 6 hours of carpet cleaner rental are given (5 hours-$40; 6 hours-$46). The representation in the form of an equation is correct (Hx6+10=C). The student indicates that the carpet cleaner cannot be rented for 9 hours if Jared has $60. The student provides a generally well developed justification, rather than an explanation (because it will cost him $64. He will be over the $60). The maximum number of hours that the cost of renting the carpet cleaner is less than the cost of buying the carpet cleaner is incorrect (15). While the justification supports the solution, the student did not use his equation correctly (I got that by doing 15x10+6=$156). This response demonstrates a clear understanding and analysis of the problem.

Score Level 3 Anchor Paper

This response indicates application of a reasonable strategy that leads to some correct solutions. The table is correctly completed. The representation in the form of an equation is correct (y=6x+10). The student indicates that the carpet cleaner cannot be rented for 9 hours if Jared has $60. The explanation supports the solution (y=6(9)+10; y=54+10; y=64). The maximum number of hours that the cost of renting the carpet cleaner is less than the cost of buying the carpet cleaner is correct (25 hours). A justification is not given. This response demonstrates a clear understanding and analysis of the problem.

Score Level 4 Anchor Paper

This response indicates application of a reasonable strategy that leads to a correct solution within the context of the problem. The table is correctly completed. The representation in the form of an equation is correct (y=6x+10). The student indicates that the carpet cleaner cannot be rented for 9 hours if Jared has $60. The explanation is clearly presented and fully developed (Frist I would fill in the x with the number of hours than solve the problem. 6·9=54+10=$64 that is to much. So he can only rent the cleaner for 8 hours). The maximum number of hours that the cost of renting the carpet cleaner is less than the cost of buying the carpet cleaner is correct (25 hours). The fully developed justification supports the solution (it would take 25 hours to cost 160 If I had it for one more hour it would be 166 and that’s more than how much it would cost to buy it. I got my answer from add 6 until I got to $160). This response demonstrates a complete understanding and analysis of the problem.

Score Level 4 Anchor Paper

This response indicates application of a reasonable strategy that leads to a correct solution within the context of the problem. The table is correctly completed. The representation in the form of an equation is correct (y=6x+10). The student indicates that the carpet cleaner cannot be rented for 9 hours if Jared has $60. The explanation is clearly presented and fully developed. The student replaces x in the equation with 9, solves for y and then writes (No, he can not he would need $4 more). The maximum number of hours that the cost of renting the carpet cleaner is less than the cost of buying the carpet cleaner is correct (25 hours or less).The fully developed symbolic justification supports the solution. The student first replaces x in the equation with 25, solves for y and then writes (under cost of buying the carpet cleaner). The student then replaces x in the equation with 26, solves for y and writes (over cost of buying the carpet cleaner). This response demonstrates a complete understanding and analysis of the problem.