Score Level 2 Paper

This response indicates an incomplete application of a reasonable strategy. The representation is correct. The value of the y-intercept and the contextual meaning are not given. The maximum number of months (15) is correct. The calculations (10+3x15) provide justification, rather than explanation. This response demonstrates a conceptual understanding and analysis of the problem. (Compare to this Level 2 anchor paper.)

Score Level 3 Paper

This response indicates application of a reasonable strategy that leads to a correct solution. The representation is correct (y=3x+10). Although the correct y-intercept (10) is given, the student, instead of providing the contextual meaning, defines the variable y. The maximum number of months (15) is correct, and the symbolic explanation supports the solution. The student replaces the y in the equation with 55 and solves for x. This response demonstrates a clear understanding and analysis of the problem. (Compare to this Level 4 anchor paper.)

Score Level 1 Paper

This response indicates little application of a reasonable strategy. The representation is incorrect (x=3x). Although the student's response to the second part of the question (don't have a y-intercept) is consistent with the student's equation, a contextual meaning is not provided. The maximum number of months (fifteen) is correct, and the explanation (she had already been given 10 CDs so I subtracted 10 from 55 and got 45, then I divided by three because that's how many CDs she gets per month) supports the solution. This response demonstrates a minimal understanding and analysis of the problem.

Score Level 4 Paper

This response indicates application of a reasonable strategy that leads to a correct solution within the context of the problem. The representation is correct (y=10+3x). The student provides the correct y-intercept (10), contextual meaning of the intercept (the amount of CDs Elizabeth gets if she joins the club), and maximum number of months (15). A fully developed and clearly presented explanation is given (replacing y in my equation with 55 because y= the number of CDs. Then I subtracted 10 from each side. Now we have 45=3x. So I divided 3 by everything to get x). This response demonstrates a complete understanding and analysis of the problem. (Compare to this Level 4 anchor paper.)

Score Level 3 Paper

This response indicates application of a reasonable strategy. The representation is correct (y=3x+10). Both the value of the y-intercept (10) and the contextual meaning (how many CDs she will have after 0 months) are correct. The maximum number of months (15) is correct; however, no explanation is provided. This response demonstrates a clear understanding and analysis of the problem. (Compare to this Level 3 anchor paper.)

Score Level 4 Paper

This response indicates application of a reasonable strategy that leads to a correct solution within the context of the problem. The representation is correct (y=3x+10). The student provides the correct y-intercept (10), and the contextual meaning also is correct (she got 10 free CDs when she joined the club). The maximum number of months (15) is correct. The symbolic explanation is clearly presented and fully developed; the student replaces the y in the equation with 55 and solves for x. This response demonstrates a complete understanding and analysis of the problem.

Score Level 1 Paper

This response indicates little application of a reasonable strategy. The representation is correct (y=3x+10). While the value of the y-intercept (10) is correct, the contextual meaning is not provided. The maximum number of months and an explanation are not given. This response demonstrates a minimal understanding and analysis of the problem.

Score Level 2 Paper

This response indicates an incomplete application of a reasonable strategy. The representation is incorrect (y=10x-3). The value of the y-intercept is correct (10 free CDs), but is not consistent with the equation. The contextual meaning is correct (number of CDs she will receive after 0 months). Although incorrect, the maximum number of months (5) is consistent with the equation. The explanation reveals a reasonable strategy of guess and check; the student replaces x in the equation with 5 and then 6 and compares the outcomes. (After 5 months she will receive 47 CDs. She can't stay in the club for 6 months because she will get 2 more CDs than she wants). This response demonstrates a conceptual understanding and analysis of the problem.