The following 16 Sample Student Responses represent a range of score points.

Score for Sample Student Response #1: Rubric Score 2

Annotation: 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 Anchor Paper #4.

Score for Sample Student Response #2: Rubric Score 3

Annotation: 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 Anchor Paper #8.

Score for Sample Student Response #3: Rubric Score 1

Annotation: 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 for Sample Student Response #4: Rubric Score 4

Annotation: 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 Anchor Paper #8.

Score for Sample Student Response #5: Rubric Score 3

Annotation: 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 Anchor Paper #6.

Score for Sample Student Response #6: Rubric Score 4

Annotation: 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 for Sample Student Response #7: Rubric Score 1

Annotation: 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 for Sample Student Response #8: Rubric Score 2

Annotation: 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.

Score for Sample Student Response #9: Rubric Score 3

Annotation: This response indicates application of a reasonable strategy that leads to some correct solutions. The representation is correct (y=10+3x). The student provides the correct y-intercept (ten); however, instead of a contextual meaning, an explanation of how to use the y-intercept (that's the number you have to add when you solve the equation for x) is given. While the maximum number of months is correct, the calculations {10+(3·15)=55 and 3·15=45 and 45+10=55} provide justification, rather than explanation. This response demonstrates a clear understanding and analysis of the problem. Compare to Anchor Paper #5.

Score for Sample Student Response #10: Rubric Score 4

Annotation: 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). Both the y-intercept (10) and the contextual meaning (Elizabeth receives 10 CDs for joining the club) are correct. A correct number of months (15) is provided. 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 for Sample Student Response #11: Rubric Score 1

Annotation: This response indicates little application of a reasonable strategy. The representation, in the form of an expression rather than an equation, is (3x+10). The value of the y-intercept (10,0) is incorrect but relevant and the student provides the definition of a y-intercept, rather than the contextual meaning (y-intercept is the amount when a line crosses through the y-axis and x=0). The maximum number of months and an explanation are not given. This response demonstrates a minimal understanding and analysis of the problem.

Score for Sample Student Response #12: Rubric Score 3

Annotation: This response indicates application of a reasonable strategy that leads to some correct solutions. The representation is correct (y=10+3x). While the student provides the correct y-intercept (10), an explanation (I know this is the y- intercept because y=10+3x is the y=mx+b formula, and the b is your y-intercept), rather than the contextual meaning, is given. The maximum number of months 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 Anchor Paper #8.

Score for Sample Student Response #13: Rubric Score 4

Annotation: 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 (she receives 10 free CDs when she joins the club), and maximum number of months (15). 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 for Sample Student Response #14: Rubric Score 2

Annotation: This response indicates an incomplete application of a reasonable strategy. The representation is correct (y=10+3x). The value of the y-intercept (13) is incorrect, and the student gives the definition of the variable y, rather than the contextual meaning of the y-intercept (number of CDs Elizabeth receives after x amount of months). The maximum number of months (15) is correct. The explanation supports the solution, but is incomplete (selecting a random number then replacing x with that number). This response demonstrates a conceptual understanding and analysis of the problem. Compare to Anchor Paper #4.

Score for Sample Student Response #15: Rubric Score 1

Annotation: This response indicates little application of a reasonable strategy. The representation is incorrect (y=3x). No value for the y-intercept is given, and the contextual meaning is incorrect (number of CDs that Liz has currently purchased after joining the music club). The maximum number of months (19) is incorrect. The explanation reveals a reasonable strategy (dividing 3 into 55 and came out with 18.3), using the student's incorrect equation. This response demonstrates a minimal understanding and analysis of the problem.

Score for Sample Student Response #16: Rubric Score 2

Annotation: This response indicates an incomplete application of a reasonable strategy. The representation is incorrect (y=10x+3). However, the y-intercept (positive three) is consistent with the student's equation. While an explanation of the y-intercept is given (In a y-intercept, x always equals zero. When you substitute 0 for x, you get zero + 3=y), the equation creates an incorrect contextual meaning (the number of CDs Elizabeth must buy each month to get 10 CDs free). The maximum number of months (5.2) is incorrect, but consistent with the student's equation. The symbolic explanation reveals a reasonable strategy; the student replaces the y in the equation with 55 and solves for x. This response demonstrates a conceptual understanding and analysis of the problem.

Anchor Papers used in scoring