The following 19 Sample Student Responses represent a range of score points.

Score for Sample Student Response #1: Rubric Score 4

Annotation: This response indicates application of a reasonable strategy that leads to correct solutions within the context of the problem. The values of y when x is 10 and when x is 11 are correct. The relationship between the x-values and the y-values is complete (y is the square of x. The equation is y=x²). The student correctly fills in the boxes to indicate the differences in y-values and gives a complete description of the pattern (it is every consecutive odd number). The difference in y-values when x is 10 and when x is 11 is correct (21) and the explanation supports the solution (finding the 10^th consecutive odd number that is between the 10^th and 11^th term for y). This response demonstrates a complete understanding and analysis of the problem. (Compare to this Level 4 anchor paper.)

Score for Sample Student Response #2: Rubric Score 2

Annotation: This response indicates an incomplete application of a reasonable strategy. The values of y when x is 10 and when x is 11 are correct (10=100; 11=121). The relationship between the x-values and the y-values is incomplete (Each time you add by the odd number one after another the y side). The student has filled in the boxes to indicate the differences in y-values and a description of the pattern is given (Add the next odd number to y starting from 3 then 5 then 7 then 9 and etc.). There is no indication that the student has responded to the fourth part of the question. This response demonstrates a conceptual understanding and analysis of the problem. (Compare to this Level 2 anchor paper.)

Score for Sample Student Response #3: Rubric Score 1

Annotation: This response indicates little application of a reasonable strategy. The values of y when x is 10 and when x is 11 are correct (y=100; y=121). The relationship between the x-values and the y-values is incorrect (the formula is x·y). While the student correctly filled in the boxes to indicate the differences in y-values, a description of the pattern is not provided. This response demonstrates a minimal understanding and analysis of the problem. (Compare to this Level 1 anchor paper.)

Score for Sample Student Response #4: Rubric Score 3

Annotation: This response indicates application of a reasonable strategy that leads to some correct solutions within the context of the problem. The values of y when x is 10 and when x is 11 are correct (100; 121). The relationship between the x-values and the y-values is correct (To get the y value you need to multiply the x value by itself). The student correctly fills in the boxes to indicate the differences in y-values. The description of the pattern is not complete (The numbers are all odd numbers). The difference in y-values when x is 10 and when x is 11 is correct and the symbolic explanation supports the solution (121-100=21). This response demonstrates a clear understanding and analysis of the problem. (Compare to this Level 3 anchor paper.)

Score for Sample Student Response #5: Rubric Score 2

Annotation: This response indicates an incomplete application of a reasonable strategy. The values of y when x is 10 and when x is 11 are correct (100; 121). The relationship between the x-values and the y-values is incomplete (x always increases by 1 and y is always increasing with an addition pattern. When you look at the pattern in the y-values, it is adding odd numbers). The student fills in the boxes to indicate the differences in y-values but does not provide a description of the pattern between the differences. There is no indication that the student has responded to the fourth part of the question. This response demonstrates a conceptual understanding and analysis of the problem. (Compare to this Level 2 anchor paper.)

Score for Sample Student Response #6: Rubric Score 3

Annotation: This response indicates application of a reasonable strategy that leads to some correct solutions within the context of the problem. The values of y when x is 10 and when x is 11 are correct (y=100; y=121). The relationship between the x-values and the y-values is correct (whatever is in x you square it). While the student correctly fills in the boxes to indicate the differences in y-values, a description of the pattern is not provided. The difference in y-values when x is 10 and when x is 11 is correct and the symbolic explanation supports the solution (121-100=21). This response demonstrates a clear understanding and analysis of the problem. (Compare to this Level 3 anchor paper.)

Score for Sample Student Response #7: Rubric Score 4

Annotation: This response indicates application of a reasonable strategy that leads to correct solutions within the context of the problem. The values of y when x is 10 and when x is 11 are correct. The relationship between the x-values and the y-values is complete (the x value is multiplied by itself, or squared, to get the y value). The student correctly fills in the boxes to indicate the differences in y-values and gives a complete description of the pattern (each one is going up by 2, and they are all odd numbers). The difference in y-values when x is 10 and when x is 11 is correct (21) and the explanation supports the solution (finding the square of 10 is 100, and the square of 11 is 121, and I subtracted 100 from 121). This response demonstrates a complete understanding and analysis of the problem. (Compare to this Level 4 anchor paper.)

Score for Sample Student Response #8: Rubric Score 1

Annotation: This response indicates little application of a reasonable strategy. The student correctly filled in the boxes to indicate the differences in y-values and a description of the pattern is provided (the differences that I found is 2, The difference in the y-values go up by 2). This response demonstrates a minimal understanding and analysis of the problem. (Compare to this Level 1 anchor paper.)

Score for Sample Student Response #9: Rubric Score 2

Annotation: This response indicates an incomplete application of a reasonable strategy. The values of y when x is 10 and when x is 11 are incorrect (102; 124) as a result of a calculation error in the table when x=9. The student correctly fills in the boxes to indicate the differences in y-values and a description of the pattern is provided (the differences between one y value to the one lower than it goes up by 2). Although the difference in y-values when x is 10 and when x is 11 is incorrect (22), it is consistent with the calculation error made in the first part of the question, and the explanation supports the solution (I subtracted 102 from 124 and got 22). This response demonstrates a conceptual understanding and analysis of the problem.

Score for Sample Student Response #10: Rubric Score 4

Annotation: This response indicates application of a reasonable strategy that leads to correct solutions within the context of the problem. The values of y when x is 10 and when x is 11 are correct. The relationship between the x-values and the y-values is complete (The x values are squared in order to get the y values). The student correctly fills in the boxes to indicate the differences in y-values and gives a complete description of the pattern (The difference in the y-values increases by 2). The difference in y-values when x is 10 and when x is 11 is correct and the complete explanation supports the solution. This response demonstrates a complete understanding and analysis of the problem. (Compare to this Level 4 anchor paper.)

Score for Sample Student Response #11: Rubric Score 2

Annotation: This response indicates an incomplete application of a reasonable strategy. The student applies an inappropriate method, a linear regression model, to describe the relationship between the x and y values, resulting in an incorrect equation (y=5x-5). The equation is then used to find the values of y when x is 10 and when x is 11 (45;50), and to find the difference in y-values when x is 10 and when x is 11 (5) and to explain that answer (I determined this by first entering the table in STAT. Then I put the line of regretion into the y=....I subtracted the y-value of 10 from 11 and go a difference of 5.). The student correctly fills in the boxes, and provides a description of the pattern which supports the solution and is plausible (adding by odds. 1, 3, 5, 7, 9 and so on). This response demonstrates a conceptual understanding and analysis of the problem. (Compare to this Level 2 anchor paper.)

Score for Sample Student Response #12: Rubric Score 3

Annotation: This response indicates application of a reasonable strategy that leads to some correct solutions within the context of the problem. The values of y when x is 10 and when x is 11 are correct (y=100; y=121). The relationship between the x-values and the y-values is correct (x²=y). The student correctly fills in the boxes to indicate the differences in y-values; however, the description of the pattern is not complete (It is going up by odd numbers). The difference in y-values when x is 10 and when x is 11 is correct and the symbolic explanation supports the solution (121-100=21). This response demonstrates a clear understanding and analysis of the problem. (Compare to this Level 3 anchor paper.)

Score for Sample Student Response #13: Rubric Score 4

Annotation: This response indicates application of a reasonable strategy that leads to correct solutions within the context of the problem. The values of y when x is 10 and when x is 11 are correct (y=100; y=121). The relationship between the x-values and the y-values is complete (The y-value is the x-value times itself; x·x=y). The student correctly fills in the boxes to indicate the differences in y-values and gives a description of the pattern (The differences are all by odd numbers. Each time it's by 2 more). The difference in y-values when x is 10 and when x is 11 is correct (21) and the symbolic explanation supports the solution (121-100=21). This response demonstrates a complete understanding and analysis of the problem. (Compare to this Level 4 anchor paper.)

Score for Sample Student Response #14: Rubric Score 1

Annotation: This response indicates little application of a reasonable strategy. The values of y when x is 10 and when x is 11 are incorrect (25; 36). The student correctly fills in the boxes to indicate the differences in y-values and a description of the pattern is given (the y values go up by consecuitive odd integers). This response demonstrates a minimal understanding and analysis of the problem. (Compare to this Level 1 anchor paper.)

Score for Sample Student Response #15: Rubric Score 4

Annotation: This response indicates application of a reasonable strategy that leads to correct solutions within the context of the problem. The values of y when x is 10 and when x is 11 are correct. The relationship between the x-values and the y-values is complete (to get y, you square x). The student correctly fills in the boxes to indicate the differences in y-values and gives a description of the pattern (The pattern I found was the difference of the y values was always increased by 2). The difference in y-values when x is 10 and when x is 11 is correct (21) and the symbolic explanation supports the solution (10²=100; 11²=121; 121-100=21). This response demonstrates a complete understanding and analysis of the problem. (Compare to this Level 4 anchor paper.)

Score for Sample Student Response #16: Rubric Score 3

Annotation: This response indicates application of a reasonable strategy that leads to some correct solutions within the context of the problem. The values of y when x is 10 and when x is 11 are correct (10²=100; 11²=121). The relationship between the x-values and the y-values is correct (y=x²; The x values squared equals the y values). The student correctly fills in the boxes to indicate the differences in y-values and a description of the pattern is provided (As the two number go up, the difference of them goes up by two). There is no indication that the student has responded to the fourth part of the question. This response demonstrates a clear understanding and analysis of the problem. (Compare to this Level 3 anchor paper.)

Score for Sample Student Response #17: Rubric Score 2

Annotation: This response indicates an incomplete application of a reasonable strategy. The values of y when x is 10 and when x is 11 are correct (100; 121). The relationship between the x-values and the y-values is correct (multiplying the x value times itself to get the y value). This response demonstrates a conceptual understanding and analysis of the problem. (Compare to this Level 2 anchor paper.)

Score for Sample Student Response #18: Rubric Score 3

Annotation: This response indicates application of a reasonable strategy that leads to some correct solutions within the context of the problem. The values of y when x is 10 and when x is 11 are correct (100; 121). The relationship between the x-values and the y-values is correct (you are just multiplying x by its self). While the student correctly fills in the boxes to indicate the differences in y-values, a description of the pattern is not provided. The difference in y-values when x is 10 and when x is 11 is correct (21); however, an explanation is not given. This response demonstrates a clear understanding and analysis of the problem. (Compare to this Level 3 anchor paper.)

Score for Sample Student Response #19: Rubric Score 1

Annotation: This response indicates little application of a reasonable strategy. The values of y when x is 10 and when x is 11 are correct (100; 121). While the student correctly filled in the boxes to indicate the differences in y-values, a description of the pattern is not provided. The response demonstrates a minimal understanding and analysis of the problem. (Compare to this Level 1 anchor paper.)

Anchor Papers used in scoring