Score Level 1 Anchor Paper

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. 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 student correctly fills in the boxes to indicate the differences in y-values and a description of the pattern is provided (each number that changes the y value increases by 2 each time). While the difference between y-values when x is 10 and when x is 11 is incorrect (19), the explanation reveals a reasonable strategy (by continueing the chart and following the pattern). This response demonstrates a minimal understanding and analysis of the problem.

Score Level 2 Anchor Paper

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). The relationship between the x-values and the y-values is correct (the numbers multiply to it's self. For example the x value is 2 so you multiply 2 times 2 and receive 4 as your y value). This response demonstrates a conceptual understanding and analysis of the problem.

Score Level 2 Anchor Paper

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 (y=100; y=121). The relationship between the x-values and the y-values is incomplete (x goes up by 1 and y goes up by adding an odd number). The student correctly fills in the boxes to indicate the differences in y-values but does not provide a description of the pattern between the differences. The student has given the difference in y-values when x is 10 and when x is 11 (21) but an explanation is not provided. This response demonstrates a conceptual understanding and analysis of the problem.

Score Level 2 Anchor Paper

This response indicates an incomplete application of a reasonable strategy. The student incorrectly assumes the pattern is linear, and therefore 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). That equation is then used to find the values of y when x is 10 (45) and x is 11 (50), and to find the difference in y-values when x is 10 and when x is 11 (5) and to explain that answer (When x is 10, the y-value was 45. When x is 11, the y-value was 50. The difference between those are 5. I subtracted 45 from 50 to get the answer.). The student correctly fills in the boxes to indicate the differences in y-values, and provides a description of the pattern which supports the solution and is plausible (odd numbers that start with 3; to find these numbers, I subtracted the numbers from back. For example, to find the difference between 9 and 16, I subtracted 9 from 16.). 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 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 (x²=y). The student correctly fills in the boxes to indicate the differences in y-values and gives a description of the pattern (you add two each time). 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.

Score Level 3 Anchor Paper

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 (The x values are the square root of y). 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) and the explanation supports the solution (10²=100 and 11²=121 and 121-100=21). 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 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 y value is eaquel to the x value squared. For exanple if x=4, then y=16 because 4²=16). The student correctly fills in the boxes to indicate the differences in y-values and gives a complete description of the pattern (the difference of the numbers increases by 2). The difference in y-values when x is 10 and when x is 11 is correct (21) and the explanation supports the solution (when x=10, y=100, and when x=11 y=121, so, the difference is 21. That's 2 up from the difference of 19 in x=9, and x=10). 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 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=x²). The student correctly fills in the boxes to indicate the differences in y-values and gives a complete description of the pattern (the difference is a pattern of consecutive odd numbers, which would make the difference of the difference 2). The difference in y-values when x is 10 and when x is 11 is correct (21) and the explanation supports the solution (when x was 10, y equaled 100, and when x was 11, y equaled 121. After subtracting 121 and 100, you get 21). This response demonstrates a complete understanding and analysis of the problem.