The following 16 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 a correct solution within the context of the problem. The student correctly completes the table for each ranger and gives correct expressions for Ranger Jones (6n+78) and for Ranger Percy (8n+78). The difference in the predicted number of deer in 10 years ("20 deer") is correct. The explanation supports the solution. ("On the graph where the points are at 10, then I know that that is my answer. Ranger J will be 138, and Ranger P will be 158.") This response demonstrates a complete understanding and analysis of the problem.

Score for Sample Student Response #2: Rubric Score 1

Annotation: This response indicates little application of a reasonable strategy. The tables are correctly completed; however, no expression is given. No attempt is made to determine the difference in the predicted number of deer in 10 years. This response demonstrates a minimal understanding and analysis of the problem. Compare to Anchor Paper #1.

Score for Sample Student Response #3: Rubric Score 3

Annotation: This response indicates application of a reasonable strategy that leads to some correct solutions. The table for Ranger Jones' predictions is correctly completed. The student correctly provides the prediction for the first year on Ranger Percy's table; however, the predictions for years two and three are incorrect. The representations, in the form of equations ("Ranger Jones y=78+6x…Ranger Percy y=78+8n"), are correct. The student indicates the difference in the total number of deer by comparing Ranger Jones' prediction ("138 deer") with Ranger Percy's ("158"). The explanation supports the solution ("by plugging ten into x and solving for y") This response demonstrates a clear understanding and analysis of the problem.

Score for Sample Student Response #4: Rubric Score 2

Annotation: This response indicates an incomplete application of a reasonable strategy. The tables are correctly completed. While the representations are essentially correct, in the form of equations, the student has not defined y, after changing it from n given in the item, and d is not defined. There is no indication that the student has responded to the third part of the question. This response demonstrates a conceptual understanding and analysis of the problem. Compare to Anchor Paper #4.

Score for Sample Student Response #5: Rubric Score 3

Annotation: This response indicates application of a reasonable strategy that leads to some correct solutions. The tables are correctly completed. The representations, in the form of equations (''Ranger Jones y=6n+78…Ranger Percy y=8n+78"), are correct. The difference in the predicted number of deer in 10 years (''Ranger Jones believes that there will be 50 fewer deer in the park than what Ranger Percy thinks") is incorrect. The symbolic explanation reveals a reasonable strategy. The student replaces n in each equation with 10 and solves for y, the predicted deer population. However, a mathematical error is made in the Ranger Jones' prediction when the student adds 60 and 78 and arrives at a total of 108, rather than 138. The student then concludes "Jones thinks that in 10 years there will be 108 deer and Percy thinks there will be 158." The difference of "50 fewer deer" is consistent with the student's numbers. This response demonstrates a clear understanding and analysis of the problem. Compare to Anchor Paper #5.

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 tables are correctly completed. Correct expressions for Ranger Jones (6N+ 78) and Ranger Percy (8N+ 78) are given. The difference in the predicted number of deer in 10 years (20) is correct. The explanation is clearly presented and fully developed; the student replaces the n in each equation with 10, solves for each ranger's prediction, and then finds the difference. 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 table for Ranger Jones is correctly completed, but the table for Ranger Percy is incorrect for 3 years. No attempt is made to write an expression or determine the difference in the predicted number of deer in 10 years. This response demonstrates a minimal understanding and analysis of the problem. Compare to Anchor Paper #1.

Score for Sample Student Response #8: Rubric Score 2

Annotation: This response indicates an incomplete application of a reasonable strategy. The tables are correctly completed. The representations, in the form of equations set equal to d (defined as "deer"), are essentially correct. The student reverses the Ranger's names when labeling. There is no indication that the student has addressed the third part of the question. 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 tables are correctly completed. The representations, in the form of expressions (''Ranger Jones 6n+78…Percy 8n+78"), are correct. The student indicates the difference in the total number of deer predicted by comparing Ranger Percy's prediction ("158") with Ranger Jones' ("138"). However, an explanation is not provided. This response demonstrates a clear understanding and analysis of the problem. Compare to Anchor Paper #6.

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 tables are correctly completed. The representations, in the form of equations, are correct. The variable d is not defined. The difference in the total number of predicted deer in 10 years ("20 deer") is correct. The symbolic explanation is fully developed and supports the solution. The student replaces the n in each equation with 10, solves for each ranger's prediction, and then finds the difference. 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 tables are correctly completed. Although the student repeats the information given in the question, no expression is provided for either Ranger Jones or Ranger Percy. There is no indication that the student has responded to the third part of the question. This response demonstrates a minimal understanding and analysis of the problem.

Score for Sample Student Response #12: Rubric Score 2

Annotation: This response indicates an incomplete application of a reasonable strategy. The tables are correctly completed. The representations, in the form of equations (''Ranger Jones d=78+6n…Ranger Percy d=78+8n"), are correct, and the variable d is defined. The difference in the predicted number of deer in 10 years ("30") is incorrect. This response demonstrates a conceptual understanding and analysis of the problem. Compare to Anchor Paper #4.

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 tables are correctly completed. The representations, in the form of expressions (''Ranger Jones 78+6n…Ranger Percy 78+8n"), are correct. The difference in the number of predicted deer in 10 years ("20 deer") is correct. The symbolic explanation is fully developed, clearly presented, and supports the solution. The student replaces the n in each equation with 10; solves for x, the predicted number of deer; and then finds the difference. This response demonstrates a complete understanding and analysis of the problem.

Score for Sample Student Response #14: Rubric Score 1

Annotation: This response indicates little application of a reasonable strategy. The tables are correctly completed. The response to the second part of the question is a restatement of information given in the item. The student provides a predicted number of deer for Ranger Percy ("would be 156 deer") and Ranger Jones ("would be 144 deer"). However, these are incorrect predictions, and the student's incomplete explanation ("by just adding eight or 6 or 8 to the deer population that year") does not reveal the error. The difference between 156 and 144 is not "21." This response demonstrates a minimal understanding and analysis of the problem.

Score for Sample Student Response #15: Rubric Score 2

Annotation: This response indicates an incomplete application of a reasonable strategy. The tables are correctly completed. The representations, in the form of equations, are correct. The student has not defined x after changing it from n as given in the item. The equations are labeled for each ranger by their locations beneath the assigned tables. The numbers "132" and "158" indicate an attempt to arrive at a predicted number of deer for each ranger; however, the difference in the predicted number of deer in 10 years ("22 deer apart") is inconsistent with these numbers, and "132" is an incorrect prediction. This response demonstrates a conceptual understanding and analysis of the problem.

Score for Sample Student Response #16: Rubric Score 3

Annotation: This response indicates application of a reasonable strategy that leads to some correct solutions. The tables are correctly completed. The representations, in the form of expressions, are correct, and the variable x is defined. The difference in the predicted number of deer in 10 years ("50 deer in 10 years is the difference of the 2 rangers predictions") is incorrect. The symbolic explanation reveals a reasonable strategy. The student replaces n in each equation with 10 and solves for the predicted deer population. For Ranger Percy's prediction, the student makes an error, arriving at a total of 182, rather than 158. The difference in deer population ("50 deer") is consistent with the student's numbers. This response demonstrates a clear understanding and analysis of the problem.

Anchor Papers used in scoring