The following 7 Anchor Papers represent a range of score points and are used in conjunction with the rubrics to assess student responses.

Score for Anchor Paper #1: Rubric Score 1

Annotation: In this response the student applies a strategy of trial and error ("...make a graphing chart...For plan A I added 10 cents plus another 10 cents to get the cost for 2 min. For Plan B I added 7 cents plus another 7 cents to get the cost 2 min. I repeated this process until I got the same cost for a call."). This strategy is reasonable and should lead to a correct solution. However, there is no indication that the student considered the monthly charges, and the provided solution is incorrect. This response demonstrates a minimal understanding and analysis of the problem.

Score for Anchor Paper #2: Rubric Score 1

Annotation: This response indicates little application of a reasonable strategy. The student makes an attempt to graph the cost per minute for each plan, but neglects to consider the monthly charge and does not label the lines. The student correctly gives, "100 minutes with Plan B," but provides no explanation for this solution. The answer of 70 for Plan A is incorrect. This response demonstrates a minimal understanding and analysis of the problem.

Score for Anchor Paper #3: Rubric Score 2

Annotation: This response indicates application of a reasonable strategy that leads to a correct solution of 100 minutes. The explanation, however, is incomplete. The student has created a table that lists each plan's y values, ending at 100 minutes. The monthly charges, though, are missing, and an equal cost for the two plans at 100 minutes is not displayed. The response demonstrates a conceptual understanding and analysis of the problem.

Score for Anchor Paper #4: Rubric Score 2

Annotation: In this response the student applies a reasonable strategy that leads to an incorrect solution. The student sets up two appropriate equations and solves for m, the number of minutes. Through a calculation error, the student arrives at a solution of m=10, rather than m=100. The student solves for the total cost of the plans by substituting 10 for m in the equation for Plan B. ("I received $8.70.") Substituting $8.70 for t in the Plan A equation then leads to an m value of 37, hence a solution of "10 min. using Plan B and 37 minutes using Plan A and the total for both plans would be $8.70." Although the student has graphed the equations on the grid, the scale intervals are too small to show a point of intersection. This response demonstrates a conceptual understanding and analysis of the problem.

Score for Anchor Paper #5: Rubric Score 3

Annotation: This response indicates application of a reasonable strategy that leads to a correct solution within the context of the problem. The student correctly identifies 100 as the number of minutes of calls it would take for the two plans to cost the same. The explanation is presented graphically; the student has determined appropriate algebraic expressions to represent the payment plans and has correctly graphed them on the grid. Although the labeling of the y-axis is not complete and a title is missing, the graph and the interpretation of the graph ("...where the two lines intersect.") provide a full explanation of how the answer of 100 minutes was derived. This response demonstrates a complete understanding and analysis of the problem.

Score for Anchor Paper #6: Rubric Score 3

Annotation: This response indicates application of a reasonable strategy that leads to a correct solution within the context of the problem. The student arrives at a correct solution of 100, with the label "phone calls" instead of "minutes" representing a minor error. The fully developed explanation reveals a strategy of trial and error; the student inserts multiples of ten into both equations until the total costs are equal. ("I multiplied .1 to every 10. And I did the same with .07. I then added each of their costs for month prices.") The results of several trials appear below the explanation and along the axis of the grid. This response indicates a complete understanding and analysis of the problem.

Score for Anchor Paper #7: Rubric Score 3

Annotation: This response indicates application of a reasonable strategy that leads to a correct solution within the context of the problem. The student arrives at the correct solution of 100 minutes. The fully developed explanation is presented symbolically; the student has determined the appropriate expressions to represent the payment plans and has set them equal to one another and solved for m, the number of minutes. This response demonstrates a complete understanding and analysis of the problem.

Additional Scored Student Responses