The following 8 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: This response indicates little application of a reasonable strategy. The student provides the correct equations for Choice A (y=$6+0.50x) and Choice B (y=$2+0.75x). The solution to the system of equations is incorrect {"...8 rides to equal the cost of ticket price A ($6.00) to ticket price B ($2.00)"}. An explanation is not given. "Ticket plan A" is an incorrect response to the third part of the question; the student does not provide a justification. 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. There is no indication that the student attempts to respond to the first two parts of the question. The student's selection of Choice B as the appropriate plan is correctly justified ("...choose B because the total comes out to be $12.50 and if he chose A he would pay $13"). This response demonstrates a minimal understanding and analysis of the problem.

Score for Anchor Paper #3: Rubric Score 2

Annotation: This response indicates an incomplete application of a reasonable strategy. The student provides the correct equations for Choice A (6+x·.5 = y) and Choice B (2 +x·.75 = y). The solution to the system of equations is correct; however, an explanation is not given. "Ticket a" is an incorrect response to the third part of the question and lacks justification. This response demonstrates a conceptual understanding and analysis of the problem.

Score for Anchor Paper #4: Rubric Score 2

Annotation: This response indicates an incomplete application of a reasonable strategy. The student gives the correct equations for Choice A (y=6+0.50x) and Choice B (y = 2 +0.75x). The solution to the system of equations is incorrect. ("The total cost will be the same at $15.90.") An explanation is not provided. The selection of Choice B is correct, and the justification supports the solution ("...it shaves her 50¢ its $12.50 and A is $13.") 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 correction solution. The student provides the correct equations for Choice A (y= .5x+6) and Choice B (y=.75x+2). The solution to the system of equations is correct, and the explanation supports the solution. The student provides a well constructed graph; however, the point of intersection is not labeled, and no reference to the graph is made. The student gives the correct answer of Choice B with the graph providing a generally well developed justification (shows that at 14 rides the line representing ticket Choice B is lower than the line representing ticket Choice A), but no reference to the graph is made. This response demonstrates a clear 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. The student gives the correct equations (y =.50x+ 6) and (y =.75x+2), but the student does not label these equations. The solution to the system of equations is correct, but the calculations ".50(16)+6=16 + .75(16)+2=16" provide justification rather than the required explanation. They also reveal a significant mathematical error (the equations, when simplified, total 14 rather than 16). The student's correct answer of Choice B is fully justified ("...because .50(14)+6=$13+.75(14)+2=$12.50.") This response demonstrates a clear understanding and analysis of the problem.

Score for Anchor Paper #7: 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 gives the correct equations for Choice A (y=.50x+6) and Choice B (y=.75x+2). The student provides the correct solution to the system of equations. The fully developed explanation is presented symbolically; the student sets the equations equal to one another and solves for x, the number of rides. The student provides the correct answer of Choice B, and the justification is logically sound, fully developed, and supports the solution. The student replaces x with 14 in each equation and solves for y, the total cost of each ticket choice. The student then concludes, "The final cost of Choice A is $13, and the final cost of Choice B is $12.50. If Terry uses Choice B, she will save 50 cents." This response demonstrates a complete understanding and analysis of the problem.

Score for Anchor Paper #8: 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 gives the correct equations for Choice A (y=.5x+6) and Choice B (y=.75x+2). The student provides the correct solution to the system of equations ("...16 rides for both choice A + B to be equal in cost"). The explanation is clearly presented, fully developed, and supports the solution. The student correctly graphs each equation, labels the point of intersection, and interprets the significance of the point of intersection. ("...Terry will have spent $14 total so far. As you can see in the graph, the intersection is where they are the same.") The mislabeling of the lines constitutes a minor error. The student's correct answer of Choice B as the appropriate plan is fully justified ("At choice B, it costs $12.50 for 14 rides, and choice A costs $13.00 at 14 rides.") This response demonstrates a complete understanding and analysis of the problem.

Additional Scored Student Responses