The following 9 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, demonstrating a minimal understanding and analysis of the problem. The representations are incomplete. The student has provided a correct equation for the charges at Bike Town ("$120x=C") and an incorrect equation for the charges at Bicycle City ("$160C+$80x"). There is no indication that the student has applied a reasonable strategy to find the number of days the charge will be the same at each store or what that charge would be. The response to when is it less or more expensive to use Bicycle City is reasonable, but it is not specific enough. There are no justifications.

Score for Anchor Paper #2: Rubric Score 1

Annotation: This response indicates little application of a reasonable strategy, demonstrating a minimal understanding and analysis of the problem. The representations are fundamentally correct ("C=160+80x for Bicycle City and C=120x for Bicycle Town"). The student does not find the correct solution to the system of equations. The student does attempt to describe when the stores are more or less expensive, but the answers contradict each other. ("Bike Town is much more expensive after 5 days in the Store. And Bicycle Town is less expensive than Bike town after 5-6 Days"). There is no justification for any of these statements.

Score for Anchor Paper #3: Rubric Score 2

Annotation: In this response, the student demonstrates a conceptual understanding and analysis of the problem. The response indicates an incomplete application of a reasonable strategy. The representations in the equations are fundamentally correct. The student also finds one of the values of the point of intersection ("4=x"), although the cost at 4 days is missing. The calculations "160 + 80x = 120x…4=x" provide explanation rather than the required justification. While the student has demonstrated a conceptual understanding of the point of intersection, it is not clear that he/she understands what happens before and after the point of intersection. The student states "Never" without making any reference to its meaning in the context of the problem.

Score for Anchor Paper #4: Rubric Score 2

Annotation: This response indicates an incomplete application of a reasonable strategy, demonstrating a conceptual understanding and analysis of the problem. The representations are fundamentally correct. The student also finds one of the values of the point of intersection ("in 4 days the store will charge the same"), although the cost at 4 days is missing and the attempted justification ("I use a table") is more of an explanation. The cost comparisons of the two stores are unclear ("It is less expensive to go to Bike City if it'll takes less or over 4 days Bike Town if it is less"). Justification for this statement is missing.

Score for Anchor Paper #5: Rubric Score 2

Annotation: This response indicates an incomplete application of a reasonable strategy, demonstrating a conceptual understanding and analysis of the problem. The representations of the equations are fundamentally correct. The student also provides the correct solution to the system of equations, indicating "The charge will be the same at each stores after 4 days. That charge will be $480 at both stores." However, the student does not demonstrate any understanding of what happens before and after the point of intersection. Justifications are missing.

Score for Anchor Paper #6: Rubric Score 3

Annotation: This response demonstrates a clear understanding and analysis of the problem. The response indicates application of a reasonable strategy that leads to a correct solution. The representations are essentially correct. The student provides the correct solution to the system of equations ("The number of days that the charge would be the same is 4. The cost is $480"). The student also understands the system of equations past the point of intersection ("It is less expensive to use bicycle city for 5 days or more. It is more expensive for 3 days or less"). However, the student has not provided any justification for these correct solutions.

Score for Anchor Paper #7: Rubric Score 3

Annotation: This response indicates application of a reasonable strategy that leads to a correct solution. Despite several minor omissions, this response demonstrates a clear understanding and analysis of the problem. The equations are present but only essentially correct, consisting of algebraic expressions that omit the charge (C), as required in the test item. The student provides the correct solution to the system of equations, but the statement, "the prices will be the same at 480," contains a minor application error in its omission of a dollar sign. The student also demonstrates an understanding of the system of equations past the point of intersection ("It is less expensive to use bike city after 4 days. It is more expensive for less than 4 days"). The table shows the costs for both shops on days 0-6 and provides justification for the student's solutions, but the table omits the identification of the equations that Y1 and Y2 represent.

Score for Anchor Paper #8: Rubric Score 4

Annotation: This response demonstrates a complete understanding and analysis of the problem. The response indicates application of a reasonable strategy that leads to a correct solution in the context of the problem. The representations are correct. The student provides the correct solution to the system of equations and justifies this solution by replacing the x in each equation with 4, arriving at 480 for both. The student also demonstrates an understanding of the system of equations before and after the point of intersection ("Less expensive - Bike City x>4…Bike Town x<4"). The justification is well developed since it includes a well-constructed graph and refers to it in the written portion of the response ("Bike City…the line is lower after 4 days…Bike Town…the line is lower before 4 days").

Score for Anchor Paper #9: Rubric Score 4

Annotation: This response indicates application of a reasonable strategy that leads to a correct solution in the context of the problem. The representations are correct. The student provides the correct solution to the system of equations. The student also correctly compares the costs of the two stores before and after 4 days through the use of brackets and arrows in a created table. The table shows the costs for both shops on days 0-6, providing fully developed justifications that support the student's solutions. The response demonstrates a complete understanding and analysis of the problem.

Additional Scored Student Responses