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 representation in the form of an equation is incorrect (1960=5063+1181). The student writes that the slope is positive but does not give the slope’s value or the contextual meaning. The estimated population for 1995 is incorrect (8140) and the explanation reveals a flaw in reasoning (1995=x+1181). The student indicates that the equation is not a good model to predict the population in 2025 and the justification supports the solution (it is a long time from now). 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 gives the correct equation for when x represents whole years (y=139.44x-268312.5). The slope is correct (139.44) but the contextual meaning is incorrect (The slope shows the direction in which the graph goes). There is no indication that the student has responded to the third part of the question. The student incorrectly indicates that the equation is a good model to predict the population in 2025. A justification is not provided. 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 an incomplete strategy. The representation in the form of an equation is correct (y=139.44x+4989.9). The slope of the equation is correct (139.44) and the contextual meaning is complete (how many people increase each year.). The estimated population for 1995 is incorrect (4292.7). The explanation reveals a mathematical error; the student replaces x in the equation with -.5 rather than 35. The student incorrectly indicates that the equation is a good model to predict the population in 2025. The justification reveals a flaw in reasoning (because it is the rate of change for the past years, 1960-1990). This response demonstrates a conceptual understanding and analysis of the problem.

Score for Anchor Paper #4: Rubric Score 2

Annotation: This response indicates application of an incomplete strategy. The student gives the correct equation for when x represents whole years (y=139.44x-268312.5). There is no indication that the student has responded to the second part of the question. The estimated population for 1995 is correct (9870.3) and the explanation supports the solution (substituting 1995 for x). Instead of stating whether the equation is or is not a good model and justifying the response, the student utilizes an incorrect strategy (In year 2025 the population would be 14053.5). 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 some correct solutions. The representation in the form of an equation is correct (y=139.44x+4989.9). The slope of the equation is correct (139.44). The contextual meaning is incomplete (the rate of change of population). The estimated population for 1995 is correct (9870) and the explanation supports the solution. The student writes (using the table in my calculator), then draws a table and circles the appropriate set of numbers. The student indicates that the equation is not a good model to predict the population in 2025; however, the student provides a non-mathematical justification (I don’t think you can predict population because of variables such as disease, birth rate etc. Something might happen to the town. For example everyone could move out of the town for the city. A lot of things could happen). 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 some correct solutions. The student gives the correct equation for when x represents years since 1900 (y=139.44x+-3376.5). The slope of the equation is incorrect and the student does not provide the contextual meaning of the slope. The estimated population for 1995 is correct (9870.3). The explanation supports the solution (y=139.44(95)+-3376.5). The student indicates that the equation is not a good model to predict the population in 2025 and provides a correct justification (2025 is so far away, you don’t have the data to support it). 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 representation in the form of an equation is correct (y=139.44x+4989.9). The slope of the equation is correct (139.44) and the contextual meaning is complete (the increase in population per year). The estimated population for 1995 is correct (9870) and the explanation is fully developed and clearly presented. The student replaces x in the equation with 35, and solves for y (I plugged 35 [years since 1960] into my equation). The student indicates that the equation is not a good model to predict the population in 2025 and the justification is fully developed (I wouldn’t expect my model to be accurate that far into the future; I think that 2025 is too far into the future for my model to be correct). 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 representation in the form of an equation is correct (y=139.44x+4989.9). The slope of the equation is correct (139.44) and the contextual meaning is complete (how much the population increased each year). The estimated population for 1995 is correct (9870.3). The explanation is fully developed and clearly presented (y=139.44(35)+4989.9; y=9870.3). The student indicates that the equation is not a good model to predict the population in 2025 and the justification is fully developed (the timespand from 1960 to 2025 is to big). This response demonstrates a complete understanding and analysis of the problem.