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 attempt to apply a reasonable strategy. The student has provided incorrect values for the areas of the garden, flowers, and sidewalk, with no explanation for how the incorrect areas were calculated. Six feet for the sidewalk were added to the wrong calculation of the flower area. This reveals a serious flaw in reasoning, since that is the value of only the width of the sidewalk, but the area is needed. The answer of 16 pounds of seed is incorrect. However, the student has attempted to subtract the incorrect values of the areas of the sidewalk and flowerbeds from the incorrect area of the garden, a relevant concept for this problem. The student has also correctly found the diameters of the circles, which could be used to correctly calculate the areas of the flowerbeds. The response demonstrates a minimal understanding and analysis of the problem.

Score for Anchor Paper #2: Rubric Score 1

Annotation: This response indicates little attempt to apply a reasonable strategy. The student has correctly calculated the area of the garden and has provided an explanation for that value (24x58=1392). However, there is no demonstration of any strategy that considers the areas that will not need grass. The response then demonstrates a strategy for calculating the amount of grass seed needed for his/her calculated area and arrives at the incorrect answer of 6 lbs. of seed. Without consideration of the areas that do not need grass, the response does not demonstrate a reasonable strategy for the entire problem. The response demonstrates a minimal understanding and analysis of the problem.

Score for Anchor Paper #3: Rubric Score 2

Annotation: This response demonstrates an incomplete application of a reasonable strategy. The strategy the student has employed estimates grass seed after considering the areas of the garden, sidewalk, and flowerbeds. The student has calculated the area of the garden and subtracted the area of the sidewalk. The explanation for this portion of the response is incomplete and not well developed. There are no values for the area of the garden and the sidewalk, just the area of the garden minus the area of the sidewalk; also, the statement, "subtracted 6 ft from the 24 ft because that much is being taken up by the sidewalk," is confusing and unclear. The student's value of 1044 square feet for the area calculated thus far is correct. 1044 square feet is close to the 1000 square feet that 4 pounds of grass seed will cover, so the student stopped working, as the "8 congruent circles would take up some space…one bag will be enough." The student has possibly assumed that grass seed comes only in 4-lb. bags; based on that assumption, he/she is correct. The student has not completed all the work that was required, but all elements were considered in a reasonable strategy of estimation. The response demonstrates a conceptual understanding and analysis of the problem.

Score for Anchor Paper #4: Rubric Score 2

Annotation: This response demonstrates an incomplete application of a reasonable strategy. The student has calculated the amount of grass seed needed after considering the areas of the garden, sidewalk, and flowerbeds. The explanation to support the solution is incomplete. The student has made an error in the explanation for how he/she found the grass area, saying, "I got the total area of the yard (1392 ft²) and subtracted that from 1008," which describes a process in which the figures have been reversed. The answer of 4 lbs. for the amount of grass seed is incorrect, with no explanation for the strategy employed. The student may have misunderstood that grass seed comes only in 4 lb. bags. The incomplete subtraction with its missing result and the answer of 4 lbs. with no explanation are two indications of incomplete application of strategy. The 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. The student has calculated the amount of grass seed needed after considering the areas of the garden, sidewalk, and flowerbeds. The explanation to support the solution reveals an error in the calculation of the area of the flowerbeds, since the student did not square the radius in his/her formula. The error is carried through in an otherwise fully explained, reasonable strategy. The student includes in the explanation the proportion used to calculate the amount of grass seed. The 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. The student has calculated the amount of grass seed needed after considering the areas of the garden, sidewalk, and flowerbeds. The explanation to support the solution reveals a computation error in the final computation for the grass area (380 ft² instead of the correct 384 ft²) and the possible misunderstanding that grass seed comes only in 4 lb. bags, resulting in an incorrect answer of 4 lbs. of grass seed. The 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 the correct solution in the context of the problem. The student has calculated the amount of grass seed needed after considering the areas of the garden, sidewalk, and flowerbeds. The explanation, showing all work supporting the solution, is clearly presented and fully developed. The student caused himself/herself a little extra work when he/she "divided (the area of the circle) by two because it is a semicircle…then multiplied it by 8 because there is a total of 8 semicircles," but the operation is correct and does not detract from the response. The student provides the correct answer of 2 pounds of grass seed. The 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 the correct solution in the context of the problem. The student has calculated the amount of grass seed needed after considering the areas of the garden, sidewalk, and flowerbeds. The explanation, showing all work supporting the solution, is clearly presented and fully developed. The student provides the correct answer of 2 pounds of grass seed. The response demonstrates a complete understanding and analysis of the problem.

Additional Scored Student Responses