The following 12 Sample Student Responses represent a range of score points.

Score for Sample Student Response #1: Rubric Score 2

Annotation: This response demonstrates a reasonable but not well-developed strategy for finding the dimensions. The correct dimensions of the fenced-in region are clearly identified. While the student has incorrectly implied division rather than multiplication, the student has correctly executed an appropriate strategy, multiplying by a factor of 1 1/2 (the equivalent of 3/2>) to calculate the dimensions of the fenced-in region ("you take the pool dimensions into 1 1/2 and you have the fence dimensions"). An incorrect value of 120 is given for the perimeter ("120 because the length sides cover the deck"). The cost to purchase fencing for the fenced-in region is the correct value of $1350. The student demonstrates a good understanding of applying a factor to dimensions and of calculating cost, two of the main components of the problem. This response demonstrates a conceptual understanding and analysis of the problem. Compare to Anchor Paper #3.

Score for Sample Student Response #2: Rubric Score 3

Annotation: This response indicates application of a reasonable strategy that leads to a correct solution in the context of the problem. The correct answers for dimensions, perimeter, and cost are clearly identified. The student clearly presents and fully develops a strategy using a factor of 1.5 (the equivalent of 3/2) to calculate the dimensions of the fenced-in region. Complete explanation is provided in work that shows the dimensions multiplied by the factor. The student correctly calculates perimeter and the cost to purchase fencing to enclose the deck. The explanations for Bullets #2 and #3 neither detract nor add to the response since they were not required. This response demonstrates a complete understanding and analysis of the problem. Compare to Anchor Paper #5.

Score for Sample Student Response #3: Rubric Score 1

Annotation: This response indicates application of an inappropriate strategy. The width, not the length, of the dimensions is correct. The student explains the strategy employed, "…I found the area of the pool, and multiplied by ," an inappropriate strategy for finding dimensions that does not even result in the dimensions given. There is no value for perimeter, as the student mistakenly calculates area rather than perimeter. The cost to purchase fencing for the fenced-in region ($9000) is incorrect. However, cost was correctly calculated using the value for area instead of perimeter (1200 x $7.50=$9000). This response demonstrates a minimal understanding and analysis of the problem. Compare to Anchor Paper #1.

Score for Sample Student Response #4: Rubric Score 2

Annotation: This response demonstrates application of a reasonable strategy that leads to the correct solution in the context of the problem. The correct answers for dimensions (although "H" is confused with width), perimeter, and cost to purchase fencing for the fenced-in region are clearly identified. There is no explanation for the strategy used to correctly find the dimensions. Without this explanation, this response demonstrates a conceptual understanding and analysis of the problem.

Score for Sample Student Response #5: Rubric Score 1

Annotation: This response indicates little or no application of a reasonable strategy to find the dimensions of the fenced in region of the pool. The answer for dimensions of the fenced-in region is incorrect. The student provides the area of the pool, rather than dimensions of the fenced-in region, revealing no understanding of applying a ratio to the given dimensions of the pool. The perimeter is incorrect, with no understanding of perimeter demonstrated. The cost of $1200 is incorrect; however, the cost was correctly calculated based on the incorrect value for perimeter. This response demonstrates a minimal understanding and analysis of the problem.

Score for Sample Student Response #6: Rubric Score 3

Annotation: This response indicates application of a reasonable strategy that leads to a correct solution in the context of the problem. The correct answers for dimensions, perimeter, and cost to purchase fencing for the fenced-in region are clearly identified. The student clearly presents and fully develops a strategy, multiplying the given dimensions of the pool by the ratio to calculate the dimensions of the fenced-in region. The computations showing all the mathematical calculations provide a complete explanation to support the solution. The student correctly calculates both the perimeter and the cost to purchase fencing to enclose the deck. This response demonstrates a complete understanding and analysis of the problem. Compare to Anchor Paper #5.

Score for Sample Student Response #7: Rubric Score 1

Annotation: This student explains the strategy employed: "I found the area of the pool and to the given ratio and put · x/800 and got 2400 sq. yds." This is an inappropriate strategy for finding dimensions that does not even result in the dimensions given. The correct length, not the width, of the dimensions is present. Area, not perimeter, was calculated from his/her dimensions. The cost of $180 to purchase fencing for the fenced-in region is incorrect, even for the student's value for perimeter. The correct length of the fenced-in region has relevance. This response demonstrates a minimal understanding and analysis of the problem. Compare to Anchor Paper #1.

Score for Sample Student Response #8: Rubric Score 2

Annotation: This student's explanation of the strategy using proportion to calculate the dimensions of the fenced-in region has an error, stating that the dimensions had to be "divisible" rather than multiplied by the ratio. The correct dimensions of the fenced-in region are clearly identified. The student calculates area instead of calculating perimeter. The cost of $13,500 to purchase fencing around the enclosed area is an incorrect answer, but the student correctly calculates the cost based on his/her incorrect value for perimeter (1,800 yds.). The student demonstrates a good understanding of applying a ratio to dimensions and of calculating cost, two of the main components of the problem. This response demonstrates a conceptual understanding and analysis of the problem. Compare to Anchor Paper #3.

Score for Sample Student Response #9: Rubric Score 3

Annotation: This response indicates application of a reasonable strategy that leads to a correct solution in the context of the problem. The correct answers for dimensions, perimeter, and cost to purchase fencing for the fenced-in region are clearly identified. The student's explanation clearly presents a reasonable strategy of multiplying the dimensions by the ratio to calculate the dimensions of the fenced-in region. The dimensions do not include the units (yards), but this is not a significant error. The student correctly calculates perimeter, and the response provides the correctly calculated cost to purchase fencing to enclose the deck. This response demonstrates a complete understanding and analysis of the problem. Compare to Anchor Paper #6.

Score for Sample Student Response #10: Rubric Score 2

Annotation: This student's explanation clearly presents a strategy of multiplying the given dimensions by the ratio (3/2) to calculate the dimensions of the fenced-in region. The correct answers for dimensions and perimeter are clearly identified. The student has correctly calculated perimeter, but there is no attempt at calculating the cost of purchasing the fencing for the enclosed region. The student demonstrates a good understanding of applying a ratio to dimensions and of calculating perimeter, two of the main components of the problem. This response demonstrates a conceptual understanding and analysis of the problem. Compare to Anchor Paper #3.

Score for Sample Student Response #11: Rubric Score 1

Annotation: This student's explanation, "The pool is similar to the deck and the sides are parallel. It is clear that the deck is 2 times as big as the pool, so the number value doubles," indicates the application of an inappropriate strategy. The dimensions are therefore incorrect. The perimeter is also incorrect. And the cost to purchase fencing for the fenced-in region ($24,000) is incorrect. However, cost was correctly calculated using the student's incorrect value for perimeter (3200 x $7.50=$24,000). This response demonstrates a minimal understanding and analysis of the problem. Compare to Anchor Paper #1.

Score for Sample Student Response #12: Rubric Score 3

Annotation: This response indicates application of a reasonable strategy that leads to a correct solution in the context of the problem. The correct answers for dimensions, perimeter, and cost to purchase fencing for the fenced-in region are clearly identified. The student clearly presents and fully develops a strategy using proportion to calculate the dimensions of the fenced-in region. The computations showing all the mathematical calculations provide a complete explanation to support the solution. The student has correctly calculated perimeter and has correctly calculated the cost to purchase fencing to enclose the deck. (The student explains how the perimeter and total cost are calculated, but these explanations are extraneous and do not add to or detract from the score.) This response demonstrates a complete understanding and analysis of the problem. Compare to Anchor Paper #5.

Anchor Papers used in scoring