The following 16 Sample Student Responses represent a range of score points.

Score for Sample Student Response #1: Rubric Score 1

Annotation: This response demonstrates a minimal understanding and analysis of the problem. While the student supplies incorrect dimensions (4 ft x 20 ft) for the guest room, those dimensions do provide an area of 80 square feet and are relevant to the question. The explanation reveals an inappropriate strategy whereby the student first finds the ratio of the areas (320/80=4) and then divides the area (80 sq. ft.) by 4, the ratio of the areas, to determine the incorrect dimension of 20 ft. Compare to Anchor Paper #2.

Score for Sample Student Response #2: Rubric Score 3

Annotation: This response demonstrates a complete understanding and analysis of the problem. The correct dimensions (8 feet x 10 feet) are given. A full explanation reveals the application of a reasonable strategy that first finds the ratio between the areas of the rooms (320:80 = 4:1). The recognition that (the ratio between the lengths and the widths of the room had to be the square root of the ratio of the areas) leads to the understanding that the ratio adjusts from 4:1 to 2:1. Therefore, the student divides 16 and 20, the dimensions of the room, by 2. Compare to Anchor Paper #8.

Score for Sample Student Response #3: Rubric Score 2

Annotation: This response demonstrates a conceptual understanding and analysis of the problem. Although the correct dimensions (8 by 10 feet) are provided and the explanation reveals the application of a reasonable strategy that uses a correct scale factor (half) of the dimensions of the family room (16 and 20) to calculate the correct dimensions, the response lacks an explanation as to how the student arrives at the correct scale factor of half. Compare to Anchor Paper #5.

Score for Sample Student Response #4: Rubric Score 1

Annotation: This response demonstrates a minimal understanding and analysis of the problem. Incorrect dimensions (4 feet by 5 feet), that fail to provide an area of 80 square feet, are supplied. The explanation gives a strategy whereby first the ratio of the areas (320/80 = 4) is found. Then, the student divides the family room's dimensions (16 x 20) by the area ratio (4), but fails to recognize that area is a squared relationship in comparison to dimensions. Compare to Anchor Paper #1.

Score for Sample Student Response #5: Rubric Score 2

Annotation: This response demonstrates a conceptual understanding and analysis of the problem. Correct dimensions (8 ft. by 10 ft.) are given. The explanation reveals a reasonable strategy of first finding the ratio of the room's dimensions (4/5) and then selecting dimensions with the same ratio. Compare to Anchor Paper #4.

Score for Sample Student Response #6: Rubric Score 3

Annotation: This response demonstrates a complete understanding and analysis of the problem. The student provides correct dimensions (8 ft by 10 ft) for the guest room. A full explanation reveals the application of a reasonable strategy of proportion. The student first calculates the ratio (4/5) of the family room's dimensions. Knowing that for the rooms to be proportional the guest room dimensions must be in the same ratio (4/5) as the family room, the student then chooses two dimensions (8 and 10) that, when multiplied together, not only equal an area of 80 square feet, but also maintain the ratio of 4/5. Compare to Anchor Paper #6.

Score for Sample Student Response #7: Rubric Score 2

Annotation: This response demonstrates a conceptual understanding and analysis of the problem. The correct dimensions (8 feet by 10 feet) are provided. The explanation reveals a reasonable strategy whereby the student first finds the ratio of the areas (80/320 = ¼) and then applies the correct scale factor (½) to the family room's dimensions (16 and 20) to calculate the correct dimensions. The explanation of how that scale factor is determined reveals a flaw in the student's strategy (¼ + ¼ = ½ the ratio of the areas is ½ the ratio of the lengths).

Score for Sample Student Response #8: Rubric Score 1

Annotation: This response demonstrates a minimal understanding and analysis of the problem. Incorrect dimensions (4 ft by 5 ft), that fail to provide an area of 80 square feet, are given. The explanation reveals an attempt to apply a strategy of proportion to calculate both dimensions. However, not recognizing that area is a squared relationship in comparison to dimension, the student incorrectly sets up the first proportion (320/16 = 80/x), rather than 320/16² = 80/x², and finds one dimension (4). The error in the set up of the first proportion is repeated in the second, resulting in a second incorrect dimension (5). Compare to Anchor Paper #3.

Score for Sample Student Response #9: Rubric Score 2

Annotation: This response demonstrates a conceptual understanding and analysis of the problem. Correct dimensions (8 x 10) are given for the guest room. The explanation reveals an application of a reasonable strategy that uses a correct scale factor (1/2) of the family room's dimensions. However, the response lacks an explanation as to how the student arrives at the correct scale factor. Compare to Anchor Paper #5.

Score for Sample Student Response #10: Rubric Score 3

Annotation: This response demonstrates a complete understanding and analysis of the problem. The student provides correct dimensions (8 ft by 10 ft) for the guest room. A full explanation reveals the application of a reasonable strategy that first finds the ratio between the areas of the rooms (320/80 = 4). The student knows that the rooms are proportional and that the ratio of the family room to guest room dimensions would be 2:1 (since area is measured in units², I found the square root of 4, which is 2). The student then verifies the dimensions by using a correct proportion. Compare to Anchor Paper #8.

Score for Sample Student Response #11: Rubric Score 2

Annotation: This response demonstrates a conceptual understanding and analysis of the problem. Correct dimensions (8 feet by 10 feet) are given. An explanation reveals the application of a reasonable strategy that uses a correct scale factor (2) and multiplies by the correct dimensions (8 x 10) to verify that they are proportional to the family room dimensions (16 x 20). However, no explanation is provided as to how the student determines that scale factor. Compare to Anchor Paper #5.

Score for Sample Student Response #12: Rubric Score 1

Annotation: This response demonstrates a minimal understanding and analysis of the problem. Incorrect dimensions (20 ft. and 4 ft.) for the guest room are given. However, because these dimensions do provide an area of 80 square feet, they are relevant. The explanation reveals an attempted strategy of proportion to determine the room's width, but the proportion is incorrectly set up. Not recognizing that area is a squared relationship in comparison to dimension, the student sets up the proportion (320/80 = 16/x), rather than the correct proportion, 320/80 = 16²/x². The guest room area (80 sq. ft.) is then divided by 4 ft., the incorrectly calculated width, resulting in a second incorrect dimension of 20 ft. Compare to Anchor Paper #2.

Score for Sample Student Response #13: Rubric Score 3

Annotation: This response demonstrates a complete understanding and analysis of the problem. The student provides the correct dimensions (8 feet by 10 feet) for the guest room, and a full explanation reveals the application of a reasonable strategy to determine a scale factor (1/2). Knowing that the dimensions of the two rooms are proportional, the student makes the first determination (when the dimensions of the larger rectangle are multiplied by the same number, x, one finds the dimensions of the smaller rectangle). Then, by setting up and solving the algebraic equation (16x · 20x = 80), the student calculates x = ½, the scale factor of the sides, and multiples 16 and 20 by that scale factor to arrive at a final answer of 8 x 10 for the dimensions of the guest room. Compare to Anchor Paper #7.

Score for Sample Student Response #14: Rubric Score 2

Annotation: This response demonstrates a conceptual understanding and analysis of the problem. Correct dimensions (8 ft by 10 ft) are provided for the guest room. The explanation reveals a strategy of dimensions and area in a proportion. After calculating the two dimensions (4 and 5), the student converts these values to the correct dimensions (8 x 10), but fails to supply any explanation regarding the application of a scale factor. Compare to Anchor Paper #4.

Score for Sample Student Response #15: Rubric Score 1

Annotation: This response demonstrates a minimal understanding and analysis of the problem. The student gives incorrect dimensions (4 x 5) that fail to provide an area of 80 square feet. In the explanation, the student first finds the ratio of the areas (320/80 = 4) and then divides the family room's dimensions, 16 x 20, by the area ratio (4). This strategy fails to recognize that area is a squared relationship in comparison to dimension. Compare to Anchor Paper #1.

Score for Sample Student Response #16: Rubric Score 3

Annotation: This response demonstrates a complete understanding and analysis of the problem. Correct dimensions (8 x 10) are provided for the guest room. A full explanation reveals the application of a reasonable strategy of proportion. Knowing that the guest room dimensions must be in the same ratio as those of the family room, the student simplifies the original 16/20 dimensions to 8/10 and then verifies that those new dimensions do result in an area of 80 square feet. Compare to Anchor Paper #6.

Anchor Papers used in scoring