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Public Release Item Scoring Information Return

Goal 2 Geometry, Measurement, And Reasoning

Expectation 2.3 The student will apply concepts of measurement using tools and technology when appropriate.

Indicator 2.3.1 The student will use algebraic and/or geometric properties to measure indirectly.

Assessment Limits:

  • “Measure indirectly” means to use mathematical concepts such as congruence, similarity, and ratio and proportion to calculate measurements.
  • Similarity and congruence will be directly stated or implied (scale drawings, enlargements).
  • Items may require the student to make comparisons.
  • This indicator may incorporate measuring.
  • This indicator does not include right-triangle trigonometry.

Brief Constructed Response (BCR) Item - Released in 2004

The Smiths designed their family room to measure 16 feet by 20 feet. They designed a guest room to have proportional dimensions with an area of 80 square feet.

Complete the following on a piece of paper and/or in the answer box below:
  • What are the dimensions of the guest room? Use mathematics to explain how you determined your answer. Use words, symbols, or both in your explanation.

The following 8 Anchor Papers represent a range of score points and are used in conjunction with the rubrics to assess student responses.

Anchor Paper #1

image of student response

Score for Anchor Paper #1: Rubric Score 1

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


Anchor Paper #2

image of student response

Score for Anchor Paper #2: Rubric Score 1

Annotation: This response demonstrates a minimal understanding and analysis of the problem. Incorrect dimensions (20 x 4 ft) are given for the guest room. However, because these dimensions do provide an area of 80 square feet, they are relevant. The explanation reveals that the student incorrectly sets up a proportion (16/320=x/80 rather than the correct 16²/320=x²/80) in an attempt to apply a proportion strategy to determine the room's width. The student then divides the guest room area (80 sq. ft.) by 4, the incorrectly calculated width, to arrive at the second incorrect dimension (20 ft.).


Anchor Paper #3

image of student response

Score for Anchor Paper #3: Rubric Score 1

Annotation: This response demonstrates a minimal understanding and analysis of the problem. Incorrect dimensions (4 ft and 5 ft) are given that fail to provide an area of 80 square feet. The explanation reveals an attempt to apply a strategy of proportion to calculate one of the guest room's dimensions. However, the student, who does not recognize that area is a squared relationship in comparison to dimension, sets up the incorrect first proportion (320/20 = 80/x), rather than the correct, 320/20² = 80/x². The incorrect dimension (5) is then substituted into a correctly set up proportion to calculate the second dimension, resulting in an incorrect second dimension (4).


Anchor Paper #4

image of student response

Score for Anchor Paper #4: 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 with the student first finding the ratio (4/5) of the 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 chooses two dimensions (8 and 10) that maintain the ratio (4/5), but then fails to verify that those two dimensions do equal an area of 80 square feet.


Anchor Paper #5

image of student response

Score for Anchor Paper #5: Rubric Score 2

Annotation: This response demonstrates a conceptual understanding and analysis of the problem. The correct dimensions (10 feet by 8 ft) are provided. The explanation reveals the application of a reasonable strategy that uses a correct scale factor (half) of the family room's dimensions (20 and 16) to calculate the correct dimensions. No explanation is given as to how the scale factor is determined.


Anchor Paper #6

image of student response

Score for Anchor Paper #6: Rubric Score 3

Annotation: This response demonstrates a complete understanding and analysis of the problem. The student gives correct dimensions (8 ft x 10 ft) and a full explanation using the reasonable strategy of proportion. Knowing that the guest room dimensions must be in the same 4/5 ratio as the family room (16 is 4/5 of 20, and 8 is 4/5 of 10), the student then tests the second parameter and determines that the new dimensions provide an area of 80 square feet {A=lw; 80 =(8)(10)}.


Anchor Paper #7

image of student response

Score for Anchor Paper #7: Rubric Score 3

Annotation: This response demonstrates a complete understanding and analysis of the problem. Correct dimensions (8' x 10') are provided. A full explanation reveals the application of a reasonable strategy using a scale factor. By first finding the ratio of the length to the width (20/16), the student then determines that the length is 1.25 times the width and solves the problem using equations (l · w = 80. Since the rooms are similar, I could set up 1.25x · x = 80. I solved for x to get the width, and I multiplied 1.25 to get the length).


Anchor Paper #8

image of student response

Score for Anchor Paper #8: Rubric Score 3

Annotation: This response demonstrates a complete understanding and analysis of the problem. The correct dimensions (8 feet by 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 reduced to 4:1). The student determines the ratio of the sides (2:1) by finding the square root of the ratio of the areas and then uses proportions to arrive at the correct guest room dimensions.


Brief Constructed Response (BCR) Rubric
Print: Scoring Rubric (pdf)
Score 3

The response indicates application of a reasonable strategy that leads to a correct solution in the context of the problem. The representations are essentially correct. The explanation and/or justification is logically sound, clearly presented, fully developed, supports the solution, and does not contain significant mathematical errors. The response demonstrates a complete understanding and analysis of the problem.

Score 2

The response indicates application of a reasonable strategy that may be incomplete or undeveloped. It may or may not lead to a correct solution. The representations are fundamentally correct. The explanation and/or justification supports the solution and is plausible, although it may not be well developed or complete. The response demonstrates a conceptual understanding and analysis of the problem.

Score 1

The response indicates little or no attempt to apply a reasonable strategy or applies an inappropriate strategy. It may or may not have the correct answer. The representations are incomplete or missing. The explanation and/or justification reveals serious flaws in reasoning. The explanation and/or justification may be incomplete or missing. The response demonstrates a minimal understanding and analysis of the problem.

Score 0

The response is completely incorrect or irrelevant. There may be no response, or the response may state, “I don't know.”

Explanation refers to the student using the language of mathematics to communicate how the student arrived at the solution.

Justification refers to the student using mathematical principles to support the reasoning used to solve the problem or to demonstrate that the solution is correct. This could include the appropriate definitions, postulates and theorems.

Essentially correct representations may contain a few minor errors such as missing labels, reversed axes, or scales that are not uniform.

Fundamentally correct representations may contain several minor errors such as missing labels, reversed axes, or scales that are not uniform.

Last Revised 8/16/00
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Resources for 2.3.1:
Skill Statements | PUBLIC RELEASE ITEMS | Lesson Plans |