School Improvement in Maryland
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 2002

The two triangles shown below are equilateral.

Complete the following in the answer box below:
  • What is the ratio of the smaller triangle's area to the larger triangle's area?
  • Use mathematics to justify your answer.

The following 3 Sample Student Responses represent a range of score points.

Sample Student Response #1

image of student response

Score for Sample Student Response #1: Rubric Score 2

Annotation: This response demonstrates a conceptual understanding and analysis of the problem. The student tries to solve the problem using an appropriate strategy of comparing the areas of the triangles. However, the incorrect ratio of 1:7.9 is found. When the student applies the formula A=1/2bh, an error is made in the area of the larger triangle. The student incorrectly uses 4 instead of 8 for the base. A justification using the correct and incorrect values for the area of each triangle is provided. Compare to Anchor Paper #3.
Sample Student Response #2

image of student response

Score for Sample Student Response #2: Rubric Score 3

Annotation: This response demonstrates a complete understanding and analysis of the problem. The work reveals that the student applies an appropriate strategy of comparing the areas of the triangles. The areas of both triangles are correct with the student arriving at a correct area ratio of 1:16. These correct area values for the triangles provide justification. Compare to Anchor Paper #6.
Sample Student Response #3

image of student response

Score for Sample Student Response #3: Rubric Score 1

Annotation: This response demonstrates a minimal understanding and analysis of the problem. The explanation shows that the student finds the correct 2:8 ratio of the sides. This is relevant work that could be used in an appropriate strategy. However, the incorrect area ratio of 1:4 (2:8 simplified) is provided as the answer. The strategy of applying the ratio of the sides to the area is inappropriate because the ratio of the sides to areas is not a linear relationship. The student fails to recognize that area is a squared function and that the area ratio is the square of the side ratio. No justification is present. Compare to Anchor Paper #2.

Additional Resources

Anchor Papers used in scoring

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 |