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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 2001

Two jogging paths go around the perimeters of two similar triangles in a park. The dimensions of the path around the smaller triangle are shown in the figure below. One complete lap around the outer edge of the longer path is 3,600 yards.

Use the answer box to complete the following. (You will need to use additional paper to complete the answer satisfactorily.)

  • What are the dimensions of the path around the larger triangle?
     
  • Use mathematics to justify your answer.

The following 7 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 minimal understanding and analysis of the problem. The work reveals that the student found the scale factor of three for the perimeter, but failed to apply the scale factor to the individual sides. This demonstrates little attempt to apply a reasonable strategy to find the dimensions of the larger triangle. The student has not provided any justification.


Anchor Paper #2

image of student response

Score for Anchor Paper #2: Rubric Score 1

Annotation: This response demonstrates minimal understanding and analysis of the problem. The student has arrived at the incorrect dimensions of "1000 by 800 by 600." The explanation reveals the student recognized "the smaller triangle is a 3,4,5 triangle;" however, the inappropriate strategy, "the dimensions are just doubled," does not account for the 3600-yard perimeter. The attempt to maintain the ratio demonstrates minimal understanding. The student has not provided any justification.


Anchor Paper #3

image of student response

Score for Anchor Paper #3: Rubric Score 2

Annotation: This response demonstrates conceptual understanding and analysis of the problem. The correct dimensions, "1500, 1200, and 900," are found "by seeing that the shorter path is 3 times longer the long side" – an appropriate strategy using the correct scale factor to multiply the dimensions of each of the sides. No justification is provided.


Anchor Paper #4

image of student response

Score for Anchor Paper #4: Rubric Score 2

Annotation: This response demonstrates conceptual understanding and analysis of the problem. The correct dimensions of "1500 yds, 1200 yds, 900 yds" are present. "Perimeter of the small one = 1200 x 3 = 3600" provides explanation of an appropriate strategy, revealing that the student found the correct scale factor of three. The student applied the scale factor to each of the sides as evidenced from the correct dimensions. Justification is absent.


Anchor Paper #5

image of student response

Score for Anchor Paper #5: Rubric Score 2

Annotation: This response demonstrates conceptual understanding and analysis of the problem. The correct dimensions of 900 yards, 1200 yards, and 1500 yards are correctly oriented on the student's hand-drawn diagram. Work, with the student applying proportion to each of the sides, provides a complete explanation of an appropriate strategy. Justification is absent.


Anchor Paper #6

image of student response

Score for Anchor Paper #6: Rubric Score 3

Annotation: This response demonstrates complete understanding and analysis of the problem. The correct dimensions of "900 yds, 1200 yds, and 1500 yds" are found using an appropriate strategy. The explanation fully supports the strategy of finding the variable by which sides of a 3-4-5 triangle should be multiplied to arrive at the desired 3600-yard perimeter. Full justification is present in the statement, "the two triangles are similar and the dimensions of the path around the smaller triangle are a Pythagorean Triple: 3,4,5 x 100; so the dimensions of the larger triangle also had to be 3,4,5 x a number."


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. The student's explanation supports a reasonable strategy to arrive at the correct dimensions of 900x1200x1500 yards. The student has applied a trial and error strategy, knowing that each side needed to be multiplied by the same scale factor (thus maintaining the ratio) and that the perimeter was equal to 3600 yards. Justification is provided in the statement, "...because they are similar, and similar shapes are proportional."


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 |