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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 2.3.2 The student will use techniques of measurement and will estimate, calculate, and/or compare perimeter, circumference, area, volume, and/or surface area of two-and three-dimensional figures and their parts.

Assessment Limits:

  • Two-dimensional shapes include polygons, circles, and composite figures.
  • Three-dimensional shapes include cubes, prisms, pyramids, cylinders, cones, spheres, and composite figures.
  • Formulas will be provided.
  • No oblique solids will be used.
  • Items may involve applications of geometric properties and relationships.
  • Students may be required to make comparisons which do not require calculations.

Extended Constructed Response (ECR) Item - Released in 2003

A golf ball has a diameter of 1.68 inches. Twelve golf balls will be packaged in a rectangular cardboard box. There are three choices for how the golf balls will be arranged.

Choice A:  12 golf balls in one row

Choice B:  2 rows of golf balls, each row 6 balls long

Choice C:  3 rows of golf balls, each row 4 balls long

Complete the following in the answer box below:

  • Which of the three choices requires the least amount of cardboard? Use mathematics to explain how you determined your answer. Use words, symbols, or both in your explanation.
 

The following 4 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 1

Annotation: This response demonstrates a minimal understanding and analysis of the problem. The student incorrectly answers "it doesn't matter which arrangement you use." The explanation reveals an inappropriate strategy that relies on the comparison of the length of each box multiplied by the number of rows per box. However, there is some relevant understanding in the student's explanation for finding the dimensions of a side of each box. Compare to Anchor Paper #2.
Sample Student Response #2

image of student response

Score for Sample Student Response #2: Rubric Score 3

Annotation: This response demonstrates a clear understanding and analysis of the problem. The student correctly answers "Choice C," and the explanation shows that application of a correct strategy of surface area is employed. However, an error in a dimension for Box C (5.68 rather than the correct value of 6.72) leads to an incorrect surface area of 93.2736 for Box C (rather than the correct value of 107.26). Compare to Anchor Paper #5.
Sample Student Response #3

image of student response

Score for Sample Student Response #3: Rubric Score 4

Annotation: This response demonstrates a complete understanding and analysis of the problem. The student correctly answers "Choice C because it uses up the least cardboard." A full explanation for finding the surface areas is supported by the correct dimensions and correct surface area values. Compare to Anchor Paper #8.
Sample Student Response #4

image of student response

Score for Sample Student Response #4: Rubric Score 2

Annotation: This response demonstrates a conceptual understanding and analysis of the problem. The student correctly answers "Choice C" and states that the surface area, an appropriate strategy, is calculated. However, the student gives the three incorrect surface area values of 67.68, 50.88, and 47.52 square inches. Work reveals that the student fails to consider the diameter of the golf ball in all the calculations of the sides of each box. This demonstrates an incomplete correct strategy. Compare to Anchor Paper #3.

Additional Resources

Anchor Papers used in scoring

Extended Constructed Response (ECR) Rubric
Print: Scoring Rubric (pdf)
Score 4

The response indicates application of a reasonable strategy that leads to a correct solution in the context of the problem. The representations are 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 3

The response indicates application of a reasonable strategy that may or may not lead to a correct solution. The representations are essentially correct. The explanation and/or justification is generally well developed, feasible, and supports the solution. The response demonstrates a clear understanding and analysis of the problem.

Score 2

The response indicates an incomplete application of a reasonable strategy that 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 application of a reasonable 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 2.3.2:
Skill Statements | PUBLIC RELEASE ITEMS | Lesson Plans |