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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 2001

The dimensions of two suitcases are shown below. Suitcase A is a trapezoidal prism, and Suitcase B is a rectangular prism.

Note: These figures are not drawn to scale.

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

  • What is the volume of Suitcase A? Use mathematics to explain how you determined the volume of Suitcase A. Use words, symbols, or both in your explanation.
     
  • Both suitcases have the same volume. What is the height of Suitcase B? Use mathematics to explain how you determined the height of Suitcase B. Use words, symbols, or both in your explanation.

The following 16 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 3

Annotation: This response demonstrates a clear understanding and analysis of the problem. The student has arrived at correct values for the volume of Suitcase A and the height of Suitcase B. The explanation of a reasonable strategy to solve the problem is generally well developed. Values in the explanation reveal that the student broke down the trapezoidal prism into parts. The correct volume value of two triangular prisms (1440) was arrived at, but the student's explanation, "Multiply five (5) times twelve (12) and split that in half to get a portion of the trapezoid, find the area, you get 1440 square inches," does not clearly indicate that strategy. The student then explains how to calculate the volume of Suitcase A. Full explanation for calculating the correct height for Suitcase B is provided in the statement, "you multiply the base times the width then divide that into the volume of Suitcase A."


Sample Student Response #2

image of student response

Score for Sample Student Response #2: Rubric Score 2

Annotation: This response demonstrates a conceptual understanding and analysis of the problem. The work reveals that the student has an incomplete reasonable strategy to solve the entire problem. The student finds an incorrect volume for Suitcase A. However, working with the incorrect volume, the student uses a reasonable strategy to solve for the height of Suitcase B. Compare to Anchor Paper #4.
Sample Student Response #3

image of student response

Score for Sample Student Response #3: Rubric Score 1

Annotation: This response demonstrates minimal understanding and analysis of the problem. Incorrect answers of "2808 in 3 " and "17.86" are provided. However, the student has correctly recognized the trapezoid shape. Work reveals the use of the formula (A=1/2(b1+b2)h) to find the volume of Suitcase A. The student has used an incorrect value for b2 and did not multiply by 24 to correctly calculate the volume. Solving for the volume of Suitcase B, the student provides an explanation of an inappropriate strategy to arrive at the incorrect answer of "17.86." Compare to Anchor Paper #2.
Sample Student Response #4

image of student response

Score for Sample Student Response #4: Rubric Score 4

Annotation: This response demonstrates complete understanding and analysis of the problem. The correct volume for Suitcase A ("2880 in.2") and the correct height of Suitcase B ("16 in.") are clearly evident. The volume of Suitcase A lacks a correct label of cubic inches. This is considered to be an error in labeling rather than in strategy, and, therefore, not a significant mathematical error. Work provides a fully developed explanation to solve the entire problem. Compare to Anchor Paper #8.
Sample Student Response #5


Sample Student Response #6


Sample Student Response #7


Sample Student Response #8


Sample Student Response #9


Sample Student Response #10


Sample Student Response #11


Sample Student Response #12


Sample Student Response #13


Sample Student Response #14


Sample Student Response #15


Sample Student Response #16


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 |