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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 2004

A cylindrical tank is shown below. The tank is refilled when the water level reaches the refill line.

Complete the following on a piece of paper and/or in the answer box below:

  • How much water can the entire tank hold? Use mathematics to explain how you determined your answer. Use words, symbols, or both in your explanation.
     
  • At the beginning of the day the tank is full. How much water can be removed from the tank before it is necessary to refill the tank? 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 provides a correct value (125.67) that lacks any unit of measure; however, there is no explanation of the strategy employed. No attempt is made to answer the second part of the problem.


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. The student provides a correct value (125.66) with an error, units of square feet rather than cubic feet. An appropriate strategy for volume (area of base x the height) is indicated; however, without any values, the explanation is weak. No attempt is made to answer the second part of the problem.


Anchor Paper #3

image of student response

Score for Anchor Paper #3: Rubric Score 2

Annotation: This response demonstrates a conceptual understanding and analysis of the problem. Although an incorrect value (40 units of water) is given, the student attempts a reasonable strategy to calculate volume. The explanation demonstrates an error (I multiplied area of base x height, and those numbers were 4 x 10). In response to the second part of the problem, the student provides an incorrect (36 units of water), but relevant, answer. An explanation of a reasonable strategy to determine the amount of water that can be removed is given, but contains the same mistake in the area of the base as the first part of the problem.


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. A correct value (126) is provided with no unit of measure, and a full explanation of a reasonable strategy to determine volume is given. No attempt is made to answer the second part of the problem.


Anchor Paper #5

image of student response

Score for Anchor Paper #5: Rubric Score 3

Annotation: This response demonstrates a clear understanding and analysis of the problem. An incorrect answer (502.7 ft³) is given. While an explanation of a reasonable strategy to determine volume is provided, the student makes the error of using the diameter, rather than radius value, in the correct formula. For the second part of the problem, an incorrect (452.43 ft³), but relevant, answer is supplied. An explanation, continuing the error from the problem's first part, is provided for a reasonable strategy to determine the amount of water that can be removed.


Anchor Paper #6

image of student response

Score for Anchor Paper #6: Rubric Score 3

Annotation: This response demonstrates a clear understanding and analysis of the problem. The student provides an incomplete answer (the cylindrical tank can hold 12.6 ft² at the refill line). An explanation of a reasonable strategy to determine volume is given; however, the student never responds to how much water the entire tank can hold. In response to the second part of the problem, a correct rounded value (113.4 ft²) with an error, units of square feet rather than cubic feet, and an explanation of a reasonable strategy are provided.


Anchor Paper #7

image of student response

Score for Anchor Paper #7: Rubric Score 4

Annotation: This response demonstrates a complete understanding and analysis of the problem. Both a correct answer (40 ft³) and a full explanation of a reasonable strategy to calculate volume are provided. For the second part of the problem, a correct answer (36 ft³) and a full explanation of a reasonable strategy to calculate the amount of water to be removed are given.


Anchor Paper #8

image of student response

Score for Anchor Paper #8: Rubric Score 4

Annotation: This response demonstrates a complete understanding and analysis of the problem. The answer (125.6 ft³) is correct; a full explanation of a reasonable strategy to calculate volume is given. In responding to the second part of the problem, a correct answer (113.04 ft³) and an explanation of a reasonable strategy are provided.


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 |