| Public Release Item Scoring Information |
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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 2.3.1 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.
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Brief Constructed Response (BCR) Item - Released in 2001 |
A gardener uses 20 gallons of water each week on his 8-foot by 10-foot vegetable
garden. He plans to enlarge his garden to 24 feet by 30 feet.
Use the answer box to complete the following. (You will need to use additional paper to complete the answer satisfactorily.)
- How much water would he expect to use on his new garden? Use
mathematics to explain how you determined your answer. Use words,
symbols, or both in your explanation.
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The following 3 Sample Student Responses represent a range of score points.
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| Sample Student Response #1 |
Score for Sample Student Response #1:
Rubric Score 2
Annotation: This response demonstrates a conceptual understanding and analysis of the problem. The student provides an incorrect answer of 720 gallons of water. The explanation describes a correct strategy to solve the problem, but an error resulted in the incorrect answer. "I calculated the answer by finding the area of both gardens, then dividing the larger area by the smaller one. Then I got that the larger garden was nine times bigger than the smaller one. So I multiplied the gal. used per week for the smaller garden by 9 and got my answer." Compare to Anchor Paper #3.
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| Sample Student Response #2 |
Score for Sample Student Response #2:
Rubric Score 3
Annotation: This response demonstrates a complete understanding and analysis of the problem. The student correctly answers that 180 gallons of water will be required for the new garden. Complete explanation of an appropriate strategy to solve the problem is present in the correct set-up of the reduced ratio of water usage in a correct proportion: "If every gallon waters 4 sq. ft., then 1/4 = x/720 = 180/720."
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| Sample Student Response #3 |
Score for Sample Student Response #3:
Rubric Score 1
Annotation: This response demonstrates minimal understanding and analysis of the problem. The student has arrived at the incorrect answer of 60 gallons of water for the new garden. The student finds the correct scale factor of the dimensions: "the old dimensions of his garden to be 1/3 the dimension of his plans for a new garden." After finding the correct scale factor, the student applied an inappropriate strategy of multiplying the water usage by the scale factor. Compare to Anchor Paper #1.
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Brief Constructed Response (BCR) Rubric |
| Print: Scoring Rubric (pdf)
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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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/share/clg/xml/public_release/mathematics/2001_231_geo17.xml
