| Public Release Item Scoring Information |
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Goal 2 Geometry, Measurement, And Reasoning |
Expectation 2.1 The student will represent and analyze two- and three-dimensional figures using tools and technology when appropriate. |
Indicator 2.1.4 The student will construct and/or draw and/or validate properties of geometric figures using appropriate tools and technology. |
Assessment Limits:
- “Validate properties” in this indicator, means justifying solutions using definitions, mathematical principles and/or measurement.
- Students may use a compass, straightedge, patty paper, a MiraTM, and/or a mirror as construction tools. Using a ruler or protractor cannot be part of the strategy.
- Students may use a compass, ruler, patty paper, a MiraTM, a mirror and/or a protractor as drawing tools.
- It is acceptable to do a construction when the item asks for a drawing.
- Paper folding and the use of MirasTM and mirrors are appropriate methods for representing, constructing, and/or analyzing figures, and their use must be referenced.
- Constructions and drawings are limited to the two-dimensional relationships listed in 2.1.1.
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Brief Constructed Response (BCR) Item - Released in 2001 |
Two factories are located near a railroad. There is a loading platform on line l
equidistant from the two factories.
Use the answer box to complete the following. (You will need to use additional paper to complete the answer satisfactorily.)
- Use geometric constructions to determine the location of the loading platform.
Label the loading platform with an X.
- Use mathematics to justify your answer.
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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 3
Annotation: This response demonstrates a complete understanding and analysis of the problem. The representation is essentially correct. The student has correctly located the point indicating where the loading platform should be. Arc marks to construct the perpendicular bisector reveal an appropriate strategy to solve the problem. Full justification is provided in the statement, "...a perpendicular line in the center...will give the equal distance from where the loading dock is to each factory." Compare to Anchor Paper #5.
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| Sample Student Response #2 |
Score for Sample Student Response #2:
Rubric Score 2
Annotation: This response demonstrates a conceptual understanding and analysis of the problem. The representation is correct. The student has correctly located the point indicating where the loading platform should be. Arc marks to construct the perpendicular bisector reveal an appropriate strategy to solve the problem. However, the student has not provided a justification. The statement, "...made a point on line L which was equidistant from A & B," repeats information from the prompt, rather than demonstrating the understanding that any point on the perpendicular bisector provides a point equidistant from the two factories. Compare to Anchor Paper #4.
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| Sample Student Response #3 |
Score for Sample Student Response #3:
Rubric Score 1
Annotation: This response demonstrates a minimal understanding and analysis of the problem. The strategy used to locate the point equidistant from the two factories was trial and error using equal radius lengths. While the representation is fundamentally correct, there is no indication that the student understood the required strategy of constructing the perpendicular bisector. There is no justification. 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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