| Public Release Item Scoring Information |
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Goal 2 Geometry, Measurement, And Reasoning |
Expectation 2.2 The student will apply geometric properties and relationships to solve problems using tools and technology when appropriate. |
Indicator 2.2.1 The student will identify and/or verify congruent and similar figures and/or apply equality or proportionality of their corresponding parts. |
Assessment Limits:
- Students will demonstrate geometric reasoning and justify conclusions. Although the focus is on geometric theory, answers to some items may include a numeric answer.
- Corresponding measurements include length, angle measure, perimeter, circumference, area, volume, surface area and lateral area.
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Extended Constructed Response (ECR) Item - Released in 2004 |
In the figure below,
ΔABD and ΔCDB are isosceles triangles. The vertex angles,  ABD and CDB and, are congruent as shown below.
Complete the following on a piece of paper and/or in the answer box below:
- Prove that quadrilateral ABCD is
a parallelogram.
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The following 4 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 has a strategy to prove congruent triangles by ASA (angle-side-angle) and utilizes corresponding congruent parts and BC // ADto prove conditions for a parallelogram. However, the ASA proof is flawed because CBD and BDA cannot be claimed congruent by the Alternate Interior Angles Theorem. The student lacks a strategy to establish these angles' congruence. The student's justification forBC // AD actually proves AB // CD. The response demonstrates an incomplete application of a reasonable strategy.
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| Sample Student Response #2 |
Score for Sample Student Response #2:
Rubric Score 1
Annotation: This response demonstrates a minimal understanding and analysis of the problem. While there is evidence of a proof process, no indication of a strategy to prove a parallelogram is given. The statement (BD=DB) is correct with correct justification (reflexive property). The statement (ΔABD  ΔCDB) could be proved true by the stated SAS (side-angle-side); however, the second pair of congruent sides are neither stated nor justified. The student fails to provide any indication of the conditions that would prove a parallelogram. Compare to Anchor Paper #1.
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| Sample Student Response #3 |
Score for Sample Student Response #3:
Rubric Score 4
Annotation: This response demonstrates a complete understanding and analysis of the problem. The student states (AB // DC) because (alternate interior angles are =, when 2 lines are cut by a transversal, then the lines are //). After establishing AB DC using the given information and the transitive property, the student proves a parallelogram (if 1 pair of sides of a quadrilateral are both = and //, the figure is a parallelogram). Compare to Anchor Paper #7.
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| Sample Student Response #4 |
Score for Sample Student Response #4:
Rubric Score 3
Annotation: This response demonstrates a clear understanding and analysis of the problem. The student attempts the strategy of using congruent isosceles triangles to prove a parallelogram; however, the triangles are only proved similar, not congruent. In order to establish a parallelogram, the student also needs to use angle addition to prove all the opposite angles are congruent.
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Extended Constructed Response (ECR) Rubric |
| Print: Scoring Rubric (pdf)
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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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