| 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 2.1.3 The student will use transformations to move figures, create designs, and/or demonstrate geometric properties. |
Assessment Limits:
- Transformations include reflections, rotations, translations, and dilations.
- Items should go beyond the identification of transformations.
- Essential properties and relationships include the following: congruence, similarity, and symmetry.
- The student's explanation of a transformation must include the following:
- translation – distance and direction
- reflection – line of reflection
- rotation – center of rotation, angle measure, direction (clockwise or counterclockwise)
- dilation – center and scale factor
- Paper folding and the use of MirasTM and mirrors are appropriate methods for performing transformations, and their use must be referenced.
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Brief Constructed Response (BCR) Item - Released in 2001 |
Figure ABCD is shown on the grid below.
Use the answer box to complete the following. (You will also need to use graph paper to complete the answer satisfactorily.)
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On a grid, reflect ABCD across the y-axis.
Label the image A'B'C'D'.
- Use mathematics to explain how a reflection across the y-axis affects the
coordinates of any point (x, y). Use words, symbols, or both in your
explanation.
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On the same grid, translate A'B'C'D' 6 units
down. Label the image of this translation A"B"C"D".
- Use mathematics to explain how a translation 6 units down affects the
coordinates of any point (x, y). 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 1
Annotation: This response demonstrates minimal understanding and analysis of the problem. The representation of the reflection is correct with labeling of the vertices demonstrating that the orientation of the points were maintained. However, there is no representation of the required translation. The explanation, "A reflection across the y-axis makes x and y opposite of what they are on the other side," is incorrect because the y coordinate is unaffected - only the x-coordinate is affected. There is no attempt to address the translation.
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| Sample Student Response #2 |
Score for Sample Student Response #2:
Rubric Score 3
Annotation: This response demonstrates complete understanding and analysis of the problem. The representations are correct; the student has correctly performed the transformations of reflection and translation, and the figures are correctly labeled. The student provides two general descriptions of the effects on the coordinates after each transformation, "the x-coordinates becomes negative, or its opposite," and "the x-coordinates stay the same, but the y-coordinate drops 6 numbers." Compare to Anchor Paper #6.
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| Sample Student Response #3 |
Score for Sample Student Response #3:
Rubric Score 2
Annotation: This response demonstrates a conceptual understanding and analysis of the problem. The representations are fundamentally correct. The student has correctly performed the reflection; however, the translation was executed correctly from the trapezoid's original position rather than its reflected image. The figures are partially labeled. The student has addressed how the coordinates are affected by each type of transformation by stating what happens to the coordinate that is changed by the transformation and by giving a specific example that shows that the other coordinate does not change. Compare to Anchor Paper #4.
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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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