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Public Release Item Scoring Information Return

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.

Brief Constructed Response (BCR) Item - Released in 2002

The plan for a new housing development is shown below. Each lot will have a house, a garage, and a driveway identical in shape to the one shown below. Driveways have already been poured for lots B, C, and D. Each driveway must attach to the garage of each house.

Complete the following in the answer box below:
  • Sketch the positions of the three new houses and their garages. Use mathematics to describe the transformation or transformations needed to reproduce the houses and garages from lot A to lot B, lot B to lot C, and lot C to lot D.

The following 12 Sample Student Responses represent a range of score points.

Sample Student Response #1

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Score for Sample Student Response #1: Rubric Score 1

Annotation: This response demonstrates a minimal understanding and analysis of the problem. The representation is correct; the houses and garages are drawn with the correct orientations. The student tries to identify, rather than fully describe, the transformations. Reflection is correctly identified but lacks the line of reflection for a full description. "From B to C was a trasition" is incorrect. Despite having a correct representation, without at least some understanding of both reflection and rotation, the response demonstrates minimal understanding of transformations. Compare to Anchor Paper #2.


Sample Student Response #2

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Score for Sample Student Response #2: Rubric Score 3

Annotation: This response demonstrates a complete understanding and analysis of the problem. The representation is correct with each house and garage correctly oriented. The first transformation is correctly described as a reflection over the clearly labeled line segment HI. The second transformation is correctly described as a translation "to the right a few units, and then rotated 90° at point K" with the point of rotation K clearly labeled. The third transformation is correctly described as a reflection over the clearly labeled line segment SM. The student provides full descriptions of all the transformations, demonstrating application of a reasonable strategy to solve the problem.


Sample Student Response #3

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Score for Sample Student Response #3: Rubric Score 2

Annotation: This response demonstrates a conceptual understanding and analysis of the problem. The representation is correct; the houses and garages are drawn with the correct orientations. The student identifies the transformations from A to B and C to D as reflections, but fails to provide the line of reflection. The student correctly describes the transformation from B to C as a 90° rotation. (Rotation suffices as the only transformation needed for the reproduction of the house and garage from B to C because the point of rotation could exist outside the shape or lot.) While a correct description of rotation has been provided, reflection was only identified and lacks a developed or complete description. Compare to Anchor Paper #4.


Sample Student Response #4

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Score for Sample Student Response #4: Rubric Score 3

Annotation: This response demonstrates a complete understanding and analysis of the problem. The representation is correct with houses and garages correctly oriented. The student provides a correct description for the transformations from lot A to lot B and lot C to lot D. "Reflected over the edge of lot B...reflected over the edge of lot D" correctly identifies reflection and provides the lines of reflection. The student gives a correct description for the transformation from lot B to lot C. "Rotated 90° and then slid over the edge of lot C" describes the translation ("slide" is an acceptable term identifying translation) and rotation.


Sample Student Response #5

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Score for Sample Student Response #5: Rubric Score 1

Annotation: This response demonstrates minimal understanding and analysis of the problem. The representation is correct; the houses and garages are drawn with the correct orientations. However, while the student tries to discuss the drawing, no description is provided for the transformations required to reproduce the houses and garages.


Sample Student Response #6

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Score for Sample Student Response #6: Rubric Score 2

Annotation: This response demonstrates a conceptual understanding and analysis of the problem. The representation is correct with all the houses and garages correctly oriented. The student correctly identifies the transformations from lot A to lot B and lot C to lot D as reflections ("flip" and "mirrored"). However, the response lacks a full description because no line of reflection is given. The transformation from lot B to lot C is correctly identified as a rotation, but the student fails to provide the degree of rotation. Compare to Anchor Paper #3.


Sample Student Response #7

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Score for Sample Student Response #7: Rubric Score 2

Annotation: This response demonstrates a conceptual understanding and analysis of the problem. The representation is correct with each house and garage correctly oriented. The student correctly identifies the transformations from A to B and C to D as reflections ("reflect" and "flip"). However, the response lacks a full description because no line of reflection is identified. The transformation from B to C is correctly identified as a rotation and translation ("slide"), but the student neglects to provide the degree of rotation, a minimal requirement for a full description of rotation. The response lacks a full description of the correctly identified transformations.


Sample Student Response #8

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Score for Sample Student Response #8: Rubric Score 1

Annotation: This response demonstrates a minimal understanding and analysis of the problem. The representation is correct; the houses and garages are drawn with the correct orientations. Whether the student understands the correct application of rotation for the transformation from lot B to lot C or if he/she believes rotation was used for all three transformations is unclear. "By rotation the houses and the garage is the same." Compare to Anchor Paper #2.


Sample Student Response #9

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Score for Sample Student Response #9: Rubric Score 3

Annotation: This response demonstrates a complete understanding and analysis of the problem. The representation is correct with each house and garage correctly oriented. The student gives a full description of the first transformation. "I made a reflection of the house and the garage across the dividing line of lots" correctly identifies reflection and provides the line of reflection. For the description of the second transformation, the student correctly states "translated the house to the right" as well as "rotated the house 90° to the left." While the direction "to the left" should be appropriately described as counterclockwise, the error in terminology is considered minor. The third transformation is described as "a reflection across the dividing line of lot C and lot D," correctly identifying reflection and providing the line of reflection. Full descriptions of all transformations demonstrate application of a reasonable strategy to solve the problem.


Sample Student Response #10

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Score for Sample Student Response #10: Rubric Score 2

Annotation: This response demonstrates a conceptual understanding and analysis of the problem. The representation is correct with the houses and garages correctly oriented. The student correctly identifies the transformations from lot A to lot B and lot C to lot D as "flips" (an acceptable term identifying reflection). However, the response lacks a full description because no line of reflection is given. The transformation from lot B to lot C is correctly identified as a rotation, but the student fails to provide the degree of rotation. Compare to Anchor Paper #3.


Sample Student Response #11

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Score for Sample Student Response #11: Rubric Score 1

Annotation: This response demonstrates minimal understanding and analysis of the problem. The representation is correct; the houses and garages are drawn with the correct orientations. However, the student tries to describe how the drawing was made rather than the transformations required. Compare to Anchor Paper #1.


Sample Student Response #12

image of student response

Score for Sample Student Response #12: Rubric Score 2

Annotation: This response demonstrates a conceptual understanding and analysis of the problem. The representation is correct; the houses and garages are drawn with the correct orientations. The student identifies the transformations from A to B and C to D as reflections ("flipped or reflected"), but fails to provide the line of reflection. The student correctly describes the transformation from B to C as a 90° rotation. However, reflection is only identified and lacks a complete description. Compare to Anchor Paper #4.


Additional Resources

Anchor Papers used in scoring

Brief Constructed Response (BCR) Rubric

Print: Scoring Rubric (pdf)
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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Resources for 2.1.3:
Skill Statements | PUBLIC RELEASE ITEMS | Lesson Plans |