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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.

Brief Constructed Response (BCR) Item - Released in 2004

Look at figure ABCDE below.

Complete the following on a piece of paper and/or in the answer box below:
  • Draw the reflection of figure ABCDE over line m. Label the corresponding vertices A'B'C'D'E'.
     
  • What is the relationship between angleABC and angleA'B'C'? Use mathematics to justify your answer.
     

The following 7 Anchor Papers represent a range of score points and are used in conjunction with the rubrics to assess student responses.

Anchor Paper #1

image of student response

Score for Anchor Paper #1: Rubric Score 1

Annotation: This response demonstrates a minimal understanding and analysis of the problem. Because the drawing resembles the shape, even though the shape is not reflected, the representation is relevant, but incorrect. The correct relationship between the angles (angleABC is is congruent to angleA'B'C') is given. No justification is provided.


Anchor Paper #2

image of student response

Score for Anchor Paper #2: Rubric Score 1

Annotation: This response demonstrates a minimal understanding and analysis of the problem. The representation is essentially correct; D' is off due to a minor error in construction. While the student gives an unrequired explanation of how the figure was constructed, neither the relationship between angleABC and angleA'B'C', nor the justification, is provided.


Anchor Paper #3

image of student response

Score for Anchor Paper #3: Rubric Score 2

Annotation: This response demonstrates a conceptual understanding and analysis of the problem. The representation is essentially correct with minor construction errors in the locations of B' and C'. The correct relationship between the angles is given (angleABC and angleA'B'C' are congruent). The student defines congruency, but fails to provide justification for why the angles are congruent.


Anchor Paper #4

image of student response

Score for Anchor Paper #4: Rubric Score 2

Annotation: This response demonstrates a conceptual understanding and analysis of the problem. The representation has three errors; points B', C', and D' are incorrectly located. However, the reflected figure closely resembles the original shape. The student provides the correct relationship between the angles (they are congruent). A full justification (both measuring about 51°) is given. Note: the student's angleB and angleB' measurement of 51° is within 2° of the angle's actual measurement of 49° and, therefore, is considered a minor error.


Anchor Paper #5

image of student response

Score for Anchor Paper #5: Rubric Score 3

Annotation: This response demonstrates a complete understanding and analysis of the problem. Due to minor construction errors in the locations of B' and D' (placed within ½ centimeter of the actual point), the representation is essentially correct. The correct relationship between angles (they are congruent) is given. Although lacking the actual angle measurement, the response provides justification (I also know that when I measure angleABC and angleA'B'C' they are congruent). This is complete justification because it is augmented by the student's method of construction.


Anchor Paper #6

image of student response

Score for Anchor Paper #6: Rubric Score 3

Annotation: This response demonstrates a complete understanding and analysis of the problem. The representation is correct, and a correct relationship (they are congruent) between the angles is given. (When you reflect something over a line, you get an exact replica of the original shape, except it is backwards) provides full justification by addressing how reflection retains size and shape.


Anchor Paper #7

image of student response

Score for Anchor Paper #7: Rubric Score 3

Annotation: This response demonstrates a complete understanding and analysis of the problem. The representation is correct. Both a correct relationship between the angles (they are equal) and a full justification (reflections preserve angle measure) are given.


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 |