School Improvement in Maryland
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 6 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 minimal understanding and analysis of the problem. The representation is correct; the house and garages are drawn with the correct orientations. However, the student makes no attempt to describe the transformations required to reproduce the houses and garages.


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 correct; the houses and garages are drawn with the correct orientations. The student tries to identify rather than fully describe the transformations, but only the reflections are correctly identified. "From A to B they just fliped around...and from C to D they fliped again." While "flip" is an acceptable term that correctly identifies reflection, the student fails to provide the line of reflection for a full description. The attempt to describe rotation is vague. "They stayed the same direction" neither correctly identifies nor describes the transformation performed. Despite having a correct representation, without at least some understanding of both reflection and rotation, the response demonstrates minimal understanding of transformations.


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 correct with the houses and garages correctly oriented. The student identifies the transformations from lot A to lot B and lot C to lot D as reflections ("flipped or reflected"). 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. (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.) Although failing to provide a full description of the transformations, the student correctly identifies the two different transformations (reflection and rotation).


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 is correct; the houses and garages are drawn with the correct orientations. The student identifies the first transformation as a " ...reflex. because it looks like it is a mirror reflecting it to make it the opposite way." The second transformation is correctly identified as a rotation; however, the description is vague. "It was turned another direction but still the same model house." "Turn" is an acceptable term describing rotation, but the student fails to provide the degree of rotation. The third transformation clearly provides a full description. "House D is another reflex house because it looks like it was fliped over the line between them" correctly identifies the reflection or "flip" (an acceptable term describing reflection) and provides the line of reflection. While a full description of reflection is given (from C to D), rotation only is identified (from B to C).


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. The representation is correct with houses and garages correctly oriented. The student provides full descriptions of the transformations from lot A to lot B and lot C to lot D, correctly identifying reflection and providing the lines of reflection. "Reflect the house garage and driveway over line B" and "reflect the house and garage over line C." The student also gives a full description of the transformations from lot B to lot C, correctly describing translation ("transcribe {slide} over line D") and rotation ("rotate the lot 90° counterclockwise").


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 with each house and garage correctly oriented. The student correctly identifies the transformations from A to B and C to D as reflections and also identifies the lines of reflection ("...flip it over the edge of lot A and lot B...flip it over the edge of lot C and lot D.") The transformation from B to C is correctly described as a "90° counter clockwise" rotation. This description is acceptable because the house could be repositioned in a single rotation (without a translation) if the point of rotation is outside the figure. The student provides full descriptions of all the transformations, demonstrating application of a reasonable strategy to solve the problem.


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
/share/clg/xml/public_release/mathematics/2002_213_geo20.xml
Resources for 2.1.3:
Skill Statements | PUBLIC RELEASE ITEMS | Lesson Plans |