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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 2.1.4 The student will construct and/or draw and/or validate properties of geometric figures using appropriate tools and technology.

Assessment Limits:

  • “Validate properties” in this indicator, means justifying solutions using definitions, mathematical principles and/or measurement.
  • Students may use a compass, straightedge, patty paper, a MiraTM, and/or a mirror as construction tools. Using a ruler or protractor cannot be part of the strategy.
  • Students may use a compass, ruler, patty paper, a MiraTM, a mirror and/or a protractor as drawing tools.
  • It is acceptable to do a construction when the item asks for a drawing.
  • Paper folding and the use of MirasTM and mirrors are appropriate methods for representing, constructing, and/or analyzing figures, and their use must be referenced.
  • Constructions and drawings are limited to the two-dimensional relationships listed in 2.1.1.

Brief Constructed Response (BCR) Item - Released in 2001

Two factories are located near a railroad. There is a loading platform on line l equidistant from the two factories.

Use the answer box to complete the following. (You will need to use additional paper to complete the answer satisfactorily.)

  • Use geometric constructions to determine the location of the loading platform. Label the loading platform with an X.
     
  • 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. The strategy used to locate the point equidistant from both factories was trial and error using equal radius lengths. While the representation is fundamentally correct, there is no indication that the student understood the required strategy of constructing the perpendicular bisector. There is no justification.


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 inappropriate strategy of measuring was employed to locate the point equidistant from both factories, as indicated by the explanation and the 2 inch lengths in the diagram. While the representation is fundamentally correct, there is no indication that the student understood the required strategy of constructing the perpendicular bisector. Since the student used measurement to locate the position of the loading dock, the measurements cannot also serve as the justification.


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 fundamentally correct. The student has correctly located the point indicating where the loading platform should be, and the explanation reveals a trial and error strategy of using equal radius lengths to determine the point equidistant from both factories. The justification by measure, "...after measuring to make sure, they are equidistant from each factory," is not fully developed since the actual measures are not present.


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 student has correctly located the point indicating where the loading platform should be, and arc marks to construct the perpendicular bisector reveal an appropriate strategy to solve the problem. There is no justification.


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 essentially correct. The student has correctly located the point indicating where the loading platform should be. Arc marks to construct the perpendicular bisector reveal an appropriate strategy to solve the problem. Full justification is provided in the statement, "...Line w is the perpendicular bisector...any point on line w is equidistant from Factory A and Factory B.


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 essentially correct. The student has correctly located the point indicating where the loading platform should be. Arc marks to construct the perpendicular bisector reveal an appropriate strategy to solve the problem. The student measures (5 cm indicated for lines from each factory to location of loading platform in diagram) to provide full justification.


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 essentially correct. The student has correctly located the point indicating where the loading platform should be and has provided explanation of an appropriate strategy using a mirror. The student measures for justification.


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 2.1.4:
Skill Statements | PUBLIC RELEASE ITEMS | Lesson Plans |