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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.

Extended Constructed Response (ECR) Item - Released in 2002

The floor plan for an office in a new building is shown below. The interior designer wishes to place a desk so that it is equidistant from all the walls in the office.

Complete the following in the answer box below:
  • Use construction techniques to locate the point where the desk should be.
  • Explain the steps you used in your construction. Use words, symbols, or both in your explanation.
  • Use mathematics to justify that the location of the desk is equidistant from the walls of the office.

The following 4 Sample Student Responses represent a range of score points.

Sample Student Response #1

image of student response

Score for Sample Student Response #1: Rubric Score 2

Annotation: This response demonstrates a conceptual understanding and analysis of the problem. The representation is correct. The student locates the point indicating correct placement of the desk. No compass arc marks are present to reveal construction. The explanation reveals that the student understands the correct concept of finding the intersection of angle bisectors, but without any indication of appropriate construction or explanation of the appropriate use of construction tools, the response indicates an application of an incomplete correct strategy. The student tries to provide justification with the statement "the intersection of all three lines should be equidistant from each wall;" however, that justification is not fully developed. Compare to Anchor Paper #3.
Sample Student Response #2

image of student response

Score for Sample Student Response #2: Rubric Score 4

Annotation: This response demonstrates a complete understanding and analysis of the problem. The representation is correct. The student locates the point indicating correct placement of the desk. The explanation and compass arc marks fully explain a complete correct strategy of constructing angle bisectors. "A theorem says that if a point is equidistant from the sides of an angle then it lies on the angle bisector of that angle...the point where all the angle bisectors intersect is the point equidistant from all sides" provides full justification. Compare to Anchor Paper #8.
Sample Student Response #3

image of student response

Score for Sample Student Response #3: Rubric Score 1

Annotation: This response demonstrates a minimal understanding and analysis of the problem. The representation is incorrect. The student is unable to locate the correct placement for the desk. Construction arc marks and an explanation reveal that the student applies an inappropriate strategy, locating the intersection of the medians. Bisecting the sides rather than the angles of the triangle approximates the centroid (center of mass) rather than the point equidistant from the walls. A minimal understanding of equidistance is present in both the inappropriate strategy of intersecting medians and the attempt to justify equidistance by measure.


Sample Student Response #4

image of student response

Score for Sample Student Response #4: Rubric Score 3

Annotation: This response demonstrates a clear understanding and analysis of the problem. The representation is correct. The student locates the point indicating correct placement of the desk. The explanation reveals a correct, but partially developed, strategy of constructing angle bisectors using patty paper. (A fully developed explanation would explain how the paper was folded in order to construct the angle bisector.) "You know its equal distance from each because if you make a circle w/the point as the center the circle would touch each wall" provides full justification. Compare to Anchor Paper #6.

Additional Resources

Anchor Papers used in scoring

Extended Constructed Response (ECR) Rubric
Print: Scoring Rubric (pdf)
Score 4

The response indicates application of a reasonable strategy that leads to a correct solution in the context of the problem. The representations are 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 3

The response indicates application of a reasonable strategy that may or may not lead to a correct solution. The representations are essentially correct. The explanation and/or justification is generally well developed, feasible, and supports the solution. The response demonstrates a clear understanding and analysis of the problem.

Score 2

The response indicates an incomplete application of a reasonable strategy that 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 application of a reasonable 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 |