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 2.1.4 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 2003

A community pool is equidistant from the three schools shown below.

Complete the following in the answer box below, and/or on a piece of paper:
  • Use geometric construction to determine the location of the pool.
     
  • Explain the steps you used in your construction. Use words, symbols, or both in your explanation.
     
  • Justify that the location you found is equidistant from all three schools.
     

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 conceptual understanding and analysis of the problem. The representation of the point indicating pool location is correct. While there is no evidence of perpendicular bisector construction, the drawn arcs and the explanation indicate a trial and error strategy employing arcs of equal radii. "Each point from the pool is 3.2 cm that is how I know that all 3 locations are equidistant from the pool" provides justification by measure. 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 complete understanding and analysis of the problem. The representation of the point indicating pool location is correct. The arc marks and the explanation fully describe the appropriate strategy of perpendicular bisector construction. "…In a triangle, the point equidistant from all three vertices lies at the intersection of the perpendicular bisectors at all three 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 minimal understanding and analysis of the problem. The representation of the point indicating pool location is fundamentally correct. While there is no evidence of perpendicular bisector construction, the student provides an explanation of a trial and error strategy (arc construction of equal radii), demonstrating an understanding of equidistance. No justification is provided. Compare to Anchor Paper #2.
Sample Student Response #4

image of student response

Score for Sample Student Response #4: Rubric Score 3

Annotation: This response demonstrates clear understanding and analysis of the problem. The representation of the point indicating pool location is correct. The arc marks and the explanation fully describe the appropriate strategy of perpendicular bisector construction. The student attempts justification with "My construction is equidistant because the lines are radii of the arcs I drew which means they are equal." However, this statement merely mentions that the arcs for each perpendicular bisector are of equal radii and fails to justify the point location. Compare to Anchor Paper #7.

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 |