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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 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 9 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 of the point indicating pool location is essentially correct. A single pair of crossed arcs is present in the diagram, conveying minimal understanding of using construction to determine equidistance. The student's explanation, "I measured an equal distance from each school," is an inappropriate strategy (lacks construction) to solve the item. While there is no evidence of perpendicular bisector construction, the student demonstrates an understanding of equidistance, "I pick 1-1/4 inch and measured that distance so that the pool was an equal distance away from each school." (When standard measure is the strategy, measure should not also be utilized as justification.)


Anchor Paper #2

image of student response

Score for Anchor Paper #2: Rubric Score 1

Annotation: This response demonstrates minimal 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 student does provide some explanation of a trial and error strategy (construction arcs of equal radii), thereby demonstrating an understanding of equidistance. No justification is provided.


Anchor Paper #3

image of student response

Score for Anchor Paper #3: Rubric Score 2

Annotation: This response demonstrates conceptual understanding and analysis of the problem. The representation of the point indicating pool location is essentially correct. While there is no evidence of perpendicular bisector construction, the student does explain a trial and error strategy (construction circles of equal radii). "All of the distances are the same because I did not change the radius of the circle and as long as the point is on each of the circles it's okay for the pool to be there" provides justification.


Anchor Paper #4

image of student response

Score for Anchor Paper #4: Rubric Score 2

Annotation: This response demonstrates conceptual understanding and analysis of the problem. The representation of the point indicating pool location is essentially correct. The student understands that the correct strategy is to find the location of the perpendicular bisectors intersection. However, all three perpendicular bisectors are only partially constructed, resulting in an incomplete correct strategy and an error in pool location. The student provides justification by measure, "By using a metric ruler I found that the pool is exactly 3mm from each school on the drawing."


Anchor Paper #5

image of student response

Score for Anchor Paper #5: Rubric Score 2

Annotation: This response demonstrates conceptual understanding and analysis of the problem. The representation of the point indicating pool location is correct. The student understands that finding the perpendicular bisectors intersection is an appropriate strategy. However, the perpendicular bisectors are not constructed, and there is no explanation to indicate that construction methods are employed (patty paper, mira). Lack of construction prevents this response from receiving a higher score. No justification is provided.


Anchor Paper #6

image of student response

Score for Anchor Paper #6: Rubric Score 3

Annotation: This response demonstrates clear understanding and analysis of the problem. The representation of the point indicating pool location is correct. Arc marks provide full explanation for the appropriate strategy of perpendicular bisector construction. No justification is provided.


Anchor Paper #7

image of student response

Score for Anchor Paper #7: 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 a justification by stating, "Since I found the midpoint of every line which is also the midpoint of the schools, where all the lines intersect should be equidistant from every school" However, this statement fails to convey any understanding that the intersection of the perpendicular bisectors of the connecting schools' segments is equidistant to all the endpoints of the connecting schools' segments.


Anchor Paper #8

image of student response

Score for Anchor Paper #8: 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. "Any point on a perpendicular bisector is equidistant from the end points of the segment. Since the point was on all three perpendicular bisectors, it was equidistant from all three points" provides full justification.


Anchor Paper #9

image of student response
image of student response

Score for Anchor Paper #9: 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. The student provides a measure of 1-5/16 of an inch for full justification.


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
/share/clg/xml/public_release/mathematics/2003_214_geo31.xml
Resources for 2.1.4:
Skill Statements | PUBLIC RELEASE ITEMS | Lesson Plans |