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 2.1.1 The student will analyze the properties of geometric figures.

Assessment Limits:

  • Essential properties, relationships, and geometric models include the following:
    • Congruence and similarity
    • line/segment/plane relationships (parallel, perpendicular, intersecting, bisecting, midpoint, median, altitude)
    • point relationships (collinear, coplanar)
    • angles and angle relationships (vertical, adjacent, complementary, supplementary, obtuse, acute, right, interior, exterior)
    • angle relationships with parallel lines
    • polygons (regular, non-regular, composite, equilateral, equiangular)
    • geometric solids (cones, cylinders, prisms, pyramids, composite figures)
    • circle/sphere (tangent, radius, diameter, chord, secant, central/inscribed angle, inscribed, circumscribed).

Extended Constructed Response (ECR) Item - Released in 2001

The Department of Public Works wants to put a water treatment plant at a point that is an equal distance from each of the three towns it will service. The location of each of the towns is shown below.

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

  • Locate the point that is an equal distance from each of the towns.
     
  • Explain how you determined this location. Use words, symbols, or both in your explanation.
     
  • Use mathematics to justify your answer.

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

Sample Student Response #1

image of student response
image of student response

Score for Sample Student Response #1: Rubric Score 3

Annotation: This response demonstrates a clear understanding and analysis of the problem. The representation is correct; the student has successfully located the point designating the location of the water treatment plant. The student has provided a complete explanation as well as having two complete sets of arc marks to provide full explanation of a correct strategy employing perpendicular bisectors. Justification is incomplete; the student has neither supported his/her understanding of equidistance with measure, nor has he/she conveyed the understanding that the intersection of the perpendicular bisectors ("Where the 2 lines that you drew intersect...") provides the point of equidistance. Compare to Anchor Paper #7.
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 is correct; the point designating the location of the water treatment plant is correct. At least two complete sets of arc marks provide a full explanation of an appropriate strategy, employing perpendicular bisectors. Full justification is provided in the statement, "The perp. bisectors of all the sides of a triangle intersect at a point equidistant to all of the triangles vertices." 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 diagram and explanation reveal that the student applied an inappropriate strategy to locate the position of the water treatment plant. Incomplete sets of arc marks are present. There is no justification. Compare to Anchor Paper #1.
Sample Student Response #4

image of student response

Score for Sample Student Response #4: Rubric Score 2

Annotation: This response demonstrates a conceptual understanding and analysis of the problem. The representation is fundamentally correct; the point is close, but not correct. The diagram and explanation reveal that the student has applied an incomplete correct strategy of using the concept of a circle's radius to find a point equidistant from all three towns. The student attempts to justify the location of the water treatment plant by measurement. The distances that are labeled 5cm are incorrectly measured. The distance between Town B and the plant is not supported. Compare to Anchor Paper #4.

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 2.1.1:
Skill Statements | PUBLIC RELEASE ITEMS | Lesson Plans |