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Public Release Item
Extended Constructed Response Item for Grade 7

Standard 2.0 Knowledge of Geometry

Topic A. Plane Geometric Figures

Indicator 2. Analyze geometric relationships

Objective a. Determine a missing angle measurement using the sum of the interior angles of polygons.

Assessment limit: Use angle measures in a quadrilateral

Look at quadrilateral KLMN.



Step A
What is the measure of ∠M?

______________degrees

Step B

  • Use what you know about the angle measures of a quadrilateral to justify why the measure you determined for angleM is correct. Use words, numbers, and/or symbols in your justification.
  • A new quadrilateral KLMN is drawn so that the measures of ∠K and ∠L do not change, but angleM and ∠N are now congruent. Use what you know about the angles of a quadrilateral to explain how this change affects the measure of ∠M. Use words, numbers, and/or symbols in your explanation.

Step A is scored 0 (Incorrect) or 1 (Correct) and assesses 2.A.2.a.
Step B is scored with a 4 point (0, 1, 2, 3) rubric and assesses Processes of Mathematics.

Note: 6 "Sample Student Responses" follow below. Each response appears on its own separate page and includes scoring information. The "Sample Student Responses" represent a range of score points.

Correct Answer
rubric. A new quadrilateral KLMN is drawn so that the measures of ∠K and ∠L do not change, but angleM and ∠N are now congruent. Use what you know about the angles of a quadrilateral to explain how this change affects the measure of ∠M. Use words, numbers, and/or symbols in your explanation.
Sample Student Response #1

image of student response

Score for Sample Student Response #1:

Step A - Content (Knowledge of Geometry): 0 Step B - Processes of Mathematics: 1

Annotation for Step B, Using the Rubric: The response demonstrates a minimal understanding and analysis of the problem. Instead of a justification for why the measure of angleM is correct, the response provides the start of an explanation ("add all of the angles together to get 292° ") for how to determine the measure of angleM . The explanation for how the change affects the measure of angleM is missing.


Sample Student Response #2

image of student response

Score for Sample Student Response #2:

Step A - Content (Knowledge of Geometry): 1 Step B - Processes of Mathematics: 1

Annotation for Step B, Using the Rubric: The response demonstrates a minimal understanding and analysis of the problem. Instead of a justification for why the measure of angleM is correct, the response provides an explanation ("you have to add all the other angles up the subtract the total from 360° ") for how to determine the measure of angleM . The explanation for how the change affects the measure of angleM is missing.


Sample Student Response #3

image of student response

Score for Sample Student Response #3:

Step A - Content (Knowledge of Geometry): 0 Step B - Processes of Mathematics: 2

Annotation for Step B, Using the Rubric: The response demonstrates a general understanding and analysis of the problem. Instead of a justification for why the measure of angleM is correct, the response provides an explanation ("I added 98 + 82 + 112 = 203 and 360 minus 203 is 157") for how to determine the measure of angleM . The minor addition mistake does not detract from the process used by the student. A complete explanation for how the change affects the measure of angleM ("then angleM and ∠N would be 75 degrees") is provided.


Sample Student Response #4

image of student response

Score for Sample Student Response #4:

Step A - Content (Knowledge of Geometry): 1 Step B - Processes of Mathematics: 2

Annotation for Step B, Using the Rubric: The response demonstrates a general understanding and analysis of the problem. Instead of a justification for why the measure of angleM is correct, the response provides an explanation ("I first added all the sides together then subtracted 360 − 292") for how to determine the measure of angleM . A complete explanation for how the change affects the measure of angleM (" M and N would have to be 75° ") is provided by giving the new measure of angleM .


Sample Student Response #5

image of student response
image of student response

Score for Sample Student Response #5:

Step A - Content (Knowledge of Geometry): 0 Step B - Processes of Mathematics: 3

Annotation for Step B, Using the Rubric: The response demonstrates a comprehensive understanding and analysis of the problem. A complete justification for why the measure of angleM is correct ("all the angles in a quadrillateral add up to 360° ; First I added the angles K + L, N up and got 292° . Then, I subtracted 292 from 360° and got 108° ") is provided. The minor subtraction error does not detract from the completeness of the justification. A complete explanation for how the change affects the measure of angleM ("they both would be 75° degrees") is provided by giving the new measure of angleM .


Sample Student Response #6

image of student response

Score for Sample Student Response #6:

Step A - Content (Knowledge of Geometry): 1 Step B - Processes of Mathematics: 3

Annotation for Step B, Using the Rubric: The response demonstrates a comprehensive understanding and analysis of the problem. A complete justification for why the measure of angleM is correct ("all four angles of a quadrilateral must have a sum of 360° ;98° +112°+82° = 292° , not 360° so 68° was needed. 292° + 68° = 360° ") is provided. A complete explanation for how the change affects the measure of angleM ("they both will have 75° angles") is provided by giving the new measure of angleM .


Extended Constructed Response (ECR) Rubric
Print: Scoring Rubric

Score 3

The response demonstrates a comprehensive understanding and analysis of a problem.

  • Application of a reasonable strategy in the context of the problem is indicated.
  • Explanation1 of and/or justification2 for the mathematical process(es) used to solve a problem is clear, fully developed, and logical.
  • Connections and/or extensions made within mathematics or outside of mathematics are clear and stated explicitly.
  • Supportive information and/or numbers are provided as appropriate. 3

Score 2

The response demonstrates a general understanding and analysis of a problem.

  • Application of a reasonable strategy in the context of the problem is indicated.
  • Explanation1 of and/or justification2 for the mathematical process(es) used to solve a problem is feasible, but may be only partially developed.
  • Connections and/or extensions made within mathematics or outside of mathematics are partial or overly general, or may be implied.
  • Supportive information and/or numbers are provided as appropriate. 3

Score 1

The response demonstrates a minimal understanding and analysis of a problem.

  • Partial application of a strategy in the context of the problem is indicated.
  • Explanation1 of and/or justification2 for the mathematical process(es) used to solve a problem is logically flawed or missing.
  • Connections and/or extensions made within mathematics or outside of mathematics are flawed or missing.
  • Supportive information and/or numbers may or may not be provided as appropriate.3

Score 0

The response is completely incorrect, irrelevant to the problem, or missing.4

Note 1:

Explanation refers to students' ability to communicate how they arrived at the solution for an item using the language of mathematics.

Note 2:

Justification refers to students' ability to support the reasoning used to solve a problem, or to demonstrate why the solution is correct using mathematical concepts and principles.

Note 3:

Students need to complete rubric criteria for explanation, justification, connections and/or extensions as cued for in a given problem.

Note 4:

Merely an exact copy or paraphrase of the problem will receive a score of "0".

Rubric Document Date: August 2003

/share/rubrics/msa/mathematics/xml/ecr.xml
/toolkit/vsc/assessment_items/msa_math_7_032.xml