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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 2.1.1 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 2004

Kerry plans to build a picnic table. She needs to create a drawing of the picnic table surface.

Complete the following on a piece of paper and/or in the answer box below:

  • Draw a regular hexagon with side lengths of 4 centimeters each. Label the vertices of your hexagon A, B, C, D, E, and F. Label the center of your hexagon O. Explain the steps you used in your drawing.
     
  • Classify ΔAOF according to its sides and/or angles. Use mathematics to justify your answers.
     
  • Classify ΔABD according to its sides and/or angles. Use mathematics to justify your answer.
     
  • Classify ΔABC according to its sides and/or angles. Use mathematics to justify your answer.
     

The following 8 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 a minimal understanding and analysis of the problem. The representation is correct; the sides of the hexagon are all 4 cm in length. While the student understands that the angles also will have equal 120° measures, no explanation is provided for how that angle measure is determined. The center 0 is given, and intersecting diagonals explain the strategy to locate that point. The information presented for ΔAOF, ΔABD, and ΔABC does not provide any correct understanding of the classification or justification of triangles.


Anchor Paper #2

image of student response

Score for Anchor Paper #2: Rubric Score 1

Annotation: This response demonstrates a minimal understanding and analysis of the problem. The representation is incorrect. Because all of the sides are labeled as 4 cm, and most of the sides measure 4 cm, the student does partially understand the term "regular." However, none of the angles measures 120°, and no indication is given that all the angles should have equal measure. While a center 0 is present, no strategy to locate that point is provided. The student correctly classifies all three triangles (ΔAOF is equilateral; ΔABD is scalene; ΔABC is isosceles), but fails to supply any justification.


Anchor Paper #3

image of student response
image of student response

Score for Anchor Paper #3: Rubric Score 2

Annotation: This response demonstrates a conceptual understanding and analysis of the problem. Although the representation is incorrect, five of the hexagon's sides are approximately 4 cm in length, and the student has an appropriate strategy of constructing equal side lengths. Arc marks convey a reasonable strategy of construction for copying angles; however, there are errors, and no indication is given of how the initial angle should be determined. While a center 0 is present, no strategy is provided to find that point. ΔAOF is correctly classified (equilateral, equiangular), and a justification is supplied (it is a regular hexagon; whenever something is equilateral, it must be equiangular as well). ΔABD is partially correctly classified (obtuse, scalene). If the drawing were correct, obtuse would not be correct; however, for this student's representation, it is appropriate. The statement (none of the sides are equal when I measured them) lacks the measure, but provides justification for scalene. ΔABC is correctly classified (obtuse, isosceles). The student provides justification for isosceles (has two congruent sides), and the statement (because the angle ABC is over 90°) justifies obtuse.


Anchor Paper #4

image of student response

Score for Anchor Paper #4: Rubric Score 2

Annotation: This response demonstrates a conceptual understanding and analysis of the problem. The representation is essentially correct. Arc marks provide a full explanation of an appropriate strategy to construct the angles and sides of a regular hexagon. An error in the application of the correct strategy makes the length of CD less than 4 cm. The compass point provides the center 0. ΔAOF is correctly classified (equilateral and equiangular); however, no justification is given. The last two parts of the problem, ΔABD and ΔABC, are not addressed.


Anchor Paper #5

image of student response

Score for Anchor Paper #5: Rubric Score 3

Annotation: This response demonstrates a clear understanding and analysis of the problem. The representation contains errors. Five of the six sides are approximately 4 cm. While none of the angles measure 120°, angle values in the representation convey some understanding of the correct measure. The justification for the equilateral triangle {(6-2)180=720, 720/6-120 for each angle} reveals a full strategy for the angle measure. Loosely drawn diagonals provide a reasonable strategy to find the center. AOF is correctly classified (equilateral). Justification is given in the statement (each side of the triangle is a diagonal, mangleFAO and angleAFO both = 60°, by 3rd angle th, the vertex is also 60°). ΔABD is correctly classified (30°-60°-90° right triangle), and full justification is provided. (angleBAD is 60° because 120-60=60. We know that angleABD is right because it is to AB at point B. Therefore the last angle is 30°.) ΔABC is correctly classified (isosceles) with a full justification. (2 sides of the Δ=4 cm by the drawing parameters. The vertex is 120, making each base 30°.)


Anchor Paper #6

image of student response

Score for Anchor Paper #6: Rubric Score 3

Annotation: This response demonstrates a clear understanding and analysis of the problem. The representation is essentially correct with the length of all the hexagon's sides at approximately 4 cm, and all the angles are 120°. An incorrect center 0 is given with no explanation of how that point was determined. ΔAOF is correctly classified (equilateral), and full justification is provided (each angle measures 60°, and each side measures 4 cm; each segment extending from a vertex of a regular hexagon is congruent to a side; all equilateral triangles are equiangular). ΔABD is correctly classified (right, scalene triangle). The statement (a rectangle can be constructed from ABDE, and angles of a rectangle are 90°) is appropriate justification for right, but not scalene, triangles. ΔABC is correctly classified (isosceles) and fully justified (sides of a regular hexagon are always congruent).


Anchor Paper #7

image of student response
image of student response

Score for Anchor Paper #7: Rubric Score 4

Annotation: This response demonstrates a complete understanding and analysis of the problem. The representation is correct. Arc marks and the student's written response provide a full explanation of an appropriate strategy to construct the angles and sides of a regular hexagon and supply the center 0. ΔAOF is correctly classified (equilateral). A full justification is provided (equilateral construction), which uses the same arc length for the arcs in the entire construction, and in the statement (regular hexagons are made up of 6 congruent, equilateral triangles). ΔABD is correctly classified (30-60-90 triangle). Principles of triangles and construction provide full justification. ΔABC is correctly classified (isosceles) and fully justified by a property of regular hexagons.


Anchor Paper #8

image of student response
image of student response

Score for Anchor Paper #8: Rubric Score 4

Annotation: This response demonstrates a complete understanding and analysis of the problem. The representation is correct with a full explanation of a strategy for drawing the sides and angles of the hexagon, as well as a strategy for finding the center. ΔAOF is correctly classified (equilateral) and fully justified by measure. ΔABD is correctly classified (right scalene triangle) and fully justified by the measure of the side for scalene and the measure of a 90° angle for right. ΔABC is correctly classified (isosceles) and fully justified by measure.


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 |