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Public Release Item Scoring Information Return

Goal 2 Geometry, Measurement, And Reasoning

Expectation 2.3 The student will apply concepts of measurement using tools and technology when appropriate.

Indicator 2.3.1 The student will use algebraic and/or geometric properties to measure indirectly.

Assessment Limits:

  • “Measure indirectly” means to use mathematical concepts such as congruence, similarity, and ratio and proportion to calculate measurements.
  • Similarity and congruence will be directly stated or implied (scale drawings, enlargements).
  • Items may require the student to make comparisons.
  • This indicator may incorporate measuring.
  • This indicator does not include right-triangle trigonometry.

Brief Constructed Response (BCR) Item - Released in 2001

A gardener uses 20 gallons of water each week on his 8-foot by 10-foot vegetable garden. He plans to enlarge his garden to 24 feet by 30 feet.

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

  • How much water would he expect to use on his new garden? Use mathematics to explain how you determined your answer. Use words, symbols, or both in your explanation.

The following 6 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 student has provided the incorrect answer of 60 gallons needed to water the new garden. The explanation reveals an inappropriate strategy. The student correctly recognizes that the dimensions of the garden increase by a scale factor of 3 ("…he just multiplyed it by 3. 8x3=24 10x3=30."), then incorrectly applies the same scale factor to the amount of water needed ("…so I multiplyed the 20 gallons of water by 3.") This strategy reveals a serious flaw in reasoning because area is not taken into account.


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 student has arrived at an incorrect answer of 120 gallons of water for the new garden. The explanation reveals the student recognized that the dimensions had increased by the correct scale factor of 3: "he must divide 24 by 8. This gets 3. The same is for 10 ÷ 30. This gets 3 also." The student then applied an inappropriate strategy: "You add them up and multiply 20 gallons times six = 120."


Anchor Paper #3

image of student response

Score for Anchor Paper #3: Rubric Score 2

Annotation: This response demonstrates a conceptual understanding and analysis of the problem. The student provides an incorrect answer of 320 gallons of water. The explanation describes a correct strategy to solve the problem, but an error resulted in the incorrect answer: "I came to this conclusion by finding the area of the enlarged garden, then divide that by the area of the old garden. Then multiply the amount of times the small garden goes into the larger area by 20 and you have the answer of 320."


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 student's work reveals an appropriate strategy for solving the problem; "20/x = 80/720" is a correct proportion that should result in the correct answer when solved for x. However, an error resulted in an incorrect answer of 38 gallons of water.


Anchor Paper #5

image of student response

Score for Anchor Paper #5: Rubric Score 3

Annotation: This response demonstrates a complete understanding and analysis of the problem. The student correctly answers that 180 gallons of water will be required for the new garden. Complete explanation of an appropriate strategy to solve the problem is present in the correct set up of the proportion:
 

"20 gallons of water
8 ft. by 10 ft.		 = x gallons of water"
24 ft. by 30 ft.


Anchor Paper #6

image of student response

Score for Anchor Paper #6: Rubric Score 3

Annotation: This response demonstrates a complete understanding and analysis of the problem. The student correctly answers that 180 gallons will be required. An appropriate strategy of dividing the new garden's area by the old garden's area to find the scale factor for water usage is fully explained: "720 ÷ 80=9, which would be the scale factor to multiply 20 gallons by."


Brief Constructed Response (BCR) Rubric
Print: Scoring Rubric (pdf)
Score 3

The response indicates application of a reasonable strategy that leads to a correct solution in the context of the problem. The representations are essentially 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 2

The response indicates application of a reasonable strategy that may be incomplete or undeveloped. It 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 attempt to apply a reasonable strategy or applies an inappropriate 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/2001_231_geo17.xml
Resources for 2.3.1:
Skill Statements | PUBLIC RELEASE ITEMS | Lesson Plans |