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Public Release Item Scoring Information Return

Goal 1 Functions and Algebra

Expectation 1.2 The student will model and interpret real-world situations using the language of mathematics and appropriate technology.

Indicator 1.2.3 The student will solve and describe using numbers, symbols, and/or graphs if and where two straight lines intersect.

Assessment Limits:

  • Functions will be of the form: Ax + By = C, Ax + By + C = 0, or y = mx + b.
  • All coefficients will be rational.
  • Vertical lines will be included.
  • Systems of linear functions will include coincident, parallel, or intersecting lines.
  • The majority of these items should be in real-world context.

Extended Constructed Response (ECR) Item - Released in 2002

Terry is going to the county fair. She has two choices for purchasing tickets, as shown in the table below.

Complete the following in the Answer Book:

  • Write an equation for Terry's total cost (y) for ticket Choice A. Write an equation for Terry's total cost (y) for ticket Choice B. Let x represent the number of rides she plans to go on.
  • How many rides would Terry have to go on for the total cost of ticket A and ticket B to be equal? Use mathematics to explain how you determined your answer. Use words, symbols, or both in your explanation. (If you choose to draw a graph, use the grid provided in the Answer Book to add to your written response.)
  • Terry plans to go on 14 rides. To spend the least amount of money, which ticket choice should Terry choose? 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

Score for Sample Student Response #1: Rubric Score 3

Annotation: This response indicates application of a reasonable strategy that leads to a correct solution. The student provides the correct equations ("y=0.50x+6") and ("y=0.75x+2"), but does not label these equations. The solution to the system of equations is correct; however, the explanation is incomplete, "I used guess a check to find the answer." The selection of Choice B as the appropriate choice is correct. The justification supports the solution ("because it is 50 cents cheaper"). This response demonstrates a clear understanding and analysis of the problem.


Sample Student Response #2

image of student response

Score for Sample Student Response #2: Rubric Score 4

Annotation: This response indicates application of a reasonable strategy that leads to a correct solution within the context of the problem. The student gives the correct equations for Choice A (y=$6+$0.50x) and Choice B (y=$2+0.75x). The student provides the correct solution to the system of equations. The explanation is fully developed and supports the solution; the student provides a series of guess and check trials. The student replaces x with 12, 13, and 16, respectively, then solves for the total cost, noting that "at 16 rides the cost of plans A and B are the same." The correct answer of choice B is given, and the justification is logically sound, fully developed, and supports the solution. This response demonstrates a complete understanding and analysis of the problem.


Sample Student Response #3

image of student response

Score for Sample Student Response #3: Rubric Score 2

Annotation: This response indicates an incomplete application of a reasonable strategy. The student gives the correct equation for Choice A. The correct equation is also provided for ticket Choice B, although the student has not defined B after changing it from y. The solution to the system of equations is correct, but an explanation is not provided. The student correctly identifies Choice B as the appropriate plan; however, the statement "because it would be cheaper" is synonymous with "least amount of money" and, therefore, does not justify the choice. This response demonstrates a conceptual understanding and analysis of the problem.


Sample Student Response #4

image of student response

Score for Sample Student Response #4: Rubric Score 1

Annotation: This response indicates little application of a reasonable strategy. The correct equations are given for both ticket choices, although the student has not defined A or B after changing them from y. The solution to the system of equations is incorrect. The student correctly identifies choice B as the appropriate plan; however, no justification is provided. This response demonstrates minimal understanding and analysis of the problem.


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
/share/clg/xml/public_release/mathematics/2002_123_alg17.xml
Resources for 1.2.3:
Skill Statements | PUBLIC RELEASE ITEMS | Lesson Plans |