School Improvement in Maryland
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.

Brief Constructed Response (BCR) Item - Released in 2001

A telephone company offers customers two payment plans for monthly service.

Plan A costs $5 per month plus $0.10 per minute for calls.

Plan B costs $8 per month plus $0.07 per minute for calls.

Complete the following in the Answer Book:

  • How many minutes of calls would it take for Plan A and Plan B to cost the same? Use mathematics to explain how you determined your answer. Use words, symbols, or both in your explanation. (If you solve the problem graphically, use the grid provided in the Answer Book to add to your written response.)

The following 3 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 within the context of the problem. The student arrives at a solution of 100 minutes. The fully developed explanation is presented symbolically; the student has determined appropriate algebraic expressions to represent the data and has set them equal to one another and solved for x. This response demonstrates a complete understanding and analysis of the problem.


Sample Student Response #2

image of student response

Score for Sample Student Response #2: Rubric Score 1

Annotation: This response indicates little application of a reasonable strategy. The student does not offer a solution for the number of minutes of calls it would take for the two plans to cost the same. The student does begin to describe a correct process for solving the problem, but does not apply the strategy. This response demonstrates minimal 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 that leads to a correct solution. The student correctly identifies 100 as the number of minutes of calls it would take for the two plans to cost the same. The explanation is presented in an incomplete graph. The student has graphed each plan with appropriate y-intercepts, slopes, and point of intersection. However, the student does not differentiate the lines, label the axes, or provide an interpretation of the significance of the point of intersection. This response demonstrates a conceptual understanding and analysis of the problem.


Additional Resources

Anchor Papers used in scoring

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_123_alg09.xml
Resources for 1.2.3:
Skill Statements | PUBLIC RELEASE ITEMS | Lesson Plans |