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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 2003

At a baseball game Sam bought 2 hamburgers and 1 order of French fries for a total of $3.75. Erica bought 1 hamburger and 2 orders of French fries for a total of $3.00.

Complete the following in the Answer Book:

  • Write an equation that represents Sam’s total cost. Write an equation that represents Erica’s total cost.
  • What is the cost of one hamburger? What is the cost of one order of French fries? Use mathematics to explain how you determined your answers. Use words, symbols, or both in your explanations. (If you choose to draw a graph, use the grid provided in the Answer Book to add to your written response.)
  • Use mathematics to justify your answers for the cost of one hamburger and the cost of one order of French fries.

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 2

Annotation: This response indicates an incomplete application of a reasonable strategy. The student provides the correct equations for both Sam's and Erica's total costs; however, the variables are not defined. The cost of one hamburger is correct, as is the cost of one order of fries. The explanation is incomplete ("plugging the costs for each into the equation and alterating different parts of the equation to make them equal the correct amount in each equation"). This response demonstrates a conceptual understanding and analysis of the problem. Compare to Anchor Paper #3.
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 Sam's total cost ($3.75=2x+y) and Erica's total cost ($3.00=x+2y), and the variables are defined. The student provides the correct costs of one hamburger ($1.50) and one order of fries ($.75). The fully developed explanation is presented symbolically. The student fully justifies the solutions by inserting the values for x and y into each equation and simplifying, showing that the found values make each equation true. 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 3

Annotation: This response indicates application of a reasonable strategy that leads to correct solutions. The student gives the correct equations for Sam's total cost (2x+y=3.75) and Erica's total cost (1x+2y=3.00) , and the variables are defined. The student provides the correct costs of one hamburger ($1.50) and one order of fries ($.75). The symbolic explanation is fully developed and supports the solution. No justification is given. This response demonstrates a clear understanding and analysis of the problem. Compare to Anchor Paper #5.
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. While the student provides the correct equations for Sam's total cost (2h+1f=$3.75) and Erica's total cost (1h+2f=$3.00), the variables are not defined. The student does not solve for the cost of one hamburger or one order of fries, and no explanation or justification is provided. This response demonstrates a 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
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Resources for 1.2.3:
Skill Statements | PUBLIC RELEASE ITEMS | Lesson Plans |