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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 2007

At the beginning of the summer, Sarah has $250. She takes a summer job and saves $150 per week. Felicia has $1,650 at the beginning of the summer. She travels during the summer and spends $200 per week.

Complete the following in the Answer Book:

  • Write an equation that represents the amount of money Sarah has at the end of each week.
  • Write an equation that represents the amount of money Felicia has at the end of each week.
  • Graph the two equations on the grid provided in the Answer Book. (Suggested graphing window: 0 ≤ weeks ≤ 10; 0 ≤ amount ≤ 2000.)
  • At the end of which week do Sarah and Felicia have the same amount of money? How much money do they have? 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 demonstrates application of a reasonable strategy that leads to some correct solutions within the context of the problem. The student has provided the correct equations for Sarah (y=250+150x) and Felicia (y=1,650-200x). The student has not responded to the third part of the question. The week Sarah and Felicia will have the same amount of money and the amount are correct (At week #4 they both have $850). The justification is incomplete ($250 plus $150 at the end of 4 weeks is the same as $1,650 minus $200 at the end of 4 weeks. They both equal $850). This response demonstrates a clear understanding and analysis of the problem. (Compare to this Level 3 anchor paper.)


Sample Student Response #2

image of student response

Score for Sample Student Response #2: Rubric Score 2

Annotation: This response demonstrates an incomplete application of a reasonable strategy. The equations are correct (S(x)=250+150x; F(x)=1,650-200x). The student has not responded to the third part of the question. The week Sarah and Felicia will have the same amount of money and the amount are correct (At the end of the 4th week, they have 850 dollars). A justification is not provided. This response demonstrates a conceptual understanding and analysis of the problem. (Compare to this Level 2 anchor paper.)


Sample Student Response #3

image of student response

Score for Sample Student Response #3: Rubric Score 1

Annotation: This response demonstrates little application of a reasonable strategy. The student has provided the correct equation for Sarah (y=150x+250) and a relevant equation for Felicia (y=200x+1650). The student has not responded to the third or fourth parts of the question. This response demonstrates a minimal understanding and analysis of the problem. (Compare to this Level 1 anchor paper.)


Sample Student Response #4

image of student response

Score for Sample Student Response #4: Rubric Score 4

Annotation: This response demonstrates application of a reasonable strategy that leads to correct solutions within the context of the problem. The student has provided the correct equations for Sarah (m=250+150w) and Felicia (m=1,650-200w). The equations are correctly graphed. The week Sarah and Felicia will have the same amount of money and the amount are correct (At the end of week 4 because on the graph the 2 lines cross [meet] at exactly 4 and 850). The justification is fully developed. The student replaces x with 4 in both equations and simplifies, showing that the outcome for each is equal at 850. This response demonstrates a complete understanding and analysis of the problem. (Compare to this Level 4 anchor paper.)


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 |