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 1.2.1 The student will determine the equation for a line, solve linear equations, and/or describe the solutions using numbers, symbols, and/or graphs.

Assessment Limits:

  • Functions are to have no more than two variables with rational coefficients.
  • Linear equations will be given in the form: Ax + By = C, Ax + By + C = 0, or y = mx + b.
  • Vertical lines are included.
  • The majority of these items should be in real-world context.

Extended Constructed Response (ECR) Item - Released in 2005

Sue has $75 to spend on shirts and shorts. The shirts are on sale for $10 each, including tax, and the shorts are on sale for $15 each, including tax.

Complete the following in the Answer Book:

  • Write an inequality that represents the situation above, where x represents the number of shirts and y represents the number of shorts.
  • What is the maximum number of shorts Sue can buy if she buys 2 shirts? Use mathematics to explain how you determined your answer. Use words, symbols, or both in your explanation. (If you need to draw a graph for your solution, use the grid provided in the Answer Book.)
  • List all the number combinations of shirts and shorts Sue can buy to spend exactly $75. 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 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 inequality (10x+15y≤75). The correct maximum number of shorts (3 shorts) is provided, and the fully developed explanation is presented symbolically. The student replaces x in the inequality with 2, then solves for y, and truncates to a whole number for the solution. A correct list of all the number combinations of shirts and shorts that total exactly $75 (0,5; 3,3; 6,1) is given, and the student fully justifies the solutions by inserting each of the values for x and y into the equation and simplifying, showing that the found values make the equation true. The response demonstrates a complete understanding and analysis of the problem. Compare to Anchor Paper #8.
Sample Student Response #2

image of student response

Score for Sample Student Response #2: Rubric Score 2

Annotation: This response indicates an incomplete application of a reasonable strategy. The representations, in the form of equations, are incorrect. The student provides the correct maximum number of shorts (3), and the explanation supports the solution (75-10-10=55 left over from 2 shirts, then 15+15+15=$45 highest, that’s closest to 55). Although the student correctly lists all the number combinations of shirts and shorts that total exactly $75, the justification is incomplete. (I just estimated by using the cost of shirts + shorts and looked to see what =75$ in the combination.) The response demonstrates a conceptual understanding and analysis of the problem. Compare to Anchor Paper #3.
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 some correct solutions. The student gives the correct inequality (75≥10x+15y). The correct maximum number of shorts (3 pairs of shorts) is provided, and the symbolic explanation is fully developed. The student replaces x in the inequality with 2, then solves for y, and truncates to a whole number for the solution. While the student correctly lists all the number combinations of shirts and shorts that total exactly $75, the justification is not fully developed. The student states (I plugged numbers into my equation and solved to see if they worked out evenly), but that substitution is not shown. The student also produced a graph but the student did not describe how the graph justifies his solution. The response demonstrates a clear 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 representation (10x+15y=75), in the form of an equation rather than an inequality, is essentially correct. The student provides the correct maximum number of shorts (3); however, the explanation is incomplete. (I got my answer by multiplying or using guess and check.) Data to support “guess and check” is needed to fully explain how the solution was determined. The student provides no response to the third part of the question. The 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
/share/clg/xml/public_release/mathematics/2005_121_alg21.xml
Resources for 1.2.1:
Skill Statements | PUBLIC RELEASE ITEMS | Lesson Plans |