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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 1.2.2 The student will solve linear inequalities and describe the solutions using numbers, symbols, and/or graphs.

Assessment Limits:

  • Inequalities will have no more than two variables with rational coefficients.
  • Acceptable forms of the problem or solution are the following:
    Ax + By < C, Ax + By < C, Ax + By > C, Ax + By > C, Ax + By + C < 0, Ax + By + C < 0, Ax + By + C > 0, Ax + By + C > 0, y < mx + b, y < mx + b, y > mx + b, y > mx + b, y < b, y < b, y > b, y > b, x < b, x < b, x > b, x > b, a < x < b, a < x < b, a < x < b, a < x < b, a < x + c < b, a < x + c < b, a < x + c < b, a < x + c < b.
  • The majority of these items should be in real-world context.
  • Systems of linear inequalities will not be included.
  • Compound inequalities will be included.
  • Disjoint inequalities will not be included.
  • Absolute value inequalities will not be included.

Extended Constructed Response (ECR) Item - Released in 2004

Elizabeth joins a CD buyer's club. She receives 10 free CDs when she joins this club. She must buy 3 CDs each month.

Complete the following in the Answer Book:

  • Write an equation that represents the number of CDs (y) Elizabeth will receive from the CD buyer's club after x months.
  • What is the y-intercept of your equation? What does the y-intercept mean in the context of this problem?
  • Elizabeth wants to receive no more than 55 CDs from this club. What is the maximum number of months Elizabeth will remain in the CD buyer's club? Use mathematics to explain how you determined your answer. Use words, symbols, or both in your explanation.

The following 8 Anchor Papers represent a range of score points and are used in conjunction with the rubrics to assess student responses.

Anchor Paper #1

image of student response

Score for Anchor Paper #1: Rubric Score 1

Annotation: This response indicates little application of a reasonable strategy. The representation is incorrect (y=3x). The value of the y-intercept is not provided, and the contextual meaning is incomplete (the number of CDs). The maximum number of months (18) is incorrect. The symbolic explanation reveals a reasonable strategy, replacing y with 55 and solving for x. The incorrect equation generates an incorrect solution. This response demonstrates a minimal understanding and analysis of the problem.


Anchor Paper #2

image of student response

Score for Anchor Paper #2: Rubric Score 1

Annotation: This response indicates little application of a reasonable strategy. The equation, the value of the y-intercept, and the intercept's contextual meaning are not provided. The maximum number of months is correct, and the incomplete explanation supports the solution (she starts out with 10 free which = 45; 45÷3=15). This response demonstrates a minimal understanding and analysis of the problem.


Anchor Paper #3

image of student response

Score for Anchor Paper #3: Rubric Score 2

Annotation: This response indicates an incomplete application of a reasonable strategy. The representation is correct (y=10+3x). While the value of the y-intercept (10) is correct, the contextual meaning is not given. The maximum number of months (15) is correct, but an explanation is not provided. This response demonstrates a conceptual understanding and analysis of the problem.


Anchor Paper #4

image of student response

Score for Anchor Paper #4: Rubric Score 2

Annotation: This response indicates an incomplete application of a reasonable strategy. The representation, in the form of an expression rather than an equation, is correct (10+3x). The value of the y-intercept is not provided, and the contextual meaning is incomplete (number of CDs). A correct maximum number of months (15) is given with the calculation (10+3·15=55) providing justification, rather than explanation. This response demonstrates a conceptual understanding and analysis of the problem.


Anchor Paper #5

image of student response

Score for Anchor Paper #5: Rubric Score 3

Annotation: This response indicates application of a reasonable strategy that leads to some correct solutions. The representation is correct (y=3x+10). The student provides the correct y-intercept, although it is given as "y=10." Rather than supplying a contextual meaning, the student supplies the definition of a y-intercept (where the line hits the y-axis). The maximum number of months (15) is correct; however, the calculations (3x15=45+10=55) provide justification, rather than explanation. This response demonstrates a clear understanding and analysis of the problem.


Anchor Paper #6

image of student response

Score for Anchor Paper #6: Rubric Score 3

Annotation: This response indicates application of a reasonable strategy that leads to some correct solutions. The representation is correct (y=3x+10). Both the value of the y-intercept (ten) and the contextual meaning (she starts with 10 CDs) are correct. Although the maximum number of months (15) is correct, no explanation is given. This response demonstrates a clear understanding and analysis of the problem.


Anchor Paper #7

image of student response

Score for Anchor Paper #7: 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 representation is correct (y=3x+10). The student provides the correct y-intercept (10), contextual meaning (it is the initial amount of CDs Elizabeth gets from the buyers club), and maximum number of months (15). The explanation is clearly presented and fully developed; the student constructs a table showing monthly x and y values for Elizabeth's membership, stopping at the 15th month when the number of CDs stood at 55. This response demonstrates a complete understanding and analysis of the problem.


Anchor Paper #8

image of student response

Score for Anchor Paper #8: 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 representation is correct (y=3x+10). The student provides both the correct y-intercept (10) and the contextual meaning (she starts out with 10 free CDs). The maximum number of months (15) is correct. The explanation is clearly presented and fully developed; the student replaces the y in the inequality with 55 and solves for x. This response demonstrates a complete understanding and analysis of the problem.


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/2004_122_alg19.xml
Resources for 1.2.2:
Skill Statements | PUBLIC RELEASE ITEMS | Lesson Plans |