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 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 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 demonstrates little application of a reasonable strategy. The student has provided the correct equations for Sarah (150x+250=y) and Felicia (1,650-200x=y). 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.


Anchor Paper #2

image of student response

Score for Anchor Paper #2: Rubric Score 1

Annotation: This response demonstrates little application of a reasonable strategy. The student has not responded to the first, second, or third parts of the question. The week Sarah and Felicia will have the same amount of money and the amount are correct (so that made it that by the 4 week both of them had 850 dollers). The justification supports the solution. The student begins a column of calculations for Sarah at 250 and adds four increments of 150, stopping at 850. A column for Felicia begins at 1,650 and subtracts four increments of 200, also stopping at 850. 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 demonstrates an incomplete application of a reasonable strategy. The representations, in the form of expressions rather than equations, are essentially correct (250+150x; 1650-200x). The equations are correctly graphed, lacking only a title and labels for the lines. The student incorrectly states that Sarah and Felicia will not have the same amount of money (No, Sarah has $700; Felicia has 1100). The justification is incomplete (Sara increased by 150, and Felicia Decreased by 200). 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 demonstrates an incomplete application of a reasonable strategy. The representations, in the form of expressions rather than equations, are essentially correct (Sarah 250+150w; Felicia 1650-200w). Although the student has assigned a scale on the y-axis, the representations are not graphed. The week Sarah and Felicia will have the same amount of money and the amount are correct (After 4 weeks they would have the same amount of money which would be at $850 for both). A justification is not provided. 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 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 (S=$250+150x) and Felicia (F=$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 (After 4 week they will have equal amounts of money). The justification supports the solution. The student replaces x with 4 in both equations, showing that the outcome for each is equal at $850. 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 demonstrates application of a reasonable strategy that leads to some correct solutions within the context of the problem. The representations, in the form of expressions rather than equations, are essentially correct (Sarah 250+150x; Felicia 1,650-200x). The graph is essentially correct. The points are plotted correctly and the scales are uniform, but labels and title are lacking. The week Sarah and Felicia will have the same amount of money and the amount are correct (At the End of the 4th week the will both have 850 dollars). A justification is not provided. 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 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 (y=250+150w) and Felicia (y=1,650-200w). The equations are correctly graphed, lacking only a title and labels for the lines. The week Sarah and Felicia will have the same amount of money and the amount are correct (they both will have 850 dollars after 4 weeks). 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.


Anchor Paper #8

image of student response

Score for Anchor Paper #8: 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 (250+150x=S) and Felicia (1650-200x=F). The equations are correctly graphed, lacking only a title. The week Sarah and Felicia will have the same amount of money and the amount are correct (At week 4 Sarah and Felicia have the same amount, They have $850). The justification is fully developed. The student replaces x with 4 in both equations, showing that the outcome for each is equal at 850. 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/2007_121_alg22.xml
Resources for 1.2.1:
Skill Statements | PUBLIC RELEASE ITEMS | Lesson Plans |