School Improvement in Maryland
Public Release Item Scoring Information Return

Goal 1 Functions and Algebra

Expectation 1.1 The student will analyze a wide variety of patterns and functional relationships using the language of mathematics and appropriate technology.

Indicator 1.1.2 The student will represent patterns and/or functional relationships in a table, as a graph, and/or by mathematical expression.

Assessment Limits:

  • The given pattern must represent a relationship of the form mx + b (linear), x2 (simple quadratic), simple arithmetic progression, or simple geometric progression with all exponents being positive.

Extended Constructed Response (ECR) Item - Released in 2002

Stephanie must complete class projects for history and mathematics. Each project is worth a maximum of 100 points if she turns it in on time. Each teacher uses a different method to calculate the maximum number of points that a student can earn for a late paper. The tables below show the two methods.

Complete the following in the Answer Book:

  • Complete the tables to show the number of possible points for projects that are 4 and 5 days late.
  • How many days late can Stephanie turn in each project and still possibly receive a score of 65 or better on each project? Use mathematics to explain how you determined your answer. Use words, symbols, or both in your explanation.
  • Stephanie can complete only one project on time. The second project will be only one day late. To receive the maximum total number of possible points, which project should she complete first? Use mathematics to justify your answer.
  • Describe the method that each teacher uses to determine the maximum possible points that a student can earn for a late paper.

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 1

Annotation: This response indicates little application of a reasonable strategy. The table for the history project is completed correctly; however, the math table is incorrect. The number of days for the history project is correct, but an explanation is not provided. The number of days for the math project is consistent with the student's table. The explanation supports the solution ("If she turned it in 4 day she will get a 64 not a 65..."). This response demonstrates minimal understanding and analysis of the problem.


Sample Student Response #2

image of student response
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 tables are correctly completed. The number of days Stephanie can turn her history project in late and still possibly receive a score of 65 is correct. The explanation is fully developed ("...in history the teacher takes 5 points off every day it is late. So by the 7th day she can turn it in and still get a 65%."). The number of days the math project can be late is also correct. The explanation is clearly presented and supports the solution ("...in the 4th day her grade will already be 60%. The math teacher calculates the maximum points by first taking 4 points then adding 4 points and keeps on adding four and that number gets subtracted from the possible points."). The student correctly identifies the history project as the project to turn in on time. This choice is fully justified ("...in history by the 1st day late she will already get a 95 however in math if it is one day late she can get a 96."). The student provides a complete description of each teacher's method of assigning points. The description of the math teacher's method is strengthened by the student's calculations on the math table, indicating that the points are to be subtracted from the previous day's total number of points. 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 2

Annotation: This response indicates an incomplete application of a reasonable strategy. The table for the history project is completed correctly; however, the math table is incorrect. The number of days for the history project is correct, and the number of days for the math project is consistent with the student's table. The student's response to the third part of the question is correct; the student indicates that the math project should be turned in one day late (consequently, the history project would be on time). The explanation supports the solution ("...she will get 1 more point than if she turned history in late"). The description of the history teacher's method is correct and provides an explanation for the history solution in the second part of the question. The description of the math teacher's method, however, is incorrect. This response demonstrates a conceptual understanding and analysis of the problem.


Sample Student Response #4

image of student response

Score for Sample Student Response #4: Rubric Score 3

Annotation: This response indicates application of a reasonable strategy that leads to a correct solution. The tables are correctly completed. The number of days for the history project is correct, as is the number of days for the math project. The student correctly identifies the history project as the project to turn in on time, and this choice is fully justified ("...one more point off for the extra day it was late"). The description of the history teacher's method is generally well developed ("...uses d-5"), although "d" has not been defined. This description provides an explanation for the history solution in the second part of the question. The description of the math teacher's method is feasible; however, it is not fully developed ("...uses -4d"). The student does not define "d" or indicate that the points are to be subtracted from the previous day's total number of points. This provides a generally well developed explanation for the math solution in the second part of the question. This response demonstrates a clear 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/2002_112_alg07.xml
Resources for 1.1.2:
Skill Statements | PUBLIC RELEASE ITEMS | Lesson Plans |