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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 1.1.1 The student will recognize, describe, and/or extend patterns and functional relationships that are expressed numerically, algebraically, and/or geometrically.

Assessment Limits:

  • The given pattern must represent a relationship of the form y = mx + b (linear), y = x2 + c (simple quadratic), y = x3 + c (simple cubic), simple arithmetic progression, or simple geometric progression with all exponents being positive.
  • The student will not be asked to draw three-dimensional figures.
  • Algebraic description of patterns is in indicator 1.1.2

Extended Constructed Response (ECR) Item - Released in 2003

Park rangers determined that the current deer population in a park is 78. Ranger Jones predicted that the deer population will increase by 6 deer each year. Ranger Percy predicted that the deer population will increase by 8 deer each year.

Complete the following in the Answer Book:

  • Complete the tables in the Answer Book for Ranger Jones and Ranger Percy.
  • For each ranger's prediction, write an expression that can be used to determine the deer population in the park n years from now.
  • What is the difference in the number of deer that Ranger Percy predicted will be in the park 10 years from now compared to Ranger Jones' 10-year prediction? 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 tables are correctly completed; however, no attempt is made to write an expression or determine the difference in the predicted number of deer in 10 years. The 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 tables are correctly completed, but the representations, in the form of equations, are incorrect. No attempt is made to determine the difference in the predicted number of deer in 10 years. 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 tables are correctly completed. While the student has not provided expressions to represent each ranger's prediction, the correct difference in the predicted number of deer in 10 years ("20 deers different") is given. The explanation supports the solution but is not fully developed. (''Ranger Jones predicts there will only be 138 deer…Ranger Percy predicts there will be 158 deer.") 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 tables are correctly completed. The representations, in the form of equations ("Jones-y=78+6n…Percy-y=78+8n"), are correct. The difference in the predicted number of deer is incorrect, and the explanation is incomplete. ("I add to get this number in both Jones and Percy's case.") 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 table for Ranger Jones' predictions is correctly completed. The student correctly provides the predictions for the first and second years on Ranger Percy's table, but for the third year adds 6 rather than 8. Correct expressions for Ranger Jones (78+6n) and Ranger Percy (78+8n) are given. The response provides an incorrect predicted number of deer for Ranger Jones ("126 deer in 10 years") and a correct prediction for Ranger Percy ("158 deer in 10 years"). The explanation describes a reasonable strategy ("I got this answer by plugging in 10 to the equations"); however, the number "126" would be the solution when substituting 8, rather than 10, into the expression for Ranger Jones. The difference of "32 more deer" is consistent with the student's numbers. 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 correct solutions. The tables are correctly completed. In the form of equations set equal to "td" (defined as the "total # of deer"), the representations are correct. The equations are labeled for each ranger by their locations beneath the assigned tables. The student provides the correct difference in the predicted number of deer in 10 years; however, an explanation is not 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 tables are correctly completed. The representations, in the form of equations ("Ranger Jones' y=6n+78…Ranger Percy's y=8n+78"), are correct. The difference in the predicted number of deer in 10 years ("20 deer") is correct. The symbolic explanation is fully developed, clearly presented, and supports the solution. The student replaces the n in each equation with 10, solves for each ranger's prediction, and then finds the difference. 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 tables are correctly completed. The representations, in the form of equations ("Ranger Jones d=6n+78…Ranger Percy d=8n+78"), are correct. The variable d is defined. The difference in the predicted number of deer in 10 years ("20 deer off') is correct. The symbolic explanation is clearly presented and fully developed. The student replaces n in each equation and solves to find the number of predicted deer for each ranger. 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
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Resources for 1.1.1:
Skill Statements | PUBLIC RELEASE ITEMS | Lesson Plans |