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Goal 3 Data Analysis And Probability

Expectation 3.2 The student will apply the basic concepts of statistics and probability to predict possible outcomes of real-world situations.

Indicator 3.2.2 The student will interpret data and/or make predictions by finding and using a line of best fit and by using a given curve of best fit.

Assessment Limits:

  • Items should include a definition of the data and what it represents.
  • Data will be given when a line of best fit is required.
  • Equation or graph will be given when a curve of best fit is required.

Brief Constructed Response (BCR) Item - Released in 2005

A tire company wants to determine how quickly the tread on its tires wears down with average use. Let x represent the number of months the tire was used. Let y represent the thickness of the tire tread, in millimeters. An equation for a line of best fit is shown below.

Complete the following in the Answer Book:

  • What is the slope of this line of best fit? What does the slope mean in the context of this problem?
  • What is the y-intercept of this line of best fit? What does the y-intercept mean in the context of this problem?
  • Tina will need to replace her new tires when they have 5 millimeters of tire tread left. According to the line of best fit, for how many months can Tina drive before she needs to replace her tires? Use mathematics to explain how you determined your answer. Use words, symbols, or both in your explanation.

The following 7 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 attempt to apply a reasonable strategy. While the correct answers are provided for both the slope (-5/9) and y-intercept (20), the meaning of slope and the y-intercept in the context of this problem are not given. The answer and explanation for when Tina should replace her tires is also not supplied. 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 attempt to apply a reasonable strategy. A correct answer (-5/9) is given for the slope. The meaning of slope is incomplete; the student needs to include that the slope is how quickly the tire wore down per month. The y-intercept is correct, and the meaning of the y-intercept (the thickness of the tire before it was used) is complete. Both the answer and the explanation for when Tina should replace her tires are incorrect. The response demonstrates a minimal understanding and analysis of the problem.


Anchor Paper #3

image of student response

Score for Anchor Paper #3: Rubric Score 1

Annotation: This response indicates little attempt to apply a reasonable strategy. The correct answers are given for both the slope and the y-intercept; however, the meanings of slope and the y-intercept are not provided. Although the correct answer for when Tina should replace her tires is given, the explanation is incomplete. The response demonstrates a minimal 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 correct answer is given for the slope, but the meaning of slope is incomplete. The student needs to include that it is the rate at which the tread is wearing off per month. The y-intercept is correct, and the meaning of y-intercept (the thickness of the tire tread originally) is complete. Although a correct answer (27 months) is given for when Tina should replace her tires, only a partial explanation is provided. The response demonstrates a conceptual understanding and analysis of the problem.


Anchor Paper #5

image of student response

Score for Anchor Paper #5: Rubric Score 2

Annotation: This response indicates an incomplete application of a reasonable strategy. The correct answer is given for slope, and the meaning of slope (how much the tire tread wears in a month) is complete. The correct answer is provided for the y-intercept, and the meaning of y-intercept (how thick the tire was from the start) is complete. The answer for when Tina should replace her tires is incorrect; however, the explanation, substituting 5 for y, would support a correct answer. The response demonstrates a conceptual 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 a correct solution in the context of the problem. The correct answer (-5/9) is given for the slope, and the meaning of slope (the amount the thickness of the tire tread decreases per month) is complete. The correct answer (20) is provided for the y-intercept. The meaning of the y-intercept (the initial thickness of the tire tread) is complete. The correct answer (27 months) is given for when Tina should replace her tires, and the explanation, substituting 5 for y, is fully developed and supports the solution. The response demonstrates a complete understanding and analysis of the problem.


Anchor Paper #7

image of student response

Score for Anchor Paper #7: Rubric Score 3

Annotation: This response indicates application of a reasonable strategy that leads to a correct solution in the context of the problem. The correct answer (-5/9) is given for the slope. The meaning of slope (how much the tire tread wears down each month) is complete. The correct answer (20) is supplied for the y-intercept, and the meaning of the y-intercept (the starting thickness of the tire tread) is complete. The correct answer (27 months) is given for when Tina should replace her tires. The explanation, substituting 5 for y, is fully developed and supports the solution. The response demonstrates a complete understanding and analysis of the problem.


Brief Constructed Response (BCR) Rubric
Print: Scoring Rubric (pdf)
Score 3

The response indicates application of a reasonable strategy that leads to a correct solution in the context of the problem. The representations are essentially 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 2

The response indicates application of a reasonable strategy that may be incomplete or undeveloped. It 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 attempt to apply a reasonable strategy or applies an inappropriate 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_322_alg16.xml
Resources for 3.2.2:
Skill Statements | PUBLIC RELEASE ITEMS |