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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 2002

The table below shows the sales for a greeting card company for the years 1990 through 1998.

Complete the following in the Answer Book:

  • Write an equation for the line of best fit for this data. Let x represent the years since 1900 and y represent the sales, in thousands of dollars. (If you choose to draw a graph, use the grid provided in the answer book.)
  • According to your equation, what were the sales in 1999? Use mathematics to explain how you determined your answer. Use words, symbols, or both in your explanation.

The following 6 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. The student plots the points from the table on the graph and draws a line of best fit. This represents relevant interaction with the data. No attempt is made to write an equation or determine sales in 1999. 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 attempt to apply a reasonable strategy. The representation is correct. An appropriate equation is given for the line of best fit based on "x" representing the years since zero. (Instead of letting "x" represent the years since 1900, the student lets "x" represent the years since zero.) The student does not explicitly redefine the variable in the response. No attempt is made to determine the sales in 1999. 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, and an appropriate equation is given for the line of best fit. The answer to the sales in 1999 is correct (although not expressed in thousands of dollars, a minor error); however, there is no explanation. 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 is correct; however, the student lets "x" represent the sales in years since zero instead of the years since 1900. An appropriate equation is given for the line of best fit based on "x" representing the years since zero. While the answer to the sales in 1999 is correct (although not expressed in thousands of dollars), there is no explanation. The explanation of how the student found the equation is unnecessary. 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 a correct solution in the context of the problem. The representation is correct. Instead of letting "x" represent the years since 1900, the student lets "x" represent the years since 1990. There is some redefinition of the variable when the student substitutes into the equation ("20.67 x 9 + 208.44 = 394.47"). Based on "x" representing the years since 1990, the equation is appropriate. The answer to the sales in 1999 is correct. The explanation (substituting into the equation) is presented clearly and supports the solution. This response demonstrates a complete 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 representation is correct. An appropriate equation is given for the line of best fit based on "x" representing the years since zero. The answer to the sales in 1999 is correct. The explanation is clearly presented and describes substituting into the equation. The graph of the line of best fit is not required and does not affect the score. This 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/2002_322_alg12.xml
Resources for 3.2.2:
Skill Statements | PUBLIC RELEASE ITEMS |