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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 2006

Erin used the equation below to model the price (y) of postage stamps, in cents, between 1950 and 1995. In Erin's model, x represents the number of years since 1950.

y = 0.014x² + 0.09x + 1.28

The graph below models the price of postage stamps, in cents, between 1950 and 1995.

Complete the following in the Answer Book:

  • According to the model, when was the price of a postage stamp 29¢? Use mathematics to explain how you determined your answer. Use words, symbols, or both in your explanation.
  • According to the model, what was the cost of postage stamps in 1970? Express your answer to the nearest cent. Use mathematics to explain how you determined your answer. Use words, symbols, or both in your explanation.

The following 3 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 3

Annotation: This response indicates application of a reasonable strategy that leads to a correct solution in the context of the problem. A correct answer (1992) is given for when the price of a postage stamp was 29 cents and the explanation is fully developed. A correct answer (9¢) is given for the cost of a stamp in 1970 and the explanation supports the solution (I figured that 50+x would equal 70; x= 20. Then, went to y-axis and found 9¢ for 1970). The response demonstrates a complete understanding and analysis of the problem. (Compare to this Level 3 anchor paper.)


Sample Student Response #2

image of student response

Score for Sample Student Response #2: Rubric Score 1

Annotation: This response indicates little attempt to apply a reasonable strategy. The student's incorrect answer for when the price of a postage stamp was 29 cents (1942) shows a misunderstanding of what "x" represents, that is, years since 1950, not years since 1900. Despite this error, the explanation is correct and would support a correct answer of 1992. An incorrect answer is given for the cost of a postage stamp in 1970 and the explanation is missing. The response demonstrates a minimal understanding and analysis of the problem. (Compare to this Level 1 anchor paper.)


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. A correct answer (1992) is given for when the price of a postage stamp was 29 cents and the explanation supports the solution. A correct answer of 9 cents is given for the cost of a stamp in 1970 but the explanation is missing. The response demonstrates a conceptual understanding and analysis of the problem.


Additional Resources

Anchor Papers used in scoring

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
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Resources for 3.2.2:
Skill Statements | PUBLIC RELEASE ITEMS |