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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.

Extended Constructed Response (ECR) Item - Released in 2006

The table below shows the relationship between the average temperature in March and the date in April when the cherry trees bloom in Washington, D.C.

Complete the following in the Answer Book:
(If you choose to draw a graph to help write the equation, use the grid provided in the Answer Book.)

  • Write an equation of a line of best fit for the data.
  • According to your equation, what would be the date in April of the bloom if the average March temperature were 3.5°C? Use mathematics to explain how you determined your answer. Use words, symbols, or both in your explanation.
  • Suppose the average March temperature is 14°C. Is it appropriate to use your equation to predict the date in April when the cherry trees will bloom in Washington, D.C.? Use mathematics to justify your answer.

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 3

Annotation: This response indicates application of a reasonable strategy that leads to some correct solutions. The student gives a correct equation for the line of best fit (y=–4.5x+32.7). The date in April, if the average March temperature were 3.5°C, is correct (17th of April) and the explanation supports the solution. The student replaces x in the equation with 3.5 and solves for y. The student states that it is inappropriate to use the equation if the average March temperature were 14°C and while the justification supports the solution, it is not mathematical (I think that the blossoms will have already bloomed). This response demonstrates a clear 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 2

Annotation: This response indicates an incomplete application of a reasonable strategy. The student gives a correct equation for the line of best fit (y=–4.457912458x+32.66801347). The date in April, if the average March temperature were 3.5°C, is correct (17th); however, an explanation is not given. Although the student correctly states that it is inappropriate to use the equation (No), a justification is not given. This response demonstrates a conceptual understanding and analysis of the problem. (Compare to this Level 2 anchor paper.)


Sample Student Response #3

image of student response

Score for Sample Student Response #3: 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 student gives a correct equation for the line of best fit (y=–4.4x+32.6). The date in April, if the average March temperature were 3.5°C, is correct (17th) and the explanation is well developed (I plugged 3.5 into my equation for x). The student states that it is inappropriate to use the equation if the average March temperature were 14°C and the justification is clearly presented (because of a negative answer). This response demonstrates a complete understanding and analysis of the problem. (Compare to this Level 4 anchor paper.)


Sample Student Response #4

image of student response

Score for Sample Student Response #4: Rubric Score 1

Annotation: This response indicates little application of a reasonable strategy. An equation for the line of best fit is not given. The date in April, if the average March temperature were 3.5°C, is incorrect (14th) and an explanation is not provided. The student states that it is inappropriate to use the equation if the average March temperature were 14°C and the justification supports the solution (14°C is a very different temperature than the others recorded in the data chart & the equation was made with the numbers in the chart. 14°C is a bigger number than the ones in the chart). This response demonstrates a minimal 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
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Resources for 3.2.2:
Skill Statements | PUBLIC RELEASE ITEMS |