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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 2003

Mike wants to know how many calories he can burn while jogging. The number of calories burned depends on the length of time Mike jogs. The table below shows the number of calories Mike burns while jogging.

Complete the following in the Answer Book:

  • Write an equation for a line of best fit. (If you choose to draw a graph, use the grid provided in the Answer Book.)
  • What is the slope of your line of best fit? What does the slope mean in the context of this problem?
  • Mike jogged for 60 minutes. According to your line of best fit, how many calories did he burn? 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 attempt to apply a reasonable strategy. No equation for the line of best fit is provided, and no attempt is made to give the slope or the meaning of slope in the context of the problem. A correct answer ("588 calories") for the number of calories burned is given and demonstrates some relevant interaction with the data. However, there is no explanation. 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. An appropriate equation is given for the line of best fit, but the slope, the context for slope, and the answer and explanation for the third bullet are not provided. While a graph of the line of best fit is not required, this student's attempt at graphing has reversed the x and y axes. 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 1

Annotation: This response indicates little attempt to apply a reasonable strategy. Although the variables are not defined, a correct equation is given for the line of best fit. No slope or context of slope is provided. The student correctly answers how many calories Mike burned ("588.7"), but gives no explanation. This 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. Although the variables are not defined, an appropriate equation is given for the line of best fit. The slope is correct, but the meaning of slope in the context of the problem is incorrect. The student states that the slope "represents the time or length of time Mike jogs (in minutes)." The. correct context for slope is the number of calories burned per minute. A correct answer is provided for the number of calories burned. The student, by substituting 60 for x in the equation, gives a fully developed explanation. 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 2

Annotation: This response indicates an incomplete application of a reasonable strategy. Although the variables are not defined, an appropriate equation is given for the line of best fit. A correct answer is provided not only for the slope, but also for the meaning of slope. ("This slope means that for everyone minute Mike exercises, he loses about 9.81 calories.") While a correct answer ("588.65") is given for the number of calories burned, there is no explanation. This response demonstrates a conceptual understanding and analysis of the problem.


Anchor Paper #6

image of student response

Score for Anchor Paper #6: Rubric Score 2

Annotation: This response indicates an incomplete application of a reasonable strategy. An appropriate equation is given for the line of best fit ("y = 9.8x + 0"). Although the variables are not defined, a correct answer ("9.8") is provided, but the meaning of slope in the context of the problem is missing. A correct answer is given for the number of calories burned ("588"); however, there is no explanation. This response demonstrates a conceptual 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. An appropriate equation is given for the line of best fit. The slope and meaning of slope are correct. ("If we jog 10 min. cal. burned 100 cal.") This context for slope is equivalent to Mike burning 10 calories a minute. A correct answer ("600") is provided for how many calories are burned, and the explanation (substitutes 60 for x in the equation) is fully developed. Although a graph is not required, an appropriate graph, with some definition of variables, is drawn for the line of best fit. 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 3

Annotation: This response indicates application of a reasonable strategy that leads to a correct solution in the context of the problem. The student defines the variables and gives an appropriate equation for the line of best fit. A correct answer is given for both the slope and the meaning of slope in the context of the problem. ("It means that for every minute jogged, Mike will burn 9.8 calories.") A correct answer for the number of calories burned ("588.048") is provided. The explanation is clearly presented and fully developed (substitutes 60 for x in the equation). 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

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Resources for 3.2.2:
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