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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 2004

Students in a nutrition class decide to sell orange juice at their school's next sports event. To determine the price, the students record prices of orange juice from various stores in their city. The table below shows the price of different-sized bottles of juice.

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 equation? What does the slope mean in the context of this problem?
  • The students are selling 8-ounce bottles of orange juice. According to your line of best fit, what is the price of an 8-ounce bottle of juice? 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 application of a reasonable strategy. An expression (.09919037199124x + .6022100656454), instead of an equation, is given for the line of best fit. The slope is correct; however, the meaning of slope in the context of the problem is incorrect. The price of a bottle of juice and the explanation are not provided. 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 application of a reasonable strategy. An appropriate equation (y=.099x + .60) is provided for the line of best fit. The slope and the meaning of slope are incorrect. The price of a bottle of juice is incorrect, and an explanation is not given. 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 application of a reasonable strategy. No equation is given for the line of best fit. The student does not provide the slope and the meaning of slope. However, in order to determine the price of a bottle of juice, the student finds a pattern from the given table. The student's recognition (the difference is .8 between 2.19 & 2.99; same with 16 & 8; there's 8 oz so take .8 off of 2.19 and get $1.39) shows relevant knowledge. 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 incomplete application of a reasonable strategy. An appropriate equation (y=.099x + .6022) is given for the line of best fit. The slope is correct, but no meaning of slope is provided. Based on the student's equation, a correct answer is supplied for the price of a bottle of juice (1.40); however, no explanation is given. 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 incomplete application of a reasonable strategy. Because the student provides an expression, instead of an equation, the representation is not complete. The slope is not given, but the meaning of slope (represents the increase in price per ounce) is correct. The price of a bottle of juice is correct, and the explanation (by plugging the number of ounces {8} into the x value of my equation and solving to get 1.392) is logically sound. 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 incomplete application of a reasonable strategy. A correct equation (y=.099x + .602) is provided for the line of best fit. The slope is correct, but the meaning of slope is incorrect (price per bottle). The price of a bottle of juice ($1.40) is correct, and the explanation supports the solution. (I determined my answer by looking on my calculator's graph and finding 8 on the x axis and the y value, the price is what the price was of an 8 ounce bottle of juice.) 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 in the context of the problem. A correct equation is given for the line of best fit. The omission of variable definitions is a minor error. Both the slope and the meaning of slope (price per ounce) are correct. The price of a bottle of juice is correct, and the explanation, substituting 8 for x in the equation, is clearly presented. 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 variables are defined, and an appropriate equation (y=.1x + .6) for the line of best fit. The slope and the meaning of slope (for every increase of one ounce, the price increases by 10 cents) are correct. The price of a bottle of juice ($1.40) is correct. The explanation, substituting 8 for x in the equation, is clearly presented and supports the solution. 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:
Skill Statements | PUBLIC RELEASE ITEMS |