School Improvement in Maryland
Public Release Item Scoring Information Return

Goal 3 Data Analysis And Probability

Expectation 3.1 The student will collect, organize, analyze, and present data.

Indicator 3.1.1 The student will design and/or conduct an investigation that uses statistical methods to analyze data and communicate results.

Assessment Limits:

  • The student will design investigations stating how data will be collected and justify the method.
  • Types of investigations may include: simple random sampling, representative sampling, and probability simulations.
  • Probability simulations may include the use of spinners, number cubes, or random number generators.
  • In simple random sampling each member of the population is equally likely to be chosen and the members of the sample are chosen independently of each other. Sample size will be given for these investigations.

Brief Constructed Response (BCR) Item - Released in 2003

The Knitwear Company wants to know what sock colors teenagers will buy. The company is considering the three options below for collecting data.

Option 1: Spend five days in the sock department of a randomly selected store and ask every person who enters what color socks they buy.

Option 2: Spend one day in the sock departments of five randomly selected stores in randomly selected cities and ask every teenager who enters what color socks they buy.

Option 3: Spend one day in eight randomly selected shopping centers and ask ten randomly selected teenagers at each shopping center what color socks they buy.

Complete the following in the Answer Book:

  • Which option gives the company the most representative sample of sock colors that teenagers will buy?
  • Use mathematics to justify why the other two options do not give the company the most representative sample.

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. The student correctly chooses Option 2 as the most representative sample of sock colors. The student addresses the concept of variety by stating that Option 2 gives "more options." The justification for Option 1 is clearly presented and indicates that the wrong population is being sampled ("you are asking every person, and you are trying to find what color socks teenagers will buy, not everyone's opinion"). The justification for Option 3 also supports the solution and indicates that the sample size is too small ("you are only asking 10"). Even though Option 3 actually asks 80 teens, the idea that the sample size is too small is the same whether the student says 10 or 80. This response demonstrates a complete understanding and analysis of the problem.


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 correctly chooses Option 2 as the most representative sample of sock colors. The justification for Option 1 correctly identifies that the wrong population is sampled. ("Option one is just asking any random person not a teenager but everyone.") However, the justification for Option 3 is unclear. ("Option 3 wont come out as a good percentage because your only getting 80% of teenagers.") Option 3 samples a total of 80 teenagers, not 80% of the teenagers. This response demonstrates a minimal understanding and analysis of the problem. Compare to Anchor Paper #2.
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. The student correctly chooses Option 2 as the most representative sample of sock colors. The justification for Option 1 correctly observes that the wrong population is sampled ("not everyone may be teenagers"). No justification is required for why Option 2 gives the most representative sample, but the student correctly states "your asking only teenagers." The justification for Option 3 correctly identifies that the sample size is too small ("only asking eighty teenagers not all"). Although the justifications support the solution, there is no indication that "variety" is necessary in a representative sample. This 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
/share/clg/xml/public_release/mathematics/2003_311_alg06.xml
Resources for 3.1.1:
Skill Statements | PUBLIC RELEASE ITEMS | Lesson Plans |