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 2001

The administration of Central High School has decided to add a new sport for next year's ninth-grade girls. They are considering adding either soccer, tennis, or track. The administration needs to design an investigation in which 30 ninth-grade girls are surveyed to decide which new sport next year's ninth-grade girls would prefer.

Complete the following in the Answer Book:

  • Based on simple random sample principles, explain at least two of the key elements that should be part of the administration's design.

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 within the context of the problem. The student points out that a random sample could be assured by assigning random numbers, then correctly addresses the key element of independent selection: "This way you aren't selecting the students dependent of each other." While "a large sample" is not a key element based on simple random sample principles, the student does go on to correctly explain a second key element: "And you want to give everyone a fair chance to be picked." 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 application of a reasonable strategy. The student does not explain the key elements of the administration's design. However, the student's discussion of the importance of a large sample size does indicate a minimal understanding of the concepts related to sampling: "pick from as many people as possible..." This response demonstrates a minimal understanding and analysis of the problem. Compare to Anchor Paper #1.
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 explains one of the key elements the administration should use in their design: "...an equal chance for all girls to be selected..." However, a "bigger random sample" is not a key element based on principles of simple random sampling. 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
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Resources for 3.1.1:
Skill Statements | PUBLIC RELEASE ITEMS | Lesson Plans |