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 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. 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 indicates a minimal understanding of the concepts related to sampling: "The administration should also get more students to participate so they would have an even better chance of getting the right sport for the students." 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. The student does not explain the key elements of the administration's design. However, the student's discussion of the importance of a sample that is representative does indicate a minimal understanding of the concepts related to sampling: "…they should have girls that play all different sports not just soccer…" 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 2

Annotation: This response indicates an incomplete application of a reasonable strategy. The student describes a process that will result in a simple random sample: "…every ones name in a basket pick out names ask those people…" While this sampling design does incorporate the key elements of equal chance and independent selection, the student's explanation of them is not complete. This response demonstrates a conceptual 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. The student correctly explains equal chance as a key element. The student also tries to address a second key element: "They should make sure that each student's survey is independent." Whether the student is referring to an unbiased vote, which is not a key element, or to an independent selection of survey respondents is not clear. With this incomplete explanation, the 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. The student identifies the need for independent selection of girls: "They should be chosen independently." However, the other two issues that the student addresses ("chosen randomly," "should not be biast") are not key elements based on simple random sample principles. 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. The student designs two simple random surveys (drawing numbers from a hat, using a random digits sheet). The student explains the key element of equal chance: "That way every girl has an opportunity to be chosen." However, while this sampling design also incorporates the key element of independent selection, the student's explanation of it is not complete. Therefore, 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 within the context of the problem. The student identifies the key elements of equal chance and independent selection and provides complete explanations for both: "…everyone has a fair chance and how they are picked shouldn't be dependent on someone else, for example if you picked every 5th name on an alphabetical list that wouldn't really be random…" 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 within the context of the problem. The student correctly explains the two key elements of equal chance and independent selection: "…every girl gets a fair chance to be surveyed…choosing one girl doesn't determine who gets chosen next." 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 3.1.1:
Skill Statements | PUBLIC RELEASE ITEMS | Lesson Plans |