School Improvement in Maryland
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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 2008

The president of the student government wants to survey the students in the school about their satisfaction with the 36 after-school activities. There are 1,000 students in the school—200 freshmen, 200 sophomores, 300 juniors, and 300 seniors. The president suggested three different sampling methods.

Method A: Randomly choose three students from each of the 36 after-school activities for the survey.

Method B: Randomly select 100 students from the honor roll list to survey.

Method C: Randomly select 20 freshmen, 20 sophomores, 30 juniors, and 30 seniors for the survey.

Complete the following in the Answer Book:

  • Which method provides the most representative sample of the student population? Use mathematics to justify your answer.
  • Use mathematics to justify why each of the other two methods does not provide a representative sample.

The following 6 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. The student incorrectly chooses Method A as providing the most representative sample. However, the justification for choosing Method A is relevant (its choosing people from each activity) since the student recognizes that all of a population must be represented. The 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. The student incorrectly chooses Method A as providing the most representative sample. Because the survey described in the item is asking about satisfaction with after-school activities, the student thinks only students in after-school activities should be able to answer the survey. The justification for choosing Method A shows that the student is drawing the sample from the wrong population; that is, students in after-school activities instead of the whole student body. However, this answer still shows some understanding of representative sampling. The justifications for not choosing Methods B and C also focus on the fact that the students selected may not be in after-school activities. The 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 correctly selects Method C as providing the most representative sample but gives no justification. Justification is given for why Method A does not provide the most representative sample (not every student in the school stays for after school activities). Justification is also given for why Method B does not provide the most representative sample (not all students are on the honor roll). The 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 selects Method C as providing the most representative sample and gives fully developed justification (you have a number of students from each grade + each number of students from that grade is 1/10 of the grade). No justification is given for why Methods A and B do not provide the most representative sample. 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 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 selects Method C as providing the most representative sample and gives justification (each class is represented by 1/10 of it’s population). Justification is provided as to why A and B were not chosen (because they bias by selecting only certain groups). The response demonstrates a complete understanding and analysis of the problem.


Anchor Paper #6

image of student response

Score for Anchor Paper #6: 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 selects Method C as providing the most representative sample and gives a justification (you are surveying a lot of students, some from each grade). Complete justification is given for why Method A does not provide the most representative sample (you are only asking kids that are in the after school activity). Fully developed justification is also given for why Method B does not provide the most representative sample (you are only surveying kids on the honor roll, not kids who aren’t). The 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 |