Comparing Test Scores

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Resource ID#: 124436 Primary Type: Formative Assessment

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Students are asked to informally determine the degree of overlap between two distributions with the same mean absolute deviation (MAD) by expressing the difference in their means as a multiple of the MAD.

General Information

Subject(s): Mathematics

Grade Level(s): 7

Intended Audience: Educators

Keywords: MFAS, dot plot, mean, mean absolute deviation, compare, mad

Instructional Component Type(s): Formative Assessment

Resource Collection: MFAS Formative Assessments

Attachments

MFAS_ComparingTestScoresWorksheet.docx
MFAS_ComparingTestScoresWorksheet.pdf

Formative Assessment Task

Instructions for Implementing the Task

This task can be implemented individually, with small groups, or with the whole class.

The teacher asks the student to complete the problems on the Comparing Test Scores worksheet.
The teacher asks follow-up questions, as needed.

TASK RUBRIC

Getting Started

Misconception/Error

The student cannot correctly identify the mean and the mean absolute deviation.

Examples of Student Work at this Level

The student does not know how to calculate either the mean, the men absolute deviation (MAD), or both.

Questions Eliciting Thinking

Were you able to determine the actual test scores from the dot plots?

Can you explain how you calculated the mean?

Can you explain how you calculated the MAD?

Instructional Implications

If needed, review how to find the mean of a set of data. Then review the calculation of the MAD. Assist the student in organizing data and calculations (e.g., a table with test scores on the left and absolute deviations from the mean on the right). Clarify that an absolute deviation is the absolute value of the difference between a data point and the mean, and the mean absolute deviation is the average of all absolute deviations. Ask the student to list the scores presented in each graph, calculate their means, and their MADs.

Provide additional sets of data (both raw data and data given in dot plots). Ask the student to calculate the mean and the MAD of each set of data. Provide feedback as needed.

Consider implementing MFAS tasks TV Ages – 1 and TV Ages – 2 if not already used.

Moving Forward

Misconception/Error

The student makes an error when calculating the mean absolute deviation.

Examples of Student Work at this Level

The student correctly calculates the mean of each distribution and demonstrates an understanding of the calculation of the MAD. However, the student makes an error in the calculation of the MAD which makes it difficult to respond to the third prompt (i.e., describe the difference between the means as a multiple of the MAD).

Questions Eliciting Thinking

Can you explain how you calculated the MAD?

You made an error in this calculation of the MAD. Can you check your work and correct your error?

Instructional Implications

Provide feedback to the student concerning any error made and ask the student to revise his or her calculation and response to the third prompt. Then determine if the student is at the Almost There or Got It level and proceed accordingly.

Almost There

Misconception/Error

The student is unable to describe the difference between the means as a multiple of the MAD.

Examples of Student Work at this Level

The student correctly calculates the mean and MAD of each distribution, but is unable to describe the difference in the means as a multiple of the MAD. The student:

Compares the means, the MADs, or some other aspect of the distributions.
Indicates he or she does not understand what is being asked.
Calculates the difference in the means but can go no further.

Questions Eliciting Thinking

What is the difference between the means of these two distributions?

What does the term multiple mean?

How is this difference related to the MAD?

Instructional Implications

Explain that the purpose of the third question is to assess the degree of overlap between the two distributions. Review the meaning of the term multiple and pose problems in which the student must write one number as a multiple of another. For example, ask the student to write 48 as a multiple of six by writing 48 = 8 x 6. Make clear which factor represents “the multiple,” (i.e., eight). Then guide the student through the process of writing the difference between the means as a multiple of the MAD.

Provide additional side-by-side dot plots (with similar spread and different means) and ask the student to describe the difference between the means as a multiple of the MAD.

Consider implementing MFAS tasks TV Ages – 1 and TV Ages – 2 if not already used.

Got It

Misconception/Error

The student provides complete and correct responses to all components of the task.

Examples of Student Work at this Level

The student indicates the following:

The mean of the pretest scores is 4 and the mean of the posttest scores is 10.
The MAD of each set of scores is 2.
The difference between the means is 6 which is three times the MAD.

Questions Eliciting Thinking

What do you think this indicates about the differences between the two distributions?

What does the multiple you found indicate about the degree of overlap of the two distributions?

Are there any other differences evident between the two distributions?

Instructional Implications

Have the student compare the two distributions in terms of their centers, spread, and shape. Ask the student to reference the context of the data in the comparison.

Introduce the student to the standard deviation and compare it to the MAD. Ask the student to calculate the standard deviation of each distribution.

Accommodations & Recommendations

Special Materials Needed:
• Comparing Test Scores worksheet

Source and Access Information

Contributed by: MFAS FCRSTEM

Name of Author/Source: MFAS FCRSTEM

District/Organization of Contributor(s): Okaloosa

Access Privileges: Public

License: CPALMS License - no distribution - non commercial

* Please note that examples of resources are not intended as complete curriculum.

Aligned Standards

This vetted resource aligns to concepts or skills in these benchmarks.

Related Resources

Other vetted resources related to this resource.

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Comparing Test Scores

General Information

Attachments

Formative Assessment Task

Instructions for Implementing the Task

TASK RUBRIC

Getting Started

Moving Forward

Almost There

Got It

Accommodations & Recommendations

Special Materials Needed:

Source and Access Information

Aligned Standards

Related Resources

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