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.
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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 â€“ 1 and TV Ages â€“ 2Â 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).
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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 â€śthe multiple,â€ť (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 sidebyside 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 â€“ 1 and TV Ages â€“ 2Â 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.
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