Deviation Detectives

Teacher Facilitation Guide

Subject

Mathematics (6-8)

Topic

Mean Absolute Deviation

Lesson Overview

This lesson introduces Mean Absolute Deviation (MAD) as a measure of variability. Students will move beyond just finding the "center" of data (mean) to understanding how "spread out" that data is. The lesson focuses on a simple 3-step procedural approach paired with deep conceptual interpretation using real-world scenarios.

Learning Objectives

Define Mean Absolute Deviation (MAD) as the average distance between each data point and the mean.
Calculate the MAD of a numerical data set using a three-step process.
Interpret the MAD in the context of real-world data to describe consistency and variability.

Materials Needed

Printables

• MAD Guided Notes
• Real-World Spread Practice

Tools

• Basic Calculators
• Whiteboards (optional for warm-up)

The 3-Step Process

1 Find the Mean (average) of the original data.
2 Find the Distance (absolute value) of each point from that mean.
3 Find the Mean of those distances.

Key Vocabulary

Variability: How spread out or different the data values are.
Deviation: The distance between a value and the mean.
Consistency: How predictable or similar data values are (Low MAD).

Facilitation Path

05

Minutes

The Hook: The Consistent Coffee

Present two coffee shops. Both average a 4-star rating. Shop A gets consistent 4s. Shop B gets 1s and 5s. Ask: "If the mean is the same, why does Shop B feel 'riskier'?" Lead them to the idea that average doesn't tell the whole story; variation does.

15

Minutes

Direct Instruction: Guided Notes

Distribute the Guided Notes. Walk students through the 3-step process using a small, simple data set (e.g., test scores: 80, 85, 90, 95, 100).

Teacher Tip: Emphasize that distance is always positive. We don't care if a value is above or below the mean, just how far away it is.

20

Minutes

Guided Practice: Data Lab

Students work on the Practice Worksheet. Monitor for Step 2 errors (students forgetting to use absolute values) and Step 3 errors (dividing by the wrong number).

10

Minutes

Discussion & Closing

Compare the results of the two scenarios on the practice sheet. Ask students:

"If Player A has a MAD of 2 and Player B has a MAD of 8, who is more predictable?"
"In what real-world situations would we want a LOW MAD?" (Safety, manufacturing, consistent grades)
"When might a HIGH MAD be interesting?" (Diverse weather, variety of snack choices)

Watch Out For

Mixing up Mean and Median

Ensure students use the Mean (Average) for Step 1. Using the Median will result in an incorrect MAD.

Negative Distances

Remind students that distance is always positive. If they get a sum of 0 in Step 3, they likely used negative numbers.

Deviation Detectives Lesson Plan Teacher Guide

Deviation Detectives Lesson Plan Teacher Guide

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