Mathematics · Grade 6

Active learning ideas

Mean Absolute Deviation (MAD)

Active learning helps students grasp variability, a concept that can feel abstract when taught through formulas alone. These activities transform the mean absolute deviation from a calculation into a meaningful tool that students can see and touch, making variability tangible in real-world contexts such as arm spans, sports scores, and reaction times.

• Ontario Curriculum Expectations
• 6.SP.B.5.C

• 30–50 min
• Pairs → Whole Class
• 4 activities

Activity 01

• Flipped Classroom
• 45 min · Small Groups

Small Groups: Arm Span Variability

Students measure arm spans within small groups and record data. Compute the mean, deviations, absolute deviations, and MAD. Compare MAD to range and discuss what it reveals about group consistency. Groups share findings on a class chart.

Explain how the mean absolute deviation describes the consistency of a data set.

Facilitation Tip

During Arm Span Variability, have students measure arm spans in centimeters and record differences from the group mean on sticky notes to build visual understanding of deviations.

What to look for

Provide students with a small data set, such as the number of minutes 5 students spent reading last night (e.g., 20, 30, 25, 35, 30). Ask them to calculate the mean, then the deviation for each data point, and finally the mean absolute deviation. Check their calculations for accuracy.

• Understand
• Apply
• Analyze
• Self-Management
• Self-Awareness

Activity 02

• Flipped Classroom
• 35 min · Pairs

Pairs: Sports Score Comparison

Provide pairs with two data sets of basketball scores. Pairs calculate mean, range, and MAD for each set. Determine which team shows more consistent scoring and justify using both measures. Pairs present to the class.

Construct the mean absolute deviation for a given data set.

Facilitation Tip

During Sports Score Comparison, provide real game score sheets so students see how variability differs between consistent and erratic performances.

What to look for

Present two data sets with the same range but different spreads (e.g., Data Set A: 10, 20, 30, 40, 50; Data Set B: 25, 28, 30, 32, 35). Ask students to calculate the MAD for both sets and write one sentence explaining which data set is more consistent and why, referencing their MAD calculations.

• Understand
• Apply
• Analyze
• Self-Management
• Self-Awareness

Activity 03

• Flipped Classroom
• 50 min · Whole Class

Whole Class: Reaction Time Challenge

Conduct a class reaction time test using a free online tool or ruler drop. Record all times on the board. As a class, step through mean and MAD calculations, noting deviations aloud. Vote on interpretations.

Compare MAD to other measures of spread like range.

Facilitation Tip

During the Reaction Time Challenge, use a free app like PsyToolkit to collect data and discuss how outliers affect MAD differently than range.

What to look for

Pose the question: 'Imagine you are comparing the daily temperatures for two cities. City X has a range of 10 degrees Celsius, and City Y also has a range of 10 degrees Celsius. Does this mean the cities have the same variability in temperature? How could calculating the Mean Absolute Deviation give us a better picture?' Facilitate a discussion where students explain the limitations of range and the utility of MAD.

• Understand
• Apply
• Analyze
• Self-Management
• Self-Awareness

Activity 04

• Flipped Classroom
• 30 min · Individual

Individual: Weekly Step Tracker

Students track daily steps for five days. Individually compute mean and MAD to assess personal consistency. Reflect in journals on factors affecting variability and share one insight with a partner.

Explain how the mean absolute deviation describes the consistency of a data set.

What to look for

Provide students with a small data set, such as the number of minutes 5 students spent reading last night (e.g., 20, 30, 25, 35, 30). Ask them to calculate the mean, then the deviation for each data point, and finally the mean absolute deviation. Check their calculations for accuracy.

• Understand
• Apply
• Analyze
• Self-Management
• Self-Awareness

A few notes on teaching this unit

Start with concrete examples before introducing formulas. Students benefit from physically moving data points on a number line to see distances from the mean, which builds intuition before abstract calculations. Avoid rushing to the algorithm; let students experience the concept through measurement and comparison. Research shows that students who construct their own understanding of deviation are more accurate and retain the concept longer.

Students will confidently explain that MAD measures consistency around the mean, not just the middle value. By the end of these activities, they will calculate MAD accurately, compare data sets using MAD, and articulate why range alone is insufficient for understanding spread.

---

Watch Out for These Misconceptions

• During Arm Span Variability, watch for students who think range is always a better measure of spread than MAD.

  Have students calculate both range and MAD for their arm span data, then compare two groups with similar ranges but different MADs to see which measure better reflects consistency within the group.

• During Sports Score Comparison, watch for students who believe deviations do not need absolute values because negatives cancel positives.

  Ask pairs to sort their score deviations into positive and negative piles, then observe how the sums cancel out. Use this to demonstrate why absolute values are necessary to capture total variability.

• During Reaction Time Challenge, watch for students who confuse MAD with the mean.

  After calculating MAD, have students physically move their data points on a number line to measure distances from the mean, reinforcing that MAD is about distances, not the data values themselves.

---

Methods used in this brief

• Flipped Classroom