Mathematics · Year 6

Active learning ideas

Calculating Mean, Median, and Mode

Active learning works well for this topic because students need repeated, hands-on practice with ordering numbers, calculating sums, and identifying central values. Manipulating real data sets helps them see how outliers shift the mean while the median stays steady, building an intuitive grasp of central tendency.

• ACARA Content Descriptions
• AC9M6ST02

• 20–50 min
• Pairs → Whole Class
• 3 activities

Activity 01

• Inquiry Circle
• 50 min · Small Groups

Inquiry Circle: The Typical Year 6 Student

Students collect data on height, arm span, or number of siblings. In groups, they calculate the mean, median, and mode for each category and create a profile of the 'average' student.

Which measure of center is most affected by an extreme outlier?

Facilitation Tip

During Collaborative Investigation: The Typical Year 6 Student, circulate and prompt groups with questions like, 'If three students move classrooms, how does that affect your mean height?' to keep them reasoning about data changes.

What to look for

Provide students with a small data set (e.g., 5-7 numbers including one outlier). Ask them to calculate the mean, median, and mode. Then, ask: 'Which measure is most affected by the outlier and why?'

• Analyze
• Evaluate
• Create
• Self-Management
• Self-Awareness

Activity 02

• Decision Matrix
• 25 min · Whole Class

Whole Class: The Outlier Effect

Calculate the mean height of a small group of students. Then, 'add' a giant (like a 3-meter tall fictional character) to the data and recalculate. Discuss how the mean changes while the median stays almost the same.

Why might a researcher choose to report the median instead of the mean?

Facilitation Tip

For Whole Class: The Outlier Effect, have students physically stand in order of shoe size before finding the median; this reinforces the importance of ordering data.

What to look for

Present two scenarios: 1) The average height of students in Year 6. 2) The median house price in a local suburb. Ask students: 'Which scenario is better described by its mean, and which by its median? Justify your answers, considering potential outliers in each case.'

• Analyze
• Evaluate
• Create
• Decision-Making
• Self-Management

Activity 03

• Think-Pair-Share
• 20 min · Pairs

Think-Pair-Share: Which Average is Best?

Students are given scenarios (e.g., shoe sizes in a shop, test scores with one zero, house prices). They must decide whether mean, median, or mode is the most useful 'average' for that specific case.

How do averages help us compare two different groups of data?

Facilitation Tip

In Think-Pair-Share: Which Average is Best?, assign each pair a different scenario so you can call on diverse responses during the whole-class discussion.

What to look for

Give each student a card with a different data set. Ask them to calculate the mean, median, and mode. On the back, they should write one sentence explaining which measure best represents the 'typical' value in their data set and why.

• Understand
• Apply
• Analyze
• Self-Awareness
• Relationship Skills

A few notes on teaching this unit

Research shows students learn central tendency best when they experience the data, not just calculate it. Use concrete examples like heights or test scores they care about. Avoid rushing to formulas; instead, build understanding through ordering numbers, spotting patterns, and discussing which average ‘feels right’ for the data. Emphasize that the mean is an equal share, the median is the middle person, and the mode is the most common value.

Students will confidently order data, calculate mean, median, and mode, and justify which measure best represents the typical value. They will also recognize when outliers distort the mean and explain why the median becomes more reliable in those cases.

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Watch Out for These Misconceptions

• During Collaborative Investigation: The Typical Year 6 Student, watch for students who default to the mean without considering the impact of outliers.

  Ask groups to add an extreme height (e.g., 200 cm) to their data set and recalculate. Have them discuss whether the new mean still feels like a typical height and why the median might be better.

• During Whole Class: The Outlier Effect, watch for students who skip ordering data before finding the median.

  Have students line up by height first, then find the middle person. If they resist ordering, ask, 'How can you find the middle person without lining up?' to highlight the importance of order.

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Methods used in this brief

• Inquiry Circle
• Decision Matrix
• Think-Pair-Share