Mathematics · Year 10

Active learning ideas

Box Plots and Five-Number Summary

Active learning works because students need to handle data directly to see how relationships between variables take shape. When they gather their own class data or debate spurious claims, abstract concepts like correlation and causation become concrete through their own reasoning and observations.

• ACARA Content Descriptions
• AC9M10ST02

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

Activity 01

• Inquiry Circle
• 50 min · Small Groups

Inquiry Circle: The Great Class Data Collection

Students work in groups to collect two pieces of data from their peers (e.g., arm span vs. height). They plot this on a shared digital scatter plot and use a 'string' or digital tool to find the line of best fit, discussing whether their data shows a strong or weak relationship.

Explain how a box plot visually represents the five-number summary.

Facilitation Tip

During The Great Class Data Collection, have students rotate through stations to collect multiple data points so everyone contributes to the full data set.

What to look for

Provide students with a data set (e.g., heights of students in class). Ask them to calculate the five-number summary and then draw a box plot. Check their calculations and the accuracy of their plot construction.

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

Activity 02

• Formal Debate
• 30 min · Pairs

Formal Debate: Spurious Correlations

The teacher provides 'crazy' correlations (e.g., ice cream sales vs. shark attacks). Students must work in pairs to identify the 'hidden variable' (e.g., summer heat) and debate why these two things are correlated but not causal.

Analyze how to identify outliers using the interquartile range.

Facilitation Tip

For Spurious Correlations, assign roles so debaters must cite specific data examples from their posters during rebuttals.

What to look for

Present students with two box plots comparing test scores from two different classes. Ask them to write two sentences comparing the central tendency and spread of the scores, and one sentence about which class performed more consistently.

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

Activity 03

• Gallery Walk
• 40 min · Small Groups

Gallery Walk: Prediction Posters

Groups are given a scatter plot with a line of best fit. They must create a poster that uses the line to make one 'safe' prediction (interpolation) and one 'risky' prediction (extrapolation), explaining the dangers of the latter. The class rotates to critique the 'riskiness' of the predictions.

Design a box plot for a given data set and interpret its skewness.

Facilitation Tip

In the Gallery Walk, place a sticky note pad at each poster so viewers can post immediate questions or insights for the creators to review after the walk.

What to look for

Pose the question: 'How can a box plot help us identify unusual data points that might warrant further investigation?' Facilitate a class discussion where students explain the concept of outliers and how the IQR is used to detect them.

• Understand
• Apply
• Analyze
• Create
• Relationship Skills
• Social Awareness

A few notes on teaching this unit

Teachers should start with familiar contexts students can relate to, like height vs. arm span, so the data feels personal. Avoid rushing to formulas; instead, have students estimate correlations by eye before calculating. Research shows that students grasp causation best when they actively test claims against their data, not just hear explanations.

Successful learning looks like students confidently constructing five-number summaries and box plots, explaining why correlation does not imply causation, and using evidence from their own data to support arguments. They should also recognize the difference between strong, weak, positive, and negative correlations in real contexts.

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Watch Out for These Misconceptions

• During The Great Class Data Collection, watch for students who label any downward trend as 'negative correlation' without considering the context or strength of the relationship.

  Ask them to quantify the trend by estimating the slope of the line of best fit and to explain whether the relationship is strong or weak using their data.

• During Spurious Correlations, watch for students who assume that any two variables moving together must have a cause-and-effect link.

  Have them use the debate format to present counterexamples and examine third variables or coincidences in their data sets.

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Methods used in this brief

• Inquiry Circle
• Formal Debate
• Gallery Walk