Mathematics · Year 10

Active learning ideas

Box Plots and Data Comparison

Active learning helps students grasp box plots because the abstract measures of quartiles and medians become concrete when they order real data and draw the plots themselves. Turning numbers into visual summaries reveals patterns and outliers in ways that passive study cannot.

• National Curriculum Attainment Targets
• GCSE: Mathematics - Statistics

• 25–45 min
• Pairs → Whole Class
• 4 activities

Activity 01

• Collaborative Problem-Solving
• 30 min · Pairs

Pairs Task: Heights Comparison

Pairs measure and record heights of 20 classmates, split by gender. Order data to calculate medians and quartiles, draw side-by-side box plots. Discuss which group has greater spread and why.

Explain what each section of a box plot reveals about data distribution.

Facilitation Tip

During the Pairs Task: Heights Comparison, circulate and ask each pair to explain why they placed the median line where they did.

What to look for

Provide students with two sets of data (e.g., test scores from two different classes). Ask them to calculate the median, Q1, Q3, and IQR for each set, and then draw comparative box plots on the same axis.

• Apply
• Analyze
• Evaluate
• Create
• Relationship Skills
• Decision-Making
• Self-Management

Activity 02

• Collaborative Problem-Solving
• 45 min · Small Groups

Small Groups: Reaction Time Challenge

Provide stopwatch for groups to test 30 reaction times to a signal, split into two conditions like rested versus tired. Construct box plots and compare medians and ranges. Groups justify which condition performs better.

Compare two datasets using their box plots, focusing on central tendency and spread.

Facilitation Tip

For the Small Groups: Reaction Time Challenge, supply stopwatches and printed data tables to ensure all students engage with the raw data before plotting.

What to look for

Present students with two box plots, one representing exam scores for a class that used a new teaching method and another for a class using the traditional method. Ask: 'Which class performed better overall, and how do you know? What does the spread of the data tell you about the consistency of learning in each class?'

• Apply
• Analyze
• Evaluate
• Create
• Relationship Skills
• Decision-Making
• Self-Management

Activity 03

• Collaborative Problem-Solving
• 40 min · Whole Class

Whole Class: Sleep Survey Analysis

Conduct a 1-minute survey on weekly sleep hours. Collate data on board, split by day types. Class draws shared box plots, then votes on interpretations of spread and outliers.

Justify the use of box plots for visual comparison of data distributions.

Facilitation Tip

In the Whole Class: Sleep Survey Analysis, display student-generated box plots side by side to encourage comparison and debate about data interpretation.

What to look for

Give each student a box plot. Ask them to write down: 1. The value of the median. 2. The range of the middle 50% of the data. 3. One observation about the distribution (e.g., is it skewed, is there a large spread?).

• Apply
• Analyze
• Evaluate
• Create
• Relationship Skills
• Decision-Making
• Self-Management

Activity 04

• Collaborative Problem-Solving
• 25 min · Individual

Individual: Invent and Interpret

Students invent two small datasets from sports scores. Draw individual box plots, swap with a partner to interpret and critique. Share strongest comparisons with class.

Explain what each section of a box plot reveals about data distribution.

What to look for

Provide students with two sets of data (e.g., test scores from two different classes). Ask them to calculate the median, Q1, Q3, and IQR for each set, and then draw comparative box plots on the same axis.

• Apply
• Analyze
• Evaluate
• Create
• Relationship Skills
• Decision-Making
• Self-Management

A few notes on teaching this unit

Teachers often start by having students order data physically with sticky notes on a board to visualise quartiles before moving to paper or digital plotting. Avoid rushing to formulas; focus on the meaning of the quartiles first. Research suggests that constructing box plots manually, even with imperfect scale, builds deeper understanding than pre-drawn templates.

Successful learning looks like students confidently calculating quartiles, identifying medians, and drawing accurate box plots with correct whiskers and outliers. Discussions should focus on comparing distributions rather than just listing values.

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Watch Out for These Misconceptions

• During Pairs Task: Heights Comparison, watch for students confusing the median line with the mean.

  Have students calculate both the mean and median from their height data, then plot both on a number line to see where they differ. Ask them to explain which measure they think best represents the typical height in their sample.

• During Small Groups: Reaction Time Challenge, watch for students dismissing extreme reaction times as errors.

  Ask groups to research real-world examples of reaction times in sports or driving, then debate whether outliers reflect genuine differences or recording mistakes. Require them to justify their reasoning with data.

• During Whole Class: Sleep Survey Analysis, watch for students assuming box plots need large datasets to be valid.

  Use the class’ 15–20 survey responses to plot a box plot live on the board, then ask students to suggest how the plot would change (or stay the same) if five more responses were added.

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Methods used in this brief

• Collaborative Problem-Solving