Mathematics · Year 9

Active learning ideas

Box Plots for Comparing Data

Active learning works for box plots because students build the visual themselves from raw data. When Year 9s collect measurements and mark their own medians and quartiles, the summary becomes meaningful, not abstract. This hands-on construction helps them trust the plot as a tool for comparing groups quickly and accurately.

• National Curriculum Attainment Targets
• KS3: Mathematics - Statistics

• 20–45 min
• Pairs → Whole Class
• 4 activities

Activity 01

• Decision Matrix
• 35 min · Pairs

Pairs Survey: Heights Box Plots

Pairs survey 20 classmates' heights, order data, calculate median and quartiles, then draw box plots for boys and girls on shared graph paper. They note differences in spread and centre, presenting one key comparison to the class. Extend by identifying any outliers.

How can we use box plots to visually compare the spread of two different groups?

Facilitation Tip

During the Pairs Survey, circulate to ensure students are ordering data before they find Q1, Q2, and Q3; unordered lists lead to incorrect medians.

What to look for

Provide students with two small, ordered data sets (e.g., heights of students in two different Year 9 classes). Ask them to calculate the median, Q1, and Q3 for each set and write down the IQR for both. Check their calculations for accuracy.

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

Activity 02

• Decision Matrix
• 45 min · Small Groups

Small Groups Stations: Sports Data Comparison

Prepare four data sets on reaction times or jump heights from sports. Groups rotate through stations every 10 minutes: calculate stats, plot box plot, compare to another set, and critique skewness. Record findings on a group sheet.

Analyze what the median and quartiles represent on a box plot.

Facilitation Tip

At the Sports Data Stations, give each group one set of data to plot and one to interpret so everyone contributes to both tasks.

What to look for

Present students with two side-by-side box plots representing, for example, the daily temperatures in two cities over a month. Ask: 'Which city had a higher average temperature? Which city had more variable temperatures? Explain your reasoning using the box plot features.'

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

Activity 03

• Decision Matrix
• 25 min · Whole Class

Whole Class Critique: Exam Scores Challenge

Display three pairs of box plots from mock exam data on the board. Class discusses in a think-pair-share: which shows greater spread, evidence of skewness, and why one set might mislead. Vote and justify best comparison method.

Critique the effectiveness of box plots for identifying skewness in data.

Facilitation Tip

In the Whole Class Critique, deliberately overlay calculated means on box plots so students see how medians resist outliers compared to averages.

What to look for

Give students a box plot that is clearly skewed. Ask them to write one sentence describing the skewness and one sentence explaining a limitation of using box plots for this type of data.

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

Activity 04

• Decision Matrix
• 20 min · Individual

Individual Plotting: Weather Data

Provide rainfall data for two UK cities over a month. Students independently order data, compute quartiles, plot box plots, and write two sentences comparing variability. Share digitally for class gallery walk.

How can we use box plots to visually compare the spread of two different groups?

What to look for

Provide students with two small, ordered data sets (e.g., heights of students in two different Year 9 classes). Ask them to calculate the median, Q1, and Q3 for each set and write down the IQR for both. Check their calculations for accuracy.

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

A few notes on teaching this unit

Teach box plots by starting with small, manageable data sets so students can manually order and split the data. Avoid rushing to software before they grasp how quartiles divide the data. Research shows that sketching builds spatial memory; students who draw their own plots retain the meaning of IQR and outliers better than those who only use digital tools. Emphasise that a box plot is a summary, not a raw display, so students learn to trust its ability to hide detail while revealing key patterns.

By the end of these activities, students should calculate quartiles correctly, plot box plots neatly, compare spreads with precise vocabulary, and explain skewness using the shape of the box and whiskers. Clear sketches and concise comparisons in pairs and groups signal solid understanding.

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Watch Out for These Misconceptions

• During Pairs Survey: Heights Box Plots, watch for students who think all data points are shown inside the box and whiskers.

  Bring students back to their raw height measurements and have them mark each plotted value on the number line; they will see only five points define the plot, clarifying that the box and whiskers summarise the rest.

• During Whole Class Critique: Exam Scores Challenge, watch for students who say the median and mean are always the same.

  Ask groups to calculate the mean score from their data and overlay it on the box plot with a dotted line; the gap between the solid median line and dotted mean line in skewed data will show the difference visually.

• During Small Groups Stations: Sports Data Comparison, watch for students who extend whiskers to the absolute min and max regardless of outliers.

  Provide outlier cards at each station and have groups decide whether a point is beyond 1.5 times IQR; if yes, they redraw whiskers to the nearest non-outlier to practice the rule.

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Methods used in this brief

• Decision Matrix