Mathematics · Grade 7

Active learning ideas

Visualizing Data: Box Plots

Active learning works for box plots because students must physically collect, order, and summarize data to see how compression into quartiles reveals distribution shape. Moving from raw numbers to visual summaries builds durable intuition about spread, skew, and outliers that textbook exercises alone cannot match.

• Ontario Curriculum Expectations
• 7.SP.B.4

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

Activity 01

• Gallery Walk
• 45 min · Small Groups

Small Groups: Survey Box Plots

Students survey classmates on a topic like daily screen time, record 20-30 values per group. Calculate quartiles and median using sorted lists, then draw box plots on grid paper. Groups present findings, noting outliers and shape.

Explain what story the shape of a data distribution tells us about the population.

Facilitation Tip

During Survey Box Plots, circulate and ask each group how their personal data point shifts the minimum, Q1, or median to keep reasoning explicit.

What to look for

Provide students with a small, ordered data set (e.g., 15-20 numbers). Ask them to calculate the five-number summary and then draw a box plot on grid paper. Check for accurate calculations and correct plot construction.

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

Activity 02

• Gallery Walk
• 30 min · Pairs

Pairs: Outlier Challenges

Provide data sets with planted outliers, such as test scores. Pairs identify outliers using the 1.5 IQR rule, replot without them, and discuss population impacts. Compare original and adjusted plots.

Justify why it is important to look at the quartiles of a data set rather than just the range.

Facilitation Tip

In Outlier Challenges, have pairs defend their outlier decisions to the class to normalize uncertainty and context-based judgment.

What to look for

Present two box plots side-by-side, one representing student test scores in Math and the other in English. Ask students: 'What does the shape of each box plot tell you about the range of scores in each subject? Which subject shows more consistency in student performance, and how do you know?'

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

Activity 03

• Gallery Walk
• 35 min · Whole Class

Whole Class: Histogram vs Box Plot

Collect class data on pet ages. Display histogram first, then build box plot on board with student input. Discuss what each reveals about central tendency and spread.

Compare and contrast the information conveyed by a box plot versus a histogram.

Facilitation Tip

For Histogram vs Box Plot, insist students label axes on both graphs to prevent confusion between count and value scales.

What to look for

Give students a box plot and a short list of data points. Ask them to identify the minimum, Q1, median, Q3, and maximum from the plot. Then, ask them to calculate the IQR and determine if any of the listed data points appear to be outliers based on the plot's appearance.

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

Activity 04

• Gallery Walk
• 25 min · Individual

Individual: Data Creation

Students generate personal data like weekly steps, compute five-number summary, and sketch box plot. Share in gallery walk for peer feedback on accuracy.

Explain what story the shape of a data distribution tells us about the population.

What to look for

Provide students with a small, ordered data set (e.g., 15-20 numbers). Ask them to calculate the five-number summary and then draw a box plot on grid paper. Check for accurate calculations and correct plot construction.

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

A few notes on teaching this unit

Experienced teachers begin with concrete data students have collected themselves so quartiles feel like natural checkpoints, not abstract rules. Avoid starting with pre-made box plots; let students struggle to order data and discover why quartiles split the set into quarters. Research shows that students who compute quartiles by hand retain the concept longer than those who use software without the manual steps.

Successful learning looks like students confidently calculating the five-number summary, accurately drawing box plots, and explaining what the plot’s features communicate about the data set. Discussions should include reasoning about skew, consistency, and potential outliers without confusing symbols with actual data points.

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Watch Out for These Misconceptions

• During Survey Box Plots, watch for students treating the box plot as a dot plot and expecting to count individual responses.

  Have groups lay their raw data cards in order on the table before plotting, then point out how the box compresses these cards into quartile groups to make the transition from raw data to summary visible.

• During Outlier Challenges, watch for automatic dismissal of any point beyond 1.5*IQR as an error.

  Require pairs to research their data’s context (e.g., test scores vs. temperature) and draft a short statement explaining whether each outlier is plausible or likely an error before marking it on the plot.

• During Histogram vs Box Plot, watch for students assuming the median line in a histogram always aligns with the tallest bar.

  Have students draw the five-number summary directly on their histogram using vertical lines and labels; this forces them to connect histogram shape to box plot features.

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Methods used in this brief

• Gallery Walk