Mathematics · Grade 6

Active learning ideas

Box Plots (Box-and-Whisker Plots)

Active learning works well for box plots because students need to physically order and measure data to see how quartiles divide the set. Moving numbers and drawing lines helps them connect abstract values to visual representations, which builds lasting understanding beyond memorizing steps.

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

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

Activity 01

• Museum Exhibit
• 30 min · Pairs

Pairs Plotting: Student Heights

Pairs measure and record classmates' heights in centimetres, then find the five-number summary. Each pair sketches a box plot on grid paper and compares it to a partner's plot. Discuss differences in medians and spreads during share-out.

Explain what specific information a box plot can show that a histogram cannot.

Facilitation Tip

During the Pairs Plotting: Student Heights activity, circulate to ensure pairs order data sets in ascending order before marking quartiles on the number line.

What to look for

Provide students with a small data set (e.g., 15-20 numbers). Ask them to calculate the five-number summary and then draw the corresponding box plot on a provided number line template. Check for accuracy in calculations and plot construction.

• Apply
• Analyze
• Create
• Self-Management
• Relationship Skills

Activity 02

• Museum Exhibit
• 45 min · Small Groups

Small Groups: Sports Data Comparison

Provide data sets on basketball free throws for two teams. Groups calculate summaries, draw box plots side by side, and note which team has greater consistency via interquartile range. Present findings to class with one insight each.

Construct a box plot from a five-number summary.

Facilitation Tip

During the Small Groups: Sports Data Comparison activity, ask groups to explain why one box plot seems more stretched out than another, focusing on IQR differences.

What to look for

Present two side-by-side box plots representing student scores on two different math quizzes. Ask students: 'Which quiz appears to have had more consistent scores? How can you tell from the box plots? What does the median tell you about the typical score on each quiz?'

• Apply
• Analyze
• Create
• Self-Management
• Relationship Skills

Activity 03

• Museum Exhibit
• 35 min · Whole Class

Whole Class: Poll and Plot

Conduct a class poll on minutes spent on screens daily. Record data on board, compute summary as a class using a number line. Draw a large box plot together and interpret median versus range.

Compare two different data sets using their box plots.

Facilitation Tip

During the Whole Class: Poll and Plot activity, have students predict where quartiles will fall before calculating to build intuition about data shape.

What to look for

Give students a box plot. Ask them to write down: 1) The minimum value, 2) The median, 3) The range of the middle 50% of the data (IQR), and 4) One observation about the spread of the data.

• Apply
• Analyze
• Create
• Self-Management
• Relationship Skills

Activity 04

• Museum Exhibit
• 25 min · Individual

Individual: Mystery Data Analysis

Give five-number summaries for three data sets. Students construct box plots individually, then rank sets by spread. Pair up to verify calculations and explain one comparison.

Explain what specific information a box plot can show that a histogram cannot.

Facilitation Tip

During the Individual: Mystery Data Analysis activity, provide a partially completed plot so students focus on interpreting rather than drawing errors.

What to look for

Provide students with a small data set (e.g., 15-20 numbers). Ask them to calculate the five-number summary and then draw the corresponding box plot on a provided number line template. Check for accuracy in calculations and plot construction.

• Apply
• Analyze
• Create
• Self-Management
• Relationship Skills

A few notes on teaching this unit

Teach box plots by having students first sort small, real-world data sets by hand to see quartiles emerge naturally. Avoid rushing to formulas; instead, use the physical act of grouping and measuring to build the concept of quartiles as natural dividers. Research suggests this kinesthetic approach reduces confusion about median placement and whisker meaning compared to abstract calculations alone.

Successful learning looks like students accurately identifying quartiles, constructing clean plots, and explaining what the box and whiskers show about data spread and center. They should also compare two plots to discuss consistency and typical values with precise terms like median and interquartile range.

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Watch Out for These Misconceptions

• During the Pairs Plotting: Student Heights activity, watch for students who assume the box spans the entire data range. Correction: Have pairs measure the box on their number line and compare it to the whiskers, then ask them to recount how many data points fall inside versus outside the box to reinforce that the box covers only the middle 50%.

• During the Small Groups: Sports Data Comparison activity, watch for students who assume the median is always centered in the box. Correction: Ask groups to physically fold their data sets in half to find the median, then slide the halves apart to show how skewness shifts the median within the box.

• During the Individual: Mystery Data Analysis activity, watch for students who dismiss points outside the whiskers as errors. Correction: Provide real data with an unusual value (e.g., a student height of 6 feet in a class where most are under 5 feet) and ask students to calculate the IQR before deciding if the point is an outlier, linking the rule to the data context.

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Methods used in this brief

• Museum Exhibit