Mathematics · Grade 6

Active learning ideas

Measures of Variability: Range and Interquartile Range

Active learning helps students grasp measures of variability because sorting, plotting, and manipulating data makes abstract concepts concrete. When students physically rearrange numbers to find quartiles or remove outliers, they see how range and IQR behave differently in real data sets.

• Ontario Curriculum Expectations
• 6.SP.A.3
• 6.SP.B.5.C

• 20–35 min
• Pairs → Whole Class
• 4 activities

Activity 01

• Think-Pair-Share
• 25 min · Pairs

Pairs Activity: Outlier Hunt

Provide pairs with data sets like student heights; one set includes an outlier. Pairs order data, calculate range and IQR for both, then graph on number lines. Discuss how the outlier changes each measure.

Explain how the range describes the overall spread of a data set.

Facilitation Tip

During Pairs Activity: Outlier Hunt, circulate to listen for pairs debating whether the range or IQR better describes the data before they calculate.

What to look for

Present students with a small data set (e.g., test scores: 75, 82, 88, 90, 95, 100). Ask them to calculate the range and the IQR. Then, ask: 'Which measure, range or IQR, better describes the typical spread of scores for most students in this group and why?'

• Understand
• Apply
• Analyze
• Self-Awareness
• Relationship Skills

Activity 02

• Think-Pair-Share
• 35 min · Small Groups

Small Groups: Survey and Analyze

Groups survey classmates on favorite activities or scores, record 20 data points. Order data to find quartiles, compute range and IQR, and present findings on posters. Compare spreads across groups.

Differentiate between range and interquartile range in terms of what they measure.

Facilitation Tip

When running Small Groups: Survey and Analyze, ensure each group assigns clear roles so all students engage with ordering data and finding quartiles.

What to look for

Provide two data sets, one with an outlier and one without, that have similar middle values. For example, Data Set A: 5, 10, 12, 15, 18, 20. Data Set B: 5, 10, 12, 15, 18, 50. Ask students to calculate the range and IQR for both. Facilitate a discussion on how the outlier in Data Set B affects the range compared to the IQR, and what this tells us about the data's distribution.

• Understand
• Apply
• Analyze
• Self-Awareness
• Relationship Skills

Activity 03

• Think-Pair-Share
• 30 min · Whole Class

Whole Class: Data Modification Challenge

Display class-generated data on board. As a class, add or remove outliers, recalculate range and IQR each time. Vote on which measure best describes the group.

Analyze how outliers affect the range compared to the interquartile range.

Facilitation Tip

For Whole Class: Data Modification Challenge, pause after each modification to ask students to predict how the range and IQR will change before recalculating.

What to look for

Give each student a card with a data set. Ask them to write down the range and the IQR. On the back, have them write one sentence explaining what the IQR tells them about the spread of the data that the range does not.

• Understand
• Apply
• Analyze
• Self-Awareness
• Relationship Skills

Activity 04

• Think-Pair-Share
• 20 min · Individual

Individual: Sports Data Review

Students select Canadian hockey stats, list top 15 points per game. Compute range and IQR, note outlier effects from star players. Write one sentence summary.

Explain how the range describes the overall spread of a data set.

What to look for

Present students with a small data set (e.g., test scores: 75, 82, 88, 90, 95, 100). Ask them to calculate the range and the IQR. Then, ask: 'Which measure, range or IQR, better describes the typical spread of scores for most students in this group and why?'

• Understand
• Apply
• Analyze
• Self-Awareness
• Relationship Skills

A few notes on teaching this unit

Teach quartiles first using small, ordered data sets on number lines so students visualize Q1 and Q3 as dividing points. Emphasize that range is a single snapshot of extremes while IQR is a stable 'window' on the middle. Avoid teaching formulas before students understand what the numbers represent; let them derive quartiles from visual grouping.

Successful learning looks like students confidently identifying which measure to use based on data shape, explaining why IQR resists outliers, and applying range and IQR to contextual questions. They should articulate how each measure summarizes spread without relying on vague phrases.

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Watch Out for These Misconceptions

• During Pairs Activity: Outlier Hunt, watch for students claiming the range shows the typical spread because it includes all data points.

  Have pairs plot their data on a dot plot and circle the middle cluster to visually demonstrate that range overstates spread and IQR captures the dense center.

• During Pairs Activity: Outlier Hunt, watch for students assuming outliers change the IQR as much as the range.

  Ask pairs to remove the outlier and recalculate both measures side-by-side, then compare how range spikes while IQR stays nearly the same.

• During Small Groups: Survey and Analyze, watch for students confusing quartiles with the mean or median.

  Ask groups to label each quartile on a number line and write Q1, Q2 (median), and Q3 above the correct points to reinforce their positions.

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Methods used in this brief

• Think-Pair-Share