Mathematics · Grade 7

Active learning ideas

Measures of Variability: Range & IQR

Active learning helps students grasp measures of variability because concrete manipulation of data builds intuition for abstract concepts. When students physically sort, plot, and modify numbers, they see how range and IQR respond to changes in a way that calculations alone cannot show.

• Ontario Curriculum Expectations
• 7.SP.B.3
• 7.SP.B.4

• 20–40 min
• Pairs → Whole Class
• 4 activities

Activity 01

• Concept Mapping
• 25 min · Pairs

Pairs Practice: Outlier Challenges

Provide pairs with two similar datasets, one including an outlier like an extreme score. Have them order data, calculate range and IQR for both, then graph box plots. Partners discuss and explain which measure best shows typical spread.

Explain how the 'spread' or variability of data impacts our confidence in a prediction.

Facilitation Tip

During Dataset Modifications, challenge early finishers to add three numbers that keep the IQR the same but change the range drastically.

What to look for

Provide students with a small data set (e.g., 7-10 numbers). Ask them to individually calculate the range and IQR, showing their steps. Review calculations for accuracy in identifying min/max and quartiles.

• Understand
• Analyze
• Create
• Self-Awareness
• Self-Management

Activity 02

• Concept Mapping
• 35 min · Small Groups

Small Groups: Survey Data Stations

Groups rotate through stations with printed datasets on topics like sports stats or weather. At each, they compute range, quartiles, and IQR, recording results on charts. Final share-out compares findings across datasets.

Differentiate between range and interquartile range as measures of variability.

What to look for

Present two data sets with similar means but different spreads (e.g., one with a small IQR and one with a large IQR). Ask students: 'Which data set represents more consistent performance? How does the IQR help us see this consistency better than the range alone?'

• Understand
• Analyze
• Create
• Self-Awareness
• Self-Management

Activity 03

• Concept Mapping
• 40 min · Whole Class

Whole Class: Live Measurement Variability

Class measures and records pulse rates before and after jumping jacks. Together, identify min/max for range, sort for quartiles and IQR. Plot on a shared box plot and vote on outlier status.

Analyze how outliers affect the range versus the interquartile range.

What to look for

Give students a data set containing an obvious outlier. Ask them to calculate both the range and the IQR. Then, ask: 'Which measure of variability is more affected by the outlier, and why?'

• Understand
• Analyze
• Create
• Self-Awareness
• Self-Management

Activity 04

• Concept Mapping
• 20 min · Individual

Individual: Dataset Modifications

Students receive a dataset, calculate initial range and IQR, then add/remove an outlier. They note changes and justify if the modification realistically alters spread in a context like exam grades.

Explain how the 'spread' or variability of data impacts our confidence in a prediction.

What to look for

Provide students with a small data set (e.g., 7-10 numbers). Ask them to individually calculate the range and IQR, showing their steps. Review calculations for accuracy in identifying min/max and quartiles.

• Understand
• Analyze
• Create
• Self-Awareness
• Self-Management

A few notes on teaching this unit

Start with physical data to build conceptual understanding before formal definitions appear. Avoid rushing to formulas—instead, let students discover patterns through repeated sorting and measuring. Research shows this approach reduces confusion between quartiles and equal-sized groups because the visual process clarifies position-based splits.

Students will confidently explain why range can mislead and why IQR better reflects a dataset’s typical spread. They will calculate both measures accurately and justify which one to use in different contexts, using clear reasoning.

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Watch Out for These Misconceptions

• During Pairs Practice: Outlier Challenges, watch for students who assume adding an outlier always increases both range and IQR equally.

  Prompt pairs to add an outlier and recalculate both measures on the board, asking them to explain why the range grows more dramatically than the IQR.

• During Small Groups: Survey Data Stations, watch for students who claim the IQR includes all data between the minimum and maximum values.

  Ask groups to physically remove the lowest and highest 25% of their stacked data cards to visually demonstrate what remains, linking the remaining cards to the definition of IQR.

• During Live Measurement Variability, watch for students who believe quartiles always split the data into four groups of equal count.

  Pause the activity and have students count the exact positions of Q1, Q2, and Q3 in the current dataset, then discuss why equal counts are not guaranteed in small or uneven datasets.

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Methods used in this brief

• Concept Mapping