Mathematics · Grade 7

Active learning ideas

Comparing Data Distributions

Active learning works for comparing data distributions because students need to manipulate real numbers, visualize shifts in data, and justify their reasoning aloud. When they adjust outliers or compare class heights, they connect abstract measures like mean and MAD to concrete outcomes they can see and debate.

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

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

Activity 01

• Case Study Analysis
• 25 min · Pairs

Pairs: Outlier Adjustment

Give pairs two datasets on cardstock, one with an outlier like extreme test score. Calculate mean, median, MAD before and after removal. Pairs sketch dot plots and note changes in a shared chart, then share with class.

Which measure of center is most affected by extreme outliers in a data set?

Facilitation Tip

During the Outlier Adjustment activity, circulate and ask pairs: 'How does removing or adding an outlier change the mean compared to the median?' to prompt immediate reflection.

What to look for

Provide students with two small data sets (e.g., test scores from two classes). Ask them to calculate the mean, median, and MAD for each set. Then, ask: 'Which measure of center best represents a typical score in each class, and why?'

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

Activity 02

• Case Study Analysis
• 45 min · Small Groups

Small Groups: Class Height Comparison

Measure heights of students in two groups, like by birth month. Groups create side-by-side dot plots, compute measures of center and MAD. Discuss which population has more typical heights and why variability matters.

How does the 'spread' or variability of data impact our confidence in a prediction?

Facilitation Tip

For the Class Height Comparison, ensure each small group measures their own heights first to create authentic data sets they care about analyzing.

What to look for

Present a scenario with two data sets, one with an outlier. Ask students: 'If you had to choose one measure of center to describe the typical value in both sets, which would you choose and why? How does the outlier affect your choice?' Facilitate a class discussion on the impact of outliers.

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

Activity 03

• Case Study Analysis
• 30 min · Whole Class

Whole Class: Prediction Challenge

Display two data sets on board, like city rainfall. Class votes on predictions, then calculates measures together. Adjust data live based on suggestions to show spread's impact on confidence.

When is the median a better representation of a 'typical' value than the mean?

Facilitation Tip

In the Prediction Challenge, intentionally include one set with high variability to highlight why MAD matters when predicting future values.

What to look for

Give students two sets of data, one with low variability and one with high variability. Ask them to write one sentence explaining how the spread (MAD) of the data affects their confidence in predicting the next value for each set.

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

Activity 04

• Case Study Analysis
• 20 min · Individual

Individual: Data Doctor

Students get mixed datasets from sports or weather. Individually identify best measures for comparison, justify in writing. Follow with pair share to refine arguments.

Which measure of center is most affected by extreme outliers in a data set?

Facilitation Tip

During Data Doctor, require students to write a brief justification for their diagnosis using at least two measures of center and variability.

What to look for

Provide students with two small data sets (e.g., test scores from two classes). Ask them to calculate the mean, median, and MAD for each set. Then, ask: 'Which measure of center best represents a typical score in each class, and why?'

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

A few notes on teaching this unit

Experienced teachers approach this topic by having students repeatedly calculate mean, median, and MAD while altering one variable at a time. They avoid teaching these measures in isolation, instead embedding them in tasks where students must defend their choices. Research suggests starting with physical manipulatives like sticky notes on a board helps students grasp how outliers skew data before moving to abstract calculations.

Successful learning looks like students selecting the most appropriate measure of center based on context, explaining how variability affects prediction confidence, and using data displays to support their comparisons. They should articulate why one set’s median is more representative than another’s mean, especially when outliers are present.

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Watch Out for These Misconceptions

• During the Outlier Adjustment activity, watch for students who automatically choose the mean as the best measure of center without considering the presence of outliers.

  After pairs adjust the outlier, ask them to recalculate both mean and median and explain which value better represents a typical data point in their adjusted set, using their plotted points as visual evidence.

• During the Class Height Comparison activity, watch for students who confuse MAD with the range because both describe spread.

  Have groups calculate both measures side by side and ask: 'Why does MAD using every data point give a clearer picture of variability than range, which only uses the highest and lowest values?'

• During the Prediction Challenge activity, watch for students who assume similar means indicate identical distributions.

  After the whole-class simulation, display two sets with close means but different MADs and ask students to predict the next value, then discuss how variability affects confidence in their predictions.

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Methods used in this brief

• Case Study Analysis