Mathematics · Grade 7

Active learning ideas

Making Inferences from Samples

Active learning works for this topic because comparing data sets requires students to move from abstract calculations to concrete, observable differences. When students physically collect and analyze real data, they can see how measures like mean and spread actually describe two populations, making the concept more meaningful and memorable.

• Ontario Curriculum Expectations
• 7.SP.A.2

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

Activity 01

• Inquiry Circle
• 40 min · Small Groups

Inquiry Circle: Reaction Time Challenge

Students use an online tool to measure their reaction times. They compare the data distribution of the 'left-hand' group vs. the 'right-hand' group, calculating mean and median for both to see if there is a significant difference.

Explain how a sample can be used to make predictions about an entire population.

Facilitation Tip

In the Reaction Time Challenge, circulate as groups collect data and ask them to predict which team’s results might have less variability before they calculate the mean absolute deviation.

What to look for

Present students with a scenario: 'A school wants to know the favourite sport of its 500 students. They survey 50 students from the Grade 7 classes only.' Ask students to identify the population and the sample, and explain one potential source of bias in this sampling method.

• Analyze
• Evaluate
• Create
• Self-Management
• Self-Awareness

Activity 02

• Think-Pair-Share
• 20 min · Pairs

Think-Pair-Share: The Outlier Effect

Give students a set of 'test scores' where one score is a 0. They calculate the mean and median. Then, they 'remove' the 0 and recalculate. They discuss with a partner which measure of center changed more and why.

Evaluate the reliability of an inference based on the sampling method used.

Facilitation Tip

During The Outlier Effect, pause pairs after their discussion to ask one group to share how the outlier changed their interpretation of 'typical'.

What to look for

Provide students with a small dataset from a sample (e.g., 20 coloured marbles drawn from a bag). Ask them to calculate the proportion of each colour in their sample and then write one sentence predicting the proportion of each colour in the full bag, explaining why their prediction is reasonable.

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

Activity 03

• Stations Rotation
• 45 min · Small Groups

Stations Rotation: Weather Watchers

At different stations, students analyze temperature data for two Canadian cities (e.g., Victoria and Winnipeg). They must calculate the mean and the spread (range) to explain which city has more 'predictable' weather and why.

Construct an argument for or against a claim based on sample data.

Facilitation Tip

In Weather Watchers, set a timer for each station so groups rotate before they become too focused on one type of comparison.

What to look for

Pose the question: 'If you wanted to know the average height of all Grade 7 students in Ontario, would it be better to measure 100 students from your own school or 100 students randomly selected from across the province? Explain your reasoning, considering the concepts of sample and population.'

• Remember
• Understand
• Apply
• Analyze
• Self-Management
• Relationship Skills

A few notes on teaching this unit

Experienced teachers start with hands-on data collection to build intuition, then introduce the formulas for mean and mean absolute deviation only after students see why they are needed. Avoid rushing to abstract calculations; instead, use real-world examples where the data itself sparks curiosity. Research suggests that students grasp spread better when they physically see the gaps between data points, so encourage them to plot their results whenever possible.

Successful learning looks like students using measures of center and spread to justify comparisons between data sets. They should explain why one set might be more consistent or typical than another, and connect their analysis to real-world decisions, such as choosing the better team or interpreting weather data.

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Watch Out for These Misconceptions

• During the Reaction Time Challenge, watch for students defaulting to the mean without considering outliers or variability in their data.

  Ask groups to calculate both the mean and median for their data set, then ask them to explain which one better represents a 'typical' reaction time in their sample.

• During The Outlier Effect, watch for students assuming that two sets with the same mean are identical.

  Have pairs compare two pre-made dot plots with the same mean but different spreads, then ask them to describe how the sets differ in practical terms.

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Methods used in this brief

• Inquiry Circle
• Think-Pair-Share
• Stations Rotation