Mathematics · Grade 7

Active learning ideas

Sampling Strategies

Active learning helps students grasp sampling strategies because they see for themselves how sample selection affects results. When students physically collect and compare data, they move beyond abstract definitions to understand why representation matters in real surveys.

• Ontario Curriculum Expectations
• 7.SP.A.1

• 30–40 min
• Pairs → Whole Class
• 3 activities

Activity 01

• Simulation Game
• 40 min · Small Groups

Simulation Game: The Jelly Bean Census

Each group gets a large jar of mixed-colour beans. They must test different sampling methods (e.g., taking the top 10 vs. shaking and picking 10) to see which method best predicts the actual percentages in the whole jar.

Justify why a random sample is usually more reliable than a convenience sample.

Facilitation Tip

During the Jelly Bean Census, have students record their sampling method and results on a shared chart so the class can compare how different groups' conclusions vary.

What to look for

Provide students with two scenarios: Scenario A describes a survey of students in the school cafeteria about their favorite lunch options. Scenario B describes a survey where every 10th student on the school's enrollment list is asked about their favorite lunch options. Ask students to identify which scenario is more likely to yield a representative sample and justify their answer.

• Apply
• Analyze
• Evaluate
• Create
• Social Awareness
• Decision-Making

Activity 02

• Formal Debate
• 30 min · Small Groups

Formal Debate: Survey Bias

Provide students with biased survey questions (e.g., 'Don't you agree that school should start later?'). Students work in teams to identify the bias, rewrite the question to be neutral, and debate why the original would produce 'bad' data.

Analyze how the way a survey question is phrased can influence the data collected.

Facilitation Tip

For the Survey Bias Debate, assign roles (e.g., 'convenience sampler,' 'random sampler') and require each side to present one piece of evidence from their method.

What to look for

Present students with three survey questions about school policies. For example: 'Do you agree that the school should have mandatory uniforms?' vs. 'Should the school consider implementing uniforms to improve safety and reduce distractions?' Ask students to identify which question is more neutral and explain how the phrasing might influence responses.

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

Activity 03

• Gallery Walk
• 35 min · Pairs

Gallery Walk: Sampling in the News

Post various news headlines that cite statistics. Students walk around and use a checklist to evaluate the likely sampling method and identify potential sources of bias (e.g., 'Only 10 people were asked' or 'The survey was only on Twitter').

Critique the risks of making a broad generalization based on a small sample size.

Facilitation Tip

Set a 10-minute time limit for the Gallery Walk so students stay focused on identifying sampling strategies in real news examples before moving to the next poster.

What to look for

Pose the following question: 'Imagine you want to know the average number of hours Grade 7 students in your city spend on homework each week. You can only survey 50 students. What are the risks of surveying only students in your own class? How could you try to get a more reliable sample, even with only 50 students?'

• Understand
• Apply
• Analyze
• Create
• Relationship Skills
• Social Awareness

A few notes on teaching this unit

Teach this topic by letting students make mistakes first, then guiding them to see why those mistakes matter. Avoid lecturing about bias; instead, let them experience it through simulations where flawed methods produce obvious contradictions. Use peer discussion to help students articulate why some samples work better than others, rather than telling them which is correct.

By the end of these activities, students will confidently explain why random samples yield valid conclusions, identify bias in survey scenarios, and design their own unbiased questions. They will also articulate the difference between convenience and representative sampling in their own words.

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Watch Out for These Misconceptions

• During the Jelly Bean Census, watch for students who claim a larger sample size always fixes bias. Redirect them by asking, 'If we only sampled students who love jelly beans, would adding more people change the result?'

  Use the class chart to compare a biased sample of 200 students from one grade to an unbiased sample of 50 students from all grades, highlighting how representation—not size—matters.

• During the Survey Bias Debate, students may argue convenience sampling is fine. Have them refer back to their 'friend group' data and ask, 'How do your results compare to a random sample of the whole school? What does that tell you about your sample?'

  Prompt them to calculate the percentage difference between their convenience sample and a provided random sample to show how much conclusions can shift.

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Methods used in this brief

• Simulation Game
• Formal Debate
• Gallery Walk