Mathematics · Grade 7

Active learning ideas

Experimental Probability

Active learning lets students physically roll dice, spin spinners, and record outcomes, which builds concrete experience before abstract reasoning. When students collect their own data, they feel the pull of chance variability and see why large samples matter more than quick guesses.

• Ontario Curriculum Expectations
• 7.SP.C.6
• 7.SP.C.7

• 25–45 min
• Pairs → Whole Class
• 4 activities

Activity 01

• Stations Rotation
• 45 min · Small Groups

Stations Rotation: Probability Stations

Prepare four stations with spinners divided into unequal sections, dice rolls for sums, coin flips, and marble draws from bags. Students predict theoretical probabilities, conduct 20 trials at each, record frequencies on charts, and compare to predictions. Rotate groups every 10 minutes.

Justify why experimental results might differ significantly from theoretical predictions in the short term.

Facilitation Tip

During Probability Stations, circulate with a quick checklist to note which students still add outcomes instead of replacing them in the sample space.

What to look for

Provide students with a set of data from 20 coin flips (e.g., 13 heads, 7 tails). Ask them to calculate the experimental probability of getting heads and compare it to the theoretical probability. Prompt: 'What is the experimental probability of heads? How does it compare to the theoretical probability of 1/2?'

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

Activity 02

• Inquiry Circle
• 30 min · Pairs

Pairs Challenge: Increasing Trials

Partners select a chance device like a six-sided die. They predict outcomes, run 10, 30, and 50 trials cumulatively, plotting relative frequencies on a class graph after each set. Discuss how the line approaches theoretical values.

Analyze how increasing the number of trials affects the reliability of experimental probability.

Facilitation Tip

In the Increasing Trials challenge, have pairs start with 10 trials, then add 10 more each round so everyone sees the cumulative graph grow.

What to look for

Pose the question: 'Imagine you flip a coin 5 times and get 5 heads. Does this mean the coin is unfair? Explain your reasoning, considering the number of trials.' Facilitate a class discussion on the law of large numbers and short-term variability.

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

Activity 03

• Inquiry Circle
• 35 min · Whole Class

Whole Class Simulation: Election Poll

Simulate an election with coloured beads in a bag representing votes. Class predicts winner based on theoretical probability, draws with replacement 50 times, tallies results, and revises predictions. Graph class data to show convergence.

Explain in what ways a simulation can accurately model a complex real-world event.

Facilitation Tip

For the Election Poll simulation, assign roles like pollster, recorder, and data analyst so every student contributes to the shared data set.

What to look for

Students are given a scenario: 'A spinner with 4 equal sections (red, blue, green, yellow) is spun 10 times, landing on red 4 times.' Ask them to write: 1. The experimental probability of landing on red. 2. One reason why this might be different from the theoretical probability.

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

Activity 04

• Inquiry Circle
• 25 min · Individual

Individual: Custom Spinner Design

Each student draws a spinner with 3-6 sections of varying sizes, calculates theoretical probabilities, runs 100 trials, and creates a bar graph comparing results. Share one insight in a quick gallery walk.

Justify why experimental results might differ significantly from theoretical predictions in the short term.

Facilitation Tip

When students design custom spinners, provide protractors and color-coded templates so geometric accuracy supports probability accuracy.

What to look for

Provide students with a set of data from 20 coin flips (e.g., 13 heads, 7 tails). Ask them to calculate the experimental probability of getting heads and compare it to the theoretical probability. Prompt: 'What is the experimental probability of heads? How does it compare to the theoretical probability of 1/2?'

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

A few notes on teaching this unit

Teach experimental probability by letting variance happen first, then guiding students to quantify it with relative frequency. Avoid rushing to the ‘correct’ answer; instead, let repeated trials demonstrate convergence. Research shows students grasp the law of large numbers best when they plot their own messy data before smoothing it into a trend.

Students will explain why experimental results differ from theory and how more trials shrink that gap. They will justify short-term deviations and connect relative frequency to theoretical probability with clear calculations and graphs.

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Watch Out for These Misconceptions

• During Probability Stations, watch for students who expect every 10-flip set to land exactly 5 heads and 5 tails.

  Pause the station rotation after the first set and ask groups to plot their results on a shared class graph, then prompt them to predict what might happen if they did 50 flips instead of 10.

• During Increasing Trials, listen for pairs who claim a fair coin is unfair after five consecutive heads.

  In that moment, have them add another 10 trials live and recalculate, then ask whether the new data changes their view before moving on.

• During the Election Poll simulation, watch for comments that the simulated poll should match the actual outcome exactly.

  Point to the shared results table and ask students to estimate the error margin by comparing different sample groups within the same class poll.

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Methods used in this brief

• Stations Rotation
• Inquiry Circle