Activity 01
Pairs Activity: Design Fair and Unfair Games
Pairs use dice or cards to invent two games, one fair and one with house edge. They calculate probabilities and expected values, then swap games with another pair for 50 trials and compare results to predictions. Discuss adjustments for fairness.
Explain how casinos or insurance companies use probability to ensure they remain profitable.
Facilitation TipDuring Pairs Activity: Design Fair and Unfair Games, circulate and prompt pairs to calculate expected values aloud before testing their games, reinforcing the connection between theory and play.
What to look forPresent students with a scenario: 'A spinner has 4 equal sections: red, blue, green, yellow. What is the theoretical probability of landing on red? If you spin it 20 times and land on red 7 times, what is the experimental probability?' Ask students to write their answers and show their calculations.
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Activity 02
Small Groups: Insurance Premium Simulation
Groups role-play as an insurance company over 20 'policyholders' using random draws for claims. They calculate average claims, set premiums to ensure profit, and run multiple rounds to see long-term stability. Graph results to analyze risk.
Analyze what it means for a game to be mathematically 'fair'.
Facilitation TipIn Small Groups: Insurance Premium Simulation, ask groups to explain how their premium prices reflect the group’s chosen risk levels and probabilities, ensuring peer accountability.
What to look forPose the question: 'Imagine a simple dice game where Player A wins if they roll a 6, and Player B wins if they roll any other number. Is this game fair? Explain your reasoning using the concept of expected value and theoretical probability.'
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Activity 03
Whole Class: Casino Spinner Trials
Create class spinners with unequal sections representing casino payouts. Predict long-term frequencies, then conduct 100 collective spins using a randomizer app or physical spinner. Tally results on a shared chart and compute house edge.
Predict how we can use probability to predict the long-term frequency of an event.
Facilitation TipDuring Whole Class: Casino Spinner Trials, model how to record results in a shared table so students can compare individual and collective data sets immediately.
What to look forAsk students to write one sentence explaining how a casino uses probability to make money and one sentence explaining how an insurance company uses probability to set prices.
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Activity 04
Individual: Long-Term Prediction Journal
Students flip coins or roll dice 100 times individually, recording outcomes daily over a week. Calculate running experimental probabilities and compare to theoretical 0.5. Reflect on law of large numbers in a journal entry.
Explain how casinos or insurance companies use probability to ensure they remain profitable.
What to look forPresent students with a scenario: 'A spinner has 4 equal sections: red, blue, green, yellow. What is the theoretical probability of landing on red? If you spin it 20 times and land on red 7 times, what is the experimental probability?' Ask students to write their answers and show their calculations.
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Generate Complete Lesson→A few notes on teaching this unit
Experienced teachers approach this topic by first letting students test simple, low-stakes games to build intuition about chance, then introducing the mathematical tools to explain their observations. Avoid rushing to formulas; instead, let students grapple with outcomes and articulate their reasoning before formalizing with expected value. Research suggests concrete experiences before abstract calculations improve retention and transfer to new contexts.
Students will explain why casinos and insurers rely on probability models, not luck, and justify fairness using expected value calculations. They will interpret experimental results in light of theoretical predictions, using language like 'house edge' and 'risk assessment' with confidence and concrete examples from their activities.
Watch Out for These Misconceptions
During Whole Class: Casino Spinner Trials, watch for students who dismiss short streaks as evidence that the game isn’t rigged, ignoring long-term trends.
Use the class’s aggregated data from 100+ trials to plot a line graph over time, explicitly pointing out how the experimental probability stabilizes near the theoretical value as trials increase.
During Pairs Activity: Design Fair and Unfair Games, watch for students who assume fairness requires equal win chances for each player.
Have pairs calculate expected values for their games and adjust payouts until the expected value reaches zero, using their own trial data as evidence that unequal probabilities can still yield fairness.
During Small Groups: Insurance Premium Simulation, watch for students who attribute insurer profits to hidden fees or cheating rather than probability-based pricing.
Ask groups to present how their premiums were set using the group’s calculated claim frequencies and expected payouts, highlighting the role of risk prediction in pricing without manipulation.
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