Likelihood of Simulated Events
Warm-up
If I flip this coin 10 times, how many times do you predict heads? (5.) Let us test. Flip 10 times, record. Class results: did everyone get exactly 5? (Likely not.) Why not? (Randomness.) If we all combined our results (30 students x 10 flips = 300 flips), would we be closer to 50%? (Yes.) Why?
Explore
Probability experiments stations: (1) Coin: predict 10 flips, record actual, calculate total heads out of 30 flips across the group. (2) Die: roll 12 times, which face appeared most? (3) Spinner: spin 20 times, compare to predicted. Pool class results at each station: do larger samples give better predictions?
Formalize
Compare predicted vs. actual: display all class results for the coin flip. Create a bar graph of heads counts across all groups (how many groups got 4 heads? 5 heads? 6 heads?). What is the most common result? (5, likely.) What is the range? This is a distribution, and Grade 3 students can describe it qualitatively.
Likelihood of Simulated Events
Snowsnake game connection: in a skill-and-chance game, what determines the outcome? (Both player skill and random variation.) Can we predict who will win before the game? Not with certainty, but we can say which outcome is more likely based on skill levels. This is applied probabilistic reasoning.
Practice
Students conduct a 20-flip coin experiment, record results, compare to prediction, and pool results with the class. Write 2 sentences about the difference between theoretical and experimental probability. Exit ticket: in a bag with 2 red and 8 blue marbles, which colour are you more likely to draw?
Exit ticket
Students conduct a 20-flip coin experiment, record results, compare to prediction, and pool results with the class. Write 2 sentences about the difference between theoretical and experimental probability. Exit ticket: in a bag with 2 red and 8 blue marbles, which colour are you more likely to draw?
Step 1: Examine the spinner: half red, quarter blue, quarter yellow. Elicit ranked predictions with reasons: red should win most spins (owns half the space); blue and yellow should roughly tie for the rest.
Step 2: Decide sample size — and let students feel why more is better: "Would 4 spins convince you? 40?" Settle on 40 as a class.
Step 3: Simulate: spin 40 times, tally live. Sample outcome: red 22, blue 9, yellow 9.
Step 4: Compare results to predictions: red ≈ half of 40 ✓; blue ≈ yellow ✓. Not EXACTLY 20-10-10 — and that's the teachable wobble: chance results hover NEAR the space-based prediction without hitting it on the nose.
Step 5: Pool all groups' tallies (suddenly 200+ spins): watch the proportions tighten toward half-quarter-quarter. Bigger samples steady the picture — the deepest idea in the room, earned with a spinner.
The game: roll two dice, add. Player A scores on a sum of 6, 7, or 8; Player B scores on 2, 3, 11, or 12. B has MORE winning numbers — is B luckier?
Step 1: Vote first (most pick B — four numbers beats three).
Step 2: Play 30 rounds in pairs and tally. The table fills with A wins.
Step 3: Hunt the reason — list the ways to roll each sum: 7 can happen as 1+6, 2+5, 3+4, 4+3, 5+2, 6+1 (six ways!); 6 and 8 have five ways each. But 2 is only 1+1, and 12 only 6+6 — one way each. A's three numbers own 16 ways; B's four numbers own just 6.
Step 4: The moral, stated for the ages: what matters is not how many WINNING LABELS you hold but how many PATHS lead to them. Middle sums are highways; edge sums are goat trails.
Step 5: Redesign the game to be fair — students propose and defend new number splits. (Fairness ≈ equal path-counts, about 18 each.)
The claim: a group flips a coin 100 times, gets 58 heads, and concludes their coin is "a heads coin."
Step 1: Take the claim seriously — what SHOULD 100 fair flips give? "About 50" — but press on the word ABOUT: exactly 50, or near 50?
Step 2: Gather evidence from the room: every group flips 100 times. The board fills: 47, 53, 58, 44, 51, 55… Nobody hit exactly 50; everyone landed in the neighbourhood.
Step 3: Place 58 in that landscape: it's on the high side of normal wobble, not outside it. A fair coin wanders this much routinely.
Step 4: Ask what evidence WOULD justify suspicion: 90 heads? 85? (Intuition: way outside everyone's wobble zone.) There's a real threshold idea here — Grade 3 meets, informally, the logic of statistical significance: don't call a coin crooked for doing what fair coins ordinarily do.
Exit sentence for journals: "Fair doesn't mean exactly even — it means close to even, most of the time."