Probability Master · For Teachers
Teacher Guide
Experiments first, vocabulary second — how to teach chance so it sticks.
📥 Printables
About this unit
Probability Master builds the mathematics of chance from experiments the students run themselves — thousands of simulated flips plus 50 real ones. Unit 6 has four lessons; Lessons 1 and 3 are ready now (Dice Detective and the Prediction Bureau are coming).
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Lesson 1 — The Coin Flip Lab
Goal: probability as a fraction; the Law of Large Numbers seen live; the gambler's fallacy defeated by experiment.
Answer keys
- Gambler's Trap: exactly 50% — the coin has no memory. (Independence!)
- Spinner: P(red) = 3/8 · most likely = blue (4/8) · 800 spins → about 100 golds (1/8 of 800 — "about," never "exactly").
- Journal big idea: one flip is unpredictable; a thousand flips are predictable; the coin has no memory; still 50%.
The teaching move that matters: open with the 5-heads-in-a-row question and collect votes before the lab — most classes split three ways. Resolve it only after students have watched the machine and flipped real coins. Changing your own mind on evidence is the science lesson hiding in the math lesson.
Look-fors: students describing the % as "calming down" (that's LLN in kid words); the word "about" appearing in predictions; anyone spontaneously testing the streak question with the machine — celebrate that.
Discussion prompts: Why do casinos love the "due for a win" feeling? · Where does the weather forecast's "70% chance" come from? · What else has no memory — dice? Spinners? Yesterday's weather?
Lesson 3 — Pascal's Amazing Triangle
Goal: generate the triangle from its one rule, find structural patterns, and use row n to count coin-flip outcomes — connecting combinatorics back to Lesson 1's experiments.
Answer keys
- Pattern hunt: row sums double (powers of 2) · second diagonal = counting numbers · perfectly symmetric.
- Coin secret: 2 heads in 4 flips = 6 ways · total = 16 · P = 6/16 (3/8).
- Kit challenge: P(3 heads in 6 flips) = 20/64. Kit bonus diagonal = the triangular numbers 1, 3, 6, 10, 15.
The beautiful why (share it!): the triangle is symmetric because getting 3 heads out of 4 is the same story as getting 1 tail out of 4 — every heads-count has a mirror twin.