No-Prep Sub Plans for Probability

Probability is one of the kindest topics to leave for a substitute. The mathematics is concrete, the props are cheap — coins, dice, a deck of cards — and students can generate their own data and check their own reasoning without a specialist watching over every step. This plan gives a guest teacher a full period on the fundamentals and tree diagrams, with timings, a worked example to read aloud, and student-facing instructions that assume no math background from the adult in the room.

Set the sub up to succeed

The single biggest failure on a math sub day is a guest teacher who cannot answer a question and freezes. Avoid that by choosing a task where the answer key does the explaining. Leave a printed key with fully worked solutions, and point the sub to the models in Probability – Fundamentals and Tree Diagrams, which walks each two-stage problem through the branch-by-branch multiplication so a non-mathematician can confirm student work with confidence.

The 50-minute plan, minute by minute

1. (0–5 min) Objective on the board: "You will calculate probabilities of single and combined events and represent them on a tree diagram."
2. (5–12 min) Warm-up: Students find the probability of rolling an even number, then rolling two evens in a row, and explain in writing why the second is smaller.
3. (12–25 min) Worked example read aloud: A bag has 3 red and 2 blue chips; draw two without replacing. The sub reads the tree diagram solution straight from the key while students copy it.
4. (25–42 min) Independent set: Six problems of increasing difficulty, all with answers on the projected key so students self-check every two minutes.
5. (42–50 min) Exit ticket: "Explain in one sentence why the branches from a single point on a tree must add to 1."

Student-facing instructions you can paste

Put this on a slide word for word: "A tree diagram is just a map of everything that could happen. Each branch gets a probability, you multiply along a path to find the chance of that whole path, and you add the paths that count as a win. Show every branch — no shortcuts — because the diagram is your proof, not just your answer." Framing tree diagrams as a proof keeps students writing full reasoning even when the usual teacher is absent.

Extensions that need no new materials

Because probability sits underneath so much later mathematics, strong students can push ahead without extra worksheets. Bank these options:

• Design a "fair game" for a $1 entry fee and prove it is fair using expected value.
• Estimate the probability of a repeated event and connect it to compounding, which sets up the growth models in The e-Function and Exponential Growth.
• Invent a two-stage word problem and swap with a partner to solve.
• Discuss where randomness hides in a periodic real-world signal, a nice bridge to the modeling in Trigonometric Functions – Sine and Cosine.

What you will find when you return

Collect the exit tickets and the independent sets. Because everything was self-checked against a key, the errors that remain are genuine misconceptions — usually adding probabilities that should be multiplied, or forgetting to change the denominator after a draw without replacement. That gives you a precise, ready-made re-teach for the next class, and it means the sub day moved learning forward instead of parking it.

Related reading from the Teacher Hub

• Bell Ringers and Warm-Ups for Probability
• Assessment Ideas for Binomial Distribution and Expected Value: Rubrics, Quizzes and Exit Tickets
• Project-Based Learning: Trigonometric Functions in the Real World