Probability models
Develop a probability model (a list of all the outcomes of a chance process with a probability for each, adding to 1) and use it to find probabilities of events: a uniform model gives every outcome the same probability (e.g. selecting a student at random from a class); a non-uniform model uses probabilities estimated from the observed frequencies of a chance process (e.g. how a tossed paper cup lands); compare a model's probabilities with observed frequencies and, when they disagree, explain whether the difference is plausibly chance variation or a sign that the model does not fit (e.g. a biased die or unequal spinner sections)
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Probability models means practising the idea at the table with counters or paper models and one clear check. We will demo once, then your child tries.
Materials: Tally sheet or simple bar/dot sketch; A short set of category counts. 1. Say the goal of Probability models in plain words once. 2. Adult tallies one category and sketches a bar or dot plot. 3. Child tallies three small data sets and compares the tallest category. 4. Fresh check: one fresh tally comparison. Record and stop. Done: three correct tallies with a comparison sentence each. Proof: parent note of examples and results. Stop: End after the fresh check; keep optional challenge for another day.
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PhET Interactive Simulations · Practice link — not the full lesson
Plinko Probability
Before you open · source notes
Plinko Probability supports hands-on exploration for Probability models. Not every lab worksheet.
Free interactive page, no sign-in required for the tested path.
Before you openAsk the learner what they changed in the sim or page and what they observed.
Opening this link does not save learning or assess mastery.
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Public PhET Interactive Simulations page. An anonymous GET on 2026-11-12 returned HTTP 200 with no login or payment prompt for this URL. Opening the link does not save practice or assess mastery. An adult should preview and guide the learner.
PhET Interactive Simulations. “Plinko Probability.” External page; Gakuva does not copy, host, embed, or redistribute materials.
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Check understanding
- Use a uniform model to find that a randomly chosen student from a class of 25 with 12 girls is Jane with probability 1/25 and is a girl with probability 12/25
- Toss a paper cup 50 times (e.g. 31 on its side, 13 open end up, 6 open end down), write a model with probabilities 0.62, 0.26 and 0.12, and explain why the three outcomes are not equally likely
- Compare 600 rolls of a die that showed 160 sixes with the 100 sixes a fair-die model predicts, and argue that a difference this large suggests the die is biased rather than just chance
“If your child flips a paper cup 50 times and records whether it lands on its side, open end up or open end down, could they turn the results into a probability for each way of landing — and say whether the three are equally likely?”
Curriculum record
- Type
- Conceptual
- Subject
- Mathematics
- Domain
- Probability
- Age range
- Ages 12–13
Standards