Math // Probability

Simple Chance Experiments

Conduct simple probability experiments — flipping a coin, rolling a die, pulling coloured counters from a bag — record results, and compare experimental outcomes with expected theoretical outcomes

Ages
9 to 10
Type
Method
Builds on
2 topics
Leads to
2 topics

Quick check

Has the learner ever done an experiment like flipping a coin or rolling a die lots of times, recorded the results in a tally chart, and noticed any patterns in what came up?

Ask this to see whether the topic is secure.

Topic // Mastery

What mastery looks like

What a learner can do once this topic is secure.
  • Flip a coin 20 times, record heads and tails in a tally chart, and describe what they notice about the results
  • Roll a die 30 times and compare how often each number came up with what they expected
  • Pull counters from a bag, record results, and explain whether the outcomes matched their prediction

Topic // Map

Where this fits

What to learn first and what this topic opens up, with the reason for each link. Required links come first.
  • RequiredMust come first
  • HelpfulHelps, but not essential

Before this

2 topics
  • Likelihood LanguageRequired

    Probability // Ages 9 to 10

    Conducting probability experiments and describing results requires knowing the language used to describe likelihood

  • Pictograms and tally chartsHelpful

    Data & Statistics // Ages 6 to 8

    Recording probability experiment results in tally charts uses the data-recording skills taught in Data & Statistics

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Simple Chance Experiments

Ages 9 to 10 // Method

Leads to

2 topics
  • Experimental vs TheoreticalRequired

    Probability // Ages 10 to 11

    Comparing experimental and theoretical probability requires prior experience conducting simple experiments and recording results

  • Probability as a FractionHelpful

    Probability // Ages 9 to 10

    Practical experiment experience provides the intuitive grounding that makes fractional probability representation meaningful

Topic // Research-informed

Teaching notes

From the Marble Skill Taxonomy. These notes have not been validated in classrooms, so treat them as a starting point for your own judgement.

The approach

Children aged 9–10 learn probability through hands-on chance experiments: predict an expected outcome, flip a coin / roll a die / draw counters many times, record each trial one-tally-at-a-time in a tally chart, and compare what happened with what was expected. Core insights: a fair device produces outcomes that cluster near but rarely exactly match the expected split, so expecting an exact match and concluding the device is biased from too few trials is the law-of-small-numbers error; each trial is independent of the last (no 'it's due' recency thinking); and a small experiment estimates rather than proves the true probability. With a fair device, running or pooling many more trials usually brings the observed proportion closer to the expected split, though not to an exact match.

Common misconceptions

  • Expecting the experiment to match the theoretical split exactly, and concluding the device is biased when it does not (law of small numbers)
  • Recency thinking — predicting the next trial from the recent run ('it's been heads four times, so tails is due', or 'heads is on a streak')
  • Recording carelessly — backfilling tallies or losing count so the total does not match the number of trials
  • Treating the result of a small experiment as the true probability rather than an estimate

Useful representations

  • Tally chart / frequency table (one row per outcome)
  • Coins, dice, and bags of counters as trial-generators
  • Bar or block chart of observed frequencies against the expected line
  • Prediction-vs-result comparison

Teaching practices

  • Have children predict the expected outcome first ('about half heads'), then run and record, so the comparison is theirs to make
  • Enforce one-tally-per-trial recording as the trial happens, not reconstruction from memory, and total the marks against the number of trials
  • Pool results across the class to show a larger sample landing closer to the expected split than any one child's 20 trials
  • Explicitly discuss why 13 heads out of 20 does NOT mean the coin is broken — short runs vary
  • Confront 'it's due' / 'heads again' talk on the spot: the coin has no memory, each flip is independent

Activities to try

  1. 1

    Predict, flip, tally: run and read a coin experiment

    Why it works: A fair device produces outcomes clustered near the expected split but not exactly matching it; disciplined one-tally-per-trial recording is part of the procedure, and the total must reconcile with the number of trials.

    1. Before flipping, predict the expected number of heads in 20 flips (about 10) and write it down.
    2. Set up a tally chart with one row per outcome (heads, tails).
    3. Flip the coin 20 times, marking exactly one tally per flip AS it happens — not reconstructing from memory afterward.
    4. Total the marks and check the total equals the number of flips (20).
    5. Describe what you notice: was it about half? Exactly ten? How close to your prediction?
  2. 2

    Watch the proportion settle: scale up the number of trials

    Why it works: For a fair coin, as the number of trials grows the observed proportion tends to move toward the expected split and steady; a lopsided 20-trial result can easily happen by chance with a fair coin, so on its own it is not evidence of bias. The small experiment gives an estimate, not the true probability.

    1. After a lopsided small sample (e.g. 13 heads in 20), keep going: pool results across the class, or keep flipping toward 100, 200, 500 trials.
    2. Track both the growing tally AND the running proportion of heads as more trials accumulate.
    3. Compare a 'small run' (20) against a 'large run' (hundreds): notice which lands closer to the expected half (usually, but not always, the large run).
    4. State what the larger sample tells you that the small one couldn't.
  3. 3

    The coin has no memory: confront recency thinking

    Why it works: Successive trials are independent: the coin has no memory, so neither 'tails is due' (negative recency) nor 'heads is on a streak' (positive recency) is correct — each flip remains 50-50 whatever preceded it.

    1. After a run of several heads in a row, predict the next flip (or say it cannot be predicted) and say WHY.
    2. Flip again and check; repeat the predict-then-flip several times.
    3. Explain whether a streak of heads makes tails any more 'due' on the next flip.
    4. State in your own words why each flip stays 50-50 regardless of what came before.

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