Year 6 Mathematics · AC9M6P02

Repeated Chance Experiments and Simulations

Compare observed frequency with expected probability and sample size

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Learning goalsSay it simply

Learning goal

Students calculate expected frequency, conduct physical and digital trials, compare relative frequencies across sample sizes and discuss why results vary while often becoming more stable.

Success criteria

  • I can represent or identify the concept.
  • I can explain the underlying relationship.
  • I can select an appropriate strategy or feature.
  • I can apply it in a new context.
  • I can justify and verify the response.

Teaching routine

  1. Represent
  2. Reason
  3. Calculate
  4. Interpret
  5. Verify
Curriculum focus: conduct repeated chance experiments and run simulations with an increasing number of trials; compare observed frequencies with expected frequencies and explain variation
Key conceptTeach from the board

Compare trial counts for a fair coin

Use the visual model first. Ask students to identify the quantities, structure or conditions before calculating or explaining.

trialsheadsrelative frequency1070.7050270.542001030.5151 0004980.498expected0.5

Larger samples often stabilise relative frequency near the model probability, but no trial count guarantees an exact match.

Audit a simulation and expected frequency

Connect the central relationship to a new context, then verify the conclusion with a second representation, estimate, inverse operation or reasonableness check.

P(red)=0.3, 200 trialsexpected red = 60
physical trialcheck device and consistent procedure
digital simulationcheck probability settings and trial count
comparisonuse relative frequency when totals differ
variationdescribe difference without changing data

A simulation is only as valid as its probability model and implementation. Verify settings before interpreting output.

Clean visual examplesOne-page board

Clean one-page examples

AC9M6P02 - Repeated Chance Experiments and Simulations
Example 1

trials heads relative frequency 10 7 0.70 50 27 0.54 200 103 0.515 1 000 498 0.498 expected 0.5

Example 2

P(red)=0.3, 200 trials expected red = 60

Example 3

Use the visual model first. Ask students to identify the quantities, structure or conditions before calculating or explaining.

Example 4

Larger samples often stabilise relative frequency near the model probability, but no trial count guarantees an exact match.

Curriculum examplesCopied content

AC9M6P02: conduct repeated chance experiments and run simulations with an increasing number of trials using digital tools; compare observations with expected results and discuss the effect on variation of increasing the number of trials

    Use the central and application models above to connect each elaboration to the same underlying concept.

    Questions and answersWith answers

    Check understanding

    • Calculate expected count.
    • Find relative frequency.
    • Compare 10/50/200 trials.
    • Explain variation.
    • Check simulation settings.

    Evidence of mastery

    • Represent or identify the concept
    • Explain the underlying relationship
    • Select an appropriate strategy or feature
    • Apply it in a new context
    • Justify and verify the response

    Decision: continue when students can explain the model, apply it to a new example and justify their check. Otherwise return to the central model and reduce the numerical or representational load.

    Practice and reviewReady for practice
    Expected frequency treated as guaranteedIt is a long-run prediction.
    Raw counts compared across unequal totalsUse proportions.
    Unwanted outcomes deletedRecord all valid trials.
    Simulation settings assumed correctAudit the model.
    Curriculum alignmentStart here

    Learning goal

    Students calculate expected frequency, conduct physical and digital trials, compare relative frequencies across sample sizes and discuss why results vary while often becoming more stable.

    Success criteria

    • I can represent or identify the concept.
    • I can explain the underlying relationship.
    • I can select an appropriate strategy or feature.
    • I can apply it in a new context.
    • I can justify and verify the response.

    Teaching routine

    1. Represent
    2. Reason
    3. Calculate
    4. Interpret
    5. Verify
    Curriculum focus: conduct repeated chance experiments and run simulations with an increasing number of trials; compare observed frequencies with expected frequencies and explain variation
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