Build and annotate the model
Represent repeated chance experiments and simulations and label the important parts, quantities or choices.
Learning goals
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
- Represent
- Reason
- Calculate
- Interpret
- 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 concept
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.
Worked examples
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.
Curriculum elaborations explicitly taught
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.
Common misconceptions
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.
Classroom activities
Compare and reason
Use the application model to compare two cases, explain the relationship and identify a likely error.
Transfer and verify
Apply the idea in an unfamiliar context and use a second method, evidence source or text feature to check it.
Revision Notes and quick mastery check
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.
Curriculum wording and references
Australian Curriculum v9.0
AC9M6P02: conduct repeated chance experiments and run simulations with an increasing number of trials; compare observed frequencies with expected frequencies and explain variation
The Australian Curriculum code and wording are exact. International teachers can use the underlying mathematical concept while matching the lesson to their local grade or year outcomes.
Resources and next steps
Teacher Slides
Project the fixed, branded four-page teaching sequence.
Open Classroom ViewHomework
Use the printable activity for written practice.
Open HomeworkPractice and Test
Use supported Practice first, then the separate Test when ready.
Open PracticeOpen Test
🎥 Optional Video Lesson
The SkillrHub lesson remains the primary learning resource. This optional video reinforces the explanation; you can complete the lesson and practice without watching.
Before you watch:
- Pause after each worked example.
- Try the examples yourself.
- Return to the SkillrHub lesson before continuing.
Recommended: What Is Experimental Probability?
Math with Mr. J — Compare experimental results with theoretical probability over repeated trials.
As you watch: Why can a short experiment give a different result from the expected probability?
Load video player Loads YouTube in this lesson. See the video notice below.
Try it: Compare the proportion of heads after 20 and 100 coin tosses. Explain why more trials can reduce variation without guaranteeing exactly half heads.
Video unavailable, inaccurate or unsuitable for this year? Report a video problem to SkillrHub by email. You can continue with the written lesson and practice resources.
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Curriculum equivalents: Victoria, NSW and international
Curriculum equivalents for Conduct repeated chance experiments and run simulations with an increasing...
Mapped skill: 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
These references identify matching or closely related learning. Curriculum sequence, terminology and depth vary, so teachers should use the mapped skill and lesson difficulty to confirm suitability.
| Region | Curriculum framework | Closest level or code |
|---|---|---|
| Australia | Australian Curriculum v9.0 | AC9M6P02 · Year 6 |
| Victoria | Victorian Curriculum F–10 Version 2.0 — Mathematics | VC2M6P02 · Level 6 |
| New South Wales | NSW Mathematics K–10 Syllabus (2022) | MA3-CHAN-01 · Stage 3 |
| United States (USA) | Common Core State Standards for Mathematics | Grade 6 |
| Canada (Ontario) | Ontario Curriculum — Mathematics | Grade 6 |
| United Kingdom (England) | National Curriculum in England — Mathematics | Year 7, Key Stage 3 |
| India | NCERT / CBSE — Mathematics | Class 6 |
Australian Curriculum v9.0 is the canonical source for this SkillrHub lesson. Victoria and NSW entries name the closest published state codes or outcomes; international entries are planning references rather than claims of identical curricula.
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Topic reference: AC9M6P02 — Repeated Chance Experiments and Simulations
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