Year 4 Mathematics · AC9M4P02

Conduct repeated chance experiments to observe relationships between outcomes; identify and describe the variation in results

Repeated experiments show variation: identical chance conditions can produce different short-run results. Larger combined samples often give a more stable picture of…

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E1: Investigate games and strategy

Official elaboration: playing games such as Noughts and Crosses or First to 20 and deciding if it makes a difference who goes first and whether you can use a particular strategy to increase your chances of winning

Play six Noughts and Crosses games, alternating starters and recording wins/draws. Discuss blocking an opponent and making a line. For First to 20, start at 0 and alternate adding 1 or 2; reaching 20 exactly wins. At 18, add 2; at 19, add 1. Record repeated games and strategies. Game outcomes can depend on decisions and skill, so these are not simply independent coin experiments; a few wins do not prove a general advantage.

E2: Record physical and virtual random generators

Official elaboration: recording and ordering the outcomes of experiments using different physical or virtual random generators such as coins, dice and a variety of spinners, and discussing how AI systems use random generators to train algorithms

Use equal-length sets with a coin, die or clearly labelled fair spinner; record every result in order and tally each category, including zeros. Compare counts and explain variation. A virtual generator may produce repeated values without being broken. Random sampling can supply varied AI training cases, but people must check examples and results for accuracy. Keep the method and trial count clear.

E3: Two coins: ordered outcomes and grouped results

Official elaboration: experimenting with tossing 2 coins at the same time, recording and commenting on the chance of outcomes after a number of tosses

Label coins A and B. Record HH, HT, TH, TT for each of 20 tosses. HT and TH both give one head and one tail, but are different ordered results. Example counts 4, 7, 5, 4 total 20; mixed outcomes total 12 and matching outcomes 8. Actual trials need not match this example or give equal category counts. Conduct a new experiment and compare actual results.

E4: Shuffle, draw, classify and repeat

Official elaboration: shuffling a set of cards, drawing a card at random, and recording whether it was a spade, club, diamond or heart, picture card or numbered; repeating the experiment a number of times and discussing the results

Use a standard 52-card deck without jokers. Record the suit and a separate card type: picture J/Q/K, numbered 2–10, or ace. A queen of clubs is clubs and picture. Return and shuffle after every draw for the same starting contents, or clearly describe an intentional no-replacement investigation. Each suit table and each type table separately totals the trial count. Report observed differences without claiming certainty about the next card.

Models, important questions and exit evidence

Important questions and answers: Must 20 fair-coin tosses give 10 heads? No: observed results can vary. Why keep HT and TH separate? The two labelled coins can produce the mixed result in two different orders.

Boundary: Use descriptive likelihood, conditions and observable evidence. Do not require numerical probability formulas, probability trees or formal statistical tests.

Support: Use physical objects and record one result at a time. Core: Explain each comparison using the stated conditions and actual records. Extend: Change one condition and justify what may change, within this code.

Exit evidence: Conduct and record a short experiment; compare two sets and explain why the counts need not match. Accept accurate actual records and a qualified variation statement, not an invented balanced result.

Learning goalsSay it simply

Repeated experiments show variation: identical chance conditions can produce different short-run results. Larger combined samples often give a more stable picture of outcome relationships, but exact frequencies are not guaranteed.

Learning routine: Define outcomes → Predict → Conduct consistent trials → Record frequencies → Repeat/aggregate → Compare observed counts → Describe variation

Success looks like

  • Conduct consistent trials
  • Record frequencies
  • Compare observed counts
  • Discuss sample size
  • Describe variation cautiously
Clean visual examplesOne-page board

Clean one-page examples

AC9M4P02 - Conduct repeated chance experiments to observe relationships between outcomes; identify and describe the variation in results
Example 1

same spinner full spin record immediately fixed number of trials no discarded results

Example 2

1. Class trial sets Each group conducts the same 20-trial experiment, then the class compares variation and combines results. A A: 11 B: 9 B A: 8 B: 12 C A: 13 B: 7 D A: 10 B: 10

Example 3

2. Repeated-set comparison Compare red counts across three sets of 20 digital spins. Explain any observed variation. Trials Red count 20 12 20 9 20 11

Example 4

3. Fairness audit Check that the device, procedure and recording stay consistent across all trials. same spinner full spin record immediately fixed number of trials no discarded results

Curriculum examplesCopied content

The content description and elaborations below show the curriculum ideas taught in this unit. Items marked as teaching context support lesson planning.

  • Content description: conduct repeated chance experiments to observe relationships between outcomes; identify and describe the variation in results
  • E1: playing games such as Noughts and Crosses or First to 20 and deciding if it makes a difference who goes first and whether you can use a particular strategy to increase your chances of winning
  • E2: recording and ordering the outcomes of experiments using different physical or virtual random generators such as coins, dice and a variety of spinners, and discussing how AI systems use random generators to train algorithms
  • E3: experimenting with tossing 2 coins at the same time, recording and commenting on the chance of outcomes after a number of tosses
  • E4: shuffling a set of cards, drawing a card at random, and recording whether it was a spade, club, diamond or heart, picture card or numbered; repeating the experiment a number of times and discussing the results
Questions and answersWith answers

Core idea: Repeated experiments show variation: identical chance conditions can produce different short-run results. Larger combined samples often give a more stable picture of outcome relationships, but exact frequencies are not guaranteed.

Remember

  • Conduct consistent trials
  • Record frequencies
  • Compare observed counts
  • Discuss sample size
  • Describe variation cautiously

Important questions

  • Explain variation across trial sets. Explain using the model or evidence above.
  • Why combine class results? Explain using the model or evidence above.
  • Compare 12 heads and 9 heads in two sets of 20 tosses. Explain using the model or evidence above.
  • What does a fair spinner with three equal red sectors and one blue sector suggest? Explain using the model or evidence above.
  • Name one procedural control. Explain using the model or evidence above.
Practice and reviewReady for practice
  • Equal chance means equal every run — Small samples can vary considerably.
  • Result changed to match prediction — Record every valid trial, including surprising outcomes.
  • Frequencies compared without sample size — Use equal trial totals when directly comparing counts.
  • One trial used to judge fairness — Repeated evidence is needed; even then conclusions should be cautious.

Read the topic guide and use the teacher slide for instruction. Students can then use the worksheet for written work, open Practice for supported feedback, or take the Test when they are ready.

Curriculum alignmentStart here

Repeated experiments show variation: identical chance conditions can produce different short-run results. Larger combined samples often give a more stable picture of outcome relationships, but exact frequencies are not guaranteed.

Learning routine: Define outcomes → Predict → Conduct consistent trials → Record frequencies → Repeat/aggregate → Compare observed counts → Describe variation

Success looks like

  • Conduct consistent trials
  • Record frequencies
  • Compare observed counts
  • Discuss sample size
  • Describe variation cautiously
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