Conduct repeated chance experiments including those with and without equally likely outcomes, observe and record the results; use frequency to compare outcomes and estimate their likelihoods

Students calculate expected frequency from probability and trial count, conduct or simulate repeated trials, compare observed frequencies and discuss natural variation and sample size.

Expected frequency = probability × number of trials; observed frequency will often differ, especially in smaller samples.

The observed counts do not need to equal expectations exactly. The differences are plausible variation under repeated chance.

Larger samples often produce more stable relative frequencies, but they do not guarantee a perfect match in every run.

Learning routine: Represent → Reason → Calculate → Interpret → Verify

Success looks like

• Construct or represent accurately
• Use correct vocabulary and notation
• Interpret relationships
• Apply to a new example
• Justify and evaluate

Content description: conduct repeated chance experiments including those with and without equally likely outcomes, observe and record the results; use frequency to compare outcomes and estimate their likelihoods.

• E1: discussing and listing all the possible outcomes of an activity and conducting experiments to estimate the probabilities; for example, using coloured cards in a card game and experimenting with shuffling the deck and turning over one card at a time, recording and discussing the results
• E2: conducting experiments, recording the outcomes and the number of times the outcomes occur, describing the relative frequency of each outcome; for example, using “I threw the coin 10 times, and the results were 3 times for a head, so that is 3 out of 10, and 7 times for a tail, so that is 7 out of 10”
• E3: experimenting with and comparing the outcomes of spinners with equal-coloured regions compared to unequal regions; responding to questions such as “How does this spinner differ to one where each of the colours has an equal chance of occurring?”, giving reasons
• E4: comparing the results of experiments using a fair dice and one that has numbers represented on faces more than once, explaining how this affects the likelihood of outcomes
• E5: using spreadsheets to record the outcomes of an activity and calculate the total frequencies of different outcomes, representing these as a fraction; for example, using coloured balls in a bag, drawing one out at a time and recording the colour, replacing them in the bag after each draw
• E6: investigating First Nations Australian children’s instructive games; for example, Diyari koolchee from the Diyari Peoples near Lake Eyre in South Australia, to conduct repeated trials and explore predictable patterns, using digital tools where appropriate

Core idea: Expected frequency = probability × number of trials; observed frequency will often differ, especially in smaller samples.

Remember

• Construct or represent accurately
• Use correct vocabulary and notation
• Interpret relationships
• Apply to a new example
• Justify and evaluate

Important questions

• Calculate expected frequency. Explain using the model or evidence above.
• Compare observed/expected. Explain using the model or evidence above.
• Find a relative frequency. Explain using the model or evidence above.
• Explain sample size. Explain using the model or evidence above.
• Audit simulation settings. Explain using the model or evidence above.

• Expected means guaranteed — It is a long-run prediction.
• Raw counts compared across different totals — Use relative frequencies.
• Unwanted trials discarded — Record all valid outcomes.
• Digital simulation accepted without checking settings — Verify probability model and number of trials.

Learn from the Topic Guide and fixed Teacher Slides, complete the Practice Sheet, use Practice for supported feedback, then take the Test when ready.

Students calculate expected frequency from probability and trial count, conduct or simulate repeated trials, compare observed frequencies and discuss natural variation and sample size.

Expected frequency = probability × number of trials; observed frequency will often differ, especially in smaller samples.

The observed counts do not need to equal expectations exactly. The differences are plausible variation under repeated chance.

Larger samples often produce more stable relative frequencies, but they do not guarantee a perfect match in every run.

Learning routine: Represent → Reason → Calculate → Interpret → Verify

Success looks like

• Construct or represent accurately
• Use correct vocabulary and notation
• Interpret relationships
• Apply to a new example
• Justify and evaluate

Australian Curriculum Version 9.0

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