AC9M5P02: 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

expected frequency

predicted count based on probability and trial total

observed frequency

count actually obtained

relative frequency

observed frequency divided by number of trials

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.

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

Project the fixed branded slide deck one slide at a time.

• 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.

Curriculum equivalents for Conduct repeated chance experiments including those with and without equally...

Mapped skill: 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

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.

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.

Australian Curriculum Version 9.0

• AC9M5N01: Decimals Beyond Hundredths
• AC9M5N02: Factors, Multiples and Divisibility
• AC9M5N03: Comparing and Ordering Fractions
• AC9M5N04: Percentages, Fractions and Decimals
• AC9M5N05: Adding and Subtracting Fractions
• AC9M5N06: Multiplying Larger Numbers