Expected level of development
Australian Curriculum Mathematics V9: AC9M8P03
Numeracy Progression: Understanding chance: P6
At this level, students are expected to draw on what they have learnt about probabilities related to compound events, and apply this knowledge in a variety of experiments. The use of digital tools and simulations allow for repeated practice of compound events and help to consolidate a deeper understanding around this topic.
Students can explore probabilities using random number generators and dynamic software such as GeoGebra to conduct chance events with large numbers of trials. Use relevant simulations to explore the difference between events that are complementary, inclusive or exclusive, or if they are related.
Where required, support students to use the correct language and notation around these simulations to ensure they communicate and describe the results correctly.
Teaching and learning summary:
- Revise previous knowledge of probability.
- Define terms clearly using correct notation.
- Demonstrate digital simulations for chance experiments involving compound events.
- Discuss and describe results for different chance experiments.
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Teaching strategies
A collection of evidence-based teaching strategies applicable to this topic. Note we have not included an exhaustive list and acknowledge that some strategies such as differentiation apply to all topics. The selected teaching strategies are suggested as particularly relevant, however you may decide to include other strategies as well.
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Mathematics investigation
By giving students meaningful problems to solve they are engaged and can apply their learning, thereby deepening their understanding.
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Explicit teaching
Explicit teaching is about making the learning intentions and success criteria clear, with the teacher using examples and working though problems, setting relevant learning tasks and checking student understanding and providing feedback.
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Concrete, Representational, Abstract (CRA)
The CRA model is a three-phased approach where students move from concrete or virtual manipulatives, to making visual representations and on to using symbolic notation.
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Questioning
A culture of questioning should be encouraged and students should be comfortable to ask for clarification when they do not understand.
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Teaching resources
A range of resources to support you to build your student's understanding of these concepts, their skills and procedures. The resources incorporate a variety of teaching strategies.
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Simulating multi-step experiments
This online resource allows teachers to pick and choose simulation activities that require repeated chance experiments to be able to make predictions and assign probabilities.
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Dice roll simulation
An online two-dice simulator allowing for thousands of trials for students to conduct chance experiments with.
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Flipping two coins
An online two-coin simulator allowing for repeated chance experiments.
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Which spinners?
Use this resource to conduct chance experiments using simulation software, and use students' reasoning skills.
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Odds and evens
Use this resource to conduct chance experiments using simulation software, and explore and discuss two types of probability: experimental and theoretical.
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Assessment
By the end of Year 8, students can conduct experiments and simulations using digital tools to determine related probabilities of compound events.
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She always wins. It’s not fair!
This activity challenges students to decide if a game is fair. Use the 'Getting started' and 'Answer' tabs at the bottom of the screen for an explanation.
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Estimating probabilities using repeated experiments
This online and interactive assessment resource questions students on the outcome of repeated trials. Students are asked to describe their results.
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