Expected level of development
Australian Curriculum Mathematics V9: AC9M9P03
Numeracy Progression: Understanding chance: P6
At this level, the focus of students designing and conducting chance experiments is to compare probabilities of simple and compound events.
Make explicit through strategies such as worked examples how to list outcomes of one-step events (simple) and and two-step events (compound) to make comparisons.
Use a relevant chance experiment such as flipping a coin and rolling a dice. Event: what is the probability of flipping a tail and rolling a number lower than 3? Use list and area models to compare the single events with the compound events. In this example, the list and area models for the compound event would be as follows:
| List | Area model |
| H1, H2, H3, H4, H5, H6, T1, T2, T3, T4, T5, T6 |
The favourable event is highlighted where the rows and columns intersect.
|
Use questioning to elicit from students that the probability for a favourable event is 2 out of 12 [T1, T2]. Students could replicate this chance experiment using digital tools such as simulators to compare expected results for the simple and compound events to their experimental results.
Support students to design and conduct their own chance experiments. Discuss and investigate the effect of chance experiments that have replacement with those without replacement. Compare the effect on the probabilities of favourable events.
Teaching and learning summary:
- Review students’ knowledge and understanding of probability.
- Revise the meaning of the terms ‘and’ and 'or’ in a probability context and the impact they have on assigning probabilities.
- Make explicit the differences between single-step chance experiments and various kinds of multi-step chance experiments.
- Encourage students to use digital tools to conduct experiments based on students’ own design.
- Encourage students to describe their experimental set-up and outcomes in order to show depth of understanding of the topic.
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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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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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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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Worked examples
A worked example is not just a pre-worked question that is given to the students. There are several types of worked examples and ways of using them.
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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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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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Doubles or evens
This activity simulates probability activities for two different experiments. Students must investigate and use the simulation to answer the question.
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Egg roulette: Part 1
In this lesson students use a fun context to learn about probability without replacement.
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Egg roulette: Part 2
In this lesson, students explore simulations to address misconceptions related to probability with and without replacement.
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Using probability to determine whether events are independent
This resource provides teacher guides, lesson plan and student practice to help teach and guide students around events that are dependent or independent from one another.
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Hot streaks
This sequence of lessons uses two different contexts to explore ideas of randomness. Students distinguish between random and non-random results to investigate the existence or otherwise of the ‘hot streak’ phenomenon in basketball.
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Dice-rolling simulation
A two-dice online simulation that allows for repeated trials, and also sums the numbers on the dice to allow for two-step chance experiments.
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Randomly pick a card and replace
This online simulation of a pack of playing cards allows for repeated experiments of different conditions, such as ‘and’ and ‘or’. Students can design their own experiments around the simulation or in combination with another simulation.
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Dice roll simulation
This simulation allows for rolling one, two or three dice and many repeated events.
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Likelihood
Use this simulation to measure and make comparisons with 'unfair' coin tosses where each coin's weight may be altered.
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