Planning tool
Year levels
Strands
Expected level of development
Australian Curriculum Mathematics V9: AC9M3P02
Numeracy Progression: Understanding chance: progression: P3
At this level, students conduct repeated chance experiments. They can identify and describe possible outcomes and record the results of the chance experiments. Students then compare results of trials and discuss the variation. It is expected that students have had an introduction to possible outcomes of chance experiments.
Use games that incorporate strategy based on probability concepts. As they play games, students record results and use these to make predictions in subsequent games. Students then compare the results of the trials and discuss the variation. Discuss the results of these games and make explicit the associated probabilities.
Elicit from students that with probability they can never know exactly what will happen next, but they can get an idea about what to expect.
Provide students with spinners, coins, dice and other equipment that can generate random outcomes. Discuss fairness and bias, for example, there is greater likelihood of winning when a spinner has a larger segment of one colour compared to the other colour segments.
Teaching and learning summary:
- Conduct repeated trials of chance experiments.
- Explain the differences between expected results and actual results in a simple chance experiment.
- Identify the variations between trials.
Students:
- identify the possible outcomes of a chance experiment
- list all possible outcomes in a simple chance situation
- conduct repeated trials of chance experiments
- predict and record all possible outcomes in a simple chance experiment
- create a tally chart to record results, carry out trials and tally results.
Some students may:
- be still developing their language skills and not fully understand the language of chance to then be able to relate it to the likelihood of an event occurring
- tend to believe in luck (e.g. they will have a better chance at rolling their favourite numbers)
- make predictions based on likes and interests (e.g. their favourite colours for spinners)
- not realise that chance has no memory (e.g. if a student has rolled four sixes in a row, they often believe the fifth roll cannot possibly be another six).
To address these misconceptions, ask students to play and create games linked with chance. This will encourage students to use the language of chance, test their findings, record the results and make generalisations. Students also need to experience playing unfair games.
The Learning from home activities are designed to be used flexibly by teachers, parents and carers, as well as the students themselves. They can be used in a number of ways including to consolidate and extend learning done at school or for home schooling.
Learning intention
- We are learning about probability, which is the likelihood of an event happening.
Why are we learning about this?
- We often use the language of chance and the probability of something happening in our daily lives, for example, there is no chance of rain today as it is forecast to be hot and sunny.
What to do
1. Find a die with the numbers 1 to 6.
2. Each roll is called a trial. You will roll the die 20 times and record the results of each trial. Before you start, predict:
- how many times you will roll 6
- what number you will roll the most
- how many of each number you expect to roll.
3. Roll the die 20 times and record the number rolled for each trial in a table like this.
Trial | 1 rolled | 2 rolled | 3 rolled | 4 rolled | 5 rolled | 6 rolled |
1 | ||||||
2 | ||||||
3 | ||||||
4 | ||||||
5 |
4. Continue to 20 trials.
5. Compare your predictions to your results. What do you notice?
Success criteria
I can:
- use chance terms to describe the likelihood of events happening
- predict and record all possible outcomes in a simple chance experiment
- compare results to my predictions and explain any differences.
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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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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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Using games and storybooks
Games and storybooks are great resources to use in the classroom and are engaging for students.
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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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Feedback
It has been shown that good feedback can make a significant difference to a student’s future performance.
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Collaborative learning
For group work to be effective students need to be taught explicitly how to work together in different settings, such as pairs or larger groups, and they need to practise these skills.
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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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That’s not fair! Up or down
Use this coin toss heads and tails game to discuss possible outcomes.
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That’s not fair! Odds and evens
Use this dice roll game to discuss possible outcomes.
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Statements about probability
In this unit, students write statements about probabilities based on the spinners they make.
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Sneaky snakes
Students construct a tally chart to investigate a game of chance.
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Dotty six
This game combines the rolling of a die and a 3 x 3 grid to play bingo. Use this game to introduce students to the language of chance.
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Where's bunny now?
The purpose of this activity is to engage students in evaluating another’s judgement about the fairness of a game of chance and investigating the fairness of their own game.
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Assessment
By the end of Year 3, students are conducting repeated chance experiments and discussing variation in results.
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Bubblegum machines: student worksheet
Use this task to assess a student’s understanding of probability and ability to describe an event using the language of chance.
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Lucky dip: student worksheet
Use this task to assess a student’s understanding of probability and ability to describe an event using the language of chance.
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