Planning tool
Year levels
Strands
Expected level of development
Australian Curriculum Mathematics V9: AC9M3P01
Numeracy Progression: Understanding chance: progression: P3
At this level, probability is formally introduced. The focus is on developing students’ knowledge of the language of chance, which is a subjective, informal estimate. Students learn to describe events as impossible, unlikely, likely, even chance, highly likely and certain.
Introduce a range of events and discuss possible outcomes. Use a probability scale to order events using the language of chance:
A string line can be used to create a probability scale. Students can peg a card to the string to locate an event according to the likelihood of the event occurring. This task can be done individually or collaboratively.
Enable students to develop their language of chance by using cards with chance terms to discuss and place in order or to sort and classify.
Present a chance experiment to the class, for example, selecting tokens from a lucky dip. Make explicit the number of each item which is represented by a coloured token. Discuss as a class what is least likely or most likely, with students explaining their reasoning. Summarise the activity using true statements.
Use a range of chance experiments to discuss possible outcomes. Using true–false statements can help discover any misconceptions students may have as they discuss and respond. For example, statements can include:
- It is harder to roll a 6 than a 2 when rolling a die.
- If I toss 4 heads in a row, it is impossible that the next will be heads.
- If there are 100 jellybeans in the bag and 99 are black, it is certain I will pick a black jellybean.
Teaching and learning summary:
- Use the language of chance in everyday contexts.
- Use the language of chance and give reasons for classifications.
- Predict what could happen next in practical activities that involve elements of chance.
Students:
- distinguish between certain and impossible events
- use the language of chance to describe and explain predictions
- classify a list of everyday events by their likelihood of occurring.
Some students may:
- be still developing their language skills and not understand the language of chance enough to be able to then 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, 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 that everyday chance situations can be described using chance vocabulary.
Why are we learning about this?
- We are learning to identify outcomes of familiar events involving chance.
What to do
Make a list of activities that could, will, won’t happen or might happen after school today. You also need to explain why. They could include activities like:
- riding a bike
- doing my homework
- watching television
- doing the dishes
- going to the movies
- playing outside.
Success criteria
I can:
- identify everyday chance situations and describe them using chance vocabulary
- use chance terms to describe the likelihood of events happening.
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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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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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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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Multiple exposures
Providing students with multiple opportunities within different contexts to practise skills and apply concepts allows them to consolidate and deepen their understanding.
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