Planning tool
Year levels
Strands
Expected level of development
Australian Curriculum Mathematics V9: AC9M7P01
Numeracy Progression: Understanding chance: P5
At this level, students are familiar with the language of probability and become adept at using the vocabulary: probability, sample space, favourable outcomes, trial, experiments and events. Students identify and draw sample spaces to create a list of all possible outcomes. This is an important step in assigning probabilities to these outcomes.
Using physical objects (coins, dice, spinners) and conducting singlestep experiments affords visualisation and engagement for students. Students can predict relative frequencies of an event by understanding that probability can also be thought of as a proportion of many outcomes and that the proportion can be represented as a ratio, decimal and percentage.
Teaching and learning summary:
 Use the language of probability.
 Demonstrate how to list the possible outcomes of an experiment systematically.
 Show how to draw sample spaces from singlestep experiments.
 Use handson materials to demonstrate an event and to calculate the probability of the event.
 Demonstrate how to predict relative frequencies from singlestep experiments and represent frequencies as ratios, decimals and percentages.
Students:
 recognise and use the language of probability confidently
 systematically list the outcomes of singlestage events
 assign probabilities to possible outcomes of singlestage events
 predict relative frequencies and represent them as ratios, decimals or percentages.
Some students may:
 misunderstand how random events can be quantified. By carefully designing and carrying out an experiment for a particular event, students can make connections about likelihood and assigning probabilities.
 find the concept of randomness trivial; by designing an experiment, using a variety of ways to record outcomes, and working systematically, connections to probabilities can be made.
Encourage students to read questions carefully as slight nuances in language are important in probability. Students whose first language is a language or dialect other than English may need particular support in this topic.
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 the language of probability (likely, unlikely, certain, impossible, possible, chance).
 We are learning to demonstrate and list the possible outcomes of an event.
 We are learning to describe and analyse the frequency of outcomes.
Why are we learning about this?
In life, it is important to know how to quantify, explore and explain likelihood and coincidence of events happening in our lives, and to reason about uncertainty. This helps us make decisions.
What to do
Game 1
The aim of this game is to distinguish between the events that have different likelihoods and explain numerically why one event is more likely than another.
 Play the game with a partner. Each player has a bag from which they take turns to randomly select a marble and then replace it.
 Each time a player selects a red marble they score a point.
 The first player to score 5 points wins the game.
 Discuss what the probability is of picking out a red marble?
Game 2
For each scenario, roll a dice 30 times and record the resulting number of points.
A point is scored every time you roll one of the following:
 an even number
 a 6
 a number < 6
 a number > 2
 a square number.
In each case, decide whether you were luckier or less lucky than expected. Explain your reasoning by recording your results in a table like the one below. Compare your results with the expected number of occurrences.
Total number of possible outcomes  
Total number of successful outcomes  
Probability of rolling an even number  
Probability of rolling a 6  
Probability of rolling a number < 6  
Probability of rolling a number > 2  
Probability of rolling a square number  
Probability of rolling a number < 10 
Success criteria
 I can use the language of probability when explaining the experiment/event.
 I can list systematically the outcomes of onestep and twostep experiments.
 I can calculate the probability of outcomes.
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Teaching strategies
A collection of evidencebased 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.

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 threephased approach where students move from concrete or virtual manipulatives, to making visual representations and on to using symbolic notation.
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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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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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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.

Fair games
This unit uses collaborative and handson activities and games to explore the number of outcomes in a sample space as different from the number of events. The activities support differentiation across the learning spectrum.
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Probability
This interactive game allows students to make predictions and observe how relative frequencies may be calculated and represented as fractions and percentages.
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Chance
This module benefits teachers who wish to consolidate their content knowledge of probability, covering history, realworld context and accompanying practice exercises.
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Probability
This teacherfacing resource provides content knowledge and examples on how to teach probability, as well as relevant practice questions for students.
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Assessment
By the end of Year 7, students can list sample spaces for singlestep experiments, assign probabilities to outcomes and predict relative frequencies for related events.

Fair games
This unit uses collaborative and handson activities and games to explore the number of outcomes in a sample space as different from the number of events. The activities support differentiation across the learning spectrum.
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Keeping track of all possible outcomes
An interactive assessment task where students can demonstrate their understanding of sample space and outcomes.
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Experimental probability
The interactive spinner and table allow students to map out a sample space and understand the concept of chance and probability.
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