Planning tool
Year levels
Strands
Expected level of development
Australian Curriculum Mathematics V9: AC9M5P02
Numeracy Progression: Understanding chance: P3 and P4
At this level, students conduct repeated chance experiments including those with and without equally likely outcomes. They then observe the outcome of their chance experiments, record data and describe the relative frequencies.
Provide opportunities for students to collaboratively conduct repeated chance experiments that have equally likely outcomes. Students can use physical materials or virtual random generators to investigate the probabilities of tossing a coin, rolling a dice or spinning a spinner with equal segments using a small number of trials. They can then compare these to chance experiments that do not have equally likely outcomes, for example, a spinner with larger sections of one colour compared to the rest or a bag containing unequal numbers of coloured marbles.
Present problemsolving challenges to students, and, where possible, use simulations to model probabilities as well as questioning students to prompt them to draw on their reasoning skills.
Look for opportunities for students to use spreadsheets to record data of chance experiments and then present the data to inform analysis and interpretation of the results. Results can be used in automated calculations of total frequency.
There is an opportunity to make connections to statistics, plan and conduct statistical investigations (AC9M5ST03).
Teaching and learning summary:
 Use physical and virtual tools to conduct and record outcomes of chance experiments.
 Use spreadsheets to record the outcomes of a chance experiment.
Students:
 discuss and list all the possible outcomes of a chance experiment
 conduct and record outcomes of a chance experiment
 describe the relative frequency of each outcome
 explain the difference between chance experiments that have equally likely outcomes and those that do not.
Some students may:
 not realise that chance has no memory (for example, if a student has rolled four sixes in a row, they often believe the fifth roll cannot possibly be another six).
 be confused when comparing observed frequencies and expected frequencies. They may not yet understand why observed frequencies might produce different results to expected frequencies. Conduct experiments where students must record the results, that is, their observations. They can then compare these to the expected results. For example:
 The probability of rolling a 6 on a die is 16 , so this would be the expected probability. This means if the dice was rolled 600 times, it would be expected the number 6 would come up 100 times.
 Conduct an experiment where the students roll the dice 10 times and record the results for each roll (a frequency table could be used to record results). At the end of the experiment, students tally the number of times a 6 appeared. For example, the number 6 may have come up 2 times in the 10 rolls. As a fraction, this would be written as 210 which simplifies to 15 . In this case, the observed frequency does not match the expected frequency. Discuss why this is the case. Ask students to think about how to achieve an observed result that is closer to the expected result. What would happen if we rolled the dice another 10 times and then another 10 times again? Digital tools enable students to do this efficiently.
 incorrectly believe that similar to rolling one die where there is a 1 in 6 chance, rolling 2 dice would have a 1 in 12 chance of rolling a total. However, this is not always the case. For example, rolling a total of 7 has a 6 out of 36 ( 16 ) chance, whereas rolling a total of 4 has only a 3 in 36 chance ( 212 ).
 confuse events with outcomes, for example, when rolling 2 dice and getting a total of 3, the outcome of [2,1] is different to [1,2] however the outcome is still a total of 3. There are 2 chances out of a possible of 36.
To address these misconceptions, ask students to conduct repeated chance experiments, recording and interpreting the results.
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 to investigate a chance experiment and list the outcomes.
Why are we learning about this?
 We are learning to list the outcomes of a chance experiment to know all of the possibilities.
What to do
 Play the Twelvepointed star game with another person.
 Open this website for the rules and instructions of how to play. You will need two dice and a printout of the board. If you do not have the materials, you can draw the board on a sheet of paper and you could use this online random dice generator.
 Record the results of your game and what you found out about the probabilities when rolling two dice.
 What totals are most likely?
 What totals are least likely?
 Use data to explain your answers.
Success criteria
I can:
 investigate probability using a simple chance experiment
 list outcomes of a chance experiment
 explain why some totals of rolling two dice are more likely to come up than others.
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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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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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Differentiated teaching
Differentiation involves teachers creating lessons that are accessible and challenging for all students.
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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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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.

In the bag
In this task, students use a digital tool to test their predictions of the colours of marbles in a bag, based on data from 10 trials.
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What does random look like?
In this task, students use a random generator to compare real data of 20 trials of a coin toss to madeup data.
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Two and one
This problem offers students the opportunity to get a feel for experimental probability and work systematically to find all possible outcomes.
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Dice roll simulation (with graph and large trials)
Use this dynamic software, which is a random generator for a die roll and includes data represented as a histogram and larger trials, to explore chance and probability.
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A bit of a dicey problem
Use this task to conduct a chance experiment to work out the probability of rolling totals using two dice.
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Roll these dice
Use this task to ask students to apply their understanding of probability and possible outcomes and to practise addition and subtraction.
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Penalty shootout
The purpose of this activity is to engage students in running an experiment to determine a probability and compare this with the results of similar practical situations.
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Assessment
By the end of Year 5, students are conducting repeated chance experiments, listing the possible outcomes, estimating likelihoods and making comparisons between those with and without equally likely outcomes.

Probably ...
Use this task to assess students’ understanding of probability.
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Mathematics: ACARA annotated student work samples
Refer to ACARA work sample 11, 'Come in spinner', to assess students’ understanding of probability through the task. Students list outcomes of chance experiments with equally likely outcomes and assign probabilities as a number from zero to one.
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