Planning tool
Year levels
Strands
Expected level of development
Australian Curriculum Mathematics V9: AC9M7P02
Numeracy Progression: Understanding chance: P5
At this level, students run repeated chance experiments using large numbers of trials with digital tools. Students make predictions before running simulations so that the differences between the predicted and the actual outcomes are shown and may be compared. Ensure students understand these differences and are comfortable with explaining them.
The purpose of running many trials is to show students the difference between the predictive power of probability when only a few trials are conducted compared with gradually increasing the number of trials. Ask students why this might be.
There is a variety of simulations online that are suitable for conducting repeated chance experiments. See the teacher resources below for class activity ideas, or prompt students to design and conduct their own repeated chance experiment, choosing from a variety of digital simulation tools.
Teaching and learning summary:
 Continue to use the vocabulary of probability.
 Discuss the difference between experimental and theoretical probability.
 Demonstrate and guide students to use online digital tools to simulate repeated chance experiments.
 Ensure students can compare and explain differences between predicted and observed results of their experiments.
Students:
 are familiar with and comfortable using the language of probability
 use online digital tools to conduct repeated chance experiments with large numbers of trials
 can predict, observe, record and distinguish between what was predicted and what has occurred during an experiment.
Some students may:
 find the concept of randomness of an event and how it may be investigated problematic. By designing and conducting experiments, students may be shown how trends can become predictable.
 confuse theoretical and experimental probability. The distinction can be shown by calculating probabilities from a sample space and then conducting the experiment. The probabilities can then be compared.
 be confused by how probability is a measure of likelihood of an event happening. It is important to show students how several trials are needed to make frequency predictions.
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 to apply the language of probability to an event (likely, unlikely, even, certain, impossible).
 We are learning to calculate and record the probability of an event occurring using the number of favourable outcomes and possible outcomes.
 We are learning to explain and understand the difference between experimental and theoretical probability.
Why are we learning about this?
To explore, describe and analyse the frequency of outcomes using our knowledge of probability, given that we encounter probability in many aspects of our daily life (for example sport, weather).
What to do
Activity 1
We can measure how likely, or unlikely, it is that an event will occur using the idea of probability, which is defined using a number between 0 and 1.
Complete the following activities and record your answers in your book.
1. All the letters of the alphabet are printed on cards and put in a bag. A card is drawn out at random. The probability that the letter on the card occurs in the word ‘PERTH’ is:
a. 126
b. 526
c. 2126
2. All the letters of the word ‘AUSTRALIA’ are written on separate pieces of paper, which are placed in a box. James randomly selects a piece of paper from the box and records the letter written. What is the probability of James choosing:
a. a T?
b. an I?
c. a vowel?
3. A bag contains 10 marbles, numbered 1 to 10. One marble is removed.
a. List the sample space.
b. Write down the outcomes favourable to the event ‘a marble with an odd number is taken out’.
c. What is the probability of getting an odd number?
Activity 2
Follow the reasoning and play these fun games with a friend. Don't worry, it’s not school.
Success criteria
 I can explain the likelihood of an event happening on a scale from impossible to certain.
 I can express probability on a scale from 0 to 1.
 I can calculate and use theoretical probabilities for single and combined events using a variety of appropriate representations, including diagrams.
Please note: This site contains links to websites not controlled by the Australian Government or ESA. More information here.
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.

Mathematics investigation
By giving students meaningful problems to solve they are engaged and can apply their learning, thereby deepening their understanding.
Go to resource 
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.
Go to resource 
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.
Go to resource 
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.
Go to resource
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.

Rock, paper, scissors
In this lesson, students compare theoretical and experimental probabilities by completing repeated trials of the game ‘Rock, paper, scissors’.
Go to resource 
Rock, paper … lizard, Spock?
In this lesson, students compare theoretical and experimental probabilities by completing repeated trials.
Go to resource 
Statistics and probability: probability
A resource focusing on how to calculate probabilities for events, including detailed explanations, worked examples and an assessment question.
Go to resource 
Roll dice simulation
A digital version of rolling dice. Useful for conducting experiments quickly and in large numbers.
Go to resource 
Coin toss simulation
Design an experiment for your students using this digital simulator to conduct the fivecoin probability experiment with many trials.
Go to resource 
Randomly pick a letter in the alphabet and replace
This interactive resource simulates picking a letter randomly from the alphabet and replacing it. It allows for many repeated simulations.
Go to resource 
What are probabilities?
Comprising lesson and practice opportunities, this resource covers vocabulary, chance events and sample spaces, and asks students to think about predictions and possibilities.
Go to resource
Assessment
By the end of Year 7, students conduct repeated singlestep chance experiments and run simulations using digital tools, giving reasons for differences between predicted and observed results.

What is probability?
This is a studentfacing interactive set of questions focusing on probability, making predictions, randomness and sample spaces.
Go to resource 
Probability and sampling
A comprehensive interactive assessment resource for all students that covers the basics, worded problems, estimation and simulation. Teacher materials complement each activity.
Go to resource