Mathematics / Year 7 / Probability

Curriculum content descriptions

identify the sample space for single-stage events; assign probabilities to the outcomes of these events and predict relative frequencies for related events (AC9M7P01)

Elaborations
  • discussing the meaning of probability terminology; for example, “probability”, “sample space”, “favourable outcome”, “trial”, “experiment” and “event”
  • listing sample spaces for games involving throwing a coin or a dice, spinners, or lucky dip
  • assigning the probability for throwing a \(6\) on a dice and using this to predict the number of times a \(6\) will occur when a dice is thrown multiple times
General capabilities
  • Numeracy Numeracy
  • Critical and creative thinking Critical and Creative Thinking
ScOT terms

Sample space,  Expected frequency,  Relative frequency

Downloadable

The wide wide world of sports betting

This lesson explores the difference between perfectly predictable events (like the roll of a die) and less certain events (such as sports). Students investigate mathematically how sports bookmakers create odds to guarantee themselves a profit and pay gamblers less for a win than they deserve. The lesson is outlined in ...

Downloadable

Can you beat the system?

In this lesson, students calculate the average expected value of losses on a roulette wheel over time, and use these values to analyse the cost of gambling on these games. They also study the flaws inherent in betting systems to determine whether these systems are weighted in the favour of game operators making a profit. ...

Downloadable

What are the odds?

Students calculate the probability for single-step events using sample spaces.

Downloadable

Introduction to games of chance

This lesson explores how to predict outcomes of games of chance. Students investigate the concepts of luck, skill and fairness, using dice games. They calculate probabilities for one and two dice rolls and compare the odds for different combinations of dice in a variety of game scenarios. The lesson is outlined in detail ...

Online

Possible outcomes: Year 7 – planning tool

This planning resource for Year 7 is for the topic of Possible outcomes. Students represent the probability of an event occurring on a scale of zero to one as decimals, fractions or percentages.

Video

Catalyst: Probability and the birthday paradox

Even when a maths problem seems simple – for example, the chance of two people sharing a birthday – the maths can run counter to our human intuition. Mathematician Lily Serna poses a maths problem to the Clovelly Bowling Club: how many people do you need to gather to get a 50 per cent chance of any two people in that group ...

Video

Catalyst: Probability and the gambler's fallacy

Mathematician Lily Serna visits Luna Park to explain a great probability pitfall. She shares a century-old tale from Monte Carlo casino, and then she puts its lesson to the test. If you flip a coin and it lands on heads three times in a row, what result would you predict for the next flip? Find out why intuition might land ...

Video

MathXplosion, Ep 49: The probability of finding matching socks

Check out this probability puzzle that requires you to weigh all the possibilities. Pick the most likely outcome when confronted with a drawer full of loose, unpaired socks! How did Eric come up with a matching pair?

Video

MathXplosion, Ep 8: Birthday probability

What is the probability there are at least two people in your class who have the same birthday? If you have at least 23 people in your class, the chances are good. Find out the maths behind this theory.

Online

Probability

This is a website designed for both teachers and students that addresses probability from the Australian Curriculum for year 7 students. It contains material on the language of probability, experiments and counting, and the probability of an event, and explains the mathematical use of the terms 'random' and 'randomly'. ...

Text

Thumb wrestling tournament

In this introductory activity students use a simple thumb-wrestling tournament to analyse a series of matches in which there can only be one victor. Students work in small groups to explore different ways of mapping out the events of a tournament, introducing the concept of constructing sample spaces and tree diagrams as ...

Downloadable

Prediction vs. reality

This lesson explores how we perceive randomness. Students toss coins and record their observations while half of the class fake their results. They will then explore the differences between the random results and fake results sets and investigate theoretical probabilities for large numbers of coin flips. The lesson is outlined ...

Online

Conduct chance experiments: Year 7 – planning tool

This planning resource for Year 7 is for the topic of Conduct chance experiments. Students predict the frequency of an outcome of repeated chance experiments. They conduct simulations using digital tools to generate and record the outcomes, and observe the effect of many trials on the outcome. They then compare observed ...

Online

TIMES Module 12: Statistics and Probability: chance, year 7 - teacher guide

This is a 13-page guide for teachers. It continues the development of probability. A careful consideration of outcomes and equally likely outcomes is undertaken. In year 7, students revisit simple situations with a clear and easily listed number of possible outcomes that can, or may, be assumed to be equally likely. In ...

Interactive

Syllabus bites: The language of Venn diagrams

Interactive activities supporting students learning to describe regions of a Venn diagram.

Interactive

Syllabus bites: Introducing Venn diagrams

An interactive resource in which students explore, interpret and draw Venn diagrams with two attributes.

Online

TIMES Module 1: Number and Algebra: sets and Venn diagrams - teacher guide

This is a 22-page guide for teachers. The module provides an introduction to set notation and demonstrates its use in logic, probability and functions.

Interactive

Syllabus bites: Using Venn diagrams to solve problems

Worked examples and guided exercises to assist students learning to use Venn diagrams as an organiser for solving mathematical problems.

Interactive

Syllabus bites: More Venn diagrams

An interactive exploration of Venn diagrams with three attributes.

Interactive

Syllabus bites: Venn diagrams and Two-way tables

An interactive exploration of the relationship between Venn diagrams and Two-way tables.