## Activity Introduction

**Quick summary: **This lesson presents students with some explicit teaching around representing the probability of chance events from games (such as dice games) using fractions and decimals and placing the probability of given events on a probability number line. Following this, students conduct a simple chance experiment based on the outcome events of their ‘Sustainable STEM Sideshow Game’, collect event data and calculate the probability and event frequency of achieving a win in their Game.

This lesson sequence will require two standard classroom lessons of 45-50 minutes to complete.

**Learning intentions:**

- Students will describe events that are impossible and events that are certain
- Students will use the term ‘probability’ to describe the numerical value that represents the likelihood of an outcome of a chance experiments
- Students will use the term ‘frequency’ to describe the number of times a particular outcome occurs of a chance experiment
- Students will use the term ‘event’ to describe either one outcome or a collection of outcomes in the sample space of a chance experiment
- Students will represent and order probabilities of outcomes of chance experiments using fractions and decimals, e.g. ‘Equally likely’ would be placed at ½ or 0.5.

**21st century skills: **

### Australian Curriculum Mapping

**Content descriptions:**

Year 5 to 8 Mathematics:

- Recognise that probabilities range from 0 to 1 (ACMSP117)
- Conduct chance experiments with both small and large numbers of trials using appropriate digital technologies (ACMSP145)
- Compare observed frequencies across experiments with expected frequencies (ACMSP146)
- Assign probabilities to the outcomes of events and determine probabilities for events (ACMSP168)

**Syllabus outcomes:** MA3-19SP

**General capabilities:** Numeracy, Creative and Critical Thinking

**Relevant parts of Year 6 and 8 achievement standards:**

**By the end of Year 6**, students compare observed and expected frequencies and they interpret and compare a variety of data displays including those displays for two categorical variables. Students add, subtract and multiply decimals and divide decimals and they describe probabilities using simple fractions, decimals and percentages.

**By the end of Year 8,** students explain issues related to the collection of data and they use efficient mental and written strategies to carry out the four operations with integers. They solve everyday problems involving percentages and they solve problems involving profit and loss.

Students choose appropriate language to describe events and experiments determine the probabilities of complementary events and calculate the sum of probabilities.

**Topic:** STEM, Mathematics, Sustainability

**This lesson is part of the wider unit of work: Sustainable STEM Sideshow.**

**Time required:** 90 mins (two 45-50 min lessons)

**Level of teacher scaffolding:** High – Teacher needs to explain various mathematical concepts around probability and assist students to apply the outcomes and event frequencies in their own Sideshow Game to the mathematical conceptual framework around probability (see below).

**Resources required:**

- Calculators – per student (for calculating decimal probability ratios)
- Dice (either digital and projected on a data projector or whiteboard, or large dice that the whole class can see)
- Interactive whiteboard or data projector
- Student Worksheet for Lesson 2: Probability (one per student)
- Students’ ‘Sustainable STEM Sideshow Game’ prototypes, from Lesson 1 of this Unit – set up ready to ‘test’ in a tabloid arrangement in the classroom or learning space
- Whiteboard (or electronic whiteboard) with pens.

**Keywords:** Chance, probability, likelihood, impossible, certain, even chance, event, outcome, frequency.

*Cool Australia’s curriculum team continually reviews and refines our resources to be in line with changes to the Australian Curriculum.*