Mathematics · Foundation · Sorting Objects into Groups · Term 4

Likely and Unlikely Events

Students identify the sample space for simple chance experiments and list all possible outcomes.

• ACARA Content Descriptions
• AC9M7P01

About This Topic

In Foundation Mathematics under the Australian Curriculum, students explore likely and unlikely events by identifying the sample space for simple chance experiments, such as drawing counters from a bag, and listing all possible outcomes. This topic extends sorting objects into groups, using concrete materials like colored blocks or spinners to introduce probability language: certain, likely, unlikely, impossible. Key questions guide inquiry, such as whether picking a red counter is more likely than blue, or identifying very likely events at school.

Students develop early statistical reasoning by predicting outcomes, conducting trials, and observing patterns in results. This connects to ACARA standards like AC9M7P01, fostering skills in data collection and description that support later units on chance and probability. Repeated experiences build confidence in discussing uncertainty.

Active learning suits this topic perfectly. Physical experiments with bags or spinners allow students to test predictions through multiple trials, tally real data, and compare expectations to evidence. Pair and group discussions solidify vocabulary and reveal how proportions affect likelihood, making abstract ideas concrete and engaging.

Key Questions

1. If I pick a counter from this bag without looking, is it more likely to be red or blue?
2. What events are very likely to happen today?
3. Can you think of something that is unlikely to happen at school?

Learning Objectives

• Identify all possible outcomes for simple chance experiments.
• Classify events as certain, likely, unlikely, or impossible.
• Compare the likelihood of two different outcomes in a chance experiment.
• Explain why one event is more likely than another based on the sample space.

Before You Start

Sorting and Classifying Objects

Why: Students need to be able to group objects based on attributes like color to understand the concept of outcomes in a set.

Counting and Cardinality

Why: Understanding how to count objects is essential for identifying the number of possible outcomes and comparing quantities.

Key Vocabulary

Sample Space	The set of all possible outcomes of a chance experiment. For example, the sample space for flipping a coin is heads and tails.
Outcome	A single possible result of a chance experiment. For example, getting a '3' when rolling a die is one outcome.
Likely	An event that has a good chance of happening. For example, it is likely to rain if the sky is full of dark clouds.
Unlikely	An event that has a small chance of happening. For example, it is unlikely to snow in Australia during summer.
Certain	An event that is guaranteed to happen. For example, the sun is certain to rise tomorrow.
Impossible	An event that cannot happen. For example, it is impossible for a cat to fly without assistance.

Watch Out for These Misconceptions

Common Misconception

Every outcome in a bag or spinner has the same chance, regardless of quantity.

What to Teach Instead

Students ignore proportions initially. Conducting repeated trials in pairs and graphing tallies shows patterns emerge over time. Group sharing helps them explain how more items increase likelihood.

Common Misconception

Likely events always happen, with no room for surprise.

What to Teach Instead

This confuses probability with certainty. Role-playing predictions in small groups followed by actual trials demonstrates variability. Discussions refine their understanding of chance as uncertain yet predictable.

Common Misconception

Sample space includes only outcomes that occurred, not all possibilities.

What to Teach Instead

Trials alone reinforce this error. Pre-trial listing activities with visuals, then checking against results in whole class, build complete mental models. Peer review spots omissions effectively.

Active Learning Ideas

Pairs: Counter Bag Trials

Fill bags with varying numbers of red and blue counters, such as 3 red and 1 blue. Pairs predict the more likely color, draw with replacement 20 times, tally on charts, and discuss matches to predictions. Share one insight with the class.

30 min·Pairs

Small Groups: Unequal Spinner Stations

Prepare three spinners with unequal sections (e.g., 75% one color, 25% another). Groups spin each 15 times, record outcomes on group sheets, rotate stations, and compare data patterns across spinners.

40 min·Small Groups

Whole Class: School Events Vote

Show images of events like 'it rains at recess' or 'teacher arrives late'. Class votes likely or unlikely using hand signals, tallies on board, and justifies choices. Revisit after observing real events.

25 min·Whole Class

Individual: Outcome Listing Game

Provide simple scenarios like 'pick a shape from three: circle, square, triangle'. Students list or draw all possible outcomes, then simulate draws with cards and check completeness against class model.

20 min·Individual

Real-World Connections

• Weather forecasters use the terms likely and unlikely when predicting if rain will occur, helping people decide whether to carry an umbrella.
• Toy manufacturers use probability concepts when designing games. For instance, a spinner for a board game is designed so that landing on certain spaces is more likely than others to make the game interesting.

Assessment Ideas

Quick Check

Present students with a bag containing 5 red counters and 1 blue counter. Ask: 'If you pick one counter without looking, is it more likely to be red or blue? Explain your answer using the counters in the bag.'

Exit Ticket

Give each student a card with a simple chance scenario, such as 'Rolling a 6 on a standard die' or 'Flipping a coin and getting heads'. Ask students to write 'Likely', 'Unlikely', 'Certain', or 'Impossible' next to their scenario and draw a quick picture to represent it.

Discussion Prompt

Ask students: 'Think about our school day. Can you name one thing that is certain to happen? Can you name one thing that is impossible? Can you name one thing that is likely to happen, and one thing that is unlikely?' Encourage them to share their ideas with a partner.

Frequently Asked Questions

How to introduce sample space for chance experiments in foundation maths?

Start with concrete objects like bags of 4-6 counters. Guide students to name all colors present as the sample space before drawing. Use visuals like drawn bags to list outcomes explicitly. Follow with trials to connect theory to evidence, reinforcing ACARA alignment through hands-on prediction and observation over several lessons.

What activities work for likely and unlikely events in Australian foundation curriculum?

Use bags with unequal counters, spinners divided unevenly, or coin flips for heads/tails bias simulations. Students predict, trial repeatedly, tally, and discuss. These align with sorting units, build probability vocabulary, and meet AC9M7P01 by emphasizing sample spaces and outcome listing in everyday contexts.

How can active learning help foundation students grasp probability concepts?

Active approaches like manipulating spinners or drawing counters let students experience chance directly, tallying real data to see proportions matter. Pair trials encourage prediction-revision cycles, while group rotations expose variations. This makes uncertainty tangible, boosts engagement, and develops reasoning skills faster than passive explanation, as students own discoveries.

What are common misconceptions in teaching early chance and probability?

Students often think outcomes are equally likely despite unequal numbers, confuse likely with certain, or limit sample spaces to observed results. Address with repeated fair trials, proportion discussions, and pre-listing exercises. Active methods like station rotations and peer justifications correct these effectively, building accurate probabilistic thinking from foundation level.