Chance and Likelihood

Active learning helps students grasp chance and likelihood because probability concepts feel abstract until experienced through real events. Hands-on experiments let students feel randomness, test predictions, and correct misunderstandings immediately.

• Year 2
• Mathematics
• 3 activities
• 20 min–40 min

Learning Objectives

1. Identify possible outcomes for familiar events.
2. Classify events as certain, likely, unlikely, or impossible.
3. Explain how changing the conditions of a game can alter the likelihood of winning.
4. Compare the likelihood of two different events occurring.

Simulation Game

⏱ 30 min·Pairs

Simulation Game: The Impossible Bag

The teacher has a bag of only blue marbles. Students must use chance language to describe the likelihood of pulling out a red marble ('impossible') or a blue one ('certain'). They then work in pairs to create their own 'likely' and 'unlikely' bags for a partner to guess.

Prepare & details

Why are some events certain while others are impossible?

Facilitation Tip: During The Impossible Bag, have each student draw one marble without looking, then record the outcome to show that even an unlikely event can happen.

Setup: Flexible space for group stations

Materials: Role cards with goals/resources, Game currency or tokens, Round tracker

• Apply
• Analyze
• Evaluate
• Create
• Social Awareness
• Decision-Making

Inquiry Circle

⏱ 40 min·Small Groups

Inquiry Circle: The Fair Game?

Groups are given a spinner that is 3/4 red and 1/4 blue. They must predict which colour will 'win' after 20 spins. After conducting the experiment, they discuss why the result happened and how they could change the spinner to make it 'fair' (even chance).

Prepare & details

How can we change a game to make it more or less likely for someone to win?

Facilitation Tip: In The Fair Game?, ask students to explain why one version of the game is fairer than another using the language of chance.

Setup: Groups at tables with access to source materials

Materials: Source material collection, Inquiry cycle worksheet, Question generation protocol, Findings presentation template

• Analyze
• Evaluate
• Create
• Self-Management
• Self-Awareness

Think-Pair-Share

⏱ 20 min·Whole Class

Think-Pair-Share: Certain or Impossible?

The teacher calls out events (e.g., 'The sun will rise tomorrow', 'An elephant will fly into the room'). Students move to different sides of the room labelled 'Certain' or 'Impossible' and then explain their choice to a partner.

Prepare & details

What does it mean for something to be likely but not certain?

Facilitation Tip: For Certain or Impossible?, pause after each scenario to ask students to show their answers on whiteboards before discussing.

Setup: Standard classroom seating; students turn to a neighbor

Materials: Discussion prompt (projected or printed), Optional: recording sheet for pairs

• Understand
• Apply
• Analyze
• Self-Awareness
• Relationship Skills

Teaching This Topic

Teach probability through guided discovery, starting with simple events and gradually introducing more complex language. Avoid over-explaining—let students experience chance first, then label it. Research shows that concrete experiences before abstract terms build stronger understanding in early years.

What to Expect

By the end of these activities, students should confidently use probability language to describe events and justify their choices with evidence from experiments. They should understand that unlikely events still have a chance to occur and that outcomes are not controlled by effort.

Watch Out for These Misconceptions

Common Misconception

During The Impossible Bag, watch for students who insist an 'unlikely' event cannot happen.

What to Teach Instead

After drawing a rare marble, have students update their thinking by saying, 'I thought it would not happen, but it did, so it is possible but unlikely.'

Common Misconception

During The Fair Game?, watch for students who believe they can influence outcomes through their actions.

What to Teach Instead

Require all students to use the same shaking technique and observe that the outcome is the same regardless of effort.

Assessment Ideas

Quick Check

After Certain or Impossible?, present scenarios like 'It will rain tomorrow' or 'A tossed coin lands on heads.' Ask students to classify each using probability language and justify one choice aloud.

Discussion Prompt

During The Fair Game?, ask students to suggest changes to a coin flip game to make it more likely for one player to win, and explain their reasoning using terms like 'likely' or 'unlikely'.

Exit Ticket

After The Impossible Bag, give each student a bag with 2 red marbles and 6 blue marbles. Ask them to write: 1. What colour is it likely to pick? 2. What colour is it unlikely to pick? 3. Is it certain or impossible to pick a green marble?

Extensions & Scaffolding

• Challenge: Ask students to design their own unfair game and explain how they made it unfair using probability terms.
• Scaffolding: Provide sentence stems like 'It is ____ that ____ will happen because...' for students to complete.
• Deeper: Introduce a two-step experiment, such as flipping a coin and spinning a spinner, to explore combined probabilities.

Key Vocabulary

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 lay an egg.
Likely	An event that has a good chance of happening, but is not guaranteed. For example, it is likely to be sunny in Australia in summer.
Unlikely	An event that has a small chance of happening. For example, it is unlikely to snow in Queensland.
Might happen	An event that could happen, but we cannot be sure. For example, you might see a kangaroo on a bushwalk.