Mathematics · Year 2

Active learning ideas

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.

• ACARA Content Descriptions
• AC9M2P01

• 20–40 min
• Pairs → Whole Class
• 3 activities

Activity 01

• 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.

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.

What to look for

Present students with scenarios like 'Rolling a 7 on a standard die' or 'The school principal having blue eyes'. Ask students to write 'Certain', 'Impossible', 'Likely', 'Unlikely', or 'Might Happen' next to each scenario.

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

Activity 02

• 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).

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.

What to look for

Pose the question: 'How could we change a simple game of chance, like flipping a coin, to make it more likely for one person to win?' Guide students to suggest changes such as flipping the coin twice and needing two heads, or having a special rule for one player.

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

Activity 03

• 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.

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.

What to look for

Give each student a bag with 3 red marbles and 1 blue marble. Ask them to write down: 1. What colour marble is it 'likely' to pick? 2. What colour marble is it 'unlikely' to pick? 3. Is it 'certain' or 'impossible' to pick a green marble?

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

A few notes on teaching this unit

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.

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.

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Watch Out for These Misconceptions

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

  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.'

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

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

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Methods used in this brief

• Simulation Game
• Inquiry Circle
• Think-Pair-Share