Mathematics · Foundation

Active learning ideas

Likely and Unlikely Events

Active learning helps students grasp likely and unlikely events because probability concepts are abstract and need concrete, repeated experiences to build intuition. Sorting, spinning, and voting make chance visible, turning words like ‘likely’ into lived understanding rather than memorized definitions.

• ACARA Content Descriptions
• AC9M7P01

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

Activity 01

• Hot Seat
• 30 min · Pairs

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.

If I pick a counter from this bag without looking, is it more likely to be red or blue?

Facilitation Tip

During Counter Bag Trials, circulate and ask pairs to predict the next draw before they pick, making likelihood a conversation rather than a guess.

What to look for

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.'

• Apply
• Analyze
• Evaluate
• Social Awareness
• Self-Awareness

Activity 02

• Hot Seat
• 40 min · Small Groups

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.

What events are very likely to happen today?

Facilitation Tip

At Unequal Spinner Stations, have students first predict the most likely section without spinning, then test their ideas to see if their reasoning matches the results.

What to look for

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.

• Apply
• Analyze
• Evaluate
• Social Awareness
• Self-Awareness

Activity 03

• Hot Seat
• 25 min · Whole Class

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.

Can you think of something that is unlikely to happen at school?

Facilitation Tip

In the School Events Vote, model how to phrase certain, likely, unlikely, and impossible using school routines before students share their own examples.

What to look for

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.

• Apply
• Analyze
• Evaluate
• Social Awareness
• Self-Awareness

Activity 04

• Hot Seat
• 20 min · Individual

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.

If I pick a counter from this bag without looking, is it more likely to be red or blue?

What to look for

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.'

• Apply
• Analyze
• Evaluate
• Social Awareness
• Self-Awareness

A few notes on teaching this unit

Teach this by balancing prediction, trial, and reflection in every activity. Avoid rushing to labels before students have experienced chance outcomes multiple times. Research shows that repeated trials with visual recording help students move from ‘all outcomes are equal’ to proportional reasoning. Keep language consistent and tie it directly to what they see and do.

Successful learning shows when students use probability language correctly, justify choices with evidence, and connect counts to likelihood without relying on guessing. They should explain why one outcome is more likely than another using the materials in front of them.

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Watch Out for These Misconceptions

• During Counter Bag Trials, watch for students who assume the first few draws represent the whole bag’s proportions.

  Pause after 10 draws and ask pairs to compare their tallies to the actual contents. Have them adjust predictions for the next 10 draws based on what they now know.

• During Unequal Spinner Stations, watch for students who think a section that ‘looks bigger’ is always more likely, regardless of proportions.

  Ask students to measure spinner sections with paper clips or mark 10 equal parts, then tally outcomes to see if the visual matches the math.

• During Outcome Listing Game, watch for students who list only outcomes they saw in early trials and miss possible but unobserved ones.

  Before any trials, have students list every possible outcome on a whiteboard and check it against actual results, circling any they missed in their initial writing.

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Methods used in this brief

• Hot Seat