Mathematics · Foundation

Active learning ideas

Certain, Possible, and Impossible Events

Foundational probability makes abstract ideas concrete through movement and discussion. Hands-on sorting, drawing, and role-playing let students feel the difference between certainty, possibility, and impossibility in familiar settings. This active engagement strengthens both language development and probabilistic reasoning.

• ACARA Content Descriptions
• AC9M7P01

• 25–40 min
• Pairs → Whole Class
• 4 activities

Activity 01

• Plan-Do-Review
• 25 min · Pairs

Sorting Game: Event Cards

Prepare cards with pictures or simple sentences describing events, like 'It rains in the desert' or 'Lunchtime bell rings'. Students work in pairs to sort cards into three labelled columns: certain, possible, impossible. Pairs share one card from each column with the class for discussion.

Is it certain, possible, or impossible that the sun will rise tomorrow?

Facilitation Tip

Before the Sorting Game, model how to discuss disagreements using sentence stems like ‘I think it is certain because…’ and ‘I see it differently because…’ to build mathematical talk.

What to look for

Provide students with three picture cards: 1) A sun rising in the morning, 2) A cat laying an egg, 3) A student wearing a blue shirt tomorrow. Ask students to write 'Certain', 'Possible', or 'Impossible' under each picture and explain their choice for one card.

• Remember
• Apply
• Analyze
• Self-Management
• Decision-Making
• Self-Awareness

Activity 02

• Plan-Do-Review
• 35 min · Small Groups

Bag Draw: Counter Predictions

Place red and blue counters in opaque bags, varying ratios. Students predict if drawing a specific colour is certain, possible, or impossible, then test by drawing with replacement. Record results on a class chart and compare predictions to outcomes.

Can a green counter come out of a bag that only has red counters?

Facilitation Tip

During Bag Draw, circulate with a checklist to note which students are predicting outcomes versus simply guessing, and gently prompt them to explain their reasoning.

What to look for

Hold up a bag containing only red counters. Ask: 'Is it possible, certain, or impossible to pick a blue counter from this bag?' Then, hold up a bag with a mix of red and blue counters and ask: 'Is it possible, certain, or impossible to pick a red counter?'

• Remember
• Apply
• Analyze
• Self-Management
• Decision-Making
• Self-Awareness

Activity 03

• Plan-Do-Review
• 30 min · Whole Class

Spinner Challenge: Class Vote

Create spinners divided into sections labelled certain, possible, impossible. Students spin, vote on event likelihoods, and justify choices. Tally votes and revisit after group trials to refine understandings.

What is something that is impossible to happen at school?

Facilitation Tip

After the Spinner Challenge, ask each group to share one spinner outcome that surprised them and explain why it changed their thinking.

What to look for

Pose the question: 'What is something that is impossible to happen at school today?' Facilitate a class discussion where students share their ideas and explain why those events are impossible, reinforcing the concept.

• Remember
• Apply
• Analyze
• Self-Management
• Decision-Making
• Self-Awareness

Activity 04

• Plan-Do-Review
• 40 min · Small Groups

School Scenarios: Role-Play

List school events on cards. In small groups, students act out scenarios, deciding and explaining if each is certain, possible, or impossible. Groups present to class with props like toy bags or clocks.

Is it certain, possible, or impossible that the sun will rise tomorrow?

Facilitation Tip

In School Scenarios, provide props like a toy or a bell so students can act out events and verbalize their reasoning in context.

What to look for

Provide students with three picture cards: 1) A sun rising in the morning, 2) A cat laying an egg, 3) A student wearing a blue shirt tomorrow. Ask students to write 'Certain', 'Possible', or 'Impossible' under each picture and explain their choice for one card.

• Remember
• Apply
• Analyze
• Self-Management
• Decision-Making
• Self-Awareness

A few notes on teaching this unit

Start with familiar contexts students can visualize, then move quickly to hands-on trials. Repeat small experiments in small groups so every child experiences consistency and variation firsthand. Teacher language should focus on ‘will always happen,’ ‘might happen,’ or ‘can never happen under these conditions’ to build precise vocabulary.

Students will confidently label events using the words certain, possible, and impossible, and give clear reasons for their choices. They will also begin to compare likelihoods by noticing patterns in repeated trials and group discussions.

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Watch Out for These Misconceptions

• During the Spinner Challenge, watch for students who say a spinner outcome is certain because the spinner ‘could’ land there at some time.

  Use the same spinner in three trials: have students record outcomes and compare the consistency of results. Ask, ‘How many times did blue land on the pointer? Does it always happen? How do we describe events that don’t always happen?’

• During the Sorting Game, watch for students who label a blue apple from a bowl of red apples as possible because ‘some apples are different colors.’

  Have students physically sort picture cards into labeled trays while explaining their choices. When a card is placed incorrectly, ask, ‘Can any red apple turn blue? What must be true for this event to happen?’

• During Bag Draw, watch for students who place a ‘green counter’ card in the possible column because ‘maybe we’ll find one someday.’

  Ask students to test the card immediately by drawing five times from a bag with only red counters. After seeing no green counters appear, prompt them to re-label the event and explain why impossibility depends on the bag’s contents.

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Methods used in this brief

• Plan-Do-Review