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.

• Foundation
• Mathematics
• 4 activities
• 25 min–40 min

Learning Objectives

1. Classify everyday events as certain, possible, or impossible based on given criteria.
2. Explain why an event is classified as certain, possible, or impossible using probabilistic language.
3. Identify real-world scenarios that represent certain, possible, and impossible outcomes.
4. Demonstrate understanding of chance by predicting outcomes of simple experiments.

Inquiry Circle

⏱ 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.

Prepare & details

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.

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

Inquiry Circle

⏱ 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.

Prepare & details

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.

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

Inquiry Circle

⏱ 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.

Prepare & details

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.

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

Inquiry Circle

⏱ 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.

Prepare & details

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.

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

Teaching This Topic

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.

What to Expect

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.

Watch Out for These Misconceptions

Common Misconception

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

What to Teach Instead

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?’

Common Misconception

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.’

What to Teach Instead

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?’

Common Misconception

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

What to Teach Instead

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.

Assessment Ideas

Exit Ticket

After the Sorting Game, give each student three picture cards: a sunrise tomorrow, a cat laying an egg, and a student wearing a blue shirt tomorrow. Ask students to write ‘Certain’, ‘Possible’, or ‘Impossible’ under each and explain one choice using their own words.

Quick Check

During the Bag Draw activity, hold up a bag with only red counters and ask, ‘Is it possible, certain, or impossible to pick a blue counter?’ Then hold up a mixed bag and ask, ‘Is it certain to pick a red counter?’ Listen for explanations that reference the bag’s contents.

Discussion Prompt

After the School Scenarios role-play, pose the question, ‘What is one thing that is impossible to happen at school today?’ Invite three students to share their ideas, then ask each to explain why it cannot happen under today’s conditions.

Extensions & Scaffolding

• Challenge: Provide a blank spinner template and ask students to design a spinner where ‘red’ is possible but not certain, then trade spinners with a partner to test predictions.
• Scaffolding: Give students a two-column chart labeled ‘Likely’ and ‘Unlikely’ to sort picture cards before introducing the three-way categories of certain, possible, impossible.
• Deeper exploration: Introduce a ‘chance continuum’ strip where students place labeled event cards along a line from impossible to certain, then add sticky notes for events they suggest themselves.

Key Vocabulary

Certain	An event that is guaranteed to happen. It will always occur.
Possible	An event that might happen, but is not guaranteed. It could happen or it might not.
Impossible	An event that cannot happen. It will never occur.
Chance	The likelihood or probability of something happening.