Mathematics · Foundation · Sorting Objects into Groups · Term 4

Certain, Possible, and Impossible Events

Students understand and calculate the probability of complementary events.

• ACARA Content Descriptions
• AC9M7P01

About This Topic

Foundation students explore basic probability by sorting events into certain, possible, and impossible categories. They examine real-world examples, such as the sun rising tomorrow (certain), drawing a green counter from a bag of only red counters (impossible), or finding a lost toy at school (possible). This builds early language for chance and encourages reasoning about likelihoods through familiar contexts.

Within the Australian Curriculum's statistics strand, this topic lays groundwork for data handling and later probability calculations, including complementary events. Students connect sorting objects to chance experiments, using concrete tools like bags of counters, spinners, and picture cards. Class discussions reinforce vocabulary and shared understanding of terms.

Active learning benefits this topic because hands-on sorting and prediction activities make abstract ideas concrete. Children test predictions with physical objects, discuss outcomes in pairs, and adjust thinking based on evidence. This approach boosts engagement, vocabulary use, and confidence in probabilistic reasoning from the start.

Key Questions

1. Is it certain, possible, or impossible that the sun will rise tomorrow?
2. Can a green counter come out of a bag that only has red counters?
3. What is something that is impossible to happen at school?

Learning Objectives

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

Before You Start

Sorting and Classifying Objects

Why: Students need to be able to group objects based on shared attributes to understand how events can be categorized.

Basic Understanding of Time (Days, Tomorrow)

Why: Understanding concepts like 'tomorrow' is necessary to discuss events that are certain or impossible in the near future.

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.

Watch Out for These Misconceptions

Common Misconception

Certain events might still not happen.

What to Teach Instead

Certain means it will always happen, like the school bell ringing at recess. Use repeated trials with spinners or bags in small groups to show consistency. Peer discussions help students contrast with possible events, building precise language.

Common Misconception

Impossible means it could happen someday.

What to Teach Instead

Impossible events cannot happen under the given conditions, like a blue apple from a fruit bowl of reds. Hands-on sorting cards and testing bags reveals no outcomes match impossibles. Group sharing corrects overgeneralising from rare possibilities.

Common Misconception

Possible events are as likely as certain ones.

What to Teach Instead

Possible means it might happen but not always. Prediction activities with varied bags show differences in frequency. Collaborative charting of draws helps students see patterns and distinguish likelihoods.

Active Learning Ideas

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.

25 min·Pairs

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.

35 min·Small Groups

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.

30 min·Whole Class

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.

40 min·Small Groups

Real-World Connections

• Weather forecasters use probability to describe the chance of rain, stating if it is certain, possible, or impossible for a given day.
• Game designers consider possibility when creating board games or card games, ensuring some outcomes are possible but not always certain to keep the game engaging.
• Traffic engineers assess the possibility of accidents at intersections, identifying impossible scenarios (like a car flying through a solid wall) versus possible ones that require safety measures.

Assessment Ideas

Exit Ticket

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.

Quick Check

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?'

Discussion Prompt

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.

Frequently Asked Questions

How to teach certain, possible, and impossible events in Foundation maths?

Start with familiar questions like sun rising or school routines. Use picture cards for sorting into columns, then test with bags of counters. Daily discussions build vocabulary. Concrete manipulatives ensure all students, including diverse learners, grasp concepts through touch and talk, aligning with ACARA's emphasis on reasoning.

What activities work best for probability in Foundation?

Hands-on tasks like bag draws, spinner votes, and event card sorts engage young learners. Vary materials to include colours, shapes, and school scenarios. Keep sessions short, 25-40 minutes, with clear prediction-test-discuss steps. These build data skills and excitement for stats strand progression.

How can active learning help students understand certain, possible, and impossible events?

Active approaches like pair sorting and group bag trials let students predict, test, and observe outcomes directly. Manipulating counters or spinners makes categories tangible, while discussions refine ideas through peer input. This reduces misconceptions, boosts language, and fosters reasoning skills essential for probability. Sessions promote inclusion as all contribute via talk and action.

Common misconceptions in teaching basic probability to Foundation students?

Students often blur certain with likely possibles or think impossibles are rare possibles. Address via repeated trials showing zero outcomes for impossibles. Use visual charts from class activities to compare frequencies. Structured pair talks correct ideas collaboratively, ensuring solid foundations for complementary events later.