Exploring Chance: Likely and Unlikely Events

Active learning helps students grasp probability because chance concepts feel abstract until students see them play out. When they spin, roll, or flip objects, repeated trials turn vague ideas into measurable data. Concrete experiences build the foundation for later abstract reasoning about likelihoods, making the topic stick long after the lesson ends.

• 2nd Year
• Foundations of Mathematical Thinking
• 4 activities
• 25 min–45 min

Learning Objectives

1. Classify everyday events as certain, likely, unlikely, or impossible based on given criteria.
2. Explain the reasoning behind classifying an event's likelihood using precise probability language.
3. Compare the probability of two different events and justify which is more or less likely.
4. Predict the outcome of a simple random event, such as a coin toss or dice roll, and describe its likelihood.

Collaborative Problem-Solving

⏱ 35 min·Pairs

Spinner Sorting: Event Probability Spinners

Provide spinners divided into unequal sections labeled certain, likely, unlikely, impossible. Students spin for given events like 'it rains in Ireland tomorrow' and sort cards with events into matching sections based on results. Pairs discuss and record why an event fits a category. Conclude with class sharing of surprising outcomes.

Prepare & details

Is it likely or unlikely that it will snow in July in Ireland?

Facilitation Tip: During Spinner Sorting, have students physically move event cards to probability zones before discussing, ensuring kinesthetic engagement.

Setup: Groups at tables with problem materials

Materials: Problem packet, Role cards (facilitator, recorder, timekeeper, reporter), Problem-solving protocol sheet, Solution evaluation rubric

• Apply
• Analyze
• Evaluate
• Create
• Relationship Skills
• Decision-Making
• Self-Management

Collaborative Problem-Solving

⏱ 45 min·Small Groups

Dice Prediction Relay: Likely Rolls

Teams line up and predict if numbers 1-6 are likely on a die, then roll 10 times per team member, tallying results on a shared chart. Rotate roles for predictor, roller, and recorder. Groups compare tallies to refine predictions about impossible rolls like 7.

Prepare & details

Can you tell me something that will definitely happen today?

Facilitation Tip: For Dice Prediction Relay, circulate and ask groups to explain their predictions before rolling, prompting them to justify their reasoning.

Setup: Groups at tables with problem materials

Materials: Problem packet, Role cards (facilitator, recorder, timekeeper, reporter), Problem-solving protocol sheet, Solution evaluation rubric

• Apply
• Analyze
• Evaluate
• Create
• Relationship Skills
• Decision-Making
• Self-Management

Collaborative Problem-Solving

⏱ 30 min·Whole Class

Weather Chance Circle: Irish Events

Sit in a circle; each student shares a July event like 'snow falls' and class votes likely or unlikely with thumbs up or down. Tally votes on a board and discuss evidence from Irish weather knowledge. Extend by creating a class probability poster.

Prepare & details

Is it possible to roll a 7 on a dice with numbers 1 to 6?

Facilitation Tip: In Weather Chance Circle, invite students to share personal experiences with Irish weather to connect abstract probabilities to lived reality.

Setup: Groups at tables with problem materials

Materials: Problem packet, Role cards (facilitator, recorder, timekeeper, reporter), Problem-solving protocol sheet, Solution evaluation rubric

• Apply
• Analyze
• Evaluate
• Create
• Relationship Skills
• Decision-Making
• Self-Management

Collaborative Problem-Solving

⏱ 25 min·Individual

Coin Flip Challenges: Personal Predictions

Students predict outcomes for 20 coin flips, marking likely heads or tails on worksheets. They flip individually, then pair to compare data and adjust predictions. Share class averages to see patterns emerge from chance.

Prepare & details

Is it likely or unlikely that it will snow in July in Ireland?

Facilitation Tip: During Coin Flip Challenges, encourage students to record results in a shared tally chart to highlight patterns emerging from multiple trials.

Setup: Groups at tables with problem materials

Materials: Problem packet, Role cards (facilitator, recorder, timekeeper, reporter), Problem-solving protocol sheet, Solution evaluation rubric

• Apply
• Analyze
• Evaluate
• Create
• Relationship Skills
• Decision-Making
• Self-Management

Teaching This Topic

Teach probability through repeated, hands-on trials so students experience randomness firsthand. Avoid relying solely on theoretical explanations, as young learners need concrete evidence to trust their conclusions. Use group work to normalize mistakes and normalize variation in outcomes, reinforcing that probability describes patterns over many trials, not single events. Research shows this approach builds lasting understanding of chance concepts better than abstract definitions alone.

What to Expect

Successful learning happens when students confidently use probability language to describe events and support their choices with evidence. They should justify their reasoning with real-world observations, not guesses, and recognize that some events are more likely than others. Evidence from their own trials becomes the basis for their conclusions.

Watch Out for These Misconceptions

Common Misconception

During Dice Prediction Relay, watch for students who assume every outcome on a die is equally likely, such as predicting a 1 or 6 with the same chance.

What to Teach Instead

Pause the relay and ask students to list all possible outcomes on a die. Then, have them roll the die 20 times as a class, tallying results to show that some numbers appear more often than others, making it clear that not all outcomes are equally probable.

Common Misconception

During Weather Chance Circle, watch for students who treat unlikely events as impossible, such as claiming it is impossible to have snow in Ireland in summer.

What to Teach Instead

Show students real weather data or news articles about rare summer snow events in Ireland. Ask them to vote on the likelihood of such events and track actual occurrences over time to illustrate that unlikely events do happen occasionally.

Common Misconception

During Coin Flip Challenges, watch for students who believe personal luck or superstition affects outcomes, such as thinking a certain student can make heads appear more often.

What to Teach Instead

Have each student flip the same coin the same number of times and compare results. Point out that the pattern of heads and tails remains random regardless of who flips, reinforcing that chance is not influenced by individuals.

Assessment Ideas

Quick Check

After Spinner Sorting, present students with cards showing scenarios like 'A dog wearing shoes' or 'The school day ending at 3:00 PM'. Ask students to hold up a card labeled 'Certain', 'Likely', 'Unlikely', 'Impossible' and explain their choice in one sentence.

Discussion Prompt

During Coin Flip Challenges, pose the question: 'Is it more likely to flip heads or tails?' Ask students to discuss in pairs, then facilitate a whole-class conversation where they justify their answers and explain why the outcomes are equally likely based on their tally charts.

Exit Ticket

After Dice Prediction Relay, give each student a slip of paper. Ask them to write one event that is 'likely' and one that is 'impossible' in their school week, with a sentence explaining why each fits its category.

Extensions & Scaffolding

• Challenge students to design a spinner that lands on 'unlikely' more often than 'likely' and test it with peers.
• Scaffolding: Provide a word bank with probability terms for students to use when justifying their choices during Spinner Sorting.
• Deeper exploration: Ask students to research weather data for Ireland and compare their predictions from Weather Chance Circle to historical records.

Key Vocabulary

Likely	An event that has a high chance of happening. For example, it is likely to rain if the sky is full of dark clouds.
Unlikely	An event that has a low chance of happening. For example, it is unlikely to see a polar bear in the Sahara Desert.
Certain	An event that is guaranteed to happen. For example, the sun is certain to rise tomorrow.
Impossible	An event that cannot happen. For example, it is impossible to jump over the moon.