Foundations of Mathematical Thinking · 2nd Year

Active learning ideas

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.

• NCCA Curriculum Specifications
• NCCA: Primary - Data
• NCCA: Primary - Problem solving

• 25–45 min
• Pairs → Whole Class
• 4 activities

Activity 01

• 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.

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.

What to look for

Present students with cards showing different scenarios (e.g., 'A cat barking', 'The next person you meet is wearing blue', 'Tomorrow's date'). Ask students to hold up a card (or point to a poster) labeled 'Certain', 'Likely', 'Unlikely', 'Impossible' that best describes each scenario and briefly explain their choice.

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

Activity 02

• 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.

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.

What to look for

Pose the question: 'Is it more likely to flip heads or tails on a fair coin?' Ask students to discuss in pairs, using the vocabulary learned. Then, facilitate a whole-class discussion, asking students to justify their answers and explain why the outcomes are equally likely.

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

Activity 03

• 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.

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.

What to look for

Give each student a slip of paper. Ask them to write down one event that is 'certain' and one event that is 'impossible' in their own lives. They should then write one sentence explaining why each event fits its category.

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

Activity 04

• 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.

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.

What to look for

Present students with cards showing different scenarios (e.g., 'A cat barking', 'The next person you meet is wearing blue', 'Tomorrow's date'). Ask students to hold up a card (or point to a poster) labeled 'Certain', 'Likely', 'Unlikely', 'Impossible' that best describes each scenario and briefly explain their choice.

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

A few notes on teaching this unit

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.

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.

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Watch Out for These Misconceptions

• 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.

  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.

• 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.

  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.

• 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.

  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.

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Methods used in this brief

• Collaborative Problem-Solving