Foundations of Mathematical Thinking · 1st Year

Active learning ideas

Likelihood and Chance

Active learning helps students grasp likelihood and chance because probability is a concrete concept best understood through hands-on experiences. When students physically sort events, spin spinners, or toss coins, they see how chance works in real time, making abstract ideas like 'unlikely' and 'likely' more tangible.

• NCCA Curriculum Specifications
• NCCA: Primary - Data

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

Activity 01

• Four Corners
• 30 min · Small Groups

Sorting Stations: Event Cards

Prepare cards with 20 everyday events, like 'it might rain' or 'pigs fly'. Students sort them into possible, impossible, likely, unlikely trays at four stations, then justify choices with a partner. Regroup to share one example per category.

Explain why some things are impossible while others are just unlikely?

Facilitation Tip

During Sorting Stations, circulate and ask students to justify their placements by pointing to specific features of the event cards.

What to look for

Present students with five scenario cards (e.g., 'A cat can bark', 'It will rain tomorrow', 'The sun will rise in the east', 'You will grow wings tonight', 'You will eat lunch today'). Ask students to sort these cards into four labeled hoops: Impossible, Unlikely, Possible, Likely. Observe their sorting and ask clarifying questions for one or two cards.

• Understand
• Analyze
• Evaluate
• Self-Awareness
• Social Awareness

Activity 02

• Four Corners
• 25 min · Pairs

Prediction Spinner Game

Create spinners divided into four colors, each labeled with a chance term. Pairs spin 10 times, predict outcomes before spinning, tally results, and discuss if predictions matched reality. Adjust spinner sections to change likelihoods mid-game.

Analyze if we can ever be 100 percent sure about what will happen next?

Facilitation Tip

For the Prediction Spinner Game, ensure students record their predictions before spinning to build anticipation and reflection.

What to look for

Pose the question: 'Can we ever be 100 percent sure about what will happen tomorrow?' Facilitate a class discussion, encouraging students to provide examples of things they are very sure about (e.g., the sun rising) and things they are less sure about (e.g., winning the lottery). Guide them to use the vocabulary terms.

• Understand
• Analyze
• Evaluate
• Self-Awareness
• Social Awareness

Activity 03

• Four Corners
• 40 min · Whole Class

Weather Chance Journal

Students track daily weather forecasts individually for a week, noting if rain is likely or unlikely, then compare journals in whole class. Vote on tomorrow's prediction and check results next day.

Predict how knowing the past helps us predict what might happen in the future?

Facilitation Tip

In the Weather Chance Journal, model how to note both the forecast and their own observations to connect data to real-life decisions.

What to look for

On a small slip of paper, ask students to write down one event they think is 'unlikely' and one event they think is 'impossible'. For each, they should write one sentence explaining their reasoning, referencing why it cannot happen or has a very low chance of happening.

• Understand
• Analyze
• Evaluate
• Self-Awareness
• Social Awareness

Activity 04

• Four Corners
• 35 min · Small Groups

Coin Toss Challenge

In small groups, predict heads or tails for 20 tosses, record actual outcomes on charts. Discuss why even likely events like heads (50% chance) do not always happen as predicted.

Explain why some things are impossible while others are just unlikely?

What to look for

Present students with five scenario cards (e.g., 'A cat can bark', 'It will rain tomorrow', 'The sun will rise in the east', 'You will grow wings tonight', 'You will eat lunch today'). Ask students to sort these cards into four labeled hoops: Impossible, Unlikely, Possible, Likely. Observe their sorting and ask clarifying questions for one or two cards.

• Understand
• Analyze
• Evaluate
• Self-Awareness
• Social Awareness

A few notes on teaching this unit

Teach probability through repeated, small trials to show patterns without implying certainty. Avoid overemphasizing single outcomes, as this reinforces the misconception that past events determine future ones. Research suggests using collaborative discussions after activities to help students articulate uncertainty and refine their understanding through peer feedback.

Successful learning is visible when students confidently use terms like possible, likely, unlikely, and impossible to describe events. They should explain their reasoning clearly and adjust their predictions based on evidence from their activities.

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Watch Out for These Misconceptions

• During Sorting Stations, watch for students labeling unlikely events as impossible.

  Direct students to test unlikely events by spinning a spinner set to favor those outcomes, then ask if the event truly cannot happen or just has a low chance.

• During Coin Toss Challenge, watch for students assuming past tosses predict future outcomes.

  Have pairs compare their results and discuss why a run of tails doesn’t guarantee the next toss will be heads, using the activity’s repeated trials as evidence.

• During Prediction Spinner Game, watch for students claiming possible events are certain.

  After the game, facilitate a class debate where students defend why possible events, like spinning red, still leave room for uncertainty in a single trial.

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Methods used in this brief

• Four Corners