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Foundations of Mathematical Thinking · 1st Class

Active learning ideas

Playing and Describing Simple Games

Active learning works for this topic because first graders build fairness concepts through repeated, hands-on trials. When children physically toss coins, spin spinners, and roll dice, they see randomness in action. Seeing data unfold in real time helps them move from guessing to noticing patterns in chance-based outcomes.

NCCA Curriculum SpecificationsNCCA: Junior Cycle - Strand 3: Statistics and Probability - SP.3.3NCCA: Junior Cycle - Strand 3: Statistics and Probability - SP.3.4
20–45 minPairs → Whole Class4 activities

Activity 01

Role Play30 min · Whole Class

Whole Class: Coin Toss Challenge

Display a large coin on the board or use a real one. Have the whole class predict heads or tails for 20 tosses, then tally results live on a shared chart. Discuss if outcomes match predictions and vote on game fairness. End with students suggesting rule changes for balance.

Is this game fair for everyone who plays? How do you know?

Facilitation TipDuring the Coin Toss Challenge, model how to hold the coin, flip it, and record results immediately to avoid later guesswork.

What to look forProvide each student with a simple game, like a coin toss for heads or tails. Ask them to play the game 10 times and record the outcomes. Then ask: 'Is this game fair? How do you know?' Observe their tallies and listen to their justifications.

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Activity 02

Role Play45 min · Small Groups

Small Groups: Spinner Fairness Stations

Prepare spinners divided into 2-4 equal or unequal sections. Groups spin 30 times at two stations, record colors or numbers on individual sheets, and compare frequencies. Rotate stations, then share which spinner seems fair and why based on tallies.

What might happen on the next turn of this game?

Facilitation TipAt the Spinner Fairness Stations, remind groups to spin the spinner only once per turn, keeping trials independent.

What to look forGive students a card with a spinner divided into 4 equal sections (2 red, 1 blue, 1 green). Ask them to predict what color is most likely to be landed on after 10 spins. On the back, they should write one sentence explaining their prediction.

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Activity 03

Role Play25 min · Pairs

Pairs: Dice Roll Predictions

Partners take turns rolling a die 20 times, predicting the most common number first. Tally results together on paper and graph them simply with tallies. Discuss who might win a game to get a six and test a new prediction round.

Can you explain the rules of a simple game and say who you think is most likely to win?

Facilitation TipFor Dice Roll Predictions, provide blank tables with rows for each turn so pairs can fill in predictions before rolling.

What to look forPresent two simple games to the class. For example, Game A: Roll a die, win if you roll a 6. Game B: Flip a coin, win if it's heads. Ask students to discuss in pairs: 'Which game do you think is fairer? Why?' Facilitate a class discussion to compare their reasoning.

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Activity 04

Role Play20 min · Individual

Individual: Design a Fair Game

Each student draws a simple game board with spinner or coin rules. Test it 10 times alone, note wins, and write one sentence on fairness. Share one with the class for quick feedback.

Is this game fair for everyone who plays? How do you know?

Facilitation TipDuring Design a Fair Game, circulate with sentence stems like 'This game is fair because...' to support verbal explanations.

What to look forProvide each student with a simple game, like a coin toss for heads or tails. Ask them to play the game 10 times and record the outcomes. Then ask: 'Is this game fair? How do you know?' Observe their tallies and listen to their justifications.

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Templates

Templates that pair with these Foundations of Mathematical Thinking activities

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A few notes on teaching this unit

Teachers should avoid over-explaining probability terms upfront. Instead, let students experience chance through play, then introduce language naturally during debriefs. Research shows that first graders grasp fairness best when they collect their own data, compare results, and explain patterns to peers. Avoid reinforcing the idea that fairness means equal wins per turn; focus on equal chances per turn.

Successful learning looks like students using terms like fair, chance, and likely while explaining their reasoning. They should compare their small-group tallies to whole-class charts and adjust their fairness judgments based on evidence. Clear rules, accurate tallies, and peer discussion show understanding beyond single-game experiences.


Watch Out for These Misconceptions

  • During the Coin Toss Challenge, watch for students believing that after five heads in a row, tails is 'due' next.

    Pause the challenge after five turns and ask the class to predict the next outcome. Record predictions, then flip again. Use the class chart to show that each flip has a 50% chance regardless of prior results.

  • During the Spinner Fairness Stations, watch for students declaring a spinner unfair after one trial where their color didn't appear.

    Prompt the group to spin 20 times and tally frequencies. Ask them to compare their color’s count to the total spins and discuss why variation is expected in short trials.

  • During Dice Roll Predictions, watch for students assuming that numbers they rolled last time are more likely this time.

    Have pairs roll the die twice to see that the numbers are independent. Ask them to predict the next roll while holding the die, then roll to check if their prediction matches.


Methods used in this brief