Mathematics · 1st Year

Active learning ideas

Fair and Unfair Games

Active learning helps students grasp probability concepts in Fair and Unfair Games by letting them test ideas in real time. When students roll dice, flip coins, and spin spinners, they connect abstract chance to something they can see and measure. This hands-on experience builds lasting understanding because students own the data they collect and analyze.

• NCCA Curriculum Specifications
• NCCA: Primary - Data

• 20–45 min
• Pairs → Whole Class
• 4 activities

Activity 01

• Stations Rotation
• 45 min · Small Groups

Stations Rotation: Chance Game Stations

Prepare three stations: coin toss (20 flips per player), dice roll (roll until 6 for win), biased spinner (unequal sections). Small groups spend 10 minutes at each, tallying wins for two players. After rotations, groups share data to classify fairness.

Differentiate between a fair game and an unfair game.

Facilitation Tip

For Predict and Play, have students write their predictions in their notebooks before playing to make their thinking visible.

What to look for

Present students with a description of a simple game (e.g., 'Player A wins if they roll an even number on a die, Player B wins if they roll an odd number'). Ask: 'Is this game fair? Explain your reasoning in one sentence.'

• Remember
• Understand
• Apply
• Analyze
• Self-Management
• Relationship Skills

Activity 02

• Plan-Do-Review
• 25 min · Pairs

Pairs: Test and Tally

Pairs play a partner-chosen game like heads/tails best of 30. Each records wins on a shared chart. They discuss if outcomes favor one player and predict adjustments for fairness.

Design a simple game that is fair for everyone playing.

What to look for

After playing a coin toss game where one player wins on heads and the other on tails, ask: 'If we tossed the coin 10 times and got 7 heads and 3 tails, what does this tell us about the fairness of the game? What would we need to do to be more certain?'

• Remember
• Apply
• Analyze
• Self-Management
• Decision-Making
• Self-Awareness

Activity 03

• Plan-Do-Review
• 35 min · Whole Class

Whole Class: Fair Game Design Challenge

Display rules for student-designed games on board. Class votes on fairness, then plays top three in rounds, updating a group tally chart. Vote again based on trial data.

Justify why a game might be unfair to some players.

What to look for

Provide students with a blank game board and dice. Ask them to design a simple game for two players. On the back, they should write one sentence explaining why their game is fair or one sentence explaining how they would make it fair.

• Remember
• Apply
• Analyze
• Self-Management
• Decision-Making
• Self-Awareness

Activity 04

• Plan-Do-Review
• 20 min · Individual

Individual: Predict and Play

Students predict fair/unfair for given games, then play 15 solo trials, logging results in notebooks. They note matches between predictions and data.

Differentiate between a fair game and an unfair game.

What to look for

Present students with a description of a simple game (e.g., 'Player A wins if they roll an even number on a die, Player B wins if they roll an odd number'). Ask: 'Is this game fair? Explain your reasoning in one sentence.'

• Remember
• Apply
• Analyze
• Self-Management
• Decision-Making
• Self-Awareness

A few notes on teaching this unit

Successful teachers begin with concrete tools like dice and spinners so students focus on outcomes rather than abstract formulas. They guide students to notice patterns over many trials, linking frequency to probability. Avoid rushing to definitions; let students discover fairness through repeated testing and discussion. Research shows that students learn probability best when they actively test predictions and adjust their views.

By the end of these activities, students will confidently define fair and unfair games by using evidence from repeated trials. They will explain fairness using probability language and adjust game rules based on data. Students will also critique claims about fairness using their own test results.

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Watch Out for These Misconceptions

• During Station Rotation, watch for students who assume a game is fair just because both players have a turn.

  Direct students to compare their tallies after 20 trials. Ask them to explain why identical rules do not guarantee equal odds, especially if the tools are biased.

• During Test and Tally, watch for students who conclude a game is unfair after only five trials.

  Have students extend their trials to 50 rolls and compare their early results to the final totals. Ask them to explain how their conclusion changed with more data.

• During Fair Game Design Challenge, watch for students who create a game using numbers without checking section sizes.

  Ask students to measure and compare spinner sections before testing. Have them calculate expected outcomes and rerun trials to confirm their design.

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Methods used in this brief

• Stations Rotation
• Plan-Do-Review