Foundations of Mathematical Thinking · 1st Year · Number Sense and Place Value · Autumn Term

Fair and Unfair Games

Students will explore simple games and determine if they are fair or unfair based on chance.

• NCCA Curriculum Specifications
• NCCA: Primary - Data

About This Topic

Fair and Unfair Games helps first-year students grasp basic probability by examining simple chance-based activities. They play games like coin tosses, dice rolls, and spinners, recording outcomes over repeated trials. Students tally wins for each player or side, then decide if results show equal chances, defining a fair game, or uneven odds, marking it unfair. This hands-on work connects to everyday play and builds confidence in using data to support claims.

In the NCCA Primary Data strand, this topic strengthens number sense through counting trials and place value in score tallies. It supports key questions on differentiating fairness, designing equitable games, and justifying imbalances with evidence. Students develop reasoning skills as they explain patterns from their records, preparing for later statistics.

Active learning excels with this topic because students discover probability through play and data collection. Testing games themselves reveals how chance evens out over trials, turning abstract ideas into personal insights. Group discussions of results encourage justification and peer teaching, deepening understanding and engagement.

Key Questions

1. Differentiate between a fair game and an unfair game.
2. Design a simple game that is fair for everyone playing.
3. Justify why a game might be unfair to some players.

Learning Objectives

• Classify games as fair or unfair based on analyzing recorded outcomes from repeated trials.
• Compare the probability of winning for each player in a given game by examining experimental data.
• Design a simple game with clear rules that demonstrates fairness for all participants.
• Justify why a specific game is unfair by explaining the uneven distribution of winning chances based on evidence.

Before You Start

Counting and Cardinality

Why: Students need to be able to count the number of trials and the number of wins for each player to analyze game outcomes.

Basic Data Recording

Why: Students must be able to record results, such as tally marks, to track game outcomes over multiple trials.

Key Vocabulary

Fair Game	A game where each player has an equal chance of winning. The outcomes are unpredictable and balanced.
Unfair Game	A game where one or more players have a greater chance of winning than others. The outcomes are unbalanced.
Probability	The likelihood or chance of a specific event happening. It helps us understand how likely something is to occur.
Outcome	The result of a single trial or event in a game, such as rolling a specific number on a die or flipping a coin to heads.
Trial	One instance of playing the game or performing an action, like one roll of a die or one coin toss. Repeating trials helps reveal patterns.

Watch Out for These Misconceptions

Common Misconception

All games are fair if rules are the same for everyone.

What to Teach Instead

Fairness in chance games requires equal winning probabilities, not just identical rules. Biased tools like weighted dice create unfairness. Small group trials expose this as students compare tallies and adjust games collaboratively.

Common Misconception

A single win or loss proves a game is unfair.

What to Teach Instead

Chance varies in few trials; fairness shows in many repeats. Students learn this by extending play and watching frequencies stabilize. Peer sharing of long-run data corrects overreliance on short experiences.

Common Misconception

Games with numbers are always fair.

What to Teach Instead

Numbers alone do not ensure equity; spinners with unequal sections skew odds. Hands-on testing lets students measure sections and rerun trials, building evidence-based judgments.

Active Learning Ideas

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.

45 min·Small Groups

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.

25 min·Pairs

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.

35 min·Whole Class

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.

20 min·Individual

Real-World Connections

• Carnival game operators design games that appear fair but are statistically weighted to ensure the house wins over time. Understanding probability helps consumers identify potentially unfair games.
• Board game designers carefully balance the mechanics of their games to ensure fairness and replayability. They use probability to ensure no single strategy or starting position guarantees a win.

Assessment Ideas

Quick Check

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.'

Discussion Prompt

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?'

Exit Ticket

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.

Frequently Asked Questions

How do students differentiate fair and unfair games?

Students play games repeatedly, tally outcomes for each player, and compare win frequencies. Equal chances over 20-30 trials indicate fairness; consistent advantages signal unfairness. Guiding questions prompt them to justify with data, reinforcing data strand skills.

What activities help students design fair games?

After testing existing games, students sketch their own with equal sections on spinners or even coin flips. Pairs test prototypes, tally results, and revise for balance. Class sharing celebrates fair designs and explains tweaks, building creativity and reasoning.

How does active learning benefit teaching fair and unfair games?

Active approaches like station rotations and paired testing let students generate their own data, making probability concrete. They observe chance patterns firsthand, discuss discrepancies, and refine ideas through play. This boosts retention, enthusiasm, and skills in data collection over passive explanation.

How to address varying abilities in this topic?

Provide ready tally sheets for some, blank charts for others. Extend challenges by adding more trials or complex spinners. Pair stronger students with peers for support, ensuring all engage in play, recording, and justification at their level.