Mastering Mathematical Reasoning · 6th-class

Active learning ideas

Probability Fair Games

Active learning lets students see probability in action rather than just calculate it on paper. When they design spinners or test games, they confront real probabilities and fairness, making abstract fractions concrete.

• NCCA Curriculum Specifications
• NCCA: Primary - Chance
• NCCA: Primary - Problem Solving

• 30–50 min
• Pairs → Whole Class
• 4 activities

Activity 01

• Experiential Learning
• 45 min · Pairs

Game Design Workshop: Custom Spinner Challenge

Pairs draw spinners on paper plates with 4-8 sections, assigning colours for wins and losses. They calculate exact win probability as a fraction and expected value per spin. Pairs test 50 spins, tally results, and graph actual versus predicted wins.

Apply probability concepts to explain whether a game of chance is fair or unfair.

Facilitation Tip

During Game Design Workshop, circulate and ask each group to justify their spinner’s probability distribution before they cut and assemble it.

What to look for

Provide students with a spinner divided into 4 unequal sections (e.g., 2 red, 1 blue, 1 green). Ask: 'What is the theoretical probability of landing on red? Is this spinner fair for a two-player game where one player wins on red and the other wins on blue or green?'

• Apply
• Analyze
• Evaluate
• Self-Awareness
• Self-Management
• Social Awareness

Activity 02

• Experiential Learning
• 50 min · Small Groups

Fairness Testing Circuit: Game Rotations

Prepare three games: biased coin, uneven die, balanced cards. Small groups rotate every 10 minutes, run 20 trials per game, record win rates, and vote on fairness. Debrief as a class compares group data to reveal patterns.

Analyze how to make an unfair game fair by adjusting its rules or outcomes.

Facilitation Tip

During Fairness Testing Circuit, set a timer for each station so students rotate quickly and collect enough data to see patterns in the results.

What to look for

Students are given a simple dice game: Player A wins if they roll a 1 or 2, Player B wins if they roll a 3, 4, 5, or 6. Ask them to write: 1. The probability of Player A winning. 2. The probability of Player B winning. 3. Is the game fair? Explain why or why not.

• Apply
• Analyze
• Evaluate
• Self-Awareness
• Self-Management
• Social Awareness

Activity 03

• Experiential Learning
• 35 min · Small Groups

Unfair to Fair Makeover: Rule Tweaks

Provide an unfair game, like a 3:1 spinner. Groups propose and test rule changes, such as adding sections or combining outcomes, to achieve 1/2 probability. They justify adjustments with calculations and trial data.

Predict the long-term results of playing a probability game multiple times.

Facilitation Tip

During Unfair to Fair Makeover, require students to present their rule changes with both probability calculations and a revised game board or card set.

What to look for

Present students with a game where Player A wins if they draw an even number from a bag of 10 numbered balls (1-10), and Player B wins if they draw an odd number. Ask: 'How could we change the rules of this game to make it fair for both players? Describe at least two different ways.'

• Apply
• Analyze
• Evaluate
• Self-Awareness
• Self-Management
• Social Awareness

Activity 04

• Experiential Learning
• 30 min · Whole Class

Long-Term Prediction Relay: Trial Marathon

Whole class simulates 200 plays of one game by passing a die or spinner. Tally cumulative wins on a shared chart. Predict and verify if results approach expected value over time.

Apply probability concepts to explain whether a game of chance is fair or unfair.

Facilitation Tip

During Long-Term Prediction Relay, have students graph class results as they accumulate; this visual helps them see the law of large numbers in action.

What to look for

Provide students with a spinner divided into 4 unequal sections (e.g., 2 red, 1 blue, 1 green). Ask: 'What is the theoretical probability of landing on red? Is this spinner fair for a two-player game where one player wins on red and the other wins on blue or green?'

• Apply
• Analyze
• Evaluate
• Self-Awareness
• Self-Management
• Social Awareness

A few notes on teaching this unit

Start with hands-on design to build intuition, then move to systematic testing to challenge misconceptions. Avoid rushing to formulas—instead, let students discover why expected value predicts long-term results through repeated trials. Research shows that students grasp fairness better when they see how small sample sizes mislead, so emphasize data collection and class sharing over single attempts.

Students will explain why probabilities matter in game design, adjust rules to create fair games, and use expected values to predict long-term outcomes. They will also justify their decisions using calculations and data from trials.

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Watch Out for These Misconceptions

• During Game Design Workshop, watch for students who claim a game is fair because 'it feels balanced' or 'we won about half in 10 spins.'

  Ask them to calculate the theoretical probability first, then collect 100 spins to compare. Have them present their data on a class chart to see how short-term results differ from long-term expectations.

• During Fairness Testing Circuit, watch for students who assume all outcomes in a custom spinner are equally likely unless told otherwise.

  Direct them to measure the angle of each section and calculate the actual probability before testing. Ask them to adjust their spinner if the sections are unequal and recalculate.

• During Long-Term Prediction Relay, watch for students who think the expected value must match every single trial outcome.

  Have them simulate 500 trials as a class and graph the results. Ask them to explain why streaks occur but the average approaches the expected value over time.

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Methods used in this brief

• Experiential Learning