Traditional Māori games (tākaro) were not just for entertainment but also taught important skills, strategy, and mathematical concepts. This lesson explores probability through three traditional games: Pūtōrino (a flute game), Poi Rākau (stick games), and Whai (string patterns).
Cultural Safety Note: When teaching Māori content, ensure you pronounce Māori words correctly (practice with students or use online resources). Acknowledge the iwi associated with these games where possible. Always approach Māori knowledge with respect.
The pūtōrino is a flute that can be played with different finger hole combinations. Let's explore the probabilities of different notes.
A pūtōrino has 6 finger holes. Each hole can be open (1) or closed (0).
How many possible note combinations exist?
If you randomly cover 3 holes, what's the probability of playing a specific note combination?
Number of favourable outcomes:
Total possible outcomes: 64
In this traditional stick game, players throw sticks between each other in patterns.
| Number of Sticks | Possible Catch Combinations | Probability of Successful Catch |
|---|---|---|
| 1 stick | 2 (left or right hand) | 1/2 = 50% |
| 2 sticks | 4 (LL, LR, RL, RR) | 1/4 = 25% |
| 3 sticks | 8 combinations | 1/8 = 12.5% |
Practical Task: In pairs, simulate the stick game using pencils. Record 20 attempts each with 1, 2, then 3 sticks. Compare your experimental probabilities with the theoretical probabilities above.
Whai involves creating patterns with a loop of string. Some patterns are more likely to appear than others based on the sequence of moves.
Basic moves:
Create a probability tree for a 3-move sequence. What's the probability of getting:
| Achievement Objective | Assessment Method |
|---|---|
| Calculate probabilities | Worksheet with probability calculations for game scenarios |
| Compare theoretical and experimental probability | Lab report comparing class data with theoretical probabilities |
| Cultural understanding | Reflection paragraph on how Māori incorporated probability in games |
| Learning Need | Adaptation |
|---|---|
| Visual learners | Provide diagrams of game setups and probability trees |
| Kinesthetic learners | Physical simulations of the games |
| ESOL students | Glossary of Māori and mathematical terms |
| Advanced students | Extension problems with compound probability |
Resources Needed: Pencils (for stick game simulation), string for whai, printed worksheets