🧺 Te Kete Ako

Physics of Traditional Māori Games

Physics of Traditional Māori Games · Years 10–12

Year LevelYears 10–12
TypeStudent handout — classroom resource

Ngā Whāinga Akoranga · Learning Intentions

  • Investigate a scientific concept or phenomenon using observation and evidence
  • Apply scientific understanding to explain natural processes and systems
  • Connect scientific knowledge to environmental decision-making and kaitiakitanga
  • Evaluate how both mātauranga Māori and Western science contribute to understanding

Paearu Angitu · Success Criteria

  • I can describe the key concept or phenomenon accurately using scientific vocabulary
  • I can explain how evidence supports my scientific understanding
  • I can connect scientific knowledge to at least one real-world environmental application
  • I can identify where mātauranga Māori and Western science perspectives intersect or differ
⚡ Physics 🏐 Kī-o-rahi, Poi, Ti Rākau 🎓 Year 10–12 🇳🇿 NZC Level 5–7

Physics of Traditional Māori Games

🌀 Force, momentum, angular velocity, and friction — through taonga tākaro
"Ka mau te wehi — mā te taiao, mā te tinana, ka ako te hinengaro" — Through the natural world, through the body, the mind learns.
(Taonga tākaro are not just games — they are embodied physics laboratories.)

Taonga tākaro — traditional Māori games — were not random play. Ti rākau developed precise neuromuscular coordination, poi trained rotational mechanics, and kī-o-rahi used complex spatial strategy. Every game encodes physics. In this handout, you will apply Newton's laws, circular motion, momentum, and friction to real data from these games — and discover that tīpuna were applied physicists.

Part 1 — Poi: Angular Velocity and Circular Motion

🌀 What is Poi?

Poi are weighted balls on a cord, swung in patterns around the body. Traditionally used to develop wrist flexibility for weapons training — and as a training tool for rangatahi to develop coordination. Modern performance poi can reach speeds of 60–80 km/h at the tip.

When a poi ball travels in a circle, it undergoes uniform circular motion. The physics:

v = 2πr / T (speed = circumference ÷ period)
F_c = mv²/r (centripetal force required)
ω = 2π / T (angular velocity in rad/s)
Poi Style String Length (r) Rotations per second Mass of ball (m)
Traditional raupo 0.35 m 2.5 rev/s 80 g
Performance LED 0.55 m 3.8 rev/s 120 g
Fire poi 0.48 m 1.8 rev/s 200 g
  1. For the traditional raupo poi, calculate:
    • The period T (hint: T = 1/frequency)
    • The speed v at the tip
    • The centripetal force F_c needed
  2. The fire poi have more than double the mass of raupo poi but spin slower. Calculate the centripetal force for fire poi and compare to raupo. Why might a performer choose different poi types for different contexts?
  3. Extension: A poi string exerts centripetal force on the ball. The ball exerts an equal and opposite force on the performer's wrist (Newton's 3rd Law). Calculate the force on the wrist for performance LED poi at maximum speed. Convert to kg-force and comment on the physical conditioning required.

Part 2 — Ti Rākau: Momentum and Catching

🪵 What is Ti Rākau?

Ti rākau are 50–60 cm rākau (sticks) tossed and caught in synchronised patterns between partners. The game develops timing, spatial reasoning, and rapid reflexes. In advanced versions, 4–6 players exchange sticks simultaneously while chanting.

When a rākau (stick) is thrown and caught, we apply:

p = mv (momentum = mass × velocity)
Impulse = Δp = FΔt (impulse = change in momentum)
KE = ½mv² (kinetic energy)
Measurement Value Notes
Rākau mass 0.18 kg Traditional hardwood
Throwing speed 4.2 m/s Measured with high-speed camera
Catch time 0.08 s Time from contact to full stop
Throw angle 72° from horizontal Standard ti rākau arc
Max height reached 0.85 m above release Used to verify with projectile motion
  1. Calculate the momentum of the rākau at release. What force is applied by the catcher's hand to stop it in 0.08 seconds?
  2. Using projectile motion, verify that a rākau thrown at 4.2 m/s at 72° would reach 0.85 m:
    h = (v_y)² / (2g) where v_y = v × sin(72°)
  3. Friction and Grip: A rākau would slip if the static friction force is less than the horizontal force needed to redirect its momentum during catching. If μ (coefficient of friction between hand and wood) = 0.55 and Normal force = 8 N, what is the maximum friction force? Is the rākau likely to slip?
    f = μN

Part 3 — Kī-o-rahi: Strategy, Angles, and Energy

🏐 What is Kī-o-rahi?

Kī-o-rahi is a fast-moving team sport played on a circular field. One team (Ki) score by touching a central pou (pole); the other team (Taniwha) score by hitting target zones on the boundary. McDonald's chose kī-o-rahi (not rugby or cricket) as "New Zealand's national sport" for a 2005 global campaign — recognising its deep roots and athletic complexity.

  1. Field Geometry: A kī-o-rahi field is circular with radius 40 m. A Ki player runs from the edge at position A to the central pou at position O (radius = 4 m), then to position B on the opposite side. If A and B are 120° apart on the circumference, what is the total distance run? What is the displacement? (Use the cosine rule for displacement: c² = a² + b² − 2ab cos C)
  2. Energy Expenditure: A 65 kg player sprints at 7.2 m/s. Calculate their kinetic energy. If they must stop in 1.5 seconds (due to a Taniwha defender), calculate the average retarding force.
  3. Cultural-Physical Analysis: Kī-o-rahi encodes the story of Rātā searching for the bones of his father Wahieroa. The Ki team represents Rātā, the Taniwha team represents obstacles in his journey. The circular field represents the cyclical nature of whakapapa.
    Write 4–5 sentences connecting the physics of the game (circular motion, energy, spatial strategy) with the whakapapa (narrative meaning) of the game. What does it mean to say the game "contains physics" and "contains story" at the same time?

🌀 Whakamutunga — The Body Knows Physics

Before Newton published his laws in 1687, Māori were already encoding physics into culture — poi demonstrates torque and centripetal force, ti rākau demonstrates impulse and momentum, kī-o-rahi demonstrates circular geometry and kinetic energy. These are not coincidences; they are evidence of a deep embodied understanding of the physical world expressed through taonga tākaro.

Final challenge: Design your own "physics measurement" experiment using poi or ti rākau. What variables would you measure? What physics concepts would you test?

🌿 Ngā Rauemi Hono — Related Resources

Hononga Marautanga · Curriculum Alignment

Science — Pūtaiao

Level 3–4: Investigate how living and physical systems work; understand relationships between organisms and their environments; collect, interpret, and evaluate scientific evidence to explain natural phenomena.

Social Sciences — Tikanga ā-Iwi

Level 3–4: Understand how human activity affects natural environments; explore the connection between ecological health and community wellbeing; recognise the role of cultural knowledge in environmental decision-making.

Tuhia ōu whakaaro · Write Your Thoughts

Reflect on your learning. What was the most important idea? What question do you still have?

Aronga Mātauranga Māori

Mātauranga Māori is a sophisticated knowledge system built through centuries of careful observation, hypothesis, testing, and refinement — the same processes that define scientific inquiry. Māori knowledge of ecology, weather patterns, seasonal change, and animal behaviour guided sustainable resource management for generations before Western science arrived in Aotearoa. Understanding science through a dual-knowledge lens — bringing mātauranga Māori and Western science into dialogue rather than hierarchy — produces richer, more contextually grounded understanding. The concept of kaitiakitanga reminds us that scientific knowledge carries obligations: understanding how natural systems work means accepting responsibility for how we treat them.

Ngā Rauemi Tautoko · Resources already provided

This handout is designed to be used alongside other resources in the same unit. Related materials are linked in the unit planner. All content is provided — no additional preparation is required to use this handout in your classroom.

📋 Teacher Planning Snapshot

Ngā Whāinga Ako — Learning Intentions

Students will engage with this resource to build understanding of Aotearoa New Zealand's ecosystems, biodiversity, and the role of kaitiakitanga in environmental stewardship.

Ngā Paearu Angitū — Success Criteria

  • ✅ Students can explain key concepts from this resource using their own words.
  • ✅ Students can connect the content to real-world environmental contexts in Aotearoa.

Differentiation & Inclusion

Scaffold support: Provide sentence starters, word banks, or graphic organisers to scaffold access for students who need it. Offer entry-level and extension tasks to address a range of readiness levels.

ELL / ESOL: Pre-teach key vocabulary and provide bilingual glossaries where available. Allow students to respond in their home language first.

Inclusion: Use accessible formats — clear font, adequate whitespace, structured tasks. Neurodiverse learners benefit from chunked instructions and choice in how they demonstrate understanding.

Prior knowledge: Best used after the relevant lesson sequence. No specialist prior knowledge required for entry-level engagement.