📐 Mathematics Y6-9

⭐ Star Navigation & Coordinates

Te Kōkōrangi me ngā Whetū • Finding Your Way by the Stars

🧭 Master Navigators

Polynesian navigators crossed the Pacific Ocean — the world's largest body of water — using only the stars, waves, winds, and their knowledge passed down through generations.

They didn't have GPS, compasses, or maps. Instead, they memorized the positions of hundreds of stars and understood how the sky changes throughout the year. This is coordinate mathematics in action!

⭐ Key Stars for Pacific Navigation

Māhutonga

Southern Cross

Points to the South Pole

Matariki

Pleiades cluster

Marks the Māori New Year

Rehua

Antares

Bright red star of summer

Tākurua

Sirius

Brightest star in the sky

📍 Coordinates in the Sky

Astronomers use a coordinate system to locate stars, just like we use coordinates on a map!

  • Altitude: How high the star is above the horizon (0° to 90°)
  • Azimuth: Direction along the horizon (0° North, 90° East, 180° South, 270° West)

Traditional navigators memorized where important stars would rise and set — their azimuth positions — at different times of year.

📝 Activity 1: Star Map Grid

Plot these stars on the coordinate grid. The first one is done for you.

Star Coordinates (across, up)
Māhutonga (Southern Cross) (3, 2) ✓
Matariki (7, 8)
Rehua (5, 5)
Tākurua (2, 7)
10
9
8
7
6
5
4
3
2
1
2
3
4
5
6
7
8
9
1

📝 Activity 2: Navigation Challenge

A navigator is sailing from point A(2, 3) to point B(8, 7).

a) Plot both points on a grid and draw the route.

b) How many units East must they travel?

c) How many units North must they travel?

d) If they sail diagonally, will the distance be more or less than traveling East then North? Explain.

📝 Activity 3: Finding South

Navigators use the Southern Cross to find South. The long axis of the cross points toward the South Celestial Pole.

If Māhutonga rises at azimuth 150° and sets at azimuth 210°, what azimuth is it at when directly South?

Why is knowing the direction of South useful for navigation?

📚 Kupu Māori — Vocabulary

Whetū

Star

Kōkōrangi

Sky

Raki / Tokerau

North

Tonga

South

Rāwhiti

East

Uru

West

👩‍🏫 Teacher Notes

Curriculum: NZC Level 3-4 Geometry — Position and orientation, Coordinate systems

Extension: Research the Hawaiian star compass (star houses); Use stellarium.org to explore the night sky; Calculate distances using Pythagoras.