📎 Learning Intentions | Ngā Whāinga Ako
Know | Mōhio
- That a Cartesian coordinate plane uses two perpendicular number lines (x-axis and y-axis) meeting at the origin (0, 0).
- That every point on a map can be described as an ordered pair (x, y).
- That Māori navigators used star paths (ara whetū) and landmarks as their own coordinate system.
Demonstrate | Whakaatu
- Overlay a Cartesian grid on the Hamilton Zoo map and correctly label the x-axis, y-axis, and origin.
- Write the coordinates of at least 5 zoo landmarks as ordered pairs (x, y).
- Explain, in your own words, how a grid reference system helps us communicate location.
📐 Curriculum Alignment | Hononga Marautanga
Use a co-ordinate system or the language of direction and distance to specify locations and describe paths.Ministry of Education (2007). The New Zealand Curriculum. Mathematics and statistics achievement objectives, Level 3.
🌿 Whakatūwhera — Cultural Opening | Opening Hook
Kia whakatōmuri te haere whakamua.
"Walk backwards into the future" — Māori navigators used the stars and whenua behind them as their reference point. In coordinate geometry, we always need a fixed reference point: the origin.
🎤 Kaiako Hook (5 min)
Begin by showing students a Google Maps screenshot of Hamilton Zoo. Ask: "How would you describe the exact location of the lion enclosure to someone who has never been here — using only numbers?"
Reveal that Māori celestial navigators (tohunga whakatere waka) used star paths and ocean swells as their own coordinate system — a sophisticated grid embedded in nature. Today's lesson connects this whakaaro (thinking) to the Cartesian plane.
🎬 Watch | Mātakitaki
Watch the full clip — 6:47. Source: Khan Academy. The clip teaches the plane itself — axes, origin, ordered pairs. The zoo map is where you then put it to work.
📚 Lesson Content | Ihirangi Akoranga
Part 1: Setting Up Our Zoo Grid (15 min)
Distribute the class zoo grid map below (print it, or display it digitally). Guide students through how it was built:
- Draw a horizontal line across the middle of the map — this is the x-axis (horizontal).
- Draw a vertical line from top to bottom — this is the y-axis (vertical).
- Where these lines cross is origin (0, 0). Choose a meaningful landmark (e.g., main entrance) as origin.
- Number the grid squares outward in both directions: positive right/up, negative left/down.
🔑 Key Concept: Ordered Pairs (x, y)
An ordered pair (x, y) tells us: first move along the x-axis, then up/down the y-axis.
Example: The Elephant enclosure is at (3, 4) → 3 units right, 4 units up from the entrance.
Remember: Always write x first, then y. The comma separates them. Parentheses hold them.
Part 2: Mapping the Zoo Animals (20 min)
Students work in pairs, reading their grid overlay to fill in the 8 locations below — six animals plus the café and the entrance:
| Animal | Kararehe | Te Reo Name | Grid Reference (x, y) |
|---|---|---|
| African Lion | Raiona | ( ___ , ___ ) |
| Chimpanzee | Timipanihi | ( ___ , ___ ) |
| Red Panda | Panda Whero | ( ___ , ___ ) |
| Giraffe | Hārepe | ( ___ , ___ ) |
| Meerkats | — | ( ___ , ___ ) |
| Kiwi (nocturnal house) | Kiwi | ( ___ , ___ ) |
| Main Café | Whare Kai | ( ___ , ___ ) |
| Main Entrance | Tatau Matua (0,0) | (0, 0) |
Part 3: Mātauranga Connection — Ara Whetū (10 min)
Māori navigators crossing Te Moana Nui a Kiwa identified star paths called ara whetū. Key stars rose at known points on the horizon, providing directional reference just like our x and y axes. The star Atutahi (Canopus) never sets below the horizon over most of Aotearoa — from about 37°S southward, which includes Hamilton and everywhere below it, so it can be used as a reference night after night. Further north, including Auckland and Te Tai Tokerau, it does dip below the horizon for part of the night. Whether a star sets at all depends on your latitude, and latitude is itself a coordinate. (Unlike our fixed origin (0, 0), Atutahi still moves across the sky through the night, as every star does — it circles without setting rather than staying put.)
Discuss: How is the Māori navigator's ara whetū system similar to a coordinate grid? What is the "origin" for a navigator at sea?
✅ Assessment | Aromatawai
🎟 Exit Ticket (5 min)
Students answer on a sticky note before leaving:
- Write the coordinates of the Kiwi nocturnal house: ( ___ , ___ )
- If you move 2 units right and 3 units down from (0, 0), what are your coordinates?
- One thing you noticed about coordinates: ___________
🔑 Kaiako answer key
- (−3, 4) — on the class zoo grid map above.
- (2, −3) — 2 right makes x = 2; 3 down makes y = −3.
- Open response — look for noticing such as "x always comes first" or "negative numbers mean left/down".
🧑🏫 Kaiako Notes
- Common Error: Students writing (y, x) instead of (x, y). Reinforce: "Along the corridor, then up the stairs".
- Extension: Ask students to write coordinates for all 4 quadrants by placing origin in the middle of the map.
- Support: Pre-label 3 animals' coordinates to scaffold the table task.
📎 Lesson Resources | Ngā Rauemi
- 🗺 Class Zoo Grid Map (above) — the four-quadrant grid used in every lesson of this unit
- 🗺 Hamilton Zoo Grid Navigation Worksheet (A–F letter-grid practice — a different reference system from the class grid)
- 📋 Star Navigation & Coordinates Handout — a shared Te Kete Ako handout; its own page names Y10 Physics: Navigation & Ocean Sciences as its parent unit. Used here for the ara whetū discussion, not for its Year 10 physics content.