Lesson 6: Grid References & Coordinate Systems — From Alphanumeric to (x,y)
Bridging the gap between alphanumeric zoo maps and the full Cartesian coordinate system — the mathematical foundation of all spatial reasoning.
🎯 Ngā Whāinga Akoranga | Learning Intentions
How alphanumeric grids (A3, C5) relate to (x,y) coordinate pairs; the Cartesian plane with four quadrants; that all mapping systems share a common mathematical structure.
Convert 8 alphanumeric grid references to (x,y) coordinate pairs; plot zoo enclosures accurately on a Cartesian coordinate grid.
🎥 Media Anchor & Mathematical Scaffold
Mathematics in Context: Hamilton Zoo
Watch the full clip — 2:07. Source: Ordnance Survey. The clip teaches the method; the zoo context is ours, and the lesson applies it to real enclosure coordinates.
🧠 1. Before Viewing
You know grid references like B4. Today we're upgrading: B4 becomes approximately (2,4) in coordinate language. How is this similar to what you already know? What's different?
👁️ 2. During Viewing
- Early in the clip: Convert grid reference D5 to an approximate (x,y) pair. What does x represent? What does y represent?
- Midway: The Cartesian plane extends into FOUR quadrants. What would negative x and negative y coordinates mean in a zoo context?
- Later in the clip: Why do mathematicians use the (x,y) system rather than alphanumeric grids? What advantages does it give?
🗣️ 3. After Viewing — Kaiako Move
Kaiako Move: Draw the Hamilton Zoo coordinate grid on the board. Demonstrate converting three enclosure grid references to (x,y) pairs. Show: what stays the same, what changes.
Task: Coordinate Conversion: Convert 8 alphanumeric zoo grid references to (x,y) pairs. Plot all 8 on a coordinate grid. Check: which animals are neighbours?
⚡ Whakaoho | Do Now (5 mins)
Quick conversion: what is the (x,y) coordinate for grid reference C4? What about F7? How did you work it out?
📐 Activity 1: Guided Mathematical Exploration (25 mins)
Coordinate mapping: working from the zoo map, students create a coordinate grid overlay and plot 12 enclosures. Compare with a partner — do your coordinates match?
✍️ Activity 2: Application & Reflection (20 mins)
Coordinate reflection: write three sentences explaining how the alphanumeric grid you already know connects to the Cartesian coordinate system. Where are they the same? Where are they different?
🏫 Kaiako Planning & Pedagogy Notes
Curriculum Alignment: Te Mātaiaho Mathematics Phase 3/4 — Geometry: understand and use Cartesian coordinates; connect alphanumeric and (x,y) positioning systems.
Hamilton Zoo Context: All tasks use authentic zoo spatial data. Print one zoo map per pair and project one for the class. Ākonga need to point at the same feature and disagree about its reference.
Cultural Connection: Māori and Pacific navigation located places by relationship — this ridge from that river mouth — before any imposed grid. A grid reference is one system among several, and it is worth asking ākonga what a grid makes easy to say and what it makes hard. A place name often carries information a coordinate cannot.