Lesson 5: Coordinate Geometry Capstone — Design Your Dream Zoo Section
The culminating challenge — designing an optimised zoo section using coordinate geometry, transformations, scale, and distance calculations to demonstrate full mathematical mastery.
🎯 Ngā Whāinga Akoranga | Learning Intentions
How to integrate coordinate grids, distance calculations, transformations, and scale into a unified design project; how professional architects and urban planners use these mathematical tools.
Design a complete zoo section on a coordinate grid, including: accurate coordinate labels, at least one transformed shape, scale-factor calculation for one enclosure, and a route distance calculation.
🎥 Media Anchor & Mathematical Scaffold
Mathematics in Context: Hamilton Zoo
Watch the full clip — 2:29. Source: Hamilton Zoo. The zoo the whole unit is built around, in its own words. Ākonga designing an enclosure should hear what the enclosure is FOR before they place a single coordinate.
🧠 1. Before Viewing
You are now a zoo architect. Your task: design a new 'Southern Ocean' section for Hamilton Zoo on a coordinate grid. You have a 10×10 unit space (1 unit = 10m). What mathematical thinking will you bring?
👁️ 2. During Viewing
- Early in the clip: List the mathematical tools you have from this unit: coordinates, distance calculation, transformation, scale factor. How will you use each in your design?
- Midway: Your penguin pool should be symmetric — use a reflection transformation to create matching pools on both sides of the central axis.
- Later in the clip: Calculate: what is the total walking distance of your planned visitor route through the section? Show the coordinate arithmetic for each leg.
🗣️ 3. After Viewing — Kaiako Move
Kaiako Move: Display an example zoo section design with mathematical annotations (coordinates, distances, transformations labelled). Discuss: what makes this mathematically rigorous? What would improve it?
Task: Zoo Design Capstone: On a 10×10 coordinate grid, design a Southern Ocean section with at least 4 species areas. Label all coordinates. Include: one reflection, one scale-factor calculation, and one route distance calculation.
⚡ Whakaoho | Do Now (5 mins)
Share your design in progress with a partner. Can they identify which enclosures are reflections of each other? Can they check your distance calculations?
📐 Activity 1: Guided Mathematical Exploration (25 mins)
Design presentation: in pairs, present your coordinate geometry zoo design to another pair. Explain the mathematical choices you made. Use correct vocabulary: coordinates, reflection, scale factor, distance.
✍️ Activity 2: Application & Reflection (20 mins)
Mathematical reflection: write a paragraph explaining which tool from this unit (coordinates, distance, transformation, scale) you found most useful and why. Give a specific example from your design.
🏫 Kaiako Planning & Pedagogy Notes
Curriculum Alignment: Te Mātaiaho Mathematics Phase 3/4 — Integrated project: apply coordinate geometry, transformations, and scale in an authentic design context.
Hamilton Zoo Context: All tasks use authentic zoo spatial data. Print the map and have every earlier lesson's marked-up copies available; the capstone assembles them.
Cultural Connection: Across this unit ākonga have used a coordinate system to describe a real place. Kaitiakitanga asks the further question the maths cannot answer on its own: what do the people responsible for this place owe the animals in it?