Mathematics Level 3
Hamilton Zoo Adventure Te Kōpere Kararehe o Kirikiriroa
Coordinate Geometry Through Zoo Exploration
Unit Overview | Tirohanga Whānui
Students explore coordinate geometry by navigating Hamilton Zoo on a class coordinate grid — a classroom overlay on the zoo map, not the zoo's exact layout — plotting animal locations across all four quadrants and calculating scaled distances between exhibits. This hands-on approach connects mathematical concepts to a familiar New Zealand location.
📐 NZ Curriculum Phase 3 Alignment
- Geometry: Locating coordinate points on a coordinate plane
- Geometry: Using grid references to identify regions and plot positions
- Geometry: Interpreting and creating grid maps with directional language
- Measurement: Using scales, compass points, and distance
🎯 Learning Intentions | Whāinga Ako
Coordinates
Students will plot and identify locations using (x,y) coordinates on the Hamilton Zoo map
Grid References
Students will use alphanumeric grid systems to locate and describe animal exhibits
Distance & Direction
Students will calculate distances and describe directions between zoo locations
Scale & Mapping
Students will interpret map scales to calculate real-world distances
📚 Unit Structure | Hoahoa Wāhanga
1
Zoo Map Orientation
Te Reo: Whakatōngatanga Mahere
- Introduction to Hamilton Zoo layout
- Basic coordinate system setup
- Identifying major landmarks and exhibits
- Creating a simple grid overlay
2
Animal Location Plotting
Te Reo: Whakatakoto Tauwāhi Kararehe
- Plotting animal locations using coordinates
- Reading coordinates from the zoo map
- Creating a zoo animal coordinate database
- Extending coordinates into all four quadrants (negative x and y values)
3
Pathways and Navigation
Te Reo: Ngā Ara me te Whakatere
- Planning efficient routes through the zoo
- Using compass directions (N, S, E, W)
- Calculating shortest paths between exhibits
- Understanding grid references for navigation
4
Distance and Scale
Te Reo: Roa me te Inenga
- Interpreting map scale for Hamilton Zoo
- Converting grid units to metres/kilometres
- Calculating walking distances between animals
- Planning time-efficient zoo visits
5
Zoo Conservation Project
Te Reo: Kaupapa Tiakitanga Kōpere
- Designing new exhibit locations using coordinates
- Considering animal habitat requirements and spacing
- Creating scaled drawings of proposed exhibits
- Presenting recommendations with mathematical justification
🦁 Key Activities | Ngā Hohenga Matua
Activity 1: Hamilton Zoo Coordinate Hunt
Duration: 40 minutes
Materials: The class zoo grid map (in Lesson 1), coordinate worksheets, coloured pencils
Steps:
- Students receive the Hamilton Zoo map with coordinate grid overlay
- Create coordinate system: Main Entrance at (0,0) as origin, with the grid extending into all four quadrants. This is the class zoo grid used in every lesson of this unit — a classroom overlay on the zoo map, not the zoo's exact layout
-
Identify and plot coordinates for:
- Elephant area: (3, 4)
- Lion enclosure: (4, 3)
- Giraffe exhibit: (4, −2)
- Kiwi nocturnal house: (−3, 4)
- Chimpanzee exhibit: (−3, 5)
- Students check their plotting by describing animal neighbours
- Extension: Plot additional facilities (toilets, food kiosk, playground)
Activity 2: Zoo Navigator Challenge
Duration: 35 minutes
Materials: Zoo map, direction compass, calculator
Navigation Challenges:
-
Efficient Zoo Visit:
Plan route visiting Elephant → Lion → Giraffe
- Calculate total grid distance
- Identify compass directions for each leg
- Find alternative routes and compare distances
-
Emergency Response:
Staff need to get from entrance to each animal quickly
- Find shortest path to each major exhibit
- Create emergency access map with coordinates
-
Family Fun Day:
Design route suitable for families with young children
- Include playground, toilets, and cafe coordinates
- Minimise backtracking and walking distance
Activity 3: Scale and Real Distance
Duration: 45 minutes
Materials: Rulers, calculators, real zoo statistics
Working with Scale 1:2000 (1cm = 20m)
-
Distance Calculations:
- Entrance (0,0) to Elephant area (3, 4): grid-path distance 7 units = 140m real distance
- Lion (4, 3) to Giraffe (4, −2): distance 5 units = 100m real distance
- Walking speed 80 m/min (≈4.8 km/h, matching Lesson 4) = time calculations for zoo visits
-
Area Calculations:
- Elephant enclosure dimensions on map vs. real area
- Kiwi enclosure area — a 4×3 grid rectangle on the class grid (see Lesson 4) — for conservation planning
- Car park capacity using area measurements
-
Practical Applications:
- How long to walk around entire zoo perimeter?
- Fuel costs for zoo maintenance vehicles
- Planning new pathways between exhibits
✅ Assessment Opportunities | Ngā Ahuatanga Aromatawai
📊 Formative Assessment
- Daily coordinate plotting accuracy checks
- Peer verification of animal locations
- Quick compass direction quizzes
- Distance calculation warm-ups
📋 Summative Assessment
- Zoo Guide Creation: Design coordinate-based visitor guide
- Conservation Proposal: Plan new exhibit with mathematical justification
- Navigation Challenge: Timed route planning with accuracy scoring
🎯 Success Criteria
- Accurately plots points using coordinate pairs
- Uses grid references to locate and describe positions
- Calculates distances using scale conversions
- Applies compass directions in navigation tasks
- Solves real-world problems using coordinate geometry
📚 Resources Required | Ngā Rauemi
🗺️ Maps and Visuals
- Hamilton Zoo map with coordinate grid overlay
- Large format classroom display map
- Individual student map copies
- Transparent coordinate grid sheets
- Compass rose reference charts
🧮 Equipment
- Rulers and measuring tools
- Calculators for scale work
- Coloured pencils for plotting
- Magnetic compass for direction work
- Graph paper for extension activities
💻 Digital Resources
- Hamilton Zoo virtual tour videos
- Online mapping tools for comparison
- Coordinate geometry apps/games
- Digital protractors and rulers
- Zoo webcam links for real-time connection
🌿 Cultural Connections
- Māori place names around Hamilton
- Traditional Māori navigation methods
- Conservation values in Māori culture
- Te reo vocabulary for directions and locations
- Local iwi connections to land and animals
🚀 Extensions and Connections | Ngā Whakawhiti
🔗 Cross-Curricular Links
- Science: Animal habitat requirements and spacing
- Social Studies: Hamilton city development and planning
- English: Writing visitor guides and direction instructions
- Technology: Designing digital zoo maps and apps
- Arts: Creating artistic maps with cultural elements
⭐ Challenge Activities
- Design a new section of Hamilton Zoo using coordinate planning
- Calculate the optimal number of pathways for visitor flow
- Compare Hamilton Zoo layout to other famous zoos worldwide
- Use GPS coordinates to connect map work to real technology
- Create a treasure hunt using coordinate clues
🏠 Community Connections
- Virtual or physical field trip to Hamilton Zoo
- Guest speaker: Zoo planner or architect
- Connect with Hamilton Zoo education team
- Community mapping project around school neighbourhood
- Share findings with Hamilton Zoo for feedback
🤔 Reflection Questions | Ngā Pātai Whakaaro
For Students | Mā Ngā Ākonga
- How do coordinates help us describe exact locations?
- What challenges did you face when calculating distances?
- How might coordinate systems be used in real jobs?
- What was surprising about the layout of Hamilton Zoo?
- How could we improve navigation around the zoo?
For Teachers | Mā Ngā Kaiako
- Which coordinate concepts required the most scaffolding?
- How effectively did students connect math to real-world applications?
- What cultural connections resonated most with students?
- How could technology enhance this unit further?
- What evidence shows students can apply coordinate geometry independently?
Kaiako Planning Snapshot
Teacher Planning Snapshot
- Year level: Years 7–8 | Duration: 5 lessons | NZC Level 3 geometry, measurement, and spatial reasoning.
- Teaching focus: Keep the map, the coordinate plane, and the real zoo context visible together so students can move between plotted points, language about location, and actual movement through space.
- Mātauranga Māori: Hamilton Zoo mapping gives a strong opening to discuss whakatere waka, wayfinding, and local place knowledge. Use te reo for direction and location, and connect coordinate reasoning to the way whakapapa and whenua help people understand where they are and how they move responsibly through a place.
- On-level: Most learners can plot ordered pairs, read grid positions, and compare route efficiency once the grid, scale, and direction language are practised repeatedly in context.
- Extension: Challenge students to redesign one zoo route or exhibit location and justify the change using coordinates, scale, walking distance, and visitor access.
Inclusion and Accessibility
- ESOL / ELL: Pre-teach location vocabulary such as left, right, north, south, grid, axis, coordinate, and scale with gestures, arrows, and model sentences.
- Accessibility: Provide enlarged maps, colour-coded coordinate grids, and tactile or high-contrast route options so students can track position changes clearly.
- Neurodiverse learners: Break navigation tasks into one-step prompts first, then build toward multi-step route planning so the spatial load increases gradually rather than all at once.
🎯 Curriculum Links | Te Hononga Marautanga
NZC (2007) · Mathematics and Statistics · Level 3 · Geometry and Measurement. The statements below are verbatim from the achievement-objective charts. Lessons 1–3 teach the position-and-orientation objective; Lesson 4 teaches the measurement objectives; Lesson 5 applies them in the conservation capstone.
Use a co-ordinate system or the language of direction and distance to specify locations and describe paths.
Use linear scales and whole numbers of metric units for length, area, volume and capacity, weight (mass), angle, temperature, and time.
Find areas of rectangles and volumes of cuboids by applying multiplication.
NZC (2007) · Social Sciences · Level 3 · Social Studies — taught through the Lesson 5 conservation design brief.
Understand how people make decisions about access to and use of resources.
Te Mātaiaho (2025, draft) · Mathematics and Statistics · Phase 3 (Years 7–8) · Algebra — Practices. The four-quadrant plotting practice below is the core of Lessons 1–2; the linear-pattern practices in the same row are not taught in this unit.
- Identifying and plotting points in the four quadrants of the coordinate plane, using ordered pairs and values from a table - Using tables, graphs in the coordinate plane, and diagrams to recognise the relationship between the ordinal position and its corresponding element in a linear pattern, develop a rule for the pattern in words, and make conjectures about further elements in the pattern - Identifying the constant increase or decrease in a linear pattern, using variables and algebraic notation to represent the rule in an equation, and using the equation to make conjectures
🔗 Unit Progression & Next Steps
The 5 lessons in this unit, in teaching order:
Pedagogical Foundations | Ngā Tūāpou Akoranga
A real place and a real map: this unit grounds coordinate geometry in Hamilton Zoo, with a classroom grid overlay giving each enclosure its coordinates. Three researchers explain why spatial learning needs genuine context, not abstract planes.
Social Constructivism
Lev Vygotsky
The Zone of Proximal Development explains why beginning with a real zoo map rather than a blank coordinate plane works pedagogically. The familiar context of Hamilton Zoo is the scaffolding object that makes the abstract coordinate system purposeful. Without concrete context, many Y7‑8 students lack the developmental readiness to grasp why coordinates are useful — the zoo provides that grounding.
Cognitive Development
Jean Piaget
Piaget’s stage transition from concrete to formal operations — actively underway at Y7‑8 — explains why this moment is both ideal and demanding for coordinate geometry. Students are learning to think in relationships rather than things; a real map provides the concrete anchor while the coordinate system builds the formal structure. The unit’s sequencing from map-reading to abstract plane follows this developmental logic.
Progressive Education
John Dewey
Dewey’s requirement that genuine learning involve real action in a real world — not preparation for a future in which real things will happen — is what separates this unit from textbook exercises. “Navigate the zoo to find the kiwi enclosure” is a real spatial problem. The coordinate system is the tool; the zoo is the problem. Real tools used on real problems is Dewey’s standard for genuine learning.
→ Explore all theorists at Te Whare Ako — Teaching Theory