📐 Hamilton Zoo Coordinate Navigator 📊 Kaiwhakarea Tauwāhi Kōpere Kirikiriroa
🎯 Mathematical Mission Brief | Whakatōhea Pāngarau
Welcome to advanced zoo navigation! You'll use proper coordinate geometry to solve real problems at Hamilton Zoo.
📊 Key Mathematical Concepts:
- Coordinate System: (x, y) notation with origin at (0, 0)
- Scale Factor: 1 grid unit = 10 metres in real life
- Distance Formula: Calculate exact distances between points
- Coordinate Plane: Quadrant I navigation (positive values only)
- Problem Solving: Apply mathematics to real-world scenarios
Scale: 1 unit = 10m, so multiply your answer by 10 for real distance!
Activity 1: Precise Coordinate Mapping
Task: Identify the exact coordinates (x, y) for each location. Remember: x is horizontal (across), y is vertical (up).
| Location | x-coordinate | y-coordinate | Coordinate Pair (x, y) |
|---|---|---|---|
| 🚗 Car Park (Origin A) | 0 | 0 | (0, 0) |
| 🦒 Giraffe Exhibit | (, ) | ||
| 🐘 Elephant Enclosure | (, ) | ||
| 🐅 Tiger Territory | (, ) | ||
| 💧 Wetlands Area | (, ) |
Activity 2: Distance Calculations
🧮 Mathematical Method:
Step 1: Identify coordinates (x₁, y₁) and (x₂, y₂)
Step 2: Apply distance formula: d = √[(x₂ - x₁)² + (y₂ - y₁)²]
Step 3: Multiply by scale factor (10m) for real distance
Calculate the exact distance from Car Park A (0, 0) to each animal exhibit:
🦒 Distance to Giraffes:
Giraffe coordinates: (, )
Calculation: d = √[( - 0)² + ( - 0)²]
d = √[² + ²]
d = √[ + ]
d = √ = units
Real distance: metres
🐘 Distance to Elephants:
Elephant coordinates: (, )
Calculation: d = √[( - 0)² + ( - 0)²]
d = units = metres
Activity 3: Route Optimization Problem
Mathematical Challenge: A zoo keeper needs to visit all animal exhibits efficiently. Using your distance calculations, determine the optimal route.
📊 Distance Summary Table:
| Route Segment | Distance (units) | Distance (metres) | Walking Time (3 km/h) |
|---|---|---|---|
| Car Park → Giraffes | min | ||
| Car Park → Elephants | min | ||
| Car Park → Tigers | min |
Optimal visiting order based on distance:
1st:
2nd:
3rd:
Mathematical justification:
Activity 4: Advanced Coordinate Geometry
Real-world Application: The zoo is planning a new pathway system. Use coordinate geometry to solve design problems.
Problem 1: Pathway Intersection
A straight pathway connects the Giraffes (coordinates: _____, _____) to the Elephants (coordinates: _____, _____).
Another pathway connects Tigers (coordinates: _____, _____) to Wetlands (coordinates: _____, _____).
Calculate: Do these pathways intersect? If so, what are the intersection coordinates?
Pathway 1 equation: y = x +
Pathway 2 equation: y = x +
Intersection point: (, )
Problem 2: Area Calculation
The zoo wants to fence a triangular area with vertices at Car Park (0, 0), Giraffes, and Elephants.
Calculate the area of this triangle using coordinates:
Area = ½|x₁(y₂ - y₃) + x₂(y₃ - y₁) + x₃(y₁ - y₂)|
Area = square units = square metres
Activity 5: Mathematical Modeling Challenge
Advanced Application: Model a real zoo management problem using coordinate geometry.
🏗️ Zoo Expansion Project
The zoo board wants to add a new café that is:
- Equidistant from all three main animal exhibits
- Within the zoo boundaries
- Accessible by existing pathways
Mathematical Task: Find the optimal café location using coordinate geometry.
Method: Circumcenter Calculation
Step 1: Find the perpendicular bisectors of the triangle formed by the three exhibits
Step 2: Calculate their intersection point
Step 3: Verify equal distances to all three points
Proposed café coordinates: (, )
Verification - Distance to each exhibit:
To Giraffes: units
To Elephants: units
To Tigers: units
Professional recommendation:
🎉 Mathematical Mastery Achieved! | Angitū Pāngarau!
Congratulations! You've mastered Phase 3 coordinate geometry!
✅ Skills Mastered:
- 📍 Precise coordinate identification
- 📐 Distance formula application
- ⚖️ Scale factor conversions
- 🎯 Route optimization
- 📊 Mathematical modeling
- 🔬 Problem-solving strategies
🚀 Ready For:
- 🔢 Four-quadrant systems
- 📈 Linear equation modeling
- 🔄 Geometric transformations
- 📊 Advanced optimization
- 🧮 Algebraic relationships
- 📐 Trigonometric applications
🎯 Teacher Notes | Ngā Kōrero Kaiako
📚 NZ Curriculum Phase 3 Alignment:
📐 Geometry & Measurement:
- Locate coordinate points on coordinate plane
- Communicate and interpret locations using coordinate systems
- Calculate distances using coordinate geometry
- Apply scale factors in practical contexts
- Use geometric relationships to solve problems
🔢 Algebra:
- Substitute values into formulas and equations
- Solve linear equations in context
- Model real situations using mathematical expressions
- Use tables and graphs to explore relationships
- Apply mathematical reasoning to justify solutions
🎓 Assessment Opportunities:
📊 Formative:
- Coordinate plotting accuracy
- Distance calculation process
- Mathematical reasoning quality
- Problem-solving approaches
📋 Summative:
- Complete zoo optimization project
- Mathematical modeling assessment
- Coordinate geometry test
- Real-world application portfolio
🌿 Cultural Integration:
- Whakatōhea: Mission/quest concept from Māori tradition
- Tauwāhi: Traditional navigation and positioning knowledge
- Kaitiakitanga: Mathematical stewardship of zoo resources
- Place Connection: Hamilton/Kirikiriroa as mathematical space