🎥 The Context: A Species on the Brink
The Kākāpō is one of New Zealand's most unique treasures (taonga). Once numbering in the hundreds of thousands, their population critically declined. Through intensive management, they are recovering. But managing a population requires maths—specifically, understanding growth rates and spatial resource management.
🌍 Kaitiakitanga (Guardianship)
Conservation isn't just science; it's an act of Kaitiakitanga. As mathematical modellers, our job is to predict future needs so we can ensure the whakapapa (lineage) of these birds continues forever.
📈 Problem 1: Modelling Recovery
In 1995, the Kākāpō population reached a low of 51 birds. Thanks to the recovery programme, the population has grown. Let's model two potential growth scenarios for a new sanctuary island.
Scenario A: Linear Growth
The population increases by exactly 5 birds per year.
Equation: \( P = 51 + 5t \)
Scenario B: Exponential Growth (Success!)
With a successful breeding season every year, the population grows by 10% per year.
Equation: \( P = 51 \times (1.10)^t \)
Your Task:
- Graph both functions on the same set of axes for \( t = 0 \) to \( t = 20 \) years.
- Calculate the population in Year 20 for both scenarios.
- Linear: ____________
- Exponential: ____________
- compare: In which year does the Exponential model overtake the Linear model significantly (by more than 20 birds)?
🚧 Problem 2: The Sanctuary Fencing Challenge
A new "Mainland Island" sanctuary is being built at Hamilton Zoo to breed Kākāpō safe from predators. You have funding for exactly 1200 metres of predator-proof fencing.
The Geometry of Safety
You need to enclose a rectangular area using this 1200m of fencing. To support the most birds, you need to maximise the Area inside the fence.
Option 1: Long and Thin
Length = 500m, Width = 100m
Perimeter = \( 2(500 + 100) = 1200m \) (Valid)
Area = 500 × 100 = 50,000 m²
Option 2: A Square
Length = ?, Width = ?
Calculate the dimensions and area for a square.
Investigation:
- Test 3 different rectangle dimensions that have a perimeter of 1200m.
- Create a table of your results: Length | Width | Area.
- Generalise: Let Length = \( x \). Then Width = \( 600 - x \).
Write an equation for Area \( A \) in terms of \( x \). - Solve: What value of \( x \) gives the maximum possible area?
💬 Critical Thinking
Quality vs Quantity
In Problem 2, we found the shape that maximises area. However, Kākāpō are solitary and territorial. They prefer complex terrain (hills, trees) over flat open fields.
discuss: Why might a mathematically "optimal" square fence NOT be the best ecological choice for the birds? Consider terrain, rivers, and existing forest lines.
Curriculum alignment
- Algebra — Practices: - The symbols + and - represent addition and subtraction, and the equal sign shows that two sides of an equation represent the same quantity. - An open number sentence is a st…
- Matter Interactions and Energy — Knowledge: transparent materials let all or most light through.
- Measurement — Practices: - Standard measuring units are universally agreed and commonly used units for making measurements that enable people to communicate clearly. - Measuring tools are usually mark…
- Measurement — Practices: - The distance around the boundary of a 2D shape gives its perimeter. - A polygon is a 2D straight-edged shape where the sides connect to form a closed shape.
- Earth and Space — Knowledge: The Earth rotates on its axis once every 24 hours.
📋 Teacher Planning Snapshot
Ngā Whāinga Ako — Learning Intentions
Students will apply mathematical thinking to authentic contexts at Te Kāhui Kararehe o Kirikiriroa (Hamilton Zoo), developing tūhuratanga (statistical inquiry) skills through real data about animal populations, habitats, and conservation. This unit connects maths to kaitiakitanga — our responsibility to care for ngā manu me ngā kararehe of Aotearoa.
Ngā Paearu Angitū — Success Criteria
- ✅ I can collect, display, and interpret data about animals using appropriate graphs and statistics.
- ✅ I can apply measurement, geometry, or number skills to solve real problems in a zoo context.
- ✅ I can connect mathematical findings to conservation and kaitiakitanga for native species.
Differentiation & Inclusion
Scaffold support: Provide pre-drawn graph templates and data tables for entry-level access. Offer extension tasks requiring students to design their own statistical investigation using zoo population data and write a conservation recommendation backed by evidence.
ELL / ESOL: Pre-teach mathematics and conservation vocabulary. Use visual supports — diagrams, models, and real objects where possible. Allow students to explain their mathematical thinking verbally before writing.
Inclusion: Offer manipulatives and calculator access to support all learners. Neurodiverse learners benefit from structured inquiry frameworks, clear success criteria, and choice in how they present mathematical findings. The hands-on, real-world context of zoo mathematics motivates engagement across learning profiles.
Mātauranga Māori lens: Connect to traditional Māori knowledge of kararehe and manu — including the significance of native species like tuatara, kiwi, and kākāpō in tikanga Māori. Use maramataka (traditional Māori lunar calendar) as a context for data and pattern recognition. Frame conservation mathematics as a practical expression of kaitiakitanga.
Prior knowledge: Best used after foundational statistics and measurement skills. Connects well to science ecology units.