📐 Week 2: Rua Kūmara Volume Calculation

Unit 10: Kai, Culture and Climate — Surviving Scarcity
Calculate how many kūmara could be stored in a rua kūmara (storage pit). This connects mathematics to understanding how Māori managed food scarcity.

🔢 Numeracy Integration: This activity uses measurement, volume calculations, and estimation. It connects to Mathematics Level 4: Measurement and Geometry.

📏 Step 1: Measure Your Model Rua

If you built a model rua kūmara, measure it. If not, use these example measurements:

Measurement Your Model Example (Real Size)
Length (cm) _____ cm 200 cm (2 m)
Width (cm) _____ cm 150 cm (1.5 m)
Depth/Height (cm) _____ cm 100 cm (1 m)

🧮 Step 2: Calculate Volume

Formula for Volume of a Rectangular Prism:
Volume = Length × Width × Height
(For a rua kūmara, we'll treat it as a rectangular box)

Your Calculations:

Volume = _____ cm × _____ cm × _____ cm

Volume = _____ cm³

Convert to cubic meters (m³):

1 m³ = 1,000,000 cm³

Volume = _____ cm³ ÷ 1,000,000 = _____ m³

🍠 Step 3: Estimate Kūmara Storage

Assumptions:

  • An average kūmara is about 15 cm long and 8 cm wide (roughly the size of a large potato)
  • Kūmara are stored with some space between them (not packed tightly)
  • About 60% of the rua space is actually filled with kūmara (40% is air space)

Calculate:

1. Volume of one kūmara (approximate):

Volume of kūmara ≈ _____ cm³

2. How many kūmara could fit (if packed tightly):

Number = Rua volume ÷ Kūmara volume

Number = _____ ÷ _____ = _____ kūmara

3. Account for air space (use 60%):

Actual storage = _____ × 0.6 = _____ kūmara

🤔 Step 4: Reflection Questions

  1. How many people could this rua feed? (Assume 1 person eats 2-3 kūmara per day, and storage needs to last 3-4 months)


  2. What if the rua was bigger/smaller? How would that change the number of kūmara stored?


  3. Why was storing kūmara important? What would happen if you couldn't store them?


💡 Extension: Research actual rua kūmara sizes from archaeological sites. Compare your calculations with historical records. How accurate were your estimates?