Garden Plot Measurement
Māra Kai — Measuring to Grow, Growing to Sustain · Mathematics in Context
Ngā Whāinga Akoranga · Learning Intentions
- Calculate perimeter, area, and volume for rectangles, triangles, and circles
- Create accurate scale drawings and use scale to find real-world dimensions
- Apply proportional reasoning to planting density and yield calculations
- Solve multi-step problems involving cost, materials, and sustainability planning
Paearu Angitu · Success Criteria
- I can calculate the area of irregular composite plots combining 3 shapes
- I can create a scale drawing at 1 cm = 2 m with labelled dimensions
- I can calculate volume of raised beds and cost of soil components
- I can use a planting formula to find how many plants fit in a given space
Hononga Marautanga · Curriculum Alignment
Level 4–5: calculate perimeter, area, and volume in context; create and interpret scale drawings; apply proportional reasoning; solve multi-step problems using appropriate units.
Recognise mathematical knowledge embedded in Māori horticultural practice; understand how the kaitiakitanga principle connects measurement to sustainability; connect māra kai design to whānau wellbeing.
Whakataukī
"He aha te mea nui o te ao? He tangata, he tangata, he tangata"
What is the greatest thing in the world? It is people, it is people, it is people. And the māra feeds the people — measurement is the practical foundation of manaakitanga.
The māra kai (food garden) is one of the oldest and most mathematically rich practices in Māori culture. Designing a garden that feeds a whānau requires calculating perimeter (how much fencing), area (how many plants fit), volume (how much soil and compost), and scale (how to draw a plan). This handout uses a real marae garden design.
Wāhi 1 · Āhua o te Māra · Garden Design — Area and Perimeter
The Mangakōtukutuku kura wants to build a new māra kai beside the wharenui. They have a rectangular plot 18 m long and 12 m wide. Inside, they want separate beds for different kai (food crops).
| Bed name | Shape | Dimensions | Crop |
|---|---|---|---|
| Kūmara bed A | Rectangle | 6 m × 4 m | Red kūmara |
| Kūmara bed B | Rectangle | 6 m × 4 m | Orange kūmara |
| Kāmokamo bed | Rectangle | 8 m × 3 m | Kāmokamo (gourds) |
| Pūhā bed | Triangle | base 4 m, height 3 m | Pūhā (sow thistle) |
| Tikumu bed | Circle | radius 1.5 m | Tikumu (mountain daisy) |
| Pathway | — | All remaining area | Gravel |
-
Calculate the area of each bed (show all working, use correct units):
Rectangle: A = l × w | Triangle: A = ½ × b × h | Circle: A = π × r²
- Calculate the total planted area. Then find the pathway area (total plot − all beds). Express the pathway as a percentage of the total plot.
- Scale drawing: Using the grid below, draw the garden to a scale of 1 cm = 2 m. Label each bed with its name and dimensions. (Grid squares = 1 cm each.)
-
The plot needs a deer/rabbit fence around its entire perimeter. Fencing costs $28.50 per metre, plus four gate posts at $45 each and one 1.5 m gate at $220. Calculate the total fencing cost.
Perimeter = 2 × (length + width)
Wāhi 2 · Wāhi Oneone · Soil Volume Calculations
Kūmara are traditionally grown in rua kūmara — raised mounds that allow excellent drainage and warmer soil. The marae is creating raised beds with these specifications:
- Kūmara beds A & B: raised to 35 cm above ground level
- Kāmokamo bed: raised to 25 cm
- Pūhā and tikumu: at ground level (no fill needed)
- Soil mix: 60% garden soil · 30% compost · 10% pumice
- Garden soil: $42/m³ · Compost: $65/m³ · Pumice: $28/m³
-
Calculate the volume of raised bed fill needed for Kūmara Bed A (6 m × 4 m × 0.35 m). Repeat for Bed B and the Kāmokamo bed.
Volume (rectangular prism) = length × width × height
- Calculate the total volume of soil, compost, and pumice needed (using 60/30/10% mix). Then calculate the cost of each component and total cost.
- Soil is sold in 50-litre bags (1 m³ = 1,000 litres). How many bags of each component are needed? (Always round UP.) If bags cost: soil $4.80, compost $6.20, pumice $3.10 — what is the total bag cost?
Wāhi 3 · Whai Hua · Planting Density and Yield
Kūmara plants are traditionally spaced 60 cm apart in rows, rows 90 cm apart. This spacing — developed over generations — optimises yield while allowing weeding access. Modern research confirms it remains optimal for NZ growing conditions.
-
How many kūmara plants fit in Bed A (6 m × 4 m) at 60 cm within rows, 90 cm between rows? Draw a diagram of the planting pattern.
Plants per row = floor(bed width ÷ 0.6) | Number of rows = floor(bed length ÷ 0.9)
- Each kūmara plant yields an average of 1.8 kg ± 0.4 kg per season. What is the expected total yield from both kūmara beds (A and B) combined? What is a realistic range (minimum and maximum)?
- The kura wants to harvest enough kūmara for a hāngī feeding 80 students and staff. Each person eats approximately 350 g of kūmara. How many plants are needed? Do both beds together provide enough? Show all working.
- Sustainability planning (kaitiakitanga): A māra needs organic matter replaced each year. The compost pile produces 0.8 m³ of finished compost per 3 months. How many m³ annually? Is this enough to replace the 30% compost layer (top 10 cm) in all raised beds each year?
Aronga Mātauranga Māori
The māra kai was not simply a garden — it was an act of relationship: with the whenua, with the ancestor crops (kūmara came with Māori from Polynesia), and with future generations. Māori horticulturalists of the 14th and 15th centuries were precision planners who understood drainage gradients, microclimates, and seasonal timing without rulers or calculators. Their knowledge lives in the patterns of māra across Aotearoa — the orientation, spacing, and bed design that ensured maximum yield on the available land.
The concept of kaitiakitanga as applied to the māra means: take what you need, replace what you took, leave the soil richer than you found it. The sustainability calculation in Part 3 is not just a mathematics exercise — it asks the same question that every kūmara grower from the 14th century to today has had to answer: will this māra still feed the mokopuna?
Ngā Rauemi Tautoko · Support Materials
Resources already provided:
- This handout with all three problem parts and specification tables
- Calculator (essential for Part 2 and Part 3 calculations)
- Ruler (essential for Part 1 scale drawing — 1 cm = 2 m)
- π ≈ 3.14 or π button on calculator
Aronga Rerekē · Differentiated Pathways
Tīmata · Entry Level
Complete Part 1 questions 1–2 (area and percentage). Draw a simplified version of the scale plan. Complete Part 3 question 1 (planting density).
Paerewa · On Level
Complete Parts 1 and 2 fully. Answer all Part 3 questions except the sustainability question. Show all working with correct units throughout.
Tūāpae · Extension
Complete all three parts including the sustainability calculation. Then design your own māra kai for a real space at school: identify dimensions, choose 4 crops, calculate area, soil volume, planting density, and total yield. Present your scale plan, calculations, and a planting schedule linked to the Maramataka growing calendar.
📋 Teacher Planning Snapshot
Ngā Whāinga Ako — Learning Intentions
Students will engage with this resource to build pāngarau (mathematical) understanding — developing number sense, pattern recognition, and mathematical reasoning through hands-on, culturally grounded activities that connect to tamariki's world.
Ngā Paearu Angitū — Success Criteria
- ✅ Students can explain their mathematical thinking using words, objects, drawings, or symbols.
- ✅ Students can apply the number or pattern concept in this resource to a real or everyday context.
Differentiation & Inclusion
Scaffold support: Use concrete materials (blocks, counters, fingers) for entry-level engagement before progressing to abstract representations. Offer extension challenges asking students to generalise a pattern, write their own word problem, or explain their strategy to a partner.
ELL / ESOL: Mathematical language is a discipline-specific barrier — pre-teach key terms (e.g., equals, more than, fewer, pattern, factor) using visual representations. Allow students to demonstrate mathematical understanding non-verbally or through drawing. Pair with a bilingual buddy where possible.
Inclusion: Embed choice in how students engage — oral, written, or diagrammatic responses are all valid. Neurodiverse learners benefit from short, chunked task sequences with immediate feedback loops. Avoid timed drills in favour of exploratory tasks that reward curiosity. Make the maths classroom a safe place to be wrong and try again.
Mātauranga Māori lens: Pāngarau is a living tradition in Te Ao Māori — from the geometric precision of tukutuku and kōwhaiwhai patterns to the navigational mathematics of waka hourua, and the seasonal calculations embedded in maramataka. Framing early number sense within these contexts shows tamariki that mathematics is a human, culturally rich endeavour — not a foreign import. Encourage students to see counting, measuring, and patterning as acts of knowing their world.
Prior knowledge: Designed for early learners. No prior formal mathematics knowledge required. Teachers should assess current number knowledge before selecting appropriate entry points.
Curriculum alignment
- Number and Algebra — Number Strategies: Use a range of counting, grouping, and equal-sharing strategies with whole numbers and fractions.
- Number and Algebra — Patterns and Relationships: Generalise that the next counting number gives the result of adding one object to a set and that counting the number of objects in a set tells how many.