Lesson 4: Distance & Scale — Roa me te Inenga

Students interpret Hamilton Zoo's map scale to convert grid distances into real-world metres, apply measurement to conservation planning, and connect scale to traditional whakatere waka navigation tools.

Phase 3 · Years 7–8 Mathematics · Pāngarau ⏱ 60 min

📎 Learning Intentions | Ngā Whāinga Ako

Know | Mōhio

  • That a map scale (e.g., 1 cm = 10 m) is a ratio showing how map distance relates to real-world distance.
  • That coordinate grid units can represent real-world measurements when scale is applied.
  • That waka hourua navigators estimated distances by measuring time and ocean-current speed — an early form of dead reckoning.

Demonstrate | Whakaatu

  • Use the zoo map scale to convert at least 5 grid distances into metres.
  • Calculate the total walking distance (in metres) of a planned zoo visit route.
  • Estimate how long a zoo visit route would take at an average walking speed of 80 m/min.

📐 Curriculum Alignment

NZC Mathematics and Statistics · Level 3 · Geometry and Measurement — Measurement
Use linear scales and whole numbers of metric units for length, area, volume and capacity, weight (mass), angle, temperature, and time.
Ministry of Education (2007). The New Zealand Curriculum. Mathematics and statistics achievement objectives, Level 3.

🌿 Whakatūwhera

Waka hourua navigators measured distance not in kilometres, but in days sailed, star-rises, and counts of ocean swell. Each of those is a ratio — a form of map scale read directly from the world rather than printed in a legend. That is the same idea you are about to use on paper.

🪶 Mātauranga Māori — handoff required (whakataukī). A whakataukī stood here that carried no source and could not be attested; its translation also rendered ki uta as "to the mountains" when it means toward the land or inland. It was removed on 2026-08-30 rather than reworded, because a saying presented as a whakataukī asserts a whakapapa it must be able to carry. If you have an appropriate whakataukī for wayfinding and scale, or can source one with kaiako Māori or kaumātua, add it here — the navigation content above stands on its own until then.

🎤 Kaiako Hook (5 min)

Hold up two maps of the same area — one at 1:1000 scale, one at 1:5000. Ask: "Which is larger on paper? Which gives more detail? If I walk 2 cm on each map, how far have I actually walked in real life?"

📚 Lesson Content

Part 1: Understanding Map Scale (10 min)

🔑 Scale Ratio

Hamilton Zoo Map Scale: 1 grid unit = 20 metres (example — adjust to match your printed map).

Formula: Real Distance = Grid Distance × Scale Factor

Example: The Lion (4, 3) to Giraffe (4, −2) = 5 grid units → 5 × 20 = 100 metres.

Part 2: Scale Conversion Practice (20 min)

Students work through these five pairs using their plotted copy of the class zoo grid map (Lesson 1) from Lesson 2. For each pair: calculate the grid distance, convert it to metres using the scale, then rank all five from shortest to longest.

  1. Entrance (0, 0) → Café (2, 4)
  2. Lion (4, 3) → Elephant (3, 4)
  3. Kiwi (−3, 4) → Chimpanzee (−3, 5)
  4. Meerkats (−4, −3) → Entrance (0, 0)
  5. Red Panda (1, 5) → Giraffe (4, −2)
🔑 Kaiako answer key — Part 2
  1. Entrance → Café: 2 + 4 = 6 units → 6 × 20 = 120 m
  2. Lion → Elephant: 1 + 1 = 2 units → 40 m
  3. Kiwi → Chimpanzee: 0 + 1 = 1 unit → 20 m
  4. Meerkats → Entrance: 4 + 3 = 7 units → 140 m
  5. Red Panda → Giraffe: 3 + 7 = 10 units → 200 m

Ranked shortest to longest: Kiwi–Chimpanzee (20 m), Lion–Elephant (40 m), Entrance–Café (120 m), Meerkats–Entrance (140 m), Red Panda–Giraffe (200 m).

These are grid-path (along the lines) distances, matching the rule set in Lesson 3 — no diagonal shortcuts.

Part 3: Zoo Visit Time Planner (15 min)

Students plan a complete zoo visit day using their best route from Lesson 3. They now calculate:

Compare with a partner: Whose route visits more animals within a 5-hour zoo day?

Part 4: Conservation Application — Enclosure Size (10 min)

On our class grid — which is our own overlay, not the zoo's real layout — suppose a kiwi enclosure occupies a 4×3 rectangle. At our scale (1 unit = 20 m), what area would that be on the ground?

Area (grid) = 4 × 3 = 12 square grid units. Area (real) = 12 × (20 m)² = 12 × 400 m² = 4,800 m².

Discuss: Is this enough space for a healthy kiwi population? Before answering, have students look up real habitat guidance from a named source (e.g. Save the Kiwi or Department of Conservation) — the answer should cite what they found, not a guess. What area would you design for a kiwi sanctuary?

✅ Assessment

🎟 Exit Ticket

  1. The Chimpanzee (−3, 5) and Red Panda (1, 5) are on the same y-level. What is their real-world distance apart (scale: 1 unit = 20 m)?
  2. A zoo path covers 7 grid units. If the scale is 1 unit = 25 m, how long is the path in metres?
  3. Why do navigators need scale? Give one real-world example.
🔑 Kaiako answer key
  1. 80 m — |1 − (−3)| = 4 grid units; 4 × 20 m = 80 m.
  2. 175 m — 7 × 25 m.
  3. Open response — e.g. a map is only useful if you can convert its distances to real ones (hiking maps, ship charts, GPS apps all state a scale).