Lesson 2: Distance Between Two Coordinates — How Far is the Giraffe from the Kiwi?
Using the distance formula and Pythagoras' theorem to calculate exact distances between zoo enclosures from their coordinates — no ruler required.
🎯 Ngā Whāinga Akoranga | Learning Intentions
How to calculate horizontal and vertical distances between coordinates; how Pythagoras' theorem (a²+b²=c²) calculates diagonal distances; when to use each method.
Calculate distances between 6 pairs of enclosure coordinates using both the simple difference method and Pythagoras; compare with map scale measurements.
🎥 Media Anchor & Mathematical Scaffold
Mathematics in Context: Hamilton Zoo
Watch the full clip — 3:40. Source: Khan Academy. The zoo context is ours; the clip teaches the method, then the lesson applies it to real enclosure coordinates.
🧠 1. Before Viewing
The kiwi house is at (2,3) and the giraffe enclosure is at (6,7). How far apart are they — directly in a straight line? Can you calculate this WITHOUT measuring the map?
👁️ 2. During Viewing
- Early in the clip: For a horizontal or vertical path, distance = |x2-x1| or |y2-y1|. Apply this to the pair (2,3) and (2,7). What's the distance?
- Midway: For a diagonal path: use Pythagoras. From (2,3) to (6,7): horizontal change = 4, vertical change = 4. Distance = √(4²+4²) = √32 ≈ 5.66 units. Verify this.
- Later in the clip: Convert your coordinate distance to real metres using the map scale. Does this match the measurement you'd make on the printed map?
🗣️ 3. After Viewing — Kaiako Move
Kaiako Move: Work through one complete distance calculation on the board: identify the two coordinates, calculate horizontal and vertical change, apply Pythagoras, convert to real metres. Let students check with their maps.
Task: Distance Calculations: For 6 pairs of zoo enclosures, calculate the distance using coordinates. For horizontal/vertical pairs — use simple difference. For diagonal pairs — apply Pythagoras.
⚡ Whakaoho | Do Now (5 mins)
Challenge: which is further from the zoo entrance at (0,0): the lion enclosure at (5,0) or the kiwi house at (3,4)? Use Pythagoras to find out.
📐 Activity 1: Guided Mathematical Exploration (25 mins)
Distance accuracy check: calculate distances using coordinates, then measure the same distances directly on the map. How close are your coordinate calculations to the measured distances?
✍️ Activity 2: Application & Reflection (20 mins)
Pythagoras reflection: explain in your own words how Pythagoras' theorem allows you to calculate a distance without measuring. Include a worked example from today.
🏫 Kaiako Planning & Pedagogy Notes
Curriculum Alignment: Te Mātaiaho Mathematics Phase 3 — Geometry and Measurement: calculate distances using coordinate arithmetic and Pythagoras' theorem.
Hamilton Zoo Context: All tasks use authentic zoo spatial data. Print the map with the scale bar clearly visible; the scale is doing the work in this lesson.
Cultural Connection: Waka navigators estimated distance from elapsed time, star altitude and swell rather than from a straight line on paper. Ask ākonga which method is more useful when the ground is not flat — the zoo paths are not straight either.