Lesson 2: Plotting Routes & Calculating Distances Using Coordinates
Using coordinate pairs to plot animal-to-animal routes and calculate exact distances using the distance formula — mathematics meets zoo navigation.
🎯 Ngā Whāinga Akoranga | Learning Intentions
How to plot a series of (x,y) coordinate points to represent a route; how to calculate distance between two coordinates using |x2-x1| and |y2-y1| for horizontal and vertical segments.
Plot a complete zoo visitor route as a series of coordinate points; calculate the total route distance using coordinate arithmetic.
🎥 Media Anchor & Mathematical Scaffold
Distance Between Two Points
Video Anchor: How to Find the Distance Between Two Points — Geometry Tutorial (Runtime: 4:35).
🧠 1. Before Viewing
If the kiwi house is at (2,3) and the giraffe enclosure is at (2,7), what is the distance between them? Can you work it out from the coordinates alone without measuring the map?
👁️ 2. During Viewing
- Full Watch: Watch the entire 6-minute video. As you watch, write down: (1) What is the distance formula? (2) Work through at least two examples from the video. (3) Try predicting the distance before the video shows the answer.
🗣️ 3. After Viewing — Kaiako Move
Kaiako Move: Model plotting a 5-stop zoo route using coordinates. Show students how to calculate horizontal and vertical distances between stops. Add them up for total route distance.
Task: Route Calculator: Plot a 6-stop zoo tour as a series of coordinates. Calculate each leg distance using coordinate arithmetic. Total route distance and compare with the map scale measurement.
⚡ Whakaoho | Do Now (5 mins)
The giraffe enclosure is at (4,6) and the café is at (7,6). What is the distance between them — and which direction (N/S/E/W) would you walk?
📐 Activity 1: Guided Mathematical Exploration (25 mins)
Route comparison: plot two different routes between the same start and end points. Calculate the distance of each. Which is shorter? Why?
✍️ Activity 2: Application & Reflection (20 mins)
Distance reflection: write a worked example showing how you calculate the distance from (1,2) to (1,8) using coordinates. What real-world measurement does this represent?
🏫 Kaiako Planning & Pedagogy Notes
Curriculum Alignment: Te Mātaiaho Mathematics Phase 3/4 — Geometry: plot coordinate routes; calculate distances using coordinate arithmetic.
Hamilton Zoo Context: All tasks use authentic zoo spatial data. Print the map per group. Groups will mark competing routes and need to lay them side by side.
Cultural Connection: A waka route was chosen against wind, current and season, not by shortest line. When ākonga plot a route through the zoo, ask what the shortest path ignores — gradient, crowding, and the animals it disturbs.