Activity 1 · a circumference from shadows
For older learners, draw two upright rods 800 km apart on a meridian under parallel rays. Supply a 7.2° signed-angle difference. Ask: what fraction of a full turn is this, and what circumference follows? The answer is 7.2/360 = 1/50, so C = 800 × 50 = 40,000 km. Now increase the angle by 0.1° and explain why the inferred circumference becomes smaller.
Activity 2 · hide the bottom, then raise the observer
For younger learners, use a ball, a small marked target and a camera. Keep the target fixed while moving the camera upward. Record the lowest visible target mark. The activity models occlusion; it does not turn the ball’s measurements into Earth’s actual radius. Extend it by comparing hidden height and tangent drop in the curvature tool.
Activity 3 · one route on three maps
Choose two southern coordinate pairs in the route tool. Compare the endpoints and bearings, then find the same arc on Mercator, equal-area and polar maps. Ask which visual bend belongs to the projection and which distance stays unchanged. The maps receive the same surface route, so a changed line shape does not add kilometres.
A record learners can complete
Before collecting outdoor shadows, record rod height, date, local solar-noon procedure, site coordinates and uncertainties. Never view the Sun through unfiltered optics. Use the observation sheet for predictions and raw readings; compare repeat scatter with a shared alignment bias.