A graph appears on the board with no numbers, no labels, no title — just axes and a shape. Three questions, always in this order: what do you notice? what do you wonder? what story could this graph be telling? In this course the horizontal axis is usually time, and the story is usually motion — which means the mathematics lives in the slope: where the curve is steep, something is happening fast, and where it flattens, something is coming to rest.
How we play
- Thirty seconds of silent looking. No hands yet.
- Notice only what is there: a steep climb, a levelling-off, a moment where the curve turns around and comes back.
- Pitch a story — then point to the feature of the graph that each part of your story explains.
Three stories for one curve that climbs, flattens, then climbs again
- “Someone walking to school who stops at a friend’s house. The flat stretch is the doorstep conversation — position frozen, clock still running.”
- “The height of water filling a vase with a bulge in the middle. The flattening is the bulge: same tap, more vase to fill, so the level rises more slowly.”
- “It is a cubic with a horizontal tangent.” True to the shape, but a story with no characters. We sent it back for some.
One variation
Same rules, but the graph on the board is a velocity-time graph — and now the story hides one layer down. A flat stretch no longer means stopped; it means cruising. The curve dipping below the axis does not mean going backward in time; it means the walker turned around. Telling the position story from the velocity graph, or the velocity story from the position graph, is the whole game of Motion on a Line — and the group that plays it here first plays it faster there.
Features have names
Steepness, flat spots, turning points, the direction of bending — using the right name for the right feature is half of every story, and this course spends a semester making those names exact. “Steepness” is about to become The Derivative, and the art of reading a whole story from slopes alone is Curve Sketching.