Graphs that come alive

Begin with a curve that can move. Trace it, notice the crossing at the centre, and describe what seems to repeat.

We would change one parameter and watch how the curve responds. Before reaching for algebra, each learner would make a prediction and test it against the graph.

Next, we would connect points on the curve to the equations x = 3 cos(t) and y = 3 sin(2t), checking what happens at a few simple values of t.

The goal would be to explain a shape using a reason, then make a new shape intentionally. This is a design example, not a real teacher's class or a bookable lesson.