Classroom
One lesson of 45 minutes per pattern: a question to predict, a short film, a worksheet at three levels (Starter, Core, Challenge) with the answers apart, and questions to discuss. Print them on A4 or save them as PDF.
All lessons in one PDF →- Probability · ages 15–18 · 45 min
The Galton board: order from random bounces
- count paths with Pascal’s triangle and binomial coefficients
- turn path counts into probabilities
- see why many random events give a predictable shape
- Numbers and geometry · ages 15–18 · 45 min
Fibonacci in a sunflower
- see how a fraction of a turn makes spokes
- meet the golden ratio as the limit of Fibonacci ratios
- explain why the golden angle fills a flower evenly
- Modular arithmetic · ages 13–18 · 45 min
Times tables on a circle
- calculate with remainders (modular arithmetic)
- draw a cardioid as the envelope of straight lines
- link the multiplier to the number of cusps
- Geometry and probability · ages 14–18 · 45 min
The chaos game: a fractal from chance
- find midpoints with coordinates
- describe the Sierpiński triangle and its self-similarity
- see how a random rule can still give an exact shape