The challenge is to produce elegant solutions. Elegance here implies simplicity. The focus is on rhombi, in particular those formed by jointing two equilateral triangles along an edge.

Explore patterns based on a rhombus. How can you enlarge the pattern - or explode it?

What shape and size of drinks mat is best for flipping and catching?

Here is a chance to create some attractive images by rotating shapes through multiples of 90 degrees, or 30 degrees, or 72 degrees or...

Can you reproduce the Yin Yang symbol using a pair of compasses?

Follow the diagrams to make this patchwork piece, based on an octagon in a square.

Design and construct a prototype intercooler which will satisfy agreed quality control constraints.

Generate three random numbers to determine the side lengths of a triangle. What triangles can you draw?

Jenny Murray describes the mathematical processes behind making patchwork in this article for students.