Construct two equilateral triangles on a straight line. There are two lengths that look the same - can you prove it?

The items in the shopping basket add and multiply to give the same amount. What could their prices be?

Take a triangular number, multiply it by 8 and add 1. What is special about your answer? Can you prove it?

By sketching a graph of a continuous increasing function, can you prove a useful result about integrals?

Can you work out the irrational numbers that belong in the circles to make the multiplication arithmagon correct?

Use graphs to gain insights into an area and perimeter problem, or use your knowledge of area and perimeter to gain insights into the graphs...

What do you get when you raise a quadratic to the power of a quadratic?