Four rods, two of length a and two of length b, are linked to form a kite. The linkage is moveable so that the angles change. What is the maximum area of the kite?
If you move the tiles around, can you make squares with different coloured edges?
This article for teachers discusses examples of problems in which there is no obvious method but in which children can be encouraged to think deeply about the context and extend their ability to. . . .
It is possible to dissect any square into smaller squares. What is the minimum number of squares a 13 by 13 square can be dissected into?
ABC is an equilateral triangle and P is a point in the interior of the triangle. We know that AP = 3cm and BP = 4cm. Prove that CP must be less than 10 cm.
How many winning lines can you make in a three-dimensional version of noughts and crosses?
Can you mentally fit the 7 SOMA pieces together to make a cube? Can you do it in more than one way?
Have a go at this 3D extension to the Pebbles problem.