A box of size a cm by b cm by c cm is to be wrapped with a square piece of wrapping paper. Without cutting the paper what is the smallest square this can be?

Discover a way to sum square numbers by building cuboids from small cubes. Can you picture how the sequence will grow?

How can you change the surface area of a cuboid but keep its volume the same? How can you change the volume but keep the surface area the same?

A ribbon runs around a box so that it makes a complete loop with two parallel pieces of ribbon on the top. How long will the ribbon be?

A spider is sitting in the middle of one of the smallest walls in a room and a fly is resting beside the window. What is the shortest distance the spider would have to crawl to catch the fly?

Jo made a cube from some smaller cubes, painted some of the faces of the large cube, and then took it apart again. 45 small cubes had no paint on them at all. How many small cubes did Jo use?

Stick some cubes together to make a cuboid. Find two of the angles by as many different methods as you can devise.