Visualising and representing

Choose a box and work out the smallest rectangle of paper needed to wrap it so that it is completely covered.

What are the next three numbers in this sequence? Can you explain why are they called pyramid numbers?

Given a 2 by 2 by 2 skeletal cube with one route `down' the cube. How many routes are there from A to B?

How many different ways can I lay 10 paving slabs, each 2 foot by 1 foot, to make a path 2 foot wide and 10 foot long from my back door into my garden, without cutting any of the paving slabs?

How can you make an angle of 60 degrees by folding a sheet of paper twice?

Can you shunt the trucks so that the Cattle truck and the Sheep truck change places and the Engine is back on the main line?

Is it possible to rearrange the numbers 1,2......12 around a clock face in such a way that every two numbers in adjacent positions differ by any of 3, 4 or 5 hours?

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?

Billy's class had a robot called Fred who could draw with chalk held underneath him. What shapes did the pupils make Fred draw?

Have you ever tried tessellating capital letters? Have a look at these examples and then try some for yourself.