Visualising and representing

If you move the tiles around, can you make squares with different coloured edges?

If you split the square into these two pieces, it is possible to fit the pieces together again to make a new shape. How many new shapes can you make?

A hundred square has been printed on both sides of a piece of paper. What is on the back of 100? 58? 23? 19?

Can you find a cuboid that has a surface area of exactly 100 square units. Is there more than one? Can you find them all?

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?

Which of these dice are right-handed and which are left-handed?

Here are shadows of some 3D shapes. What shapes could have made them?

Investigate how networks can be used to solve a problem for the 18th Century inhabitants of Konigsberg.

If you can copy a network without lifting your pen off the paper and without drawing any line twice, then it is traversable. Decide which of these diagrams are traversable.