Visualising and representing

A game has a special dice with a colour spot on each face. These three pictures show different views of the same dice. What colour is opposite blue?

Follow the journey taken by this bird and let us know for how long and in what direction it must fly to return to its starting point.

Imagine a wheel with different markings painted on it at regular intervals. Can you predict the colour of the 18th mark? The 100th mark?

A dog is looking for a good place to bury his bone. Can you work out where he started and ended in each case? What possible routes could he have taken?

Imagine a 3 by 3 by 3 cube made of 9 small cubes. Each face of the large cube is painted a different colour. How many small cubes will have two painted faces? Where are they?

Here are more buildings to picture in your mind's eye. Watch out - they become quite complicated!

Have a look at what happens when you pull a reef knot and a granny knot tight. Which do you think is best for securing things together? Why?

In how many ways can you fit two of these yellow triangles together? Can you predict the number of ways two blue triangles can be fitted together?