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?

A 3x3x3 cube may be reduced to unit cubes in six saw cuts. If after every cut you can rearrange the pieces before cutting straight through, can you do it in fewer?

What is the total area of the four outside triangles which are outlined in red in this arrangement of squares inside each other?

Two buses leave at the same time from two towns Shipton and Veston on the same long road, travelling towards each other. At each mile along the road are milestones. The buses' speeds are constant and in the ratio 5 to 4. The buses travel to and fro between the towns. What milestones are at Shipton and Veston?

Bilbo goes on an adventure, before arriving back home. Using the information given about his journey, can you work out where Bilbo lives?

A bicycle passes along a path and leaves some tracks. Is it possible to say which track was made by the front wheel and which by the back wheel?

Can you find ways of joining cubes together so that 28 faces are visible?

Can you make the numbers around each face of this solid add up to the same total?

Explain why, when moving heavy objects on rollers, the object moves twice as fast as the rollers. Try a similar experiment yourself.