Visualising and representing

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?

Can you arrange the shapes in a chain so that each one shares a face (or faces) that are the same shape as the one that follows it?

Each of the nets of nine solid shapes has been cut into two pieces. Can you see which pieces go together?

A bus route has a total duration of 40 minutes. Every 10 minutes, two buses set out, one from each end. How many buses will one bus meet on its way from one end to the other end?

Charlie and Alison have been drawing patterns on coordinate grids. Can you picture where the patterns lead?

Place a red counter in the top left corner of a 4x4 array, which is covered by 14 other smaller counters, leaving a gap in the bottom right hand corner (HOME). What is the smallest number of moves it will take to move the red counter to HOME?

Choose a couple of the sequences. Try to picture how to make the next, and the next, and the next... Can you describe your reasoning?

Think of a number and follow the machine's instructions... I know what your number is! Can you explain how I know?

Explore the area of families of parallelograms and triangles. Can you find rules to work out the areas?

The sums of the squares of three related numbers is also a perfect square - can you explain why?