Visualising and representing

Imagine a pyramid which is built in square layers of small cubes. If we number the cubes from the top, starting with 1, can you picture which cubes are directly below this first cube?

Can you picture where this letter "F" will be on the grid if you flip it in these different ways?

Nearly all of us have made table patterns on hundred squares, that is 10 by 10 grids. This problem looks at the patterns on differently sized square grids.

Try adding fractions using A4 paper.

Can you compare these bars with each other and express their lengths as fractions of the black bar?

What fraction of the black bar are the other bars? Have a go at this challenging task!

There are lots of different methods to find out what the shapes are worth - how many can you find?

This task, written for the National Young Mathematicians' Award 2016, involves open-topped boxes made with interlocking cubes. Explore the number of units of paint that are needed to cover the boxes and the small cubes that would fit inside each one.