Visualising and representing

problem
Tower of Hanoi

Age

11 to 14

Challenge level

The Tower of Hanoi is an ancient mathematical challenge. Working on the building blocks may help you to explain the patterns you notice.
problem
Christmas chocolates

Age

11 to 14

Challenge level

How could Penny, Tom and Matthew work out how many chocolates there are in different sized boxes?
problem
Mach attack

Age

16 to 18

Challenge level

Have you got the Mach knack? Discover the mathematics behind exceeding the sound barrier.
problem
Ford circles

Age

16 to 18

Challenge level

Can you find the link between these beautiful circle patterns and Farey Sequences?
problem
Classical means

Age

16 to 18

Challenge level

Use the diagram to investigate the classical Pythagorean means.
problem
Summing squares

Age

14 to 16

Challenge level

Discover a way to sum square numbers by building cuboids from small cubes. Can you picture how the sequence will grow?
problem
Coordinated crystals

Age

16 to 18

Challenge level

Explore the lattice and vector structure of this crystal.
problem
Vector walk

Age

14 to 18

Challenge level

Starting with two basic vector steps, which destinations can you reach on a vector walk?
problem
Coded hundred square

Age

7 to 11

Challenge level

This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?
problem
Surprising transformations

Age

14 to 16

Challenge level

I took the graph y=4x+7 and performed four transformations. Can you find the order in which I could have carried out the transformations?