How many trains can you make which are the same length as Matt's, using rods that are identical?

Can you make a train the same length as Laura's but using three differently coloured rods? Is there only one way of doing it?

Using the picture of the fraction wall, can you find equivalent fractions?

Use the fraction wall to compare the size of these fractions - you'll be amazed how it helps!

Can you find all the different ways of lining up these Cuisenaire rods?

Find out what a "fault-free" rectangle is and try to make some of your own.

Pick two rods of different colours. Given an unlimited supply of rods of each of the two colours, how can we work out what fraction the shorter rod is of the longer one?

Using only the red and white rods, how many different ways are there to make up the other colours of rod?

Make a line of green and a line of yellow rods so that the lines differ in length by one (a white rod)

Imagine a strip with a mark somewhere along it. Fold it in the middle so that the bottom reaches back to the top. Stetch it out to match the original length. Now where's the mark?

Can you see how to build a harmonic triangle? Can you work out the next two rows?

Data is sent in chunks of two different sizes - a yellow chunk has 5 characters and a blue chunk has 9 characters. A data slot of size 31 cannot be exactly filled with a combination of yellow and. . . .

What have Fibonacci numbers got to do with Pythagorean triples?

What have Fibonacci numbers to do with solutions of the quadratic equation x^2 - x - 1 = 0 ?

Make and prove a conjecture about the value of the product of the Fibonacci numbers $F_{n+1}F_{n-1}$.

Maisy has thought carefully about how to make chairs and tables out of cubes which match each other for size.

This article for teachers suggests teaching strategies and resources that can help to develop children's number sense.

This article for teachers describes a project which explores thepower of storytelling to convey concepts and ideas to children.