Here are some rods that are different colours. How could I make a dark green rod using yellow and white rods?

In this maze of hexagons, you start in the centre at 0. The next hexagon must be a multiple of 2 and the next a multiple of 5. What are the possible paths you could take?

These sixteen children are standing in four lines of four, one behind the other. They are each holding a card with a number on it. Can you work out the missing numbers?

Can you see why 2 by 2 could be 5? Can you predict what 2 by 10 will be?

If the numbers 5, 7 and 4 go into this function machine, what numbers will come out?

In sheep talk the only letters used are B and A. A sequence of words is formed by following certain rules. What do you notice when you count the letters in each word?

Square numbers can be represented as the sum of consecutive odd numbers. What is the sum of 1 + 3 + ..... + 149 + 151 + 153?

When number pyramids have a sequence on the bottom layer, some interesting patterns emerge...

A mathematician goes into a supermarket and buys four items. Using a calculator she multiplies the cost instead of adding them. How can her answer be the same as the total at the till?

Can you find a rule which connects consecutive triangular numbers?

Can you find a rule which relates triangular numbers to square numbers?

Show that all pentagonal numbers are one third of a triangular number.

This function involves absolute values. To find the slope on the slide use different equations to define the function in different parts of its domain.

Draw graphs of the sine and modulus functions and explain the humps.

The family of graphs of x^n + y^n =1 (for even n) includes the circle. Why do the graphs look more and more square as n increases?

Pupils from St Nicolas CE Junior School found two ways to share out the butterfly cards fairly.

Esther's detective work and several students' algebraic thinking helped to shed light on Arithmagons.

Shaun from Nottingham High School produced an excellent method of representation for Spot the Card.

When we add, subtract, multiply or divide we draw numbers from infinite sets. Here we see that sometimes we are working with an infinite group and sometimes not.

A game for 2 or more players with a pack of cards. Practise your skills of addition, subtraction, multiplication and division to hit the target score.

Start with any number of counters in any number of piles. 2 players take it in turns to remove any number of counters from a single pile. The winner is the player to take the last counter.

Infinity is not a number, and trying to treat it as one tends to be a pretty bad idea. At best you're likely to come away with a headache, at worse the firm belief that 1 = 0. This article discusses the different types of infinity.