A counter is placed in the bottom right hand corner of a grid. You toss a coin and move the star according to the following rules: ... What is the probability that you end up in the top left-hand. . . .

Use this animation to experiment with lotteries. Choose how many balls to match, how many are in the carousel, and how many draws to make at once.

This interactivity invites you to make conjectures and explore probabilities of outcomes related to two independent events.

Four cards are shuffled and placed into two piles of two. Starting with the first pile of cards - turn a card over... You win if all your cards end up in the trays before you run out of cards in. . . .

A simple spinner that is equally likely to land on Red or Black. Useful if tossing a coin, dropping it, and rummaging about on the floor have lost their appeal. Needs a modern browser; if IE then at. . . .

Six balls of various colours are randomly shaken into a trianglular arrangement. What is the probability of having at least one red in the corner?

The aim of the game is to slide the green square from the top right hand corner to the bottom left hand corner in the least number of moves.

The opposite vertices of a square have coordinates (a,b) and (c,d). What are the coordinates of the other vertices?

7 balls are shaken in a container. You win if the two blue balls touch. What is the probability of winning?

Identical discs are flipped in the air. You win if all of the faces show the same colour. Can you calculate the probability of winning with n discs?

To avoid losing think of another very well known game where the patterns of play are similar.

Discover a handy way to describe reorderings and solve our anagram in the process.

Can you beat Piggy in this simple dice game? Can you figure out Piggy's strategy, and is there a better one?

Show that for any triangle it is always possible to construct 3 touching circles with centres at the vertices. Is it possible to construct touching circles centred at the vertices of any polygon?

Is this a fair game? How many ways are there of creating a fair game by adding odd and even numbers?

Can you work out which spinners were used to generate the frequency charts?

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.

A point P is selected anywhere inside an equilateral triangle. What can you say about the sum of the perpendicular distances from P to the sides of the triangle? Can you prove your conjecture?

If you continue the pattern, can you predict what each of the following areas will be? Try to explain your prediction.

Can you put the 25 coloured tiles into the 5 x 5 square so that no column, no row and no diagonal line have tiles of the same colour in them?

Do you know how to find the area of a triangle? You can count the squares. What happens if we turn the triangle on end? Press the button and see. Try counting the number of units in the triangle now. . . .

A right-angled isosceles triangle is rotated about the centre point of a square. What can you say about the area of the part of the square covered by the triangle as it rotates?

Charlie likes tablecloths that use as many colours as possible, but insists that his tablecloths have some symmetry. Can you work out how many colours he needs for different tablecloth designs?

Use Excel to explore multiplication of fractions.

Can you give the coordinates of the vertices of the fifth point in the patterm on this 3D grid?

Given the nets of 4 cubes with the faces coloured in 4 colours, build a tower so that on each vertical wall no colour is repeated, that is all 4 colours appear.

Can you make a right-angled triangle on this peg-board by joining up three points round the edge?

What is the relationship between the angle at the centre and the angles at the circumference, for angles which stand on the same arc? Can you prove it?

Learn how to use the Shuffles interactivity by running through these tutorial demonstrations.

in how many ways can you place the numbers 1, 2, 3 … 9 in the nine regions of the Olympic Emblem (5 overlapping circles) so that the amount in each ring is the same?

The classic vector racing game brought to a screen near you.

You can move the 4 pieces of the jigsaw and fit them into both outlines. Explain what has happened to the missing one unit of area.

A game for 2 players. Can be played online. One player has 1 red counter, the other has 4 blue. The red counter needs to reach the other side, and the blue needs to trap the red.

These formulae are often quoted, but rarely proved. In this article, we derive the formulae for the volumes of a square-based pyramid and a cone, using relatively simple mathematical concepts.

A and B are two interlocking cogwheels having p teeth and q teeth respectively. One tooth on B is painted red. Find the values of p and q for which the red tooth on B contacts every gap on the. . . .

There are 27 small cubes in a 3 x 3 x 3 cube, 54 faces being visible at any one time. Is it possible to reorganise these cubes so that by dipping the large cube into a pot of paint three times you. . . .

Can you spot the similarities between this game and other games you know? The aim is to choose 3 numbers that total 15.

Here is a chance to play a fractions version of the classic Countdown Game.

Can you beat the computer in the challenging strategy game?

A collection of our favourite pictorial problems, one for each day of Advent.

A tool for generating random integers.

This set of resources for teachers offers interactive environments to support work on loci at Key Stage 4.

A metal puzzle which led to some mathematical questions.

This resource contains interactive problems to support work on number sequences at Key Stage 4.

How good are you at finding the formula for a number pattern ?

Practise your skills of proportional reasoning with this interactive haemocytometer.

Meg and Mo need to hang their marbles so that they balance. Use the interactivity to experiment and find out what they need to do.

Players take it in turns to choose a dot on the grid. The winner is the first to have four dots that can be joined to form a square.