A java applet that takes you through the steps needed to solve a Diophantine equation of the form Px+Qy=1 using Euclid's algorithm.

This is an interactivity in which you have to sort the steps in the completion of the square into the correct order to prove the formula for the solutions of quadratic equations.

Prove Pythagoras' Theorem using enlargements and scale factors.

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

Slide the pieces to move Khun Phaen past all the guards into the position on the right from which he can escape to freedom.

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 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.

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?

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. . . .

A game for 2 players that can be played online. Players take it in turns to select a word from the 9 words given. The aim is to select all the occurrences of the same letter.

A circle rolls around the outside edge of a square so that its circumference always touches the edge of the square. Can you describe the locus of the centre of the circle?

Ask a friend to choose a number between 1 and 63. By identifying which of the six cards contains the number they are thinking of it is easy to tell them what the number is.

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.

Use an Excel to investigate division. Explore the relationships between the process elements using an interactive spreadsheet.

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

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. . . .

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

Find all the ways of placing the numbers 1 to 9 on a W shape, with 3 numbers on each leg, so that each set of 3 numbers has the same total.

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. . . .

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?

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

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.

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.

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

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?

Have you seen this way of doing multiplication ?

Use Excel to explore multiplication of fractions.

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. . . .

Euler discussed whether or not it was possible to stroll around Koenigsberg crossing each of its seven bridges exactly once. Experiment with different numbers of islands and bridges.

We can show that (x + 1)² = x² + 2x + 1 by considering the area of an (x + 1) by (x + 1) square. Show in a similar way that (x + 2)² = x² + 4x + 4

Cellular is an animation that helps you make geometric sequences composed of square cells.

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

Practise your skills of proportional reasoning with this interactive haemocytometer.

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 ?

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

A tool for generating random integers.

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

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. . . .

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.

Work out how to light up the single light. What's the rule?

This game challenges you to locate hidden triangles in The White Box by firing rays and observing where the rays exit the Box.

Can you set the logic gates so that the number of bulbs which are on is the same as the number of switches which are on?

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

There are thirteen axes of rotational symmetry of a unit cube. Describe them all. What is the average length of the parts of the axes of symmetry which lie inside the cube?

Triangle numbers can be represented by a triangular array of squares. What do you notice about the sum of identical triangle numbers?

What are the areas of these triangles? What do you notice? Can you generalise to other "families" of triangles?