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.

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. . . .

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?

Use the interactivity to play two of the bells in a pattern. How do you know when it is your turn to ring, and how do you know which bell to ring?

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

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

Here is a solitaire type environment for you to experiment with. Which targets can you reach?

Use the interactivity to listen to the bells ringing a pattern. Now it's your turn! Play one of the bells yourself. How do you know when it is your turn to ring?

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.

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

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.

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 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.

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. . . .

This rectangle is cut into five pieces which fit exactly into a triangular outline and also into a square outline where the triangle, the rectangle and the square have equal areas.

Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.

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

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

Can you locate the lost giraffe? Input coordinates to help you search and find the giraffe in the fewest guesses.

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. . . .

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.

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?

Draw some isosceles triangles with an area of $9$cm$^2$ and a vertex at (20,20). If all the vertices must have whole number coordinates, how many is it possible to draw?

A tilted square is a square with no horizontal sides. Can you devise a general instruction for the construction of a square when you are given just one of its sides?

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

Practise your diamond mining skills and your x,y coordination in this homage to Pacman.

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?

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

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?

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

Try entering different sets of numbers in the number pyramids. How does the total at the top change?

Two engines, at opposite ends of a single track railway line, set off towards one another just as a fly, sitting on the front of one of the engines, sets off flying along the railway line...

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

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.

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

Place a red counter in the top left corner of a 4x4 array, which is covered by 14 other smaller counters, leaving a gap in the bottom right hand corner (HOME). What is the smallest number of moves. . . .

Show how this pentagonal tile can be used to tile the plane and describe the transformations which map this pentagon to its images in the tiling.

Experiment with the interactivity of "rolling" regular polygons, and explore how the different positions of the red dot affects its speed at each stage.

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

Two circles of equal radius touch at P. One circle is fixed whilst the other moves, rolling without slipping, all the way round. How many times does the moving coin revolve before returning to P?

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.

It's easy to work out the areas of most squares that we meet, but what if they were tilted?

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

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.

There are nine teddies in Teddy Town - three red, three blue and three yellow. There are also nine houses, three of each colour. Can you put them on the map of Teddy Town according to the rules?

Imagine picking up a bow and some arrows and attempting to hit the target a few times. Can you work out the settings for the sight that give you the best chance of gaining a high score?

Carry out some time trials and gather some data to help you decide on the best training regime for your rowing crew.

Mo has left, but Meg is still experimenting. Use the interactivity to help you find out how she can alter her pouch of marbles and still keep the two pouches balanced.