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. . . .

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. . . .

On the 3D grid a strange (and deadly) animal is lurking. Using the tracking system can you locate this creature as quickly as possible?

Square It game for an adult and child. Can you come up with a way of always winning this game?

This is an interactive net of a Rubik's cube. Twists of the 3D cube become mixes of the squares on the 2D net. Have a play and see how many scrambles you can undo!

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?

This resources contains a series of interactivities designed to support work on transformations at Key Stage 4.

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.

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.

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.

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

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

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.

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?

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.

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

A game for 1 person to play on screen. Practise your number bonds whilst improving your memory

P is a point on the circumference of a circle radius r which rolls, without slipping, inside a circle of radius 2r. What is the locus of P?

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?

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

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

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

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.

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

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

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

The interactive diagram has two labelled points, A and B. It is designed to be used with the problem "Cushion Ball"

An environment that enables you to investigate tessellations of regular polygons

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

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

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?

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.

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.

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

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?

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.

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

A red square and a blue square overlap so that the corner of the red square rests on the centre of the blue square. Show that, whatever the orientation of the red square, it covers a quarter of the. . . .

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

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?

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. . . .

Use Excel to explore multiplication of fractions.

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

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

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

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?