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.

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.

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?

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

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

Match pairs of cards so that they have equivalent ratios.

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.

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. . . .

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

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.

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!

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. . . .

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

An environment that enables you to investigate tessellations of regular polygons

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

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.

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.

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.

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. . . .

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 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?

Use Excel to explore multiplication of fractions.

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. . . .

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

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.

Help the bee to build a stack of blocks far enough to save his friend trapped in the tower.

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

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

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?

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

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

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

A metal puzzle which led to some mathematical questions.

An Excel spreadsheet with an investigation.

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

Use Excel to practise adding and subtracting fractions.

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

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

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?

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

Have you seen this way of doing multiplication ?

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?

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

Use an interactive Excel spreadsheet to investigate factors and multiples.

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.