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.

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.

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.

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.

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?

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. 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. . . .

Use Excel to explore multiplication of fractions.

An environment that enables you to investigate tessellations of regular polygons

Use Excel to investigate the effect of translations around a number grid.

Use an interactive Excel spreadsheet to explore number in this exciting game!

A simple file for the Interactive whiteboard or PC screen, demonstrating equivalent fractions.

Use an Excel spreadsheet to explore long multiplication.

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.

Match pairs of cards so that they have equivalent ratios.

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

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.

This problem is about investigating whether it is possible to start at one vertex of a platonic solid and visit every other vertex once only returning to the vertex you started at.

Can you beat the computer in the challenging strategy game?

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

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

Can you explain the strategy for winning this game with any target?

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

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.

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

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?

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. . . .

Use an interactive Excel spreadsheet to investigate factors and multiples.

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?

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

Triangular 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?

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. . . .

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

The number of plants in Mr McGregor's magic potting shed increases overnight. He'd like to put the same number of plants in each of his gardens, planting one garden each day. How can he do it?

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

An Excel spreadsheet with an investigation.

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 Excel to practise adding and subtracting fractions.

A game for 1 person. Can you work out how the dice must be rolled from the start position to the finish? Play on line.