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?

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

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?

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.

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.

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. . . .

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

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 make a right-angled triangle on this peg-board by joining up three points round the edge?

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

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

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

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

A group of interactive resources to support work on percentages Key Stage 4.

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.

Use Excel to explore multiplication of fractions.

An environment that enables you to investigate tessellations of regular polygons

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

Discover a handy way to describe reorderings and solve our anagram in the process.

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. . . .

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

This resource contains a range of problems and interactivities on the theme of coordinates in two and three dimensions.

Match pairs of cards so that they have equivalent ratios.

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

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?

A collection of resources to support work on Factors and Multiples at Secondary level.

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.

A tool for generating random integers.

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

How good are you at finding the formula for a number pattern ?

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

Use an Excel spreadsheet to explore long multiplication.

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

A metal puzzle which led to some mathematical questions.

An Excel spreadsheet with an investigation.

Use Excel to practise adding and subtracting fractions.

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

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

Use an interactive Excel spreadsheet to investigate factors and multiples.

This resource contains interactive problems to support work on number sequences at Key Stage 4.

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. . . .

An environment that simulates a protractor carrying a right- angled triangle of unit hypotenuse.

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

A point P is selected anywhere inside an equilateral triangle. What can you say about the sum of the perpendicular distances from P to the sides of the triangle? Can you prove your conjecture?

Can you beat the computer in the challenging strategy game?

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

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.