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.

A metal puzzle which led to some mathematical questions.

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.

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 investigate the effect of translations around a number grid.

Use an interactive Excel spreadsheet to explore number in this exciting 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 group of interactive resources to support work on percentages Key Stage 4.

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

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

Match pairs of cards so that they have equivalent ratios.

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

Use Excel to explore multiplication of fractions.

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. . . .

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?

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

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

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

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. . . .

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.

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

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 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. . . .

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

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

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.

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

Match the cards of the same value.

Use an interactive Excel spreadsheet to investigate factors and multiples.

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

An Excel spreadsheet with an investigation.

Use an Excel spreadsheet to explore long multiplication.

A tool for generating random integers.

Use Excel to practise adding and subtracting fractions.

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.

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.

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?

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. . . .

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

If you continue the pattern, can you predict what each of the following areas will be? Try to explain your prediction.

A counter is placed in the bottom right hand corner of a grid. You toss a coin and move the star according to the following rules: ... What is the probability that you end up in the top left-hand. . . .

in how many ways can you place the numbers 1, 2, 3 … 9 in the nine regions of the Olympic Emblem (5 overlapping circles) so that the amount in each ring is the same?

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