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.

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.

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?

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?

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

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

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

Triangle ABC has equilateral triangles drawn on its edges. Points P, Q and R are the centres of the equilateral triangles. What can you prove about the triangle PQR?

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

An environment that enables you to investigate tessellations of regular polygons

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

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

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

Use Excel to explore multiplication of fractions.

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.

Use an Excel spreadsheet to explore long multiplication.

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

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

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

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

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

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.

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

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

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

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

Can you beat the computer in the challenging strategy game?

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.

Use Excel to practise adding and subtracting fractions.

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.

Use an interactive Excel spreadsheet to investigate factors and multiples.

An Excel spreadsheet with an investigation.

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.

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

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?

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

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