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?

A metal puzzle which led to some mathematical questions.

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

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

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

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.

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

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

An environment that enables you to investigate tessellations of regular polygons

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

Practise your skills of proportional reasoning with this interactive haemocytometer.

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

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

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

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

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

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

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. . . .

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.

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?

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

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. . . .

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

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.

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. . . .

Use Excel to explore multiplication of 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.

Match pairs of cards so that they have equivalent ratios.

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 an Excel spreadsheet to explore long multiplication.

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

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

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

Use an interactive Excel spreadsheet to investigate factors and multiples.

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

An Excel spreadsheet with an investigation.

Use Excel to practise adding and subtracting fractions.

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.

A tool for generating random integers.

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?

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

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

Cellular is an animation that helps you make geometric sequences composed of square cells.

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. . . .

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