Make and prove a conjecture about the cyclic quadrilateral inscribed in a circle of radius r that has the maximum perimeter and the maximum area.

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.

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

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?

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.

An environment that enables you to investigate tessellations of regular polygons

Try this interactivity to familiarise yourself with the proof that the square root of 2 is irrational. Sort the steps of the proof into the correct order.

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

Match pairs of cards so that they have equivalent ratios.

Use Excel to explore multiplication of 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?

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

Re-arrange the pieces of the puzzle to form a rectangle and then to form an equilateral triangle. Calculate the angles and lengths.

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. . . .

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. . . .

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

Can you beat the computer in the challenging strategy game?

A weekly challenge concerning prime numbers.

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

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. . . .

A tool for generating random integers.

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

Match the cards of the same value.

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

A metal puzzle which led to some mathematical questions.

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

Can you locate these values on this interactive logarithmic scale?

A spherical balloon lies inside a wire frame. How much do you need to deflate it to remove it from the frame if it remains a sphere?

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?

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

Use an Excel spreadsheet to explore long multiplication.

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

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

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

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

Use an interactive Excel spreadsheet to investigate factors and multiples.

Use Excel to practise adding and subtracting fractions.

Take any parallelogram and draw squares on the sides of the parallelogram. What can you prove about the quadrilateral formed by joining the centres of these squares?

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

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.

An Excel spreadsheet with an investigation.

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!

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

How can we solve equations like 13x + 29y = 42 or 2x +4y = 13 with the solutions x and y being integers? Read this article to find out.