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.

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.

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.

An environment that enables you to investigate tessellations of regular polygons

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

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

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

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

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

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

A metal puzzle which led to some mathematical questions.

Match pairs of cards so that they have equivalent ratios.

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

Can you locate these values on this interactive logarithmic scale?

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

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 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?

Use Excel to explore multiplication of fractions.

Charlie likes tablecloths that use as many colours as possible, but insists that his tablecloths have some symmetry. Can you work out how many colours he needs for different tablecloth designs?

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. . . .

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.

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

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.

Can you beat the computer in the challenging strategy game?

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

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

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 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.

Use an interactive Excel spreadsheet to investigate factors and multiples.

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.

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

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?

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

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

Use an Excel spreadsheet to explore long multiplication.

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