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.

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 metal puzzle which led to some mathematical questions.

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

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

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

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

Can you locate these values on this interactive logarithmic scale?

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

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.

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

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?

Six circles around a central circle make a flower. Watch the flower as you change the radii in this circle packing. Prove that with the given ratios of the radii the petals touch and fit perfectly.

Use Excel to explore multiplication of fractions.

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 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?

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. . . .

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. . . .

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

Can you beat the computer in the challenging strategy game?

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.

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

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 weekly challenge concerning prime numbers.

An Excel spreadsheet with an investigation.

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.

Use an interactive Excel spreadsheet to investigate factors and multiples.

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

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

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

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 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.

Use an Excel spreadsheet to explore long multiplication.

Use Excel to practise adding and subtracting fractions.

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

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

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

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