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.

Three equilateral triangles ABC, AYX and XZB are drawn with the point X a moveable point on AB. The points P, Q and R are the centres of the three triangles. What can you say about triangle PQR?

Can you work through these direct proofs, using our interactive proof sorters?

Can you correctly order the steps in the proof of the formula for the sum of a geometric series?

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.

Can you beat the computer in the challenging strategy game?

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.

Prove Pythagoras' Theorem using enlargements and scale factors.

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.

Use this interactivity to sort out the steps of the proof of the formula for the sum of an arithmetic series. The 'thermometer' will tell you how you are doing

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

A counter is placed in the bottom right hand corner of a grid. You toss a coin and move the star according to the following rules: ... What is the probability that you end up in the top left-hand. . . .

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?

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?

The opposite vertices of a square have coordinates (a,b) and (c,d). What are the coordinates of the other vertices?

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

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?

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

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.

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

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

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

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?

Find all the ways of placing the numbers 1 to 9 on a W shape, with 3 numbers on each leg, so that each set of 3 numbers has the same total.

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 interactive Excel spreadsheet to investigate factors and multiples.

Use an Excel spreadsheet to explore long multiplication.

Use Excel to practise adding and subtracting fractions.

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

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

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

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.

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

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

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

An Excel spreadsheet with an investigation.

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

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

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 Excel to explore multiplication of fractions.

There are thirteen axes of rotational symmetry of a unit cube. Describe them all. What is the average length of the parts of the axes of symmetry which lie inside the cube?

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.

Play a more cerebral countdown using complex numbers.