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.

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

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.

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

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

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

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

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?

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

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

Ask a friend to choose a number between 1 and 63. By identifying which of the six cards contains the number they are thinking of it is easy to tell them what the number is.

Prove Pythagoras' Theorem using enlargements and scale factors.

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?

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.

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 graphical interpretation at Key Stage 4.

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

Can you locate these values on this interactive logarithmic scale?

Use this animation to experiment with lotteries. Choose how many balls to match, how many are in the carousel, and how many draws to make at once.

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. . . .

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 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.

Play a more cerebral countdown using complex numbers.

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.

Mathmo is a revision tool for post-16 mathematics. It's great installed as a smartphone app, but it works well in pads and desktops and notebooks too. Give yourself a mathematical workout!

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

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. . . .

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.

It is possible to identify a particular card out of a pack of 15 with the use of some mathematical reasoning. What is this reasoning and can it be applied to other numbers of cards?

Can you beat the computer in the challenging strategy game?

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

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

Practise your skills of proportional reasoning with this interactive haemocytometer.

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

Use Excel to explore multiplication of fractions.

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. . . .

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!

P is a point on the circumference of a circle radius r which rolls, without slipping, inside a circle of radius 2r. What is the locus of P?

An Excel spreadsheet with an investigation.

Use Excel to practise adding and subtracting fractions.

Use an interactive Excel spreadsheet to investigate factors and multiples.

Use an Excel spreadsheet to explore long multiplication.

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