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.

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

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

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?

When number pyramids have a sequence on the bottom layer, some interesting patterns emerge...

This is an interactivity in which you have to sort into the correct order the steps in the proof of the formula for the sum of a geometric series.

Prove Pythagoras Theorem using enlargements and scale factors.

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.

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.

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

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 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.

Rotate a copy of the trapezium about the centre of the longest side of the blue triangle to make a square. Find the area of the square and then derive a formula for the area of the trapezium.

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.

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

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.

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

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

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.

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.

With red and blue beads on a circular wire; 'put a red bead between any two of the same colour and a blue between different colours then remove the original beads'. Keep repeating this. What happens?

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. . . .

Four cards are shuffled and placed into two piles of two. Starting with the first pile of cards - turn a card over... You win if all your cards end up in the trays before you run out of cards in. . . .

Use Excel to explore multiplication of fractions.

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

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?

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?

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

Can you beat Piggy in this simple dice game? Can you figure out Piggy's strategy, and is there a better one?

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. . . .

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?

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.

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. . . .

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.

A tool for generating random integers.

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.

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

Practise your skills of proportional reasoning with this interactive haemocytometer.

Can you locate these values on this interactive logarithmic scale?

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

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?

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?