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?

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.

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.

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

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

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

Prove Pythagoras' Theorem using enlargements and scale factors.

Practise your skills of proportional reasoning with this interactive haemocytometer.

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

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.

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.

On the 3D grid a strange (and deadly) animal is lurking. Using the tracking system can you locate this creature as quickly as possible?

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

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.

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.

Use Excel to explore multiplication of fractions.

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

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 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. . . .

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

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?

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

A tool for generating random integers.

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

A weekly challenge concerning prime numbers.

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

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

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

Can you locate these values on this interactive logarithmic scale?

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.

Can you beat the computer in the challenging strategy game?

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

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

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

A metal puzzle which led to some mathematical questions.

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. . . .

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

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

Triangle ABC has equilateral triangles drawn on its edges. Points P, Q and R are the centres of the equilateral triangles. What can you prove about the triangle PQR?

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

Use an Excel spreadsheet to explore long multiplication.

Use Excel to practise adding and subtracting fractions.