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?

Take any parallelogram and draw squares on the sides of the parallelogram. What can you prove about the quadrilateral formed by joining the centres of these squares?

The shortest path between any two points on a snooker table is the straight line between them but what if the ball must bounce off one wall, or 2 walls, or 3 walls?

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?

Use Excel to explore multiplication of fractions.

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?

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

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?

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

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. . . .

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.

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. . . .

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

An environment that enables you to investigate tessellations of regular polygons

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?

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?

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

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?

Match the cards of the same value.

A weekly challenge concerning prime numbers.

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

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 tool for generating random integers.

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

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"

A metal puzzle which led to some mathematical questions.

Can you locate these values on this interactive logarithmic scale?

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

Practise your skills of proportional reasoning with this interactive haemocytometer.

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.

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?

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?

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

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 explore number in this exciting game!

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

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

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

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

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

Overlaying pentominoes can produce some effective patterns. Why not use LOGO to try out some of the ideas suggested here?

Use an interactive Excel spreadsheet to investigate factors and multiples.

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

Match pairs of cards so that they have equivalent ratios.

Use Excel to practise adding and subtracting fractions.