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?

A metal puzzle which led to some mathematical questions.

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?

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

This resources contains a series of interactivities designed to support work on transformations at Key Stage 4.

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

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

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.

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

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.

Use Excel to explore multiplication of fractions.

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

Use Excel to practise adding and subtracting fractions.

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

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.

Two circles of equal radius touch at P. One circle is fixed whilst the other moves, rolling without slipping, all the way round. How many times does the moving coin revolve before returning to P?

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

A tool for generating random integers.

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

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

An Excel spreadsheet with an investigation.

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

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

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

Explore displacement/time and velocity/time graphs with this mouse motion sensor.

It's easy to work out the areas of most squares that we meet, but what if they were tilted?

Match pairs of cards so that they have equivalent ratios.

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

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?

An environment that enables you to investigate tessellations of regular polygons

This rectangle is cut into five pieces which fit exactly into a triangular outline and also into a square outline where the triangle, the rectangle and the square have equal areas.

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 graphical interpretation at Key Stage 4.

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

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

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.

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?

Do you know how to find the area of a triangle? You can count the squares. What happens if we turn the triangle on end? Press the button and see. Try counting the number of units in the triangle now. . . .

Can you break down this conversion process into logical steps?

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.

Which dilutions can you make using 10ml pipettes and 100ml measuring cylinders?

A point P is selected anywhere inside an equilateral triangle. What can you say about the sum of the perpendicular distances from P to the sides of the triangle? Can you prove your conjecture?

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

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. . . .