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?

Can you find a way to turn a rectangle into a square?

Use Excel to explore multiplication of fractions.

Use an interactive Excel spreadsheet to investigate factors and multiples.

An environment that enables you to investigate tessellations of regular polygons

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"

Match pairs of cards so that they have equivalent ratios.

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

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

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

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

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

Use an Excel spreadsheet to explore long multiplication.

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

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

Use Excel to practise adding and subtracting fractions.

An Excel spreadsheet with an investigation.

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 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 find triangles on a 9-point circle? Can you work out their angles?

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?

Show how this pentagonal tile can be used to tile the plane and describe the transformations which map this pentagon to its images in the tiling.

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. . . .

Semi-regular tessellations combine two or more different regular polygons to fill the plane. Can you find all the semi-regular tessellations?

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?

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?

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. . . .

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

What is the relationship between the angle at the centre and the angles at the circumference, for angles which stand on the same arc? Can you prove it?

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

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

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?

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

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 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?

Euler discussed whether or not it was possible to stroll around Koenigsberg crossing each of its seven bridges exactly once. Experiment with different numbers of islands and bridges.

A red square and a blue square overlap so that the corner of the red square rests on the centre of the blue square. Show that, whatever the orientation of the red square, it covers a quarter of the. . . .

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

Some treasure has been hidden in a three-dimensional grid! Can you work out a strategy to find it as efficiently as possible?

Can you find a reliable strategy for choosing coordinates that will locate the treasure in the minimum number of guesses?

Draw some isosceles triangles with an area of $9$cm$^2$ and a vertex at (20,20). If all the vertices must have whole number coordinates, how many is it possible to draw?

Which dilutions can you make using only 10ml pipettes?

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?

The computer has made a rectangle and will tell you the number of spots it uses in total. Can you find out where the rectangle is?

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

A tilted square is a square with no horizontal sides. Can you devise a general instruction for the construction of a square when you are given just one of its sides?