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.

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

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. . . .

An environment that enables you to investigate tessellations of regular polygons

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

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

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.

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?

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.

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.

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

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 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?

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?

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

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

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?

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

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.

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 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. . . .

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. . . .

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

This problem is about investigating whether it is possible to start at one vertex of a platonic solid and visit every other vertex once only returning to the vertex you started at.

Use this animation to experiment with lotteries. Choose how many balls to match, how many are in the carousel, and how many draws to make at once.

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.

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

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.

Can you explain the strategy for winning this game with any target?

Can you beat the computer in the challenging strategy game?

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

A circle rolls around the outside edge of a square so that its circumference always touches the edge of the square. Can you describe the locus of the centre of the circle?

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.

We can show that (x + 1)² = x² + 2x + 1 by considering the area of an (x + 1) by (x + 1) square. Show in a similar way that (x + 2)² = x² + 4x + 4

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

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. . . .

Triangular numbers can be represented by a triangular array of squares. What do you notice about the sum of identical triangle numbers?

Try entering different sets of numbers in the number pyramids. How does the total at the top change?

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