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?

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?

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?

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. . . .

Use Excel to explore multiplication of fractions.

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

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

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

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

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

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?

Use an Excel spreadsheet to explore long multiplication.

An environment that enables you to investigate tessellations of regular polygons

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

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

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

An Excel spreadsheet with an investigation.

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

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.

Use an interactive Excel spreadsheet to investigate factors and multiples.

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?

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?

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. . . .

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?

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?

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?

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

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

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

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

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

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

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?

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.

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

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

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.

Ask a friend to choose a number between 1 and 63. By identifying which of the six cards contains the number they are thinking of it is easy to tell them what the number is.

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?

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.

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 fill in the mixed up numbers in this dilution calculation?

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