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

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?

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?

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.

Use an Excel spreadsheet to explore long multiplication.

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

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.

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.

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

Use an interactive Excel spreadsheet to investigate factors and multiples.

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. . . .

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

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

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.

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

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.

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

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?

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

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?

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?

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

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

Which dilutions can you make using only 10ml pipettes?

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

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.

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.

Practise your skills of proportional reasoning with this interactive haemocytometer.

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?

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

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.

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?

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. . . .

Can you find a relationship between the number of dots on the circle and the number of steps that will ensure that all points are hit?