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?

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?

Take any parallelogram and draw squares on the sides of the parallelogram. What can you prove about the quadrilateral formed by joining the centres of these squares?

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

Use Excel to explore multiplication of fractions.

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

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

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

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?

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.

A tool for generating random integers.

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 spreadsheet to explore long multiplication.

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.

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

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

Use Excel to practise adding and subtracting fractions.

An Excel spreadsheet with an investigation.

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

A metal puzzle which led to some mathematical questions.

An environment that enables you to investigate tessellations of regular polygons

Match pairs of cards so that they have equivalent ratios.

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

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

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

Try this interactivity to familiarise yourself with the proof that the square root of 2 is irrational. Sort the steps of the proof into the correct order.

How can we solve equations like 13x + 29y = 42 or 2x +4y = 13 with the solutions x and y being integers? Read this article to find out.

Can you beat the computer in the challenging strategy game?

Make and prove a conjecture about the cyclic quadrilateral inscribed in a circle of radius r that has the maximum perimeter and the maximum area.

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

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.

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.

A spherical balloon lies inside a wire frame. How much do you need to deflate it to remove it from the frame if it remains a sphere?

Six circles around a central circle make a flower. Watch the flower as you change the radii in this circle packing. Prove that with the given ratios of the radii the petals touch and fit perfectly.

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. . . .

Players take it in turns to choose a dot on the grid. The winner is the first to have four dots that can be joined to form a square.

Practise your skills of proportional reasoning with this interactive haemocytometer.