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?

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

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. . . .

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?

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

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

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.

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.

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?

Help the bee to build a stack of blocks far enough to save his friend trapped in the tower.

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?

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

These formulae are often quoted, but rarely proved. In this article, we derive the formulae for the volumes of a square-based pyramid and a cone, using relatively simple mathematical concepts.

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?

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

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

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

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

Find all the ways of placing the numbers 1 to 9 on a W shape, with 3 numbers on each leg, so that each set of 3 numbers has the same total.

Rotate a copy of the trapezium about the centre of the longest side of the blue triangle to make a square. Find the area of the square and then derive a formula for the area of the trapezium.

Use Excel to explore multiplication of fractions.

Start with any number of counters in any number of piles. 2 players take it in turns to remove any number of counters from a single pile. The winner is the player to take the last counter.

Slide the pieces to move Khun Phaen past all the guards into the position on the right from which he can escape to freedom.

Match pairs of cards so that they have equivalent ratios.

When number pyramids have a sequence on the bottom layer, some interesting patterns emerge...

A game for 2 players that can be played online. Players take it in turns to select a word from the 9 words given. The aim is to select all the occurrences of the same letter.

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

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. . . .

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

What are the areas of these triangles? What do you notice? Can you generalise to other "families" of triangles?

A point P is selected anywhere inside an equilateral triangle. What can you say about the sum of the perpendicular distances from P to the sides of the triangle? Can you prove your conjecture?

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

How good are you at finding the formula for a number pattern ?

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

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

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

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

A collection of our favourite pictorial problems, one for each day of Advent.

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.

An Excel spreadsheet with an investigation.

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

Use an Excel spreadsheet to explore long multiplication.

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

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

A tool for generating random integers.

Use an interactive Excel spreadsheet to investigate factors and multiples.

Use Excel to practise adding and subtracting fractions.