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?

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. . . .

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?

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

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

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

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.

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.

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.

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

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

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

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

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

Match pairs of cards so that they have equivalent ratios.

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?

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

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

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

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

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.

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

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?

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

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?

A tool for generating random integers.

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.

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

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.

Use Excel to explore multiplication of fractions.

A and B are two interlocking cogwheels having p teeth and q teeth respectively. One tooth on B is painted red. Find the values of p and q for which the red tooth on B contacts every gap on the. . . .

Cellular is an animation that helps you make geometric sequences composed of square cells.

There are 27 small cubes in a 3 x 3 x 3 cube, 54 faces being visible at any one time. Is it possible to reorganise these cubes so that by dipping the large cube into a pot of paint three times you. . . .

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

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?

Given the nets of 4 cubes with the faces coloured in 4 colours, build a tower so that on each vertical wall no colour is repeated, that is all 4 colours appear.

in how many ways can you place the numbers 1, 2, 3 … 9 in the nine regions of the Olympic Emblem (5 overlapping circles) so that the amount in each ring is the same?

You can move the 4 pieces of the jigsaw and fit them into both outlines. Explain what has happened to the missing one unit of area.

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 beat Piggy in this simple dice game? Can you figure out Piggy's strategy, and is there a better one?

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.

Can you beat the computer in the challenging strategy game?

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?

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

Two engines, at opposite ends of a single track railway line, set off towards one another just as a fly, sitting on the front of one of the engines, sets off flying along the railway line...