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. . . .

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

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

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

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.

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

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?

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.

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

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.

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

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

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?

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.

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.

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

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

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?

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

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

Use Excel to explore multiplication of fractions.

This resource contains interactive problems to support work on number sequences at Key Stage 4.

A tool for generating random integers.

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?

Prove Pythagoras' Theorem using enlargements and scale factors.

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

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.

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?

Learn how to use the Shuffles interactivity by running through these tutorial demonstrations.

Can you make a right-angled triangle on this peg-board by joining up three points round the edge?

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

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

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. . . .

A game for 2 players. Can be played online. One player has 1 red counter, the other has 4 blue. The red counter needs to reach the other side, and the blue needs to trap the red.

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 diamond mining skills and your x,y coordination in this homage to Pacman.

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.

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?

It's easy to work out the areas of most squares that we meet, but what if they were tilted?

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...

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

Can you spot the similarities between this game and other games you know? The aim is to choose 3 numbers that total 15.

A game for two people, or play online. Given a target number, say 23, and a range of numbers to choose from, say 1-4, players take it in turns to add to the running total to hit their target.