Semi-regular tessellations combine two or more different regular polygons to fill the plane. Can you find all the semi-regular tessellations?

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. . . .

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

Here is a solitaire type environment for you to experiment with. Which targets can you reach?

The idea of this game is to add or subtract the two numbers on the dice and cover the result on the grid, trying to get a line of three. Are there some numbers that are good to aim for?

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

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.

Can you use small coloured cubes to make a 3 by 3 by 3 cube so that each face of the bigger cube contains one of each colour?

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.

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.

A game in which players take it in turns to choose a number. Can you block your opponent?

How many different triangles can you make which consist of the centre point and two of the points on the edge? Can you work out each of their angles?

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

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?

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?

Do you know how to find the area of a triangle? You can count the squares. What happens if we turn the triangle on end? Press the button and see. Try counting the number of units in the triangle now. . . .

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

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

Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.

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 put the 25 coloured tiles into the 5 x 5 square so that no column, no row and no diagonal line have tiles of the same colour in them?

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.

There are nine teddies in Teddy Town - three red, three blue and three yellow. There are also nine houses, three of each colour. Can you put them on the map of Teddy Town according to the rules?

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.

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

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

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

This rectangle is cut into five pieces which fit exactly into a triangular outline and also into a square outline where the triangle, the rectangle and the square have equal areas.

Use Excel to explore multiplication of fractions.

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. . . .

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.

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?

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.

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?

Match the cards of the same value.

Can you beat the computer in the challenging strategy game?

Could games evolve by natural selection? Take part in this web experiment to find out!

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

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

Is this a fair game? How many ways are there of creating a fair game by adding odd and even numbers?

Meg and Mo need to hang their marbles so that they balance. Use the interactivity to experiment and find out what they need to do.

Can you set the logic gates so that the number of bulbs which are on is the same as the number of switches which are on?

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...

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

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.