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

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?

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

Square It game for an adult and child. Can you come up with a way of always winning this game?

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.

Use the interactivity to listen to the bells ringing a pattern. Now it's your turn! Play one of the bells yourself. How do you know when it is your turn to ring?

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 the interactivity to play two of the bells in a pattern. How do you know when it is your turn to ring, and how do you know which bell to ring?

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.

You have 4 red and 5 blue counters. How many ways can they be placed on a 3 by 3 grid so that all the rows columns and diagonals have an even number of red counters?

Can you beat the computer in the challenging strategy 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. . . .

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 are the coordinates of the coloured dots that mark out the tangram? Try changing the position of the origin. What happens to the coordinates now?

How many times in twelve hours do the hands of a clock form a right angle? Use the interactivity to check your answers.

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. . . .

Work out the fractions to match the cards with the same amount of money.

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.

A tetromino is made up of four squares joined edge to edge. Can this tetromino, together with 15 copies of itself, be used to cover an eight by eight chessboard?

You have 27 small cubes, 3 each of nine colours. Use the small cubes to make a 3 by 3 by 3 cube so that each face of the bigger cube contains one of every colour.

Use the interactivity to investigate what kinds of triangles can be drawn on peg boards with different numbers of pegs.

Use the interactivity or play this dice game yourself. How could you make it fair?

Explore the different tunes you can make with these five gourds. What are the similarities and differences between the two tunes you are given?

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?

Match pairs of cards so that they have equivalent ratios.

Use the interactivity to create some steady rhythms. How could you create a rhythm which sounds the same forwards as it does backwards?

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

Can you work out what is wrong with the cogs on a UK 2 pound coin?

Can you see why 2 by 2 could be 5? Can you predict what 2 by 10 will be?

Use the Cuisenaire rods environment to investigate ratio. Can you find pairs of rods in the ratio 3:2? How about 9:6?

Choose the size of your pegboard and the shapes you can make. Can you work out the strategies needed to block your opponent?

A game for 2 people that everybody knows. You can play with a friend or online. If you play correctly you never lose!

How many different triangles can you make on a circular pegboard that has nine pegs?

Ahmed has some wooden planks to use for three sides of a rabbit run against the shed. What quadrilaterals would he be able to make with the planks of different lengths?

Find out how we can describe the "symmetries" of this triangle and investigate some combinations of rotating and flipping it.

Starting with the number 180, take away 9 again and again, joining up the dots as you go. Watch out - don't join all the dots!

A game for 1 person. Can you work out how the dice must be rolled from the start position to the finish? Play on line.

An interactive game to be played on your own or with friends. Imagine you are having a party. Each person takes it in turns to stand behind the chair where they will get the most chocolate.

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

Use the interactivity to make this Islamic star and cross design. Can you produce a tessellation of regular octagons with two different types of triangle?

Can you fit the tangram pieces into the outline of this telephone?

Can you fit the tangram pieces into the outline of Little Fung at the table?

Can you fit the tangram pieces into the outlines of these people?

Can you fit the tangram pieces into the outline of this brazier for roasting chestnuts?

Hover your mouse over the counters to see which ones will be removed. Click to remover them. The winner is the last one to remove a counter. How you can make sure you win?

Three beads are threaded on a circular wire and are coloured either red or blue. Can you find all four different combinations?