Each light in this interactivity turns on according to a rule. What happens when you enter different numbers? Can you find the smallest number that lights up all four lights?

Mr Gilderdale is playing a game with his class. What rule might he have chosen? How would you test your idea?

Create a pattern on the left-hand grid. How could you extend your pattern on the right-hand grid?

A shape and space game for 2,3 or 4 players. Be the last person to be able to place a pentomino piece on the playing board. Play with card, or on the computer.

Work out how to light up the single light. What's the rule?

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

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

Sort the houses in my street into different groups. Can you do it in any other ways?

Investigate which numbers make these lights come on. What is the smallest number you can find that lights up all the lights?

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

If you can post the triangle with either the blue or yellow colour face up, how many ways can it be posted altogether?

Choose 13 spots on the grid. Can you work out the scoring system? What is the maximum possible score?

Use the interactivity to find out how many quarter turns the man must rotate through to look like each of the pictures.

Use the interactivity to sort these numbers into sets. Can you give each set a name?

Use the blue spot to help you move the yellow spot from one star to the other. How are the trails of the blue and yellow spots related?

The computer has made a rectangle and will tell you the number of spots it uses in total. Can you find out where the rectangle is?

Can you make the green spot travel through the tube by moving the yellow spot? Could you draw a tube that both spots would follow?

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

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 fit the tangram pieces into the outline of the child walking home from school?

Can you fit the tangram pieces into the outlines of the lobster, yacht and cyclist?

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

Can you fit the tangram pieces into the outlines of the chairs?

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?

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

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

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?

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?

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?

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.

Cut four triangles from a square as shown in the picture. How many different shapes can you make by fitting the four triangles back together?

An interactive activity for one to experiment with a tricky tessellation

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.

How many different rhythms can you make by putting two drums on the wheel?

A game for two or more players that uses a knowledge of measuring tools. Spin the spinner and identify which jobs can be done with the measuring tool shown.

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?

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

Exchange the positions of the two sets of counters in the least possible number of moves

An interactive game for 1 person. You are given a rectangle with 50 squares on it. Roll the dice to get a percentage between 2 and 100. How many squares is this? Keep going until you get 100. . . .

Place six toy ladybirds into the box so that there are two ladybirds in every column and every row.

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?

A game for 1 or 2 people. Use the interactive version, or play with friends. Try to round up as many counters as possible.

A game for 2 people that can be played on line or with pens and paper. Combine your knowledege of coordinates with your skills of strategic thinking.

A game to be played against the computer, or in groups. Pick a 7-digit number. A random digit is generated. What must you subract to remove the digit from your number? the first to zero wins.

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

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