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

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?

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.

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?

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

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

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

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

Yasmin and Zach have some bears to share. Which numbers of bears can they share so that there are none left over?

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.

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?

Can you logically construct these silhouettes using the tangram pieces?

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

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?

Try to stop your opponent from being able to split the piles of counters into unequal numbers. Can you find a strategy?

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

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

Use the information about Sally and her brother to find out how many children there are in the Brown family.

Imagine a wheel with different markings painted on it at regular intervals. Can you predict the colour of the 18th mark? The 100th mark?

What shaped overlaps can you make with two circles which are the same size? What shapes are 'left over'? What shapes can you make when the circles are different sizes?

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

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

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

An interactive activity for one to experiment with a tricky tessellation

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?

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?

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.

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

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.

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

Investigate the different sounds you can make by putting the owls and donkeys on the wheel.

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. . . .

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.

A game for two people that can be played with pencils and paper. Combine your knowledge of coordinates with some strategic thinking.

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

Arrange any number of counters from these 18 on the grid to make a rectangle. What numbers of counters make rectangles? How many different rectangles can you make with each number of counters?

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

How many right angles can you make using two sticks?

Is it possible to place 2 counters on the 3 by 3 grid so that there is an even number of counters in every row and every column? How about if you have 3 counters or 4 counters or....?

There are three versions of this challenge. The idea is to change the colour of all the spots on the grid. Can you do it in fewer throws of the dice?

What is the greatest number of squares you can make by overlapping three squares?

Our 2008 Advent Calendar has a 'Making Maths' activity for every day in the run-up to Christmas.

These interactive dominoes can be dragged around the screen.