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?

Can you make a cycle of pairs that add to make a square number using all the numbers in the box below, once and once only?

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!

Play this well-known game against the computer where each player is equally likely to choose scissors, paper or rock. Why not try the variations too?

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

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?

You'll need two dice to play this game against a partner. Will Incey Wincey make it to the top of the drain pipe or the bottom of the drain pipe first?

Incey Wincey Spider game for an adult and child. Will Incey get to the top of the drainpipe?

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

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

How can the same pieces of the tangram make this bowl before and after it was chipped? Use the interactivity to try and work out what is going on!

An interactive activity for one to experiment with a tricky tessellation

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?

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.

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.

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

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?

Investigate how the four L-shapes fit together to make an enlarged L-shape. You could explore this idea with other shapes too.

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

Choose four of the numbers from 1 to 9 to put in the squares so that the differences between joined squares are odd.

Take it in turns to place a domino on the grid. One to be placed horizontally and the other vertically. Can you make it impossible for your opponent to play?

Place the numbers from 1 to 9 in the squares below so that the difference between joined squares is odd. How many different ways can you do this?

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

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

Move just three of the circles so that the triangle faces in the opposite direction.

Make one big triangle so the numbers that touch on the small triangles add to 10. You could use the interactivity to help you.

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

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?

Take it in turns to make a triangle on the pegboard. Can you block your opponent?

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?

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

Place the numbers 1 to 10 in the circles so that each number is the difference between the two numbers just below it.

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

Place the numbers 1 to 6 in the circles so that each number is the difference between the two numbers just below it.

Explore this interactivity and see if you can work out what it does. Could you use it to estimate the area of a shape?

If you have only four weights, where could you place them in order to balance this equaliser?

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

Board Block game for two. Can you stop your partner from being able to make a shape on the board?

Stop the Clock game for an adult and child. How can you make sure you always win this game?

Train game for an adult and child. Who will be the first to make the train?

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?