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

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

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

What happens when you try and fit the triomino pieces into these two grids?

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 work out how to balance this equaliser? You can put more than one weight on a hook.

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?

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?

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

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?

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.

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 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.

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.

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?

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

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

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

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?

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

An interactive activity for one to experiment with a tricky tessellation

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!

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

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

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

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

How many triangles can you make using sticks that are 3cm, 4cm and 5cm long?

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!

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

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

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....?

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?

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

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

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

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

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?

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

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

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

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

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?