Complete the squares - but be warned some are trickier than they look!

How many different ways can you find to join three equilateral triangles together? Can you convince us that you have found them all?

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?

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?

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

This activity challenges you to make collections of shapes. Can you give your collection a name?

What shape is the overlap when you slide one of these shapes half way across another? Can you picture it in your head? Use the interactivity to check your visualisation.

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?

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.

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

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 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.

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

Start by putting one million (1 000 000) into the display of your calculator. Can you reduce this to 7 using just the 7 key and add, subtract, multiply, divide and equals as many times as you like?

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.

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

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

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

An interactive activity for one to experiment with a tricky tessellation

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?

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

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

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

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?

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

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

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?

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?

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 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?

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

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!

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

If there are 3 squares in the ring, can you place three different numbers in them so that their differences are odd? Try with different numbers of squares around the ring. What do you notice?

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

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

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?

This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?

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?

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?

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?