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

This was a problem for our birthday website. Can you use four of these pieces to form a square? How about making a square with all five pieces?

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

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?

NRICH December 2006 advent calendar - a new tangram for each day in the run-up to Christmas.

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?

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

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

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?

Use your mouse to move the red and green parts of this disc. Can you make images which show the turnings described?

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

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

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

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?

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 this telephone?

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?

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

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.

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

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?

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

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. . . .

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

An interactive activity for one to experiment with a tricky tessellation

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

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?

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

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

How many trains can you make which are the same length as Matt's, using rods that are identical?

Can you find all the different ways of lining up these Cuisenaire rods?

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

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

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?