Cut four triangles from a square as shown in the picture. How many
different shapes can you make by fitting the four triangles back
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?
Three beads are threaded on a circular wire and are coloured either red or blue. Can you find all four different combinations?
Find out how we can describe the "symmetries" of this triangle and
investigate some combinations of rotating and flipping it.
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?
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?
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?
NRICH December 2006 advent calendar - a new tangram for each day in
the run-up to Christmas.
Our 2008 Advent Calendar has a 'Making Maths' activity for every
day in the run-up to Christmas.
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....?
Explore the different tunes you can make with these five gourds.
What are the similarities and differences between the two tunes you
Work out the fractions to match the cards with the same amount of
A generic circular pegboard resource.
Investigate how the four L-shapes fit together to make an enlarged L-shape. You could explore this idea with other shapes too.
Ahmed has some wooden planks to use for three sides of a rabbit run
against the shed. What quadrilaterals would he be able to make with
the planks of different lengths?
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!
Place the numbers 1 to 10 in the circles so that each number is the
difference between the two numbers just below it.
Can you fit the tangram pieces into the outline of this junk?
Can you fit the tangram pieces into the outlines of the candle and sundial?
Can you fit the tangram pieces into the outline of Wai Ping, Wah Ming and Chi Wing?
Investigate the smallest number of moves it takes to turn these
mats upside-down if you can only turn exactly three at a time.
Can you fit the tangram pieces into the outlines of the chairs?
Use the interactivity to find all the different right-angled triangles you can make by just moving one corner of the starting triangle.
A card pairing game involving knowledge of simple ratio.
A train building game for 2 players.
Can you find all the different ways of lining up these Cuisenaire
Choose the size of your pegboard and the shapes you can make. Can you work out the strategies needed to block your opponent?
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?
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.
Can you fit the tangram pieces into the outline of this brazier for roasting chestnuts?
Can you fit the tangram pieces into the outlines of these people?
Can you fit the tangram pieces into the outlines of the lobster, yacht and cyclist?
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 these clocks?
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. . . .
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 outline of Mai Ling?
Use the Cuisenaire rods environment to investigate ratio. Can you
find pairs of rods in the ratio 3:2? How about 9:6?
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?
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 activity for one to experiment with a tricky tessellation
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 many different triangles can you make on a circular pegboard that has nine pegs?
Can you fit the tangram pieces into the outline of Granma T?
Can you fit the tangram pieces into the outlines of the watering can and man in a boat?
Can you fit the tangram pieces into the outlines of Mai Ling and Chi Wing?