Cut four triangles from a square as shown in the picture. How many
different shapes can you make by fitting the four triangles back
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?
Find out how we can describe the "symmetries" of this triangle and
investigate some combinations of rotating and flipping it.
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?
Can you put the 25 coloured tiles into the 5 x 5 square so that no
column, no row and no diagonal line have tiles of the same colour
NRICH December 2006 advent calendar - a new tangram for each day in
the run-up to Christmas.
Three beads are threaded on a circular wire and are coloured either red or blue. Can you find all four different combinations?
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?
Our 2008 Advent Calendar has a 'Making Maths' activity for every
day in the run-up to Christmas.
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?
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 Little Fung at the table?
Can you fit the tangram pieces into the outline of this telephone?
Can you fit the tangram pieces into the outlines of these people?
Can you fit the tangram pieces into the outlines of these clocks?
Can you fit the tangram pieces into the outlines of the lobster, yacht and cyclist?
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 outline of the child walking home from school?
Can you fit the tangram pieces into the outline of this junk?
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.
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 Little Ming?
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....?
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 Mai Ling?
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?
Can you fit the tangram pieces into the outlines of the chairs?
Can you fit the tangram pieces into the outline of Granma T?
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?
A simulation of target archery practice
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?
There are nine teddies in Teddy Town - three red, three blue and three yellow. There are also nine houses, three of each colour. Can you put them on the map of Teddy Town according to the rules?
Choose the size of your pegboard and the shapes you can make. Can
you work out the strategies needed to block your opponent?
Use the blue spot to help you move the yellow spot from one star to
the other. How are the trails of the blue and yellow spots related?
Use the Cuisenaire rods environment to investigate ratio. Can you
find pairs of rods in the ratio 3:2? How about 9:6?
A generic circular pegboard resource.
A game for 2 people that everybody knows. You can play with a
friend or online. If you play correctly you never lose!
An interactive activity for one to experiment with a tricky tessellation
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!
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 card pairing game involving knowledge of simple ratio.
Use the interactivity to find all the different right-angled
triangles you can make by just moving one corner of the starting
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.
Investigate how the four L-shapes fit together to make an enlarged
L-shape. You could explore this idea with other shapes too.
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. . . .
Work out the fractions to match the cards with the same amount of
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?
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?