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 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
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?
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?
NRICH December 2006 advent calendar - a new tangram for each day in
the run-up to Christmas.
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 triangles can you make on a circular pegboard that has nine pegs?
This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?
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
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 find all the different ways of lining up these Cuisenaire
Can you put the numbers from 1 to 15 on the circles so that no
consecutive numbers lie anywhere along a continuous straight line?
Find out how we can describe the "symmetries" of this triangle and
investigate some combinations of rotating and flipping it.
Three beads are threaded on a circular wire and are coloured either red or blue. Can you find all four different combinations?
Can you put the numbers 1 to 8 into the circles so that the four
calculations are correct?
Our 2008 Advent Calendar has a 'Making Maths' activity for every
day in the run-up to Christmas.
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?
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 Mai Ling?
A card pairing game involving knowledge of simple ratio.
Can you fit the tangram pieces into the outline of this brazier for roasting chestnuts?
Use the interactivity to find all the different right-angled
triangles you can make by just moving one corner of the starting
Can you fit the tangram pieces into the outline of Granma T?
Can you fit the tangram pieces into the outline of Wai Ping, Wah Ming and Chi Wing?
An interactive activity for one to experiment with a tricky tessellation
Can you fit the tangram pieces into the outline of this junk?
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 train building game for 2 players.
Find out what a "fault-free" rectangle is and try to make some of
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.
This problem is based on a code using two different prime numbers
less than 10. You'll need to multiply them together and shift the
alphabet forwards by the result. Can you decipher the code?
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 Cuisenaire rods environment to investigate ratio. Can you
find pairs of rods in the ratio 3:2? How about 9:6?
Can you find all the different triangles on these peg boards, and
find their angles?
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!
A simulation of target archery practice
Can you fit the tangram pieces into the outline of this telephone?
Can you fit the tangram pieces into the outline of Little Fung at the table?
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?
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.
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?
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10
Work out the fractions to match the cards with the same amount of
Arrange the four number cards on the grid, according to the rules,
to make a diagonal, vertical or horizontal line.
A generic circular pegboard resource.
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?
A game for 2 people that everybody knows. You can play with a
friend or online. If you play correctly you never lose!