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?
Cut four triangles from a square as shown in the picture. How many
different shapes can you make by fitting the four triangles back
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.
How many different triangles can you make on a circular pegboard that has nine pegs?
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?
This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?
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 find all the different ways of lining up these Cuisenaire
Find out how we can describe the "symmetries" of this triangle and
investigate some combinations of rotating and flipping it.
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
NRICH December 2006 advent calendar - a new tangram for each day in
the run-up to Christmas.
Investigate the smallest number of moves it takes to turn these
mats upside-down if you can only turn exactly three at a time.
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 from 1 to 15 on the circles so that no
consecutive numbers lie anywhere along a continuous straight line?
Can you put the numbers 1 to 8 into the circles so that the four
calculations are correct?
A train building game for 2 players.
Can you fit the tangram pieces into the outline of Granma T?
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?
Can you fit the tangram pieces into the outlines of these people?
Use the interactivity to find all the different right-angled triangles you can make by just moving one corner of the starting triangle.
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!
Find out what a "fault-free" rectangle is and try to make some of
A card pairing game involving knowledge of simple ratio.
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?
A game for 2 people that everybody knows. You can play with a
friend or online. If you play correctly you never lose!
Can you fit the tangram pieces into the outline of this junk?
An interactive activity for one to experiment with a tricky tessellation
Can you fit the tangram pieces into the outlines of the candle and sundial?
Train game for an adult and child. Who will be the first to make the train?
What is the greatest number of squares you can make by overlapping
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?
Exchange the positions of the two sets of counters in the least possible number of moves
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?
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?
Use the Cuisenaire rods environment to investigate ratio. Can you
find pairs of rods in the ratio 3:2? How about 9:6?
Choose the size of your pegboard and the shapes you can make. Can you work out the strategies needed to block your opponent?
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?
Work out the fractions to match the cards with the same amount of
A generic circular pegboard resource.
Board Block game for two. Can you stop your partner from being able to make a shape on the board?
Can you find all the different triangles on these peg boards, and
find their angles?
Square It game for an adult and child. Can you come up with a way of always winning this game?
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10
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?
A simulation of target archery practice
Try to stop your opponent from being able to split the piles of counters into unequal numbers. Can you find a strategy?
Investigate how the four L-shapes fit together to make an enlarged L-shape. You could explore this idea with other shapes too.