Here are some rods that are different colours. How could I make a dark green rod using yellow and white rods?
How many trains can you make which are the same length as Matt's, using rods that are identical?
Use the clues to colour each square.
What happens when you try and fit the triomino pieces into these
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?
Can you cover the camel with these pieces?
How many different rhythms can you make by putting two drums on the
Can you find all the different ways of lining up these Cuisenaire
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?
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?
Sort the houses in my street into different groups. Can you do it in any other ways?
Can you make a train the same length as Laura's but using three differently coloured rods? Is there only one way of doing it?
How many different ways can you find to join three equilateral
triangles together? Can you convince us that you have found them
A train building game for 2 players.
Find out what a "fault-free" rectangle is and try to make some of
How many different triangles can you draw on the dotty grid which each have one dot in the middle?
Use the interactivity to help get a feel for this problem and to find out all the possible ways the balls could land.
Cut four triangles from a square as shown in the picture. How many
different shapes can you make by fitting the four triangles back
Use your mouse to move the red and green parts of this disc. Can
you make images which show the turnings described?
How many triangles can you make using sticks that are 3cm, 4cm and 5cm long?
Can you work out how to balance this equaliser? You can put more
than one weight on a hook.
Explore the different tunes you can make with these five gourds.
What are the similarities and differences between the two tunes you
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?
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....?
Ben and his mum are planting garlic. Use the interactivity to help
you find out how many cloves of garlic they might have had.
Three beads are threaded on a circular wire and are coloured either red or blue. Can you find all four different combinations?
Place the numbers 1 to 6 in the circles so that each number is the
difference between the two numbers just below it.
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 put the numbers from 1 to 15 on the circles so that no
consecutive numbers lie anywhere along a continuous straight line?
How many different triangles can you make on a circular pegboard that has nine pegs?
Find out how we can describe the "symmetries" of this triangle and
investigate some combinations of rotating and flipping it.
Can you put the numbers 1 to 8 into the circles so that the four
calculations are correct?
Investigate the different sounds you can make by putting the owls
and donkeys on the wheel.
Our 2008 Advent Calendar has a 'Making Maths' activity for every
day in the run-up to Christmas.
Place the numbers 1 to 10 in the circles so that each number is the
difference between the two numbers just below it.
Train game for an adult and child. Who will be the first to make the train?
NRICH December 2006 advent calendar - a new tangram for each day in
the run-up to Christmas.
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 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?
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!
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.
In your bank, you have three types of coins. The number of spots shows how much they are worth. Can you choose coins to exchange with the groups given to make the same total?
Can you fit the tangram pieces into the outlines of the chairs?
A game for 2 people that everybody knows. You can play with a
friend or online. If you play correctly you never lose!
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?
Arrange the four number cards on the grid, according to the rules,
to make a diagonal, vertical or horizontal line.
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?