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?
What happens when you try and fit the triomino pieces into these
Can you cover the camel with these pieces?
Three beads are threaded on a circular wire and are coloured either red or blue. Can you find all four different combinations?
How many different triangles can you draw on the dotty grid which each have one dot in the middle?
This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?
How many triangles can you make using sticks that are 3cm, 4cm and 5cm long?
Sort the houses in my street into different groups. Can you do it in any other ways?
Investigate the smallest number of moves it takes to turn these
mats upside-down if you can only turn exactly three at a time.
How many different rhythms can you make by putting two drums on the
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?
Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?
How many different triangles can you make on a circular pegboard that has nine pegs?
Use your mouse to move the red and green parts of this disc. Can
you make images which show the turnings described?
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?
How many different ways can you find to join three equilateral
triangles together? Can you convince us that you have found them
Ben and his mum are planting garlic. Use the interactivity to help
you find out how many cloves of garlic they might have had.
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
Here are some rods that are different colours. How could I make a dark green rod using yellow and white rods?
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?
Use the clues to colour each square.
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 the interactivity to help get a feel for this problem and to find out all the possible ways the balls could land.
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?
How many trains can you make which are the same length as Matt's,
using rods that are identical?
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.
Place six toy ladybirds into the box so that there are two
ladybirds in every column and every row.
Place the numbers 1 to 6 in the circles so that each number is the
difference between the two numbers just below it.
Can you work out how to balance this equaliser? You can put more
than one weight on a hook.
Can you find all the different ways of lining up these Cuisenaire
Find out what a "fault-free" rectangle is and try to make some of
A game for 2 people that everybody knows. You can play with a
friend or online. If you play correctly you never lose!
A train building game for 2 players.
An interactive activity for one to experiment with a tricky tessellation
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 make a train the same length as Laura's but using three
differently coloured rods? Is there only one way of doing it?
Can you find all the different triangles on these peg boards, and
find their angles?
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.
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?
Move just three of the circles so that the triangle faces in the
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?
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. . . .
Twenty four games for the run-up to Christmas.
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?
Use the Cuisenaire rods environment to investigate ratio. Can you
find pairs of rods in the ratio 3:2? How about 9:6?
Take it in turns to make a triangle on the pegboard. Can you block your opponent?