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?
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
Sort the houses in my street into different groups. Can you do it in any other ways?
How many different rhythms can you make by putting two drums on the
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 interactivity to help get a feel for this problem and to find out all the possible ways the balls could land.
Our 2008 Advent Calendar has a 'Making Maths' activity for every
day in the run-up to Christmas.
Use your mouse to move the red and green parts of this disc. Can
you make images which show the turnings described?
Use the clues to colour each square.
Can you cover the camel with these pieces?
Find out how we can describe the "symmetries" of this triangle and
investigate some combinations of rotating and flipping it.
What happens when you try and fit the triomino pieces into these
NRICH December 2006 advent calendar - a new tangram for each day in
the run-up to Christmas.
Can you work out how to balance this equaliser? You can put more
than one weight on a hook.
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?
Cut four triangles from a square as shown in the picture. How many
different shapes can you make by fitting the four triangles back
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.
A generic circular pegboard resource.
Can you work out what is wrong with the cogs on a UK 2 pound coin?
How many different triangles can you make on a circular pegboard that has nine pegs?
Complete the squares - but be warned some are trickier than they
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?
Take it in turns to make a triangle on the pegboard. Can you 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?
How many trains can you make which are the same length as Matt's, using rods that are identical?
Try to stop your opponent from being able to split the piles of counters into unequal numbers. Can you find a strategy?
Place the numbers 1 to 6 in the circles so that each number is the
difference between the two numbers just below it.
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?
An odd version of tic tac toe
Twenty four games for the run-up to Christmas.
A train building game for 2 players.
Move just three of the circles so that the triangle faces in the
Can you find all the different ways of lining up these Cuisenaire
Use the interactivity to find out how many quarter turns the man
must rotate through to look like each of the pictures.
Take it in turns to place a domino on the grid. One to be placed horizontally and the other vertically. Can you make it impossible for your opponent to play?
Can you fit the tangram pieces into the outline of this telephone?
Match the halves.
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. . . .
Can you fit the tangram pieces into the outlines of the chairs?
If there are 3 squares in the ring, can you place three different numbers in them so that their differences are odd? Try with different numbers of squares around the ring. What do you notice?
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.
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.
How many right angles can you make using two sticks?
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....?
Work out the fractions to match the cards with the same amount of
How many triangles can you make using sticks that are 3cm, 4cm and 5cm long?