How many trains can you make which are the same length as Matt's,
using rods that are identical?
Here are some rods that are different colours. How could I make a dark green rod using yellow and white rods?
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.
Can you find all the different ways of lining up these Cuisenaire
Work out the fractions to match the cards with the same amount of
How many different triangles can you draw on the dotty grid which each have one dot in the middle?
Can you work out how to balance this equaliser? You can put more
than one weight on a hook.
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?
Sort the houses in my street into different groups. Can you do it in any other ways?
What do the numbers shaded in blue on this hundred square have in common? What do you notice about the pink numbers? How about the shaded numbers in the other squares?
Cut four triangles from a square as shown in the picture. How many
different shapes can you make by fitting the four triangles back
How many different rhythms can you make by putting two drums on the
How many different ways can you find to join three equilateral
triangles together? Can you convince us that you have found them
Match the halves.
Use your mouse to move the red and green parts of this disc. Can
you make images which show the turnings described?
Can you cover the camel with these pieces?
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?
Investigate the smallest number of moves it takes to turn these
mats upside-down if you can only turn exactly three at a time.
What happens when you try and fit the triomino pieces into these
Ben and his mum are planting garlic. Use the interactivity to help
you find out how many cloves of garlic they might have had.
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....?
Place six toy ladybirds into the box so that there are two
ladybirds in every column and every row.
How many triangles can you make using sticks that are 3cm, 4cm and 5cm long?
Find out what a "fault-free" rectangle is and try to make some of
Use the interactivity to help get a feel for this problem and to find out all the possible ways the balls could land.
A train building game for 2 players.
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?
Our 2008 Advent Calendar has a 'Making Maths' activity for every
day in the run-up to Christmas.
Use the clues to colour each square.
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
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?
Can you put the numbers from 1 to 15 on the circles so that no
consecutive numbers lie anywhere along a continuous straight line?
Place the numbers 1 to 10 in the circles so that each number is the
difference between the two numbers just below it.
Place the numbers 1 to 6 in the circles so that each number is the
difference between the two numbers just below it.
Use the Cuisenaire rods environment to investigate ratio. Can you
find pairs of rods in the ratio 3:2? How about 9:6?
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?
Try out the lottery that is played in a far-away land. What is the
chance of winning?
NRICH December 2006 advent calendar - a new tangram for each day in
the run-up to Christmas.
Can you fit the tangram pieces into the outline of Little Fung at the table?
Can you fit the tangram pieces into the outline of this telephone?
Make one big triangle so the numbers that touch on the small triangles add to 10. You could use the interactivity to help you.
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 outlines of these clocks?
Can you fit the tangram pieces into the outline of this brazier for roasting chestnuts?
Can you fit the tangram pieces into the outlines of these people?
Can you fit the tangram pieces into the outlines of the lobster, yacht and cyclist?
A variant on the game Alquerque
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?
Exchange the positions of the two sets of counters in the least possible number of moves
A game for 2 people that everybody knows. You can play with a
friend or online. If you play correctly you never lose!