How many trains can you make which are the same length as Matt's, using rods that are identical?
Can you work out how to balance this equaliser? You can put more
than one weight on a hook.
Ben and his mum are planting garlic. Use the interactivity to help
you find out how many cloves of garlic they might have had.
Here are some rods that are different colours. How could I make a dark green rod using yellow and white rods?
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 ways can you find to join three equilateral
triangles together? Can you convince us that you have found them
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?
What happens when you try and fit the triomino pieces into these
How many different triangles can you draw on the dotty grid which each have one dot in the middle?
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?
Train game for an adult and child. Who will be the first to make the train?
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 cover the camel with these pieces?
How many different rhythms can you make by putting two drums on the
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 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.
Find out what a "fault-free" rectangle is and try to make some of
How many triangles can you make using sticks that are 3cm, 4cm and 5cm long?
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?
Arrange the four number cards on the grid, according to the rules,
to make a diagonal, vertical or horizontal line.
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?
Use the clues to colour each square.
Our 2008 Advent Calendar has a 'Making Maths' activity for every
day in the run-up to Christmas.
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
How many different triangles can you make on a circular pegboard that has nine pegs?
Place six toy ladybirds into the box so that there are two
ladybirds in every column and every row.
Can you put the numbers 1 to 8 into the circles so that the four
calculations are correct?
Can you put the numbers from 1 to 15 on the circles so that no
consecutive numbers lie anywhere along a continuous straight line?
NRICH December 2006 advent calendar - a new tangram for each day in
the run-up to Christmas.
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 find all the different right-angled
triangles you can make by just moving one corner of the starting
Use the interactivity to find out how many quarter turns the man
must rotate through to look like each of the pictures.
Use the information about Sally and her brother to find out how many children there are in the Brown family.
Choose 13 spots on the grid. Can you work out the scoring system? What is the maximum possible score?
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?
An odd version of tic tac toe
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?
Try to stop your opponent from being able to split the piles of counters into unequal numbers. Can you find a strategy?
A card pairing game involving knowledge of simple ratio.
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?
Use your mouse to move the red and green parts of this disc. Can
you make images which show the turnings described?
Try out the lottery that is played in a far-away land. What is the
chance of winning?
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?
Use the Cuisenaire rods environment to investigate ratio. Can you
find pairs of rods in the ratio 3:2? How about 9:6?
Move just three of the circles so that the triangle faces in the
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 find all the different triangles on these peg boards, and
find their angles?