This 100 square jigsaw is written in code. It starts with 1 and
ends with 100. Can you build it up?
Place the numbers 1 to 6 in the circles so that each number is the
difference between the two numbers just below it.
Place six toy ladybirds into the box so that there are two
ladybirds in every column and every row.
How many different triangles can you draw on the dotty grid which each have one dot in the middle?
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?
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?
Use your mouse to move the red and green parts of this disc. Can
you make images which show the turnings described?
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?
How many triangles can you make using sticks that are 3cm, 4cm and 5cm long?
How many different rhythms can you make by putting two drums on the
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
Three beads are threaded on a circular wire and are coloured either red or blue. Can you find all four different combinations?
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
Can you cover the camel with these pieces?
Can you hang weights in the right place to make the equaliser
How many different ways can you find to join three equilateral
triangles together? Can you convince us that you have found them
Can you work out how to balance this equaliser? You can put more
than one weight on a hook.
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?
Ben and his mum are planting garlic. Use the interactivity to help
you find out how many cloves of garlic they might have had.
Use the information about Sally and her brother to find out how many children there are in the Brown family.
Here are some rods that are different colours. How could I make a dark green rod using yellow and white rods?
Can you put the numbers 1 to 8 into the circles so that the four
calculations are correct?
Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?
Find out how we can describe the "symmetries" of this triangle and
investigate some combinations of rotating and flipping it.
Choose four of the numbers from 1 to 9 to put in the squares so that the differences between joined squares are odd.
Make one big triangle so the numbers that touch on the small triangles add to 10. You could use the interactivity to help you.
Can you make the green spot travel through the tube by moving the
yellow spot? Could you draw a tube that both spots would follow?
Place the numbers 1 to 10 in the circles so that each number is the
difference between the two numbers just below it.
If you hang two weights on one side of this balance, in how many
different ways can you hang three weights on the other side for it
to be balanced?
Cut four triangles from a square as shown in the picture. How many
different shapes can you make by fitting the four triangles back
Our 2008 Advent Calendar has a 'Making Maths' activity for every
day in the run-up to Christmas.
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 triangles can you make on a circular pegboard
that has nine pegs?
Use the interactivity to help get a feel for this problem and to find out all the possible ways the balls could land.
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?
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?
NRICH December 2006 advent calendar - a new tangram for each day in
the run-up to Christmas.
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.
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?
Can you fit the tangram pieces into the outlines of the lobster, yacht and cyclist?
Can you fit the tangram pieces into the outlines of the chairs?
Can you fit the tangram pieces into the outline of the child walking home from school?
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.
Try out the lottery that is played in a far-away land. What is the
chance of winning?
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. . . .
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!