What happens when you try and fit the triomino pieces into these
Use the clues to colour each square.
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?
Can you cover the camel with these pieces?
Use the interactivity to help get a feel for this problem and to find out all the possible ways the balls could land.
How many different rhythms can you make by putting two drums on the
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....?
Cut four triangles from a square as shown in the picture. How many
different shapes can you make by fitting the four triangles back
Here are some rods that are different colours. How could I make a dark green rod using yellow and white rods?
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.
Can you work out how to balance this equaliser? You can put more
than one weight on a hook.
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 find all the different ways of lining up these Cuisenaire
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 numbers 1 to 8 into the circles so that the four
calculations are correct?
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?
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 trains can you make which are the same length as Matt's, using rods that are identical?
Explore the different tunes you can make with these five gourds.
What are the similarities and differences between the two tunes you
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.
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 all?
Ben and his mum are planting garlic. Use the interactivity to help
you find out how many cloves of garlic they might have had.
Three beads are threaded on a circular wire and are coloured either red or blue. Can you find all four different combinations?
How many triangles can you make using sticks that are 3cm, 4cm and 5cm long?
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 triangles can you draw on the dotty grid which each have one dot in the middle?
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10
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?
Use the interactivity to find all the different right-angled triangles you can make by just moving one corner of the starting triangle.
Use the information about Sally and her brother to find out how many children there are in the Brown family.
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?
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.
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!
Sort the houses in my street into different groups. Can you do it in any other ways?
Try out the lottery that is played in a far-away land. What is the
chance of winning?
Make one big triangle so the numbers that touch on the small triangles add to 10. You could use the interactivity to help you.
Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?
Our 2008 Advent Calendar has a 'Making Maths' activity for every
day in the run-up to Christmas.
Can you make a cycle of pairs that add to make a square number
using all the numbers in the box below, once and once only?
Investigate the different sounds you can make by putting the owls
and donkeys on the wheel.
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?
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?
Place six toy ladybirds into the box so that there are two ladybirds in every column and every row.
Can you fit the tangram pieces into the outline of this telephone?