Can you work out how to balance this equaliser? You can put more
than one weight on a hook.
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?
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?
Use the interactivity to find all the different right-angled triangles you can make by just moving one corner of the starting triangle.
How many trains can you make which are the same length as Matt's, using rods that are identical?
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?
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.
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?
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?
Ben and his mum are planting garlic. Use the interactivity to help
you find out how many cloves of garlic they might have had.
Investigate the smallest number of moves it takes to turn these
mats upside-down if you can only turn exactly three at a time.
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?
What happens when you try and fit the triomino pieces into these
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....?
An environment which simulates working with Cuisenaire rods.
Use the clues to colour each square.
Can you find all the different ways of lining up these Cuisenaire
Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?
Place six toy ladybirds into the box so that there are two ladybirds in every column and every row.
Can you put the numbers from 1 to 15 on the circles so that no
consecutive numbers lie anywhere along a continuous straight line?
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?
Try out the lottery that is played in a far-away land. What is the
chance of winning?
Can you put the numbers 1 to 8 into the circles so that the four
calculations are correct?
How many triangles can you make using sticks that are 3cm, 4cm and 5cm long?
Here are some rods that are different colours. How could I make a dark green rod using yellow and white rods?
Make one big triangle so the numbers that touch on the small triangles add to 10. You could use the interactivity to help you.
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?
Can you hang weights in the right place to make the equaliser
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 find all the different triangles on these peg boards, and
find their angles?
How many different ways can you find to join three equilateral triangles together? Can you convince us that you have found them all?
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 information about Sally and her brother to find out how many children there are in the Brown family.
Use the number weights to find different ways of balancing the equaliser.
How many different rhythms can you make by putting two drums on the
Can you complete this jigsaw of the multiplication square?
How many different triangles can you make on a circular pegboard that has nine pegs?
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?
Find out what a "fault-free" rectangle is and try to make some of
Can you use the numbers on the dice to reach your end of the number line before your partner beats you?
If you have only four weights, where could you place them in order
to balance this equaliser?
This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?
NRICH December 2006 advent calendar - a new tangram for each day in
the run-up to Christmas.
Here is a chance to play a version of the classic Countdown Game.
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!
Our 2008 Advent Calendar has a 'Making Maths' activity for every
day in the run-up to Christmas.
Choose a symbol to put into the number sentence.
How many different triangles can you draw on the dotty grid which each have one dot in the middle?