Find out what a "fault-free" rectangle is and try to make some of your own.
Ben and his mum are planting garlic. Use the interactivity to help you find out how many cloves of garlic they might have had.
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?
Place the numbers 1 to 10 in the circles so that each number is the difference between the two numbers just below it.
What happens when you try and fit the triomino pieces into these two grids?
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?
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 clues to colour each square.
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?
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....?
Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?
Can you cover the camel with these pieces?
Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.
Try out the lottery that is played in a far-away land. What is the chance of winning?
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 different ways can you find to join three equilateral triangles together? Can you convince us that you have found them all?
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?
Cut four triangles from a square as shown in the picture. How many different shapes can you make by fitting the four triangles back together?
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?
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?
Place six toy ladybirds into the box so that there are two ladybirds in every column and every row.
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 work out how to balance this equaliser? You can put more than one weight on a hook.
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 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 wheel?
Can you find all the different ways of lining up these Cuisenaire rods?
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?
Can you put the numbers from 1 to 15 on the circles so that no consecutive numbers lie anywhere along a continuous straight line?
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 trains can you make which are the same length as Matt's, using rods that are identical?
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10 will be?
Our 2008 Advent Calendar has a 'Making Maths' activity for every day in the run-up to Christmas.
Use the interactivity to investigate what kinds of triangles can be drawn on peg boards with different numbers of pegs.
Can you find all the different triangles on these peg boards, and find their angles?
Place the numbers from 1 to 9 in the squares below so that the difference between joined squares is odd. How many different ways can you do this?
This article gives you a few ideas for understanding the Got It! game and how you might find a winning strategy.
Explore the different tunes you can make with these five gourds. What are the similarities and differences between the two tunes you are given?
Here is a chance to play a version of the classic Countdown Game.
How many different triangles can you draw on the dotty grid which each have one dot in the middle?
First Connect Three game for an adult and child. Use the dice numbers and either addition or subtraction to get three numbers in a straight line.
The idea of this game is to add or subtract the two numbers on the dice and cover the result on the grid, trying to get a line of three. Are there some numbers that are good to aim for?
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?
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 Wai Ping, Wah Ming and Chi Wing?
This is a game for two players. Can you find out how to be the first to get to 12 o'clock?
Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.
A game for 2 people that everybody knows. You can play with a friend or online. If you play correctly you never lose!