Filter by: Content type: ALL Problems Articles Games Stage: All Stage 1&2 Stage 2&3 Stage 3&4 Stage 4&5 Challenge level:
A game for two or more players that uses a knowledge of measuring tools. Spin the spinner and identify which jobs can be done with the measuring tool shown.
Use the interactivity to find all the different right-angled triangles you can make by just moving one corner of the starting triangle.
Can you find all the different triangles on these peg boards, and find their angles?
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?
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....?
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?
How many different triangles can you make on a circular pegboard that has nine pegs?
Sort the houses in my street into different groups. Can you do it in any other ways?
Can you work out how to balance this equaliser? You can put more than one weight on a hook.
Use the clues to colour each square.
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?
This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?
How many different triangles can you draw on the dotty grid which each have one dot in the middle?
How many triangles can you make using sticks that are 3cm, 4cm and 5cm long?
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 interactivity to move Mr Pearson and his dog. Can you move him so that the graph shows a curve?
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?
Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?
Use your mouse to move the red and green parts of this disc. Can you make images which show the turnings described?
How many different ways can you find to join three equilateral triangles together? Can you convince us that you have found them all?
Can you create a story that would describe the movement of the man shown on these graphs? Use the interactivity to try out our ideas.
What happens when you try and fit the triomino pieces into these two grids?
Can you cover the camel with these pieces?
Try out the lottery that is played in a far-away land. What is the chance of winning?
Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.
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?
How many different rhythms can you make by putting two drums on the wheel?
Can you put the numbers 1 to 8 into the circles so that the four calculations are correct?
Use the number weights to find different ways of balancing the equaliser.
If you have only four weights, where could you place them in order to balance this equaliser?
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?
Find out what a "fault-free" rectangle is and try to make some of your own.
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 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 in them?
Place the numbers 1 to 6 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?
Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.
Can you put these shapes in order of size? Start with the smallest.
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?
Place six toy ladybirds into the box so that there are two ladybirds in every column and every row.
Can you find all the different ways of lining up these Cuisenaire rods?
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 10 in the circles so that each number is the difference between the two numbers just below it.
Our 2008 Advent Calendar has a 'Making Maths' activity for every day in the run-up to Christmas.
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?
Use the interactivity to help get a feel for this problem and to find out all the possible ways the balls could land.
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?
This is a game for two players. Can you find out how to be the first to get to 12 o'clock?