Filter by: Content type: ALL Problems Articles Games Stage: All Stage 1&2 Stage 2&3 Stage 3&4 Stage 4&5 Challenge level:
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?
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 6 in the circles so that each number is the difference between the two numbers just below it.
Can you put the numbers 1 to 8 into the circles so that the four calculations are correct?
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 number weights to find different ways of balancing the equaliser.
Place six toy ladybirds into the box so that there are two ladybirds in every column and every row.
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?
Can you use the numbers on the dice to reach your end of the number line before your partner beats you?
Can you hang weights in the right place to make the equaliser balance?
Place the numbers 1 to 10 in the circles so that each number is the difference between the two numbers just below it.
Use the interactivities to fill in these Carroll diagrams. How do you know where to place the numbers?
Use the information about Sally and her brother to find out how many children there are in the Brown family.
Ben and his mum are planting garlic. Use the interactivity to help you find out how many cloves of garlic they might have had.
Find out what a "fault-free" rectangle is and try to make some of your own.
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 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?
How have the numbers been placed in this Carroll diagram? Which labels would you put on each row and column?
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?
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10 will be?
Make one big triangle so the numbers that touch on the small triangles add to 10. You could use the interactivity to help you.
Choose four of the numbers from 1 to 9 to put in the squares so that the differences between joined squares are odd.
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 put the numbers from 1 to 15 on the circles so that no consecutive numbers lie anywhere along a continuous straight line?
This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?
Can you cover the camel with these pieces?
What happens when you try and fit the triomino pieces into these two grids?
An environment which simulates working with Cuisenaire rods.
How many triangles can you make using sticks that are 3cm, 4cm and 5cm long?
Start by putting one million (1 000 000) into the display of your calculator. Can you reduce this to 7 using just the 7 key and add, subtract, multiply, divide and equals as many times as you like?
How many different rhythms can you make by putting two drums on the wheel?
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?
How many different triangles can you make on a circular pegboard that has nine pegs?
Can you find all the different triangles on these peg boards, and find their angles?
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!
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?
Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.
How many different ways can you find to join three equilateral triangles together? Can you convince us that you have found them all?
Use the interactivity to find all the different right-angled triangles you can make by just moving one corner of the starting triangle.
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....?
Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.
Here are some rods that are different colours. How could I make a dark green rod using yellow and white rods?
If you have only four weights, where could you place them in order to balance this equaliser?
Choose a symbol to put into the number sentence.
Try out the lottery that is played in a far-away land. What is the chance of winning?
Can you find all the different ways of lining up these Cuisenaire rods?
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?
Here is a chance to play a version of the classic Countdown Game.
NRICH December 2006 advent calendar - a new tangram for each day in the run-up to Christmas.
Our 2008 Advent Calendar has a 'Making Maths' activity for every day in the run-up to Christmas.