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!
Mr McGregor has a magic potting shed. Overnight, the number of plants in it doubles. He'd like to put the same number of plants in each of three gardens, planting one garden each day. Can he do it?
Place six toy ladybirds into the box so that there are two ladybirds in every column and every row.
If you have only four weights, where could you place them in order to balance this equaliser?
A game for 2 people that everybody knows. You can play with a friend or online. If you play correctly you never lose!
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?
Choose a symbol to put into the number sentence.
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 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.
Place the numbers 1 to 10 in the circles so that each number is the difference between the two numbers just below it.
An environment which simulates working with Cuisenaire rods.
Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10 will be?
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?
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?
Can you put the numbers 1 to 8 into the circles so that the four calculations are correct?
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?
How have the numbers been placed in this Carroll diagram? Which labels would you put on each row and column?
Can you complete this jigsaw of the multiplication square?
Practise your diamond mining skills and your x,y coordination in this homage to Pacman.
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?
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?
Try to stop your opponent from being able to split the piles of counters into unequal numbers. Can you find a strategy?
Imagine a wheel with different markings painted on it at regular intervals. Can you predict the colour of the 18th mark? The 100th mark?
Can you spot the similarities between this game and other games you know? The aim is to choose 3 numbers that total 15.
An interactive game to be played on your own or with friends. Imagine you are having a party. Each person takes it in turns to stand behind the chair where they will get the most chocolate.
Interactive game. Set your own level of challenge, practise your table skills and beat your previous best score.
Use the interactivity to find all the different right-angled triangles you can make by just moving one corner of the starting triangle.
A card pairing game involving knowledge of simple ratio.
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?
This article gives you a few ideas for understanding the Got It! game and how you might find a winning strategy.
A generic circular pegboard resource.
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?
What are the coordinates of the coloured dots that mark out the tangram? Try changing the position of the origin. What happens to the coordinates now?
An interactive game for 1 person. You are given a rectangle with 50 squares on it. Roll the dice to get a percentage between 2 and 100. How many squares is this? Keep going until you get 100. . . .
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 interactive activity for one to experiment with a tricky tessellation
Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.
A game for 2 people that can be played on line or with pens and paper. Combine your knowledege of coordinates with your skills of strategic thinking.
The number of plants in Mr McGregor's magic potting shed increases overnight. He'd like to put the same number of plants in each of his gardens, planting one garden each day. How can he do it?
Work out the fractions to match the cards with the same amount of money.
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?
Train game for an adult and child. Who will be the first to make the train?
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.
Our 2008 Advent Calendar has a 'Making Maths' activity for every day in the run-up to Christmas.
This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?
Can you make the green spot travel through the tube by moving the yellow spot? Could you draw a tube that both spots would follow?
NRICH December 2006 advent calendar - a new tangram for each day in the run-up to Christmas.
A train building game for 2 players.