If you have only four weights, where could you place them in order to balance this equaliser?
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 train building game for 2 players.
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10 will be?
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?
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.
A generic circular pegboard resource.
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.
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. . . .
A game for 2 people that everybody knows. You can play with a friend or online. If you play correctly you never lose!
Work out the fractions to match the cards with the same amount of money.
Choose 13 spots on the grid. Can you work out the scoring system? What is the maximum possible score?
A card pairing game involving knowledge of simple ratio.
Train game for an adult and child. Who will be the first to make the train?
Can you put the numbers 1 to 8 into the circles so that the four calculations are correct?
Can you find all the different ways of lining up these Cuisenaire rods?
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?
Place six toy ladybirds into the box so that there are two ladybirds in every column and every row.
Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.
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?
Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.
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?
An interactive activity for one to experiment with a tricky tessellation
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?
A simulation of target archery practice
Try to stop your opponent from being able to split the piles of counters into unequal numbers. Can you find a strategy?
Place the numbers 1 to 10 in the circles so that each number is the difference between the two numbers just below it.
Find out how we can describe the "symmetries" of this triangle and investigate some combinations of rotating and flipping it.
Here is a chance to play a version of the classic Countdown Game.
Use the Cuisenaire rods environment to investigate ratio. Can you find pairs of rods in the ratio 3:2? How about 9:6?
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....?
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?
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?
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?
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?
Watch this film carefully. Can you find a general rule for explaining when the dot will be this same distance from the horizontal axis?
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?
Board Block game for two. Can you stop your partner from being able to make a shape on the board?
NRICH December 2006 advent calendar - a new tangram for each day in the run-up to Christmas.
Use the interactivities to fill in these Carroll diagrams. How do you know where to place the numbers?
How have the numbers been placed in this Carroll diagram? Which labels would you put on each row and column?
Can you put the numbers from 1 to 15 on the circles so that no consecutive numbers lie anywhere along a continuous straight line?
In this activity, the computer chooses a times table and shifts it. Can you work out the table and the shift each time?
Use the interactivity to create some steady rhythms. How could you create a rhythm which sounds the same forwards as it does backwards?
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?
Can you complete this jigsaw of the multiplication square?
What shaped overlaps can you make with two circles which are the same size? What shapes are 'left over'? What shapes can you make when the circles are different sizes?
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.