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 interactivity to find all the different right-angled triangles you can make by just moving one corner of the starting triangle.
Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?
Find out what a "fault-free" rectangle is and try to make some of your own.
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?
Our 2008 Advent Calendar has a 'Making Maths' activity for every day in the run-up to Christmas.
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 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?
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?
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?
Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10 will be?
Can you find all the different triangles on these peg boards, and find their angles?
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 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?
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?
NRICH December 2006 advent calendar - a new tangram for each day in the run-up to Christmas.
Try out the lottery that is played in a far-away land. What is the chance of winning?
Hover your mouse over the counters to see which ones will be removed. Click to remove them. The winner is the last one to remove a counter. How you can make sure you win?
Place six toy ladybirds into the box so that there are two ladybirds in every column and every row.
Can you put the numbers from 1 to 15 on the circles so that no consecutive numbers lie anywhere along a continuous straight line?
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?
Can you put the numbers 1 to 8 into the circles so that the four calculations are correct?
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?
Use the interactivity to investigate what kinds of triangles can be drawn on peg boards with different numbers of pegs.
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?
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?
Can you fit the tangram pieces into the outline of this telephone?
Can you fit the tangram pieces into the outline of Mai Ling?
Can you fit the tangram pieces into the outline of Wai Ping, Wah Ming and Chi Wing?
Imagine picking up a bow and some arrows and attempting to hit the target a few times. Can you work out the settings for the sight that give you the best chance of gaining a high score?
Choose a symbol to put into the number sentence.
Can you fit the tangram pieces into the outlines of the candle and sundial?
Here is a chance to play a version of the classic Countdown Game.
Explore the different tunes you can make with these five gourds. What are the similarities and differences between the two tunes you are given?
This article gives you a few ideas for understanding the Got It! game and how you might find a winning strategy.
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?
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 locate the lost giraffe? Input coordinates to help you search and find the giraffe in the fewest guesses.
A generic circular pegboard resource.
Three beads are threaded on a circular wire and are coloured either red or blue. Can you find all four different combinations?
Can you fit the tangram pieces into the outline of Granma T?
Can you fit the tangram pieces into the outline of Little Ming?
Carry out some time trials and gather some data to help you decide on the best training regime for your rowing crew.
Try entering different sets of numbers in the number pyramids. How does the total at the top change?
Ahmed has some wooden planks to use for three sides of a rabbit run against the shed. What quadrilaterals would he be able to make with the planks of different lengths?
Find out how we can describe the "symmetries" of this triangle and investigate some combinations of rotating and flipping it.
Can you fit the tangram pieces into the outlines of the chairs?