Use the interactivity to find all the different right-angled triangles you can make by just moving one corner of the starting triangle.
Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.
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?
Try out the lottery that is played in a far-away land. What is the chance of winning?
Place the numbers 1 to 10 in the circles so that each number is the difference between the two numbers just below it.
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?
How many different triangles can you make on a circular pegboard that has nine pegs?
Can you put the numbers from 1 to 15 on the circles so that no consecutive numbers lie anywhere along a continuous straight line?
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....?
Can you put the numbers 1 to 8 into the circles so that the four calculations are correct?
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?
Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?
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 find all the different triangles on these peg boards, and find their angles?
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 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.
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?
Find out what a "fault-free" rectangle is and try to make some of your own.
Explore the different tunes you can make with these five gourds. What are the similarities and differences between the two tunes you are given?
Find out how we can describe the "symmetries" of this triangle and investigate some combinations of rotating and flipping it.
Our 2008 Advent Calendar has a 'Making Maths' activity for every day in the run-up to Christmas.
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?
Three beads are threaded on a circular wire and are coloured either red or blue. Can you find all four different combinations?
NRICH December 2006 advent calendar - a new tangram for each day in the run-up to Christmas.
Use the interactivity to investigate what kinds of triangles can be drawn on peg boards with different numbers of pegs.
Can you fit the tangram pieces into the outlines of these people?
A train building game for 2 players.
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 fit the tangram pieces into the outlines of the lobster, yacht and cyclist?
Can you fit the tangram pieces into the outline of Granma T?
An interactive activity for one to experiment with a tricky tessellation
Can you fit the tangram pieces into the outline of Little Fung at the table?
Can you use the interactive to complete the tangrams in the shape of butterflies?
Can you fit the tangram pieces into the outline of this brazier for roasting chestnuts?
Explore this interactivity and see if you can work out what it does. Could you use it to estimate the area of a shape?
Can you fit the tangram pieces into the outlines of the chairs?
If you have only four weights, where could you place them in order to balance this equaliser?
Try to stop your opponent from being able to split the piles of counters into unequal numbers. Can you find a strategy?
A game for 2 people that everybody knows. You can play with a friend or online. If you play correctly you never lose!
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!
Can you fit the tangram pieces into the outlines of these clocks?
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10 will be?
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?
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 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 fit the tangram pieces into the outline of the child walking home from school?