How many triangles can you make using sticks that are 3cm, 4cm and 5cm long?
How many different triangles can you make on a circular pegboard that has nine pegs?
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?
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?
Use the interactivity to find all the different right-angled triangles you can make by just moving one corner of the starting triangle.
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 the numbers 1 to 10 in the circles so that each number is the difference between the two numbers just below it.
Use the clues to colour each square.
Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.
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 rhythms can you make by putting two drums on the wheel?
What happens when you try and fit the triomino pieces into these two grids?
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 find all the different ways of lining up these Cuisenaire rods?
Place six toy ladybirds into the box so that there are two ladybirds in every column and every row.
Can you find all the different triangles on these peg boards, and find their angles?
Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?
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 from 1 to 15 on the circles so that no consecutive numbers lie anywhere along a continuous straight line?
Try out the lottery that is played in a far-away land. What is the chance of winning?
Use the interactivity to investigate what kinds of triangles can be drawn on peg boards with different numbers of pegs.
Here are some rods that are different colours. How could I make a dark green rod using yellow and white rods?
Board Block game for two. Can you stop your partner from being able to make a shape on the board?
Three beads are threaded on a circular wire and are coloured either red or blue. Can you find all four different combinations?
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?
Explore the different tunes you can make with these five gourds. What are the similarities and differences between the two tunes you are given?
Can you cover the camel with these pieces?
Find out how we can describe the "symmetries" of this triangle and investigate some combinations of rotating and flipping it.
Can you work out how to balance this equaliser? You can put more than one weight on a hook.
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?
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?
Find out what a "fault-free" rectangle is and try to make some of your own.
NRICH December 2006 advent calendar - a new tangram for each day in the run-up to Christmas.
Place the numbers 1 to 6 in the circles so that each number is the difference between the two numbers just below it.
Our 2008 Advent Calendar has a 'Making Maths' activity for every day in the run-up to Christmas.
Can you put the numbers 1 to 8 into the circles so that the four calculations are correct?
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 fit the tangram pieces into the outlines of the lobster, yacht and cyclist?
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.
Move just three of the circles so that the triangle faces in the opposite direction.
Can you fit the tangram pieces into the outlines of the chairs?
Can you fit the tangram pieces into the outline of the child walking home from school?
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?
Choose the size of your pegboard and the shapes you can make. Can you work out the strategies needed to block your opponent?
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 game for 2 people that everybody knows. You can play with a friend or online. If you play correctly you never lose!
Take it in turns to make a triangle on the pegboard. Can you block your opponent?
An interactive activity for one to experiment with a tricky tessellation
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. . . .
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?