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?
Can you find all the different ways of lining up these Cuisenaire rods?
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 put the numbers from 1 to 15 on the circles so that no consecutive numbers lie anywhere along a continuous straight line?
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?
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?
Place six toy ladybirds into the box so that there are two ladybirds in every column and every row.
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?
How many different triangles can you make on a circular pegboard that has nine pegs?
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?
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?
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?
Find out how we can describe the "symmetries" of this triangle and investigate some combinations of rotating and flipping it.
Three beads are threaded on a circular wire and are coloured either red or blue. Can you find all four different combinations?
Use the interactivity to find all the different right-angled triangles you can make by just moving one corner of the starting triangle.
NRICH December 2006 advent calendar - a new tangram for each day in the run-up to Christmas.
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?
Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.
Use the interactivity to make this Islamic star and cross design. Can you produce a tessellation of regular octagons with two different types of triangle?
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 what a "fault-free" rectangle is and try to make some of your own.
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.
Our 2008 Advent Calendar has a 'Making Maths' activity for every day in the run-up to Christmas.
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 see why 2 by 2 could be 5? Can you predict what 2 by 10 will be?
Use the Cuisenaire rods environment to investigate ratio. Can you find pairs of rods in the ratio 3:2? How about 9:6?
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!
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?
Choose the size of your pegboard and the shapes you can make. Can you work out the strategies needed to block your opponent?
Can you use the interactive to complete the tangrams in the shape of butterflies?
Can you find all the different triangles on these peg boards, and find their angles?
Choose 13 spots on the grid. Can you work out the scoring system? What is the maximum possible score?
This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?
A generic circular pegboard resource.
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.
Can you fit the tangram pieces into the outline of Granma T?
Choose a symbol to put into the number sentence.
Can you fit the tangram pieces into the outlines of the chairs?
A game for 2 people that everybody knows. You can play with a friend or online. If you play correctly you never lose!
An interactive activity for one to experiment with a tricky tessellation
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?
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 outlines of the lobster, yacht and cyclist?
Can you fit the tangram pieces into the outline of the child walking home from school?
Can you fit the tangram pieces into the outlines of these clocks?
Can you fit the tangram pieces into the outlines of these people?
Can you fit the tangram pieces into the outline of this brazier for roasting chestnuts?
Can you fit the tangram pieces into the outline of Little Fung at the table?