Can you find all the different triangles on these peg boards, and find their angles?
How many different triangles can you make on a circular pegboard that has nine pegs?
Use the interactivity to investigate what kinds of triangles can be drawn on peg boards with different numbers of pegs.
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?
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?
Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?
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?
Find out what a "fault-free" rectangle is and try to make some of your own.
Can you find all the different ways of lining up these Cuisenaire rods?
Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.
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....?
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?
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?
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?
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?
Board Block game for two. Can you stop your partner from being able to make a shape on the board?
Can you put the numbers 1 to 8 into the circles so that the four calculations are correct?
Try out the lottery that is played in a far-away land. What is the chance of winning?
Use the interactivity to find all the different right-angled triangles you can make by just moving one corner of the starting triangle.
This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?
Explore the different tunes you can make with these five gourds. What are the similarities and differences between the two tunes you are given?
What is the relationship between the angle at the centre and the angles at the circumference, for angles which stand on the same arc? Can you prove it?
A generic circular pegboard resource.
Can you find triangles on a 9-point circle? Can you work out their angles?
Find out how we can describe the "symmetries" of this triangle and investigate some combinations of rotating and flipping it.
NRICH December 2006 advent calendar - a new tangram for each day in the run-up to Christmas.
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?
Three beads are threaded on a circular wire and are coloured either red or blue. Can you find all four different combinations?
Our 2008 Advent Calendar has a 'Making Maths' activity for every day in the run-up to Christmas.
Choose the size of your pegboard and the shapes you can make. Can you work out the strategies needed to block your opponent?
Choose a symbol to put into the number sentence.
Can you fit the tangram pieces into the outline of Granma T?
If you have only four weights, where could you place them in order to balance this equaliser?
An environment which simulates working with Cuisenaire rods.
A game to be played against the computer, or in groups. Pick a 7-digit number. A random digit is generated. What must you subract to remove the digit from your number? the first to zero wins.
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.
Can you fit the tangram pieces into the outline of this telephone?
Can you fit the tangram pieces into the outlines of the chairs?
Here is a chance to play a version of the classic Countdown Game.
Can you fit the tangram pieces into the outlines of the candle and sundial?
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.
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?
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!
Use the Cuisenaire rods environment to investigate ratio. Can you find pairs of rods in the ratio 3:2? How about 9:6?
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 this brazier for roasting chestnuts?