Use the three triangles to fill these outline shapes. Perhaps you can create some of your own shapes for a friend to fill?
In how many ways can you fit two of these yellow triangles together? Can you predict the number of ways two blue triangles can be fitted together?
Using different numbers of sticks, how many different triangles are you able to make? Can you make any rules about the numbers of sticks that make the most triangles?
You have a set of the digits from 0 – 9. Can you arrange these in the five boxes to make two-digit numbers as close to the targets as possible?
Can you make the most extraordinary, the most amazing, the most unusual patterns/designs from these triangles which are made in a special way?
This practical problem challenges you to create shapes and patterns with two different types of triangle. You could even try overlapping them.
Did you know mazes tell stories? Find out more about mazes and make one of your own.
Can you see which tile is the odd one out in this design? Using the basic tile, can you make a repeating pattern to decorate our wall?
What do these two triangles have in common? How are they related?
We can cut a small triangle off the corner of a square and then fit the two pieces together. Can you work out how these shapes are made from the two pieces?
Make a mobius band and investigate its properties.
Ideas for practical ways of representing data such as Venn and Carroll diagrams.
Have you noticed that triangles are used in manmade structures? Perhaps there is a good reason for this? 'Test a Triangle' and see how rigid triangles are.
NRICH December 2006 advent calendar - a new tangram for each day in the run-up to Christmas.
Surprise your friends with this magic square trick.
Kaia is sure that her father has worn a particular tie twice a week in at least five of the last ten weeks, but her father disagrees. Who do you think is right?
It's hard to make a snowflake with six perfect lines of symmetry, but it's fun to try!
Follow these instructions to make a five-pointed snowflake from a square of paper.
Follow the diagrams to make this patchwork piece, based on an octagon in a square.
Can you work out what shape is made by folding in this way? Why not create some patterns using this shape but in different sizes?
Is there a best way to stack cans? What do different supermarkets do? How high can you safely stack the cans?
Take 5 cubes of one colour and 2 of another colour. How many different ways can you join them if the 5 must touch the table and the 2 must not touch the table?
Have a go at drawing these stars which use six points drawn around a circle. Perhaps you can create your own designs?
How many different cuboids can you make when you use four CDs or DVDs? How about using five, then six?
This problem focuses on Dienes' Logiblocs. What is the same and what is different about these pairs of shapes? Can you describe the shapes in the picture?
Make a flower design using the same shape made out of different sizes of paper.
Kate has eight multilink cubes. She has two red ones, two yellow, two green and two blue. She wants to fit them together to make a cube so that each colour shows on each face just once.
What is the largest number of circles we can fit into the frame without them overlapping? How do you know? What will happen if you try the other shapes?
These practical challenges are all about making a 'tray' and covering it with paper.
You will need a long strip of paper for this task. Cut it into different lengths. How could you find out how long each piece is?
This practical activity involves measuring length/distance.
In this activity focusing on capacity, you will need a collection of different jars and bottles.
For this activity which explores capacity, you will need to collect some bottles and jars.
You'll need a collection of cups for this activity.
Arrange your fences to make the largest rectangular space you can. Try with four fences, then five, then six etc.
Can you create more models that follow these rules?
Watch the video to see how to fold a square of paper to create a flower. What fraction of the piece of paper is the small triangle?
This is a simple paper-folding activity that gives an intriguing result which you can then investigate further.
Can you work out what shape is made when this piece of paper is folded up using the crease pattern shown?
How can you make a curve from straight strips of paper?
This practical activity challenges you to create symmetrical designs by cutting a square into strips.
This challenge invites you to create your own picture using just straight lines. Can you identify shapes with the same number of sides and decorate them in the same way?
Take a rectangle of paper and fold it in half, and half again, to make four smaller rectangles. How many different ways can you fold it up?
Our 2008 Advent Calendar has a 'Making Maths' activity for every day in the run-up to Christmas.
The ancient Egyptians were said to make right-angled triangles using a rope with twelve equal sections divided by knots. What other triangles could you make if you had a rope like this?
These pictures show squares split into halves. Can you find other ways?
Make a chair and table out of interlocking cubes, making sure that the chair fits under the table!
Can you split each of the shapes below in half so that the two parts are exactly the same?
Have a go at making a few of these shapes from paper in different sizes. What patterns can you create?
Follow these instructions to make a three-piece and/or seven-piece tangram.