This practical problem challenges you to create shapes and patterns with two different types of triangle. You could even try overlapping them.
Follow these instructions to make a five-pointed snowflake from a square of paper.
It's hard to make a snowflake with six perfect lines of symmetry, but it's fun to try!
Cut a square of paper into three pieces as shown. Now,can you use the 3 pieces to make a large triangle, a parallelogram and the square again?
Have a go at making a few of these shapes from paper in different sizes. What patterns can you create?
Can you recreate this Indian screen pattern? Can you make up similar patterns of your own?
This practical activity challenges you to create symmetrical designs by cutting a square into strips.
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?
Make a flower design using the same shape made out of different sizes of paper.
What do these two triangles have in common? How are they related?
Move four sticks so there are exactly four triangles.
Looking at the picture of this Jomista Mat, can you decribe what you see? Why not try and make one yourself?
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?
Follow the diagrams to make this patchwork piece, based on an octagon in a square.
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?
Can you make the most extraordinary, the most amazing, the most unusual patterns/designs from these triangles which are made in a special way?
Ideas for practical ways of representing data such as Venn and Carroll diagrams.
Here's a simple way to make a Tangram without any measuring or ruling lines.
Use the lines on this figure to show how the square can be divided into 2 halves, 3 thirds, 6 sixths and 9 ninths.
NRICH December 2006 advent calendar - a new tangram for each day in the run-up to Christmas.
Use the three triangles to fill these outline shapes. Perhaps you can create some of your own shapes for a friend to fill?
Can you make the birds from the egg tangram?
Can you fit the tangram pieces into the outline of this junk?
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 the chairs?
Can you fit the tangram pieces into the outline of this shape. How would you describe it?
Can you fit the tangram pieces into the outlines of the candle and sundial?
Can you fit the tangram pieces into the outlines of Mai Ling and Chi Wing?
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?
What happens to the area of a square if you double the length of the sides? Try the same thing with rectangles, diamonds and other shapes. How do the four smaller ones fit into the larger one?
Make a cube out of straws and have a go at this practical challenge.
Have a go at drawing these stars which use six points drawn around a circle. Perhaps you can create your own designs?
Can you fit the tangram pieces into the outline of this telephone?
Can you fit the tangram pieces into the outline of Little Fung at the table?
Can you fit the tangram pieces into the outline of Little Ming playing the board game?
Watch this "Notes on a Triangle" film. Can you recreate parts of the film using cut-out triangles?
Have you ever noticed the patterns in car wheel trims? These questions will make you look at car wheels in a different way!
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?
Can you create more models that follow these rules?
A group of children are discussing the height of a tall tree. How would you go about finding out its height?
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?
This is a simple paper-folding activity that gives an intriguing result which you can then investigate further.
How can you make a curve from straight strips of paper?
Make new patterns from simple turning instructions. You can have a go using pencil and paper or with a floor robot.
How do you know if your set of dominoes is complete?
Arrange your fences to make the largest rectangular space you can. Try with four fences, then five, then six etc.
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?