These pictures show squares split into halves. Can you find other ways?
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?
Can you make the birds from the egg tangram?
If you split the square into these two pieces, it is possible to fit the pieces together again to make a new shape. How many new shapes can you make?
Use the lines on this figure to show how the square can be divided into 2 halves, 3 thirds, 6 sixths and 9 ninths.
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 practical investigation invites you to make tessellating
shapes in a similar way to the artist Escher.
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 create more models that follow these rules?
Try continuing these patterns made from triangles. Can you create
your own repeating pattern?
A group of children are discussing the height of a tall tree. How would you go about finding out its height?
What is the greatest number of counters you can place on the grid below without four of them lying at the corners of a square?
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?
Here is a version of the game 'Happy Families' for you to make and
NRICH December 2006 advent calendar - a new tangram for each day in
the run-up to Christmas.
Can you make the most extraordinary, the most amazing, the most
unusual patterns/designs from these triangles which are made in a
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?
We went to the cinema and decided to buy some bags of popcorn so we
asked about the prices. Investigate how much popcorn each bag holds
so find out which we might have bought.
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?
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
Can you split each of the shapes below in half so that the two parts are exactly the same?
Our 2008 Advent Calendar has a 'Making Maths' activity for every
day in the run-up to Christmas.
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
In this challenge, you will work in a group to investigate circular
fences enclosing trees that are planted in square or triangular
Can you make five differently sized squares from the tangram
Explore the triangles that can be made with seven sticks of the
Is there a best way to stack cans? What do different supermarkets
do? How high can you safely stack the cans?
Can you fit the tangram pieces into the outline of this telephone?
Can you fit the tangram pieces into the outline of Little Ming playing the board game?
Can you lay out the pictures of the drinks in the way described by
the clue cards?
Can you fit the tangram pieces into the outlines of the workmen?
This practical activity challenges you to create symmetrical
designs by cutting a square into strips.
Have a go at drawing these stars which use six points drawn around
a circle. Perhaps you can create your own designs?
Make new patterns from simple turning instructions. You can have a
go using pencil and paper or with a floor robot.
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?
How can you make a curve from straight strips of paper?
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 this shape. How would you describe it?
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 the lobster, yacht and cyclist?
Can you fit the tangram pieces into the outlines of the chairs?
Can you fit the tangram pieces into the outlines of these clocks?
Can you fit the tangram pieces into the outline of this junk?
Can you fit the tangram pieces into the outline of this brazier for roasting chestnuts?
Can you fit the tangram pieces into the outlines of these people?
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?
Looking at the picture of this Jomista Mat, can you decribe what
you see? Why not try and make one yourself?
The Man is much smaller than us. Can you use the picture of him
next to a mug to estimate his height and how much tea he drinks?