These pictures show squares split into halves. Can you find other
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?
Use the three triangles to fill these outline shapes. Perhaps you can create some of your own shapes for a friend to fill?
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?
This practical investigation invites you to make tessellating
shapes in a similar way to the artist Escher.
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.
Use the lines on this figure to show how the square can be divided
into 2 halves, 3 thirds, 6 sixths and 9 ninths.
Can you split each of the shapes below in half so that the two
parts are exactly the same?
NRICH December 2006 advent calendar - a new tangram for each day in
the run-up to Christmas.
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?
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?
Can you make the most extraordinary, the most amazing, the most
unusual patterns/designs from these triangles which are made in a
Here is a version of the game 'Happy Families' for you to make and
Our 2008 Advent Calendar has a 'Making Maths' activity for every
day in the run-up to Christmas.
Try continuing these patterns made from triangles. Can you create
your own repeating pattern?
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?
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 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?
Is there a best way to stack cans? What do different supermarkets
do? How high can you safely stack the cans?
Can you make five differently sized squares from the tangram
Explore the triangles that can be made with seven sticks of the
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?
In this challenge, you will work in a group to investigate circular
fences enclosing trees that are planted in square or triangular
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
Sara and Will were sorting some pictures of shapes on cards. "I'll collect the circles," said Sara. "I'll take the red ones," answered Will. Can you see any cards they would both want?
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?
Can you fit the tangram pieces into the outline of this telephone?
Can you fit the tangram pieces into the outline of this junk?
Can you lay out the pictures of the drinks in the way described by
the clue cards?
Let's say you can only use two different lengths - 2 units and 4
units. Using just these 2 lengths as the edges how many different
cuboids can you make?
Can you recreate this Indian screen pattern? Can you make up
similar patterns of your own?
Can you fit the tangram pieces into the outline of Wai Ping, Wah Ming and Chi Wing?
Can you fit the tangram pieces into the outline of Little Ming playing the board game?
This practical problem challenges you to create shapes and patterns
with two different types of triangle. You could even try
Can you fit the tangram pieces into the outline of Little Fung at the table?
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 Mai Ling and Chi Wing?
Can you fit the tangram pieces into the outlines of the candle and sundial?
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?
You have a set of the digits from 0 – 9. Can you arrange
these in the 5 boxes to make two-digit numbers as close to the
targets as possible?
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?
Can you fit the tangram pieces into the outlines of these people?
Can you fit the tangram pieces into the outlines of these clocks?
Looking at the picture of this Jomista Mat, can you decribe what
you see? Why not try and make one yourself?