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?
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?
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
These pictures show squares split into halves. Can you find other ways?
This practical investigation invites you to make tessellating
shapes in a similar way to the artist Escher.
How many different cuboids can you make when you use four CDs or
DVDs? How about using five, then six?
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.
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 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?
Exploring and predicting folding, cutting and punching holes and
Here is a version of the game 'Happy Families' for you to make and
Can you make the birds from the egg tangram?
Try continuing these patterns made from triangles. Can you create your own repeating pattern?
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
In this challenge, you will work in a group to investigate circular
fences enclosing trees that are planted in square or triangular
These practical challenges are all about making a 'tray' and covering it with paper.
Explore the triangles that can be made with seven sticks of the
A group of children are discussing the height of a tall tree. How would you go about finding out its height?
Can you create more models that follow these rules?
Is there a best way to stack cans? What do different supermarkets
do? How high can you safely stack the cans?
Arrange your fences to make the largest rectangular space you can. Try with four fences, then five, then six etc.
Can you fit the tangram pieces into the outlines of these clocks?
Can you fit the tangram pieces into the outline of this brazier for roasting chestnuts?
Here's a simple way to make a Tangram without any measuring or
Can you fit the tangram pieces into the outlines of these people?
Ideas for practical ways of representing data such as Venn and
Make a cube out of straws and have a go at this practical
Can you fit the tangram pieces into the outline of the child walking home from school?
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 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?
An activity making various patterns with 2 x 1 rectangular tiles.
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?
Can you recreate this Indian screen pattern? Can you make up
similar patterns of your own?
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?
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?
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?
Can you fit the tangram pieces into the outline of this junk?
This practical problem challenges you to create shapes and patterns
with two different types of triangle. You could even try
Have a go at drawing these stars which use six points drawn around
a circle. Perhaps you can create your own designs?
Follow the diagrams to make this patchwork piece, based on an
octagon in a square.
Can you fit the tangram pieces into the outline of Little Fung at the table?
Looking at the picture of this Jomista Mat, can you decribe what
you see? Why not try and make one yourself?
Can you fit the tangram pieces into the outline of Little Ming playing the board game?
Can you fit the tangram pieces into the outline of this telephone?
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?
Can you work out what shape is made when this piece of paper is folded up using the crease pattern shown?
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?