What shapes can you make by folding an A4 piece of paper?
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 visualise what shape this piece of paper will make when it is folded?
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?
Our 2008 Advent Calendar has a 'Making Maths' activity for every
day in the run-up to Christmas.
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?
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?
What do these two triangles have in common? How are they related?
Investigate the smallest number of moves it takes to turn these
mats upside-down if you can only turn exactly three at a time.
Can you cut a regular hexagon into two pieces to make a
parallelogram? Try cutting it into three pieces to make a rhombus!
NRICH December 2006 advent calendar - a new tangram for each day in
the run-up to Christmas.
How many triangles can you make on the 3 by 3 pegboard?
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?
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.
These practical challenges are all about making a 'tray' and covering it with paper.
Arrange your fences to make the largest rectangular space you can. Try with four fences, then five, then six etc.
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 make the most extraordinary, the most amazing, the most
unusual patterns/designs from these triangles which are made in a
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?
Follow the diagrams to make this patchwork piece, based on an
octagon in a square.
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?
Here's a simple way to make a Tangram without any measuring or
Can you make the birds from the egg tangram?
Are all the possible combinations of two shapes included in this
set of 27 cards? How do you know?
If you'd like to know more about Primary Maths Masterclasses, this
is the package to read! Find out about current groups in your
region or how to set up your own.
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?
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 junk?
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 Little Ming playing the board game?
An activity making various patterns with 2 x 1 rectangular tiles.
Can you fit the tangram pieces into the outline of this brazier for roasting chestnuts?
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 outlines of these clocks?
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 fit the tangram pieces into the outline of Wai Ping, Wah Ming 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 telephone?
How many differently shaped rectangles can you build using these
equilateral and isosceles triangles? Can you make a square?
Can you create more models that follow these rules?
How many models can you find which obey 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.
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.
Can you order pictures of the development of a frog from frogspawn
and of a bean seed growing into a plant?