What shapes can you make by folding an A4 piece of paper?
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.
Using these kite and dart templates, you could try to recreate part
of Penrose's famous tessellation or design one yourself.
Follow these instructions to make a three-piece and/or seven-piece
Follow the diagrams to make this patchwork piece, based on an
octagon in a square.
This is a simple paper-folding activity that gives an intriguing result which you can then investigate further.
Here are some ideas to try in the classroom for using counters to investigate number patterns.
Have a go at drawing these stars which use six points drawn around
a circle. Perhaps you can create your own designs?
Can you cut up a square in the way shown and make the pieces into a
How can you make a curve from straight strips of paper?
Make a cube with three strips of paper. Colour three faces or use
the numbers 1 to 6 to make a die.
Make a ball from triangles!
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?
Make a mobius band and investigate its properties.
Here's a simple way to make a Tangram without any measuring or
Ideas for practical ways of representing data such as Venn and
This practical activity involves measuring length/distance.
Have a look at what happens when you pull a reef knot and a granny
knot tight. Which do you think is best for securing things
Can you visualise what shape this piece of paper will make when it is folded?
Did you know mazes tell stories? Find out more about mazes and make
one of your own.
It's hard to make a snowflake with six perfect lines of symmetry,
but it's fun to try!
Arrange your fences to make the largest rectangular space you can. Try with four fences, then five, then six etc.
Surprise your friends with this magic square trick.
Follow these instructions to make a five-pointed snowflake from a
square of paper.
Paint a stripe on a cardboard roll. Can you predict what will
happen when it is rolled across a sheet of paper?
Can you fit the tangram pieces into the outlines of Mai Ling and Chi Wing?
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 workmen?
Can you fit the tangram pieces into the outlines of the candle and sundial?
Can you fit the tangram pieces into the outline of Little Ming and Little Fung dancing?
Can you fit the tangram pieces into the outlines of the chairs?
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?
How many different cuboids can you make when you use four CDs or
DVDs? How about using five, then six?
Can you fit the tangram pieces into the outline of this plaque design?
Can you fit the tangram pieces into the outline of the telescope and microscope?
Can you fit the tangram pieces into the outline of this goat and giraffe?
Can you fit the tangram pieces into the outline of these rabbits?
Can you fit the tangram pieces into the outline of Little Fung at the table?
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 make the most extraordinary, the most amazing, the most
unusual patterns/designs from these triangles which are made in a
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?
Looking at the picture of this Jomista Mat, can you decribe what
you see? Why not try and make one yourself?
This practical problem challenges you to create shapes and patterns
with two different types of triangle. You could even try
NRICH December 2006 advent calendar - a new tangram for each day in
the run-up to Christmas.
This practical problem challenges you to make quadrilaterals with a loop of string. You'll need some friends to help!
Use the lines on this figure to show how the square can be divided into 2 halves, 3 thirds, 6 sixths and 9 ninths.
Make a cube out of straws and have a go at this practical
Exploring and predicting folding, cutting and punching holes and
Can you make the birds from the egg tangram?
This problem invites you to build 3D shapes using two different
triangles. Can you make the shapes from the pictures?