Here are some ideas to try in the classroom for using counters to investigate number patterns.
Follow these instructions to make a three-piece and/or seven-piece
This is a simple paper-folding activity that gives an intriguing result which you can then investigate further.
Follow the diagrams to make this patchwork piece, based on an
octagon in a square.
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?
Have a go at drawing these stars which use six points drawn around
a circle. Perhaps you can create your own designs?
Using these kite and dart templates, you could try to recreate part
of Penrose's famous tessellation or design one yourself.
How can you make a curve from straight strips of paper?
Can you cut up a square in the way shown and make the pieces into a
Make new patterns from simple turning instructions. You can have a go using pencil and paper or with a floor robot.
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!
How do you know if your set of dominoes is complete?
Make a mobius band and investigate its properties.
Arrange your fences to make the largest rectangular space you can. Try with four fences, then five, then six etc.
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
This practical activity involves measuring length/distance.
Here's a simple way to make a Tangram without any measuring or
Follow these instructions to make a five-pointed snowflake from a
square of paper.
Did you know mazes tell stories? Find out more about mazes and make
one of your own.
Paint a stripe on a cardboard roll. Can you predict what will
happen when it is rolled across a sheet of paper?
Surprise your friends with this magic square trick.
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.
It's hard to make a snowflake with six perfect lines of symmetry,
but it's fun to try!
What shapes can you make by folding an A4 piece of paper?
Ideas for practical ways of representing data such as Venn and
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 chairs?
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 workmen?
Can you fit the tangram pieces into the outlines of the lobster, yacht and cyclist?
How many different cuboids can you make when you use four CDs or
DVDs? How about using five, then six?
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?
Can you fit the tangram pieces into the outline of this plaque design?
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 the telescope and microscope?
Can you fit the tangram pieces into the outline of Little Ming and Little Fung dancing?
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?
This practical problem challenges you to create shapes and patterns
with two different types of triangle. You could even try
This problem invites you to build 3D shapes using two different
triangles. Can you make the shapes from the pictures?
Can you deduce the pattern that has been used to lay out these
Can you make the most extraordinary, the most amazing, the most
unusual patterns/designs from these triangles which are made in a
NRICH December 2006 advent calendar - a new tangram for each day in
the run-up to Christmas.
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?