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
This practical investigation invites you to make tessellating
shapes in a similar way to the artist Escher.
Can you make the most extraordinary, the most amazing, the most
unusual patterns/designs from these triangles which are made in a
How many different cuboids can you make when you use four CDs or
DVDs? How about using five, then six?
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?
Our 2008 Advent Calendar has a 'Making Maths' activity for every
day in the run-up to Christmas.
In this challenge, you will work in a group to investigate circular
fences enclosing trees that are planted in square or triangular
The challenge for you is to make a string of six (or more!) graded cubes.
Where can you put the mirror across the square so that you can still "see" the whole square? How many different positions are possible?
Take a counter and surround it by a ring of other counters that
MUST touch two others. How many are needed?
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?
How can you put five cereal packets together to make different
shapes if you must put them face-to-face?
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?
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?
Here is a version of the game 'Happy Families' for you to make and
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.
Make a ball from triangles!
A group of children are discussing the height of a tall tree. How would you go about finding out its height?
NRICH December 2006 advent calendar - a new tangram for each day in
the run-up to Christmas.
These practical challenges are all about making a 'tray' and covering it with paper.
These squares have been made from Cuisenaire rods. Can you describe
the pattern? What would the next square look like?
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?
Can you make the birds from the egg tangram?
Can you create more models that follow these rules?
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?
An activity making various patterns with 2 x 1 rectangular tiles.
If these balls are put on a line with each ball touching the one in front and the one behind, which arrangement makes the shortest line of balls?
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?
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
Follow the diagrams to make this patchwork piece, based on an
octagon in a square.
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 Little Fung at the table?
Can you fit the tangram pieces into the outline of the child walking home from school?
Can you fit the tangram pieces into the outlines of these clocks?
Can you fit the tangram pieces into the outlines of the lobster, yacht and cyclist?
Can you fit the tangram pieces into the outlines of the chairs?
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 these people?
Can you fit the tangram pieces into the outline of this brazier for roasting chestnuts?
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 junk?
Can you fit the tangram pieces into the outline of this telephone?
Can you fit the tangram pieces into the outline of Little Ming playing the board game?
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 fit the tangram pieces into the outline of Wai Ping, Wah Ming and Chi Wing?
Make a cube out of straws and have a go at this practical
Make new patterns from simple turning instructions. You can have a go using pencil and paper or with a floor robot.
This is a simple paper-folding activity that gives an intriguing result which you can then investigate further.