Explore the triangles that can be made with seven sticks of the
Try continuing these patterns made from triangles. Can you create
your own repeating pattern?
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?
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?
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?
Make a chair and table out of interlocking cubes, making sure that
the chair fits under the table!
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?
This practical investigation invites you to make tessellating
shapes in a similar way to the artist Escher.
These pictures show squares split into halves. Can you find other
Move four sticks so there are exactly four triangles.
Use the three triangles to fill these outline shapes. Perhaps you can create some of your own shapes for a friend to fill?
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.
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?
How many different cuboids can you make when you use four CDs or
DVDs? How about using five, then six?
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?
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?
Here is a version of the game 'Happy Families' for you to make and
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
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?
Our 2008 Advent Calendar has a 'Making Maths' activity for every
day in the run-up to Christmas.
How many triangles can you make on the 3 by 3 pegboard?
Can you create more models that follow these rules?
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.
Can you make a rectangle with just 2 dominoes? What about 3, 4, 5,
What shapes can you make by folding an A4 piece of paper?
A group of children are discussing the height of a tall tree. How would you go about finding out its height?
Is there a best way to stack cans? What do different supermarkets
do? How high can you safely stack the cans?
Can you make five differently sized squares from the tangram
Using a loop of string stretched around three of your fingers, what
different triangles can you make? Draw them and sort them into
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?
We have a box of cubes, triangular prisms, cones, cuboids,
cylinders and tetrahedrons. Which of the buildings would fall down
if we tried to make them?
In this challenge, you will work in a group to investigate circular
fences enclosing trees that are planted in square or triangular
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
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 outline of this junk?
You have a set of the digits from 0 – 9. Can you arrange
these in the 5 boxes to make two-digit numbers as close to the
targets as possible?
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?
Can you recreate this Indian screen pattern? Can you make up
similar patterns of your own?
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?
This practical problem challenges you to create shapes and patterns
with two different types of triangle. You could even try
Watch this "Notes on a Triangle" film. Can you recreate parts of
the film using cut-out triangles?
Sara and Will were sorting some pictures of shapes on cards. "I'll collect the circles," said Sara. "I'll take the red ones," answered Will. Can you see any cards they would both want?
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 telephone?
Can you fit the tangram pieces into the outlines of these clocks?
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 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 these people?