What shapes can you make by folding an A4 piece of paper?
Using a loop of string stretched around three of your fingers, what
different triangles can you make? Draw them and sort them into
Make a chair and table out of interlocking cubes, making sure that
the chair fits under the table!
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?
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?
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?
Try continuing these patterns made from triangles. Can you create
your own repeating pattern?
Investigate the smallest number of moves it takes to turn these
mats upside-down if you can only turn exactly three at a time.
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.
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.
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 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?
Explore the triangles that can be made with seven sticks of the
How many triangles can you make on the 3 by 3 pegboard?
Can you make a rectangle with just 2 dominoes? What about 3, 4, 5,
Can you make five differently sized squares from the tangram
This practical problem challenges you to create shapes and patterns
with two different types of triangle. You could even try
Looking at the picture of this Jomista Mat, can you decribe what
you see? Why not try and make one yourself?
Watch this "Notes on a Triangle" film. Can you recreate parts of
the film using cut-out triangles?
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?
A group of children are discussing the height of a tall tree. How would you go about finding out its height?
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?
NRICH December 2006 advent calendar - a new tangram for each day in
the run-up to Christmas.
These are pictures of the sea defences at New Brighton. Can you
work out what a basic shape might be in both images of the sea wall
and work out a way they might fit together?
Can you make the most extraordinary, the most amazing, the most
unusual patterns/designs from these triangles which are made in a
Kimie and Sebastian were making sticks from interlocking cubes and
lining them up. Can they make their lines the same length? Can they
make any other lines?
Can you recreate this Indian screen pattern? Can you make up
similar patterns of your own?
Can you order pictures of the development of a frog from frogspawn
and of a bean seed growing into a plant?
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?
Can you fit the tangram pieces into the outline of this junk?
Can you fit the tangram pieces into the outlines of these clocks?
Can you fit the tangram pieces into the outlines of these people?
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 outline of this shape. How would you describe it?
Can you fit the tangram pieces into the outlines of the chairs?
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?
Can you fit the tangram pieces into the outline of Little Fung at the table?
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?
Can you make the birds from the egg tangram?
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?
Can you fit the tangram pieces into the outline of this telephone?
Can you fit the tangram pieces into the outline of Wai Ping, Wah Ming and Chi Wing?
Here's a simple way to make a Tangram without any measuring or
These pictures show squares split into halves. Can you find other
This is a simple paper-folding activity that gives an intriguing result which you can then investigate further.
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?