Using a loop of string stretched around three of your fingers, what
different triangles can you make? Draw them and sort them into
What shapes can you make by folding an A4 piece of paper?
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?
Try continuing these patterns made from triangles. Can you create
your own repeating pattern?
How many triangles can you make on the 3 by 3 pegboard?
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?
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!
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?
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.
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.
Explore the triangles that can be made with seven sticks of the
In this activity focusing on capacity, you will need a collection of different jars and bottles.
For this activity which explores capacity, you will need to collect some bottles and jars.
Investigate the smallest number of moves it takes to turn these
mats upside-down if you can only turn exactly three at a time.
Can you make five differently sized squares from the tangram
You will need a long strip of paper for this task. Cut it into different lengths. How could you find out how long each piece is?
Can you make a rectangle with just 2 dominoes? What about 3, 4, 5,
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?
Here's a simple way to make a Tangram without any measuring or
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?
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 birds from the egg tangram?
Can you make the most extraordinary, the most amazing, the most
unusual patterns/designs from these triangles which are made in a
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 Little Fung at the table?
Can you fit the tangram pieces into the outline of Little Ming playing the board game?
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 this brazier for roasting chestnuts?
Can you fit the tangram pieces into the outlines of these people?
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 the child walking home from school?
Can you fit the tangram pieces into the outlines of these clocks?
Have a go at drawing these stars which use six points drawn around
a circle. Perhaps you can create your own designs?
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?
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?
Watch this "Notes on a Triangle" film. Can you recreate parts of
the film using cut-out triangles?
This practical problem challenges you to create shapes and patterns
with two different types of triangle. You could even try
Can you recreate this Indian screen pattern? Can you make up
similar patterns of your own?
An activity making various patterns with 2 x 1 rectangular tiles.
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 fit the tangram pieces into the outline of this junk?
Looking at the picture of this Jomista Mat, can you decribe what
you see? Why not try and make one yourself?
How can you put five cereal packets together to make different
shapes if you must put them face-to-face?
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.
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?