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?
How many triangles can you make on the 3 by 3 pegboard?
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?
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?
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?
Can you split each of the shapes below in half so that the two parts are exactly the same?
Try continuing these patterns made from triangles. Can you create your own repeating pattern?
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?
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.
Have a go at making a few of these shapes from paper in different sizes. What patterns can you create?
Can you visualise what shape this piece of paper will make when it is folded?
For this task, you'll need an A4 sheet and two A5 transparent sheets. Decide on a way of arranging the A5 sheets on top of the A4 sheet and explore ...
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.
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?
Explore the triangles that can be made with seven sticks of the
Can you describe a piece of paper clearly enough for your partner to know which piece it is?
In this activity focusing on capacity, you will need a collection of different jars and bottles.
You'll need a collection of cups for this activity.
Can you make a rectangle with just 2 dominoes? What about 3, 4, 5,
For this activity which explores capacity, you will need to collect some bottles and jars.
Can you fit the tangram pieces into the outline of Little Fung at the table?
Can you make the birds from the egg tangram?
Here's a simple way to make a Tangram without any measuring or
Use the lines on this figure to show how the square can be divided into 2 halves, 3 thirds, 6 sixths and 9 ninths.
Use the three triangles to fill these outline shapes. Perhaps you can create some of your own shapes for a friend to fill?
Make a cube out of straws and have a go at this practical
Ideas for practical ways of representing data such as Venn and
An activity making various patterns with 2 x 1 rectangular tiles.
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?
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 fit the tangram pieces into the outline of this brazier for roasting chestnuts?
Can you fit the tangram pieces into the outline of this telephone?
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?
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 fit the tangram pieces into the outline of this junk?
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?
Looking at the picture of this Jomista Mat, can you decribe what
you see? Why not try and make one yourself?
We can cut a small triangle off the corner of a square and then fit
the two pieces together. Can you work out how these shapes are made
from the two pieces?
NRICH December 2006 advent calendar - a new tangram for each day in
the run-up to Christmas.
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 most extraordinary, the most amazing, the most
unusual patterns/designs from these triangles which are made in a
Have a go at drawing these stars which use six points drawn around
a circle. Perhaps you can create your own designs?
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?