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?
You'll need a collection of cups for this activity.
Make a chair and table out of interlocking cubes, making sure that the chair fits under the table!
For this activity which explores capacity, you will need to collect some bottles and jars.
Using a loop of string stretched around three of your fingers, what
different triangles can you make? Draw them and sort them into
In this activity focusing on capacity, you will need a collection of different jars and bottles.
What shapes can you make by folding an A4 piece of paper?
Can you create more models that follow these rules?
Have you ever tried tessellating capital letters? Have a look at
these examples and then try some for yourself.
This practical activity challenges you to create symmetrical designs by cutting a square into strips.
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 work out what shape is made when this piece of paper is folded up using the crease pattern shown?
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?
Arrange your fences to make the largest rectangular space you can. Try with four fences, then five, then six etc.
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.
Can you make a rectangle with just 2 dominoes? What about 3, 4, 5,
Try continuing these patterns made from triangles. Can you create your own repeating pattern?
Follow the diagrams to make this patchwork piece, based on an
octagon in a square.
Looking at the picture of this Jomista Mat, can you decribe what
you see? Why not try and make one yourself?
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 make the most extraordinary, the most amazing, the most
unusual patterns/designs from these triangles which are made in a
Here's a simple way to make a Tangram without any measuring or
Ideas for practical ways of representing data such as Venn and
Where can you put the mirror across the square so that you can still "see" the whole square? How many different positions are possible?
Can you make the birds from the egg tangram?
NRICH December 2006 advent calendar - a new tangram for each day in
the run-up to Christmas.
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?
This practical problem challenges you to create shapes and patterns
with two different types of triangle. You could even try
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?
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 brazier for roasting chestnuts?
Can you fit the tangram pieces into the outline of Little Fung at the table?
Can you fit the tangram pieces into the outlines of these people?
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 outline of the child walking home from school?
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?
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 recreate this Indian screen pattern? Can you make up
similar patterns of your own?
Can you fit the tangram pieces into the outline of this junk?
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?
Have a go at drawing these stars which use six points drawn around
a circle. Perhaps you can create your own designs?
Use the lines on this figure to show how the square can be divided into 2 halves, 3 thirds, 6 sixths and 9 ninths.
Watch this "Notes on a Triangle" film. Can you recreate parts of the film using cut-out triangles?
Make a flower design using the same shape made out of different sizes of paper.
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.