What shapes can you make by folding an A4 piece of paper?
How can you make an angle of 60 degrees by folding a sheet of paper
Watch the video to see how to fold a square of paper to create a flower. What fraction of the piece of paper is the small triangle?
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?
This activity investigates how you might make squares and pentominoes from Polydron.
Make an equilateral triangle by folding paper and use it to make
patterns of your own.
What is the greatest number of counters you can place on the grid below without four of them lying at the corners of a square?
Can you cut a regular hexagon into two pieces to make a
parallelogram? Try cutting it into three pieces to make a rhombus!
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?
How many triangles can you make on the 3 by 3 pegboard?
Are all the possible combinations of two shapes included in this
set of 27 cards? How do you know?
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.
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?
Arrange your fences to make the largest rectangular space you can. Try with four fences, then five, then six etc.
Can you visualise what shape this piece of paper will make when it is folded?
These practical challenges are all about making a 'tray' and covering it with paper.
What do these two triangles have in common? How are they related?
What is the greatest number of squares you can make by overlapping
This practical problem challenges you to make quadrilaterals with a loop of string. You'll need some friends to help!
Cut a square of paper into three pieces as shown. Now,can you use
the 3 pieces to make a large triangle, a parallelogram and the
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?
Use the lines on this figure to show how the square can be divided into 2 halves, 3 thirds, 6 sixths and 9 ninths.
Investigate the smallest number of moves it takes to turn these
mats upside-down if you can only turn exactly three at a time.
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?
An activity making various patterns with 2 x 1 rectangular tiles.
You could use just coloured pencils and paper to create this
design, but it will be more eye-catching if you can get hold of
hammer, nails and string.
Here's a simple way to make a Tangram without any measuring or
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?
Take a counter and surround it by a ring of other counters that
MUST touch two others. How many are needed?
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?
Can you fit the tangram pieces into the outline of this junk?
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 Little Ming playing the board game?
Can you fit the tangram pieces into the outline of this telephone?
Have a go at drawing these stars which use six points drawn around
a circle. Perhaps you can create your own designs?
The triangle ABC is equilateral. The arc AB has centre C, the arc
BC has centre A and the arc CA has centre B. Explain how and why
this shape can roll along between two parallel tracks.
Here is a solitaire type environment for you to experiment with. Which targets can you reach?
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?
Follow the diagrams to make this patchwork piece, based on an
octagon in a square.
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.
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?
Starting with four different triangles, imagine you have an
unlimited number of each type. How many different tetrahedra can
you make? Convince us you have found them all.
Can you deduce the pattern that has been used to lay out these