Build a scaffold out of drinking-straws to support a cup of water
What shape would fit your pens and pencils best? How can you make it?
This article for students gives some instructions about how to make some different braids.
Design and construct a prototype intercooler which will satisfy agreed quality control constraints.
How does the time of dawn and dusk vary? What about the Moon, how does that change from night to night? Is the Sun always the same? Gather data to help you explore these questions.
Can Jo make a gym bag for her trainers from the piece of fabric she has?
This article for pupils gives an introduction to Celtic knotwork
patterns and a feel for how you can draw them.
Make a spiral mobile.
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.
In this article for teachers, Bernard uses some problems to suggest
that once a numerical pattern has been spotted from a practical
starting point, going back to the practical can help explain. . . .
Exploring balance and centres of mass can be great fun. The
resulting structures can seem impossible. Here are some images to
encourage you to experiment with non-breakable objects of your own.
As part of Liverpool08 European Capital of Culture there were a
huge number of events and displays. One of the art installations
was called "Turning the Place Over". Can you find our how it works?
It might seem impossible but it is possible. How can you cut a
playing card to make a hole big enough to walk through?
What shape and size of drinks mat is best for flipping and catching?
What shapes should Elly cut out to make a witch's hat? How can she make a taller hat?
Make a clinometer and use it to help you estimate the heights of
A brief video looking at how you can sometimes use symmetry to
distinguish knots. Can you use this idea to investigate the
differences between the granny knot and the reef knot?
Logo helps us to understand gradients of lines and why Muggles Magic is not magic but mathematics. See the problem Muggles magic.
Here's a simple way to make a Tangram without any measuring or
Can you make the birds from the egg tangram?
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.
Investigate the smallest number of moves it takes to turn these
mats upside-down if you can only turn exactly three at a time.
Are all the possible combinations of two shapes included in this
set of 27 cards? How do you know?
Where can you put the mirror across the square so that you can still "see" the whole square? How many different positions are possible?
Use the lines on this figure to show how the square can be divided into 2 halves, 3 thirds, 6 sixths and 9 ninths.
How is it possible to predict the card?
Time for a little mathemagic! Choose any five cards from a pack and show four of them to your partner. How can they work out the fifth?
Ideas for practical ways of representing data such as Venn and
An activity making various patterns with 2 x 1 rectangular tiles.
Follow the diagrams to make this patchwork piece, based on an
octagon in a square.
Can you recreate this Indian screen pattern? Can you make up
similar patterns of your own?
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?
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.
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 this junk?
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?
Take a counter and surround it by a ring of other counters that
MUST touch two others. How many are needed?
Here is a solitaire type environment for you to experiment with. Which targets can you reach?
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?
Can you make the most extraordinary, the most amazing, the most
unusual patterns/designs from these triangles which are made in a
NRICH December 2006 advent calendar - a new tangram for each day in
the run-up to Christmas.
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?
Make a cube out of straws and have a go at this practical
Looking at the picture of this Jomista Mat, can you decribe what
you see? Why not try and make one yourself?
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.
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?
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?
Move your counters through this snake of cards and see how far you
can go. Are you surprised by where you end up?