Make a clinometer and use it to help you estimate the heights of
Make an equilateral triangle by folding paper and use it to make
patterns of your own.
This article for pupils gives an introduction to Celtic knotwork
patterns and a feel for how you can draw them.
Turn through bigger angles and draw stars with Logo.
Galileo, a famous inventor who lived about 400 years ago, came up
with an idea similar to this for making a time measuring
instrument. Can you turn your pendulum into an accurate minute
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.
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.
How can you make an angle of 60 degrees by folding a sheet of paper
Can you order pictures of the development of a frog from frogspawn
and of a bean seed growing into a plant?
It might seem impossible but it is possible. How can you cut a
playing card to make a hole big enough to walk through?
Make some celtic knot patterns using tiling techniques
More Logo for beginners. Learn to calculate exterior angles and draw regular polygons using procedures and variables.
This practical activity involves measuring length/distance.
Make a spiral mobile.
This package contains hands-on code breaking activities based on
the Enigma Schools Project. Suitable for Stages 2, 3 and 4.
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. . . .
This article for students gives some instructions about how to make some different braids.
Logo helps us to understand gradients of lines and why Muggles Magic is not magic but mathematics. See the problem Muggles magic.
What happens when a procedure calls itself?
Can you puzzle out what sequences these Logo programs will give? Then write your own Logo programs to generate sequences.
Make a cube out of straws and have a go at this practical
Exploring and predicting folding, cutting and punching holes and
How many differently shaped rectangles can you build using these
equilateral and isosceles triangles? Can you make a square?
More Logo for beginners. Now learn more about the REPEAT command.
Use the lines on this figure to show how the square can be divided into 2 halves, 3 thirds, 6 sixths and 9 ninths.
Learn about Pen Up and Pen Down in Logo
Write a Logo program, putting in variables, and see the effect when you change the variables.
An activity making various patterns with 2 x 1 rectangular tiles.
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.
Follow the diagrams to make this patchwork piece, based on an
octagon in a square.
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?
This practical problem challenges you to create shapes and patterns
with two different types of triangle. You could even try
I start with a red, a green and a blue marble. I can trade any of
my marbles for two others, one of each colour. Can I end up with
five more blue marbles than red after a number of such trades?
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.
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?
Can you make the most extraordinary, the most amazing, the most
unusual patterns/designs from these triangles which are made in a
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?
What do these two triangles have in common? How are they related?
Ideas for practical ways of representing data such as Venn and
Here's a simple way to make a Tangram without any measuring or
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.
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?
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.
Where can you put the mirror across the square so that you can still "see" the whole square? How many different positions are possible?
Learn how to draw circles using Logo. Wait a minute! Are they really circles? If not what are they?