A jigsaw where pieces only go together if the fractions are
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?
I start with a red, a blue, a green and a yellow marble. I can
trade any of my marbles for three others, one of each colour. Can I
end up with exactly two marbles of each colour?
Make a clinometer and use it to help you estimate the heights of
Delight your friends with this cunning trick! Can you explain how
Here is a chance to create some attractive images by rotating
shapes through multiples of 90 degrees, or 30 degrees, or 72
Arrange your fences to make the largest rectangular space you can. Try with four fences, then five, then six etc.
How can you make an angle of 60 degrees by folding a sheet of paper
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?
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?
Here is a solitaire type environment for you to experiment with. Which targets can you reach?
Learn how to draw circles using Logo. Wait a minute! Are they really circles? If not what are they?
Move your counters through this snake of cards and see how far you
can go. Are you surprised by where you end up?
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
Make an equilateral triangle by folding paper and use it to make
patterns of your own.
This article for students gives some instructions about how to make some different braids.
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?
This article for pupils gives an introduction to Celtic knotwork
patterns and a feel for how you can draw them.
An activity making various patterns with 2 x 1 rectangular tiles.
Make your own double-sided magic square. But can you complete both
sides once you've made the pieces?
Are all the possible combinations of two shapes included in this
set of 27 cards? How do you know?
What shapes should Elly cut out to make a witch's hat? How can she make a taller hat?
Can you order pictures of the development of a frog from frogspawn
and of a bean seed growing into a plant?
What do these two triangles have in common? How are they related?
If these balls are put on a line with each ball touching the one in
front and the one behind, which arrangement makes the shortest line
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.
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.
Ideas for practical ways of representing data such as Venn and
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.
Here's a simple way to make a Tangram without any measuring or
Investigate the smallest number of moves it takes to turn these
mats upside-down if you can only turn exactly three at a time.
This practical problem challenges you to create shapes and patterns
with two different types of triangle. You could even try
Can you fit the tangram pieces into the outline of this junk?
Can you fit the tangram pieces into the outline of Wai Ping, Wah Ming and Chi Wing?
Can you recreate this Indian screen pattern? Can you make up
similar patterns of your own?
Take a counter and surround it by a ring of other counters that
MUST touch two others. How many are needed?
Have a go at drawing these stars which use six points drawn around
a circle. Perhaps you can create your own designs?
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?
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.
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?
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?
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.
More Logo for beginners. Learn to calculate exterior angles and draw regular polygons using procedures and variables.
Looking at the picture of this Jomista Mat, can you decribe what
you see? Why not try and make one yourself?
Can you make the most extraordinary, the most amazing, the most
unusual patterns/designs from these triangles which are made in a
How can you put five cereal packets together to make different
shapes if you must put them face-to-face?