A jigsaw where pieces only go together if the fractions are
Here is a chance to create some attractive images by rotating
shapes through multiples of 90 degrees, or 30 degrees, or 72
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
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?
Make an equilateral triangle by folding paper and use it to make
patterns of your own.
Delight your friends with this cunning trick! Can you explain how
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
Make your own double-sided magic square. But can you complete both
sides once you've made the pieces?
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 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
What shapes should Elly cut out to make a witch's hat? How can she make a taller hat?
These practical challenges are all about making a 'tray' and covering it with paper.
Move your counters through this snake of cards and see how far you
can go. Are you surprised by where you end up?
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?
An activity making various patterns with 2 x 1 rectangular tiles.
Learn how to draw circles using Logo. Wait a minute! Are they really circles? If not what are they?
Are all the possible combinations of two shapes included in this
set of 27 cards? How do you know?
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?
Investigate the smallest number of moves it takes to turn these
mats upside-down if you can only turn exactly three at a time.
Can you predict when you'll be clapping and when you'll be clicking
if you start this rhythm? How about when a friend begins a new
rhythm at the same time?
Can you fit the tangram pieces into the outline of Granma T?
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.
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.
Ideas for practical ways of representing data such as Venn and
More Logo for beginners. Learn to calculate exterior angles and draw regular polygons using procedures and variables.
Generate three random numbers to determine the side lengths of a triangle. What triangles can you draw?
What shapes can you make by folding an A4 piece of paper?
Can Jo make a gym bag for her trainers from the piece of fabric she has?
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 do you know if your set of dominoes is complete?
Where can you put the mirror across the square so that you can still "see" the whole square? How many different positions are possible?
NRICH December 2006 advent calendar - a new tangram for each day in
the run-up to Christmas.
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?
These squares have been made from Cuisenaire rods. Can you describe
the pattern? What would the next square look like?
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 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?
How many models can you find which obey these rules?
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?
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
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?