Can you describe what happens in this film?
Can you recreate this Indian screen pattern? Can you make up
similar patterns of your own?
How many differently shaped rectangles can you build using these
equilateral and isosceles triangles? Can you make a square?
Here is a chance to create some attractive images by rotating
shapes through multiples of 90 degrees, or 30 degrees, or 72
It's hard to make a snowflake with six perfect lines of symmetry,
but it's fun to try!
This practical problem challenges you to make quadrilaterals with a loop of string. You'll need some friends to help!
Follow these instructions to make a five-pointed snowflake from a
square of paper.
Here is a chance to create some Celtic knots and explore the mathematics behind them.
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?
What shapes can you make by folding an A4 piece of paper?
This practical problem challenges you to create shapes and patterns
with two different types of triangle. You could even try
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.
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.
How many triangles can you make on the 3 by 3 pegboard?
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?
This activity investigates how you might make squares and pentominoes from Polydron.
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?
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?
Generate three random numbers to determine the side lengths of a triangle. What triangles can you draw?
Can you deduce the pattern that has been used to lay out these
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?
What do these two triangles have in common? How are they related?
These practical challenges are all about making a 'tray' and covering it with paper.
Where can you put the mirror across the square so that you can still "see" the whole square? How many different positions are possible?
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?
Arrange your fences to make the largest rectangular space you can. Try with four fences, then five, then six etc.
A jigsaw where pieces only go together if the fractions are
Are all the possible combinations of two shapes included in this
set of 27 cards? How do you know?
An activity making various patterns with 2 x 1 rectangular tiles.
Investigate the smallest number of moves it takes to turn these
mats upside-down if you can only turn exactly three at a time.
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
Ideas for practical ways of representing data such as Venn and
Can you make the birds from the egg tangram?
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 can you put five cereal packets together to make different
shapes if you must put them face-to-face?
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?
Exploring and predicting folding, cutting and punching holes and
Make a cube out of straws and have a go at this practical
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.
We went to the cinema and decided to buy some bags of popcorn so we
asked about the prices. Investigate how much popcorn each bag holds
so find out which we might have bought.
NRICH December 2006 advent calendar - a new tangram for each day in
the run-up to Christmas.
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?
Delight your friends with this cunning trick! Can you explain how
Here is a solitaire type environment for you to experiment with. Which targets can you reach?
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 Wai Ping, Wah Ming and Chi Wing?
A game in which players take it in turns to choose a number. Can you block your opponent?
Looking at the picture of this Jomista Mat, can you decribe what
you see? Why not try and make one yourself?