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
Make a clinometer and use it to help you estimate the heights of
What do these two triangles have in common? How are they related?
What shapes should Elly cut out to make a witch's hat? How can she make a taller hat?
Make your own double-sided magic square. But can you complete both
sides once you've made the pieces?
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
This practical activity involves measuring length/distance.
These practical challenges are all about making a 'tray' and covering it with paper.
How can you make an angle of 60 degrees by folding a sheet of paper
Arrange 9 red cubes, 9 blue cubes and 9 yellow cubes into a large 3 by 3 cube. No row or column of cubes must contain two cubes of the same colour.
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?
This practical problem challenges you to create shapes and patterns
with two different types of triangle. You could even try
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?
Can you order pictures of the development of a frog from frogspawn
and of a bean seed growing into a plant?
Here is a chance to create some attractive images by rotating
shapes through multiples of 90 degrees, or 30 degrees, or 72
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?
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?
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 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?
A jigsaw where pieces only go together if the fractions are
Cut a square of paper into three pieces as shown. Now,can you use
the 3 pieces to make a large triangle, a parallelogram and the
Arrange your fences to make the largest rectangular space you can. Try with four fences, then five, then six etc.
This article for pupils gives an introduction to Celtic knotwork
patterns and a feel for how you can draw them.
More Logo for beginners. Learn to calculate exterior angles and draw regular polygons using procedures and variables.
Where can you put the mirror across the square so that you can still "see" the whole square? How many different positions are possible?
Ideas for practical ways of representing data such as Venn and
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.
Can you fit the tangram pieces into the outline of Granma T?
Use the lines on this figure to show how the square can be divided into 2 halves, 3 thirds, 6 sixths and 9 ninths.
Make a cube out of straws and have a go at this practical
How can you put five cereal packets together to make different
shapes if you must put them face-to-face?
Use the interactivity to play two of the bells in a pattern. How do
you know when it is your turn to ring, and how do you know which
bell to ring?
Can you fit the tangram pieces into the outline of Wai Ping, Wah Ming and Chi Wing?
How many differently shaped rectangles can you build using these
equilateral and isosceles triangles? Can you make a square?
Turn through bigger angles and draw stars with Logo.
Exploring and predicting folding, cutting and punching holes and
Here's a simple way to make a Tangram without any measuring or
Can you recreate this Indian screen pattern? Can you make up
similar patterns of your own?
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.
Looking at the picture of this Jomista Mat, can you decribe what
you see? Why not try and make one yourself?
Here is a solitaire type environment for you to experiment with. Which targets can you reach?
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?
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 make the most extraordinary, the most amazing, the most
unusual patterns/designs from these triangles which are made in a
This practical problem challenges you to make quadrilaterals with a loop of string. You'll need some friends to help!