Draw three straight lines to separate these shapes into four groups
- each group must contain one of each shape.
This practical problem challenges you to make quadrilaterals with a loop of string. You'll need some friends to help!
Try this interactive strategy game for 2
How many DIFFERENT quadrilaterals can be made by joining the dots
on the 8-point circle?
A group activity using visualisation of squares and triangles.
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?
This article looks at levels of geometric thinking and the types of
activities required to develop this thinking.
Can you cut a regular hexagon into two pieces to make a
parallelogram? Try cutting it into three pieces to make a rhombus!
Billy's class had a robot called Fred who could draw with chalk
held underneath him. What shapes did the pupils make Fred draw?
Four rods, two of length a and two of length b, are linked to form
a kite. The linkage is moveable so that the angles change. What is
the maximum area of the kite?
This task depends on groups working collaboratively, discussing and
reasoning to agree a final product.
How many different triangles can you make on a circular pegboard
that has nine pegs?
Generate three random numbers to determine the side lengths of a triangle. What triangles can you draw?
This article for teachers describes a project which explores
thepower of storytelling to convey concepts and ideas to children.
Which of the following cubes can be made from these nets?
This problem invites you to build 3D shapes using two different
triangles. Can you make the shapes from the pictures?
Where can you put the mirror across the square so that you can
still "see" the whole square? How many different positions are
Can you fit the tangram pieces into the outlines of the chairs?
Can you fit the tangram pieces into the outline of Little Ming?
Can you fit the tangram pieces into the outline of this shape. How would you describe it?
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 recreate these designs? What are the basic units? What
movement is required between each unit? Some elegant use of
procedures will help - variables not essential.
Imagine a wheel with different markings painted on it at regular
intervals. Can you predict the colour of the 18th mark? The 100th
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10
Can you fit the tangram pieces into the outline of Wai Ping, Wah Ming and Chi Wing?
How can the same pieces of the tangram make this bowl before and after it was chipped? Use the interactivity to try and work out what is going on!
A magician took a suit of thirteen cards and held them in his hand
face down. Every card he revealed had the same value as the one he
had just finished spelling. How did this work?
Can you fit the tangram pieces into the outline of Granma T?
A game for 2 people. Take turns joining two dots, until your opponent is unable to move.
Can you work out what is wrong with the cogs on a UK 2 pound coin?
Can you fit the tangram pieces into the outlines of the lobster, yacht and cyclist?
Use the interactivity to listen to the bells ringing a pattern. Now
it's your turn! Play one of the bells yourself. How do you know
when it is your turn to ring?
On which of these shapes can you trace a path along all of its
edges, without going over any edge twice?
The whole set of tiles is used to make a square. This has a green and blue border. There are no green or blue tiles anywhere in the square except on this border. How many tiles are there in the set?
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?
Can you picture where this letter "F" will be on the grid if you
flip it in these different ways?
How many different cuboids can you make when you use four CDs or
DVDs? How about using five, then six?
Take a rectangle of paper and fold it in half, and half again, to
make four smaller rectangles. How many different ways can you fold
Use the lines on this figure to show how the square can be divided
into 2 halves, 3 thirds, 6 sixths and 9 ninths.
Cut four triangles from a square as shown in the picture. How many
different shapes can you make by fitting the four triangles back
Can you fit the tangram pieces into the outline of this telephone?
We start with one yellow cube and build around it to make a 3x3x3
cube with red cubes. Then we build around that red cube with blue
cubes and so on. How many cubes of each colour have we used?
Can you fit the tangram pieces into the outlines of these clocks?
Can you fit the tangram pieces into the outline of the child walking home from school?
Can you fit the tangram pieces into the outlines of these people?
Can you fit the tangram pieces into the outline of this brazier for roasting chestnuts?
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 Little Fung at the table?
Can you fit the tangram pieces into the outline of the telescope and microscope?
You have 27 small cubes, 3 each of nine colours. Use the small
cubes to make a 3 by 3 by 3 cube so that each face of the bigger
cube contains one of every colour.