This article looks at levels of geometric thinking and the types of
activities required to develop this thinking.
This task depends on groups working collaboratively, discussing and
reasoning to agree a final product.
Try this interactive strategy game for 2
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?
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 the lobster, yacht and cyclist?
Can you fit the tangram pieces into the outlines of these clocks?
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?
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 for teachers describes a project which explores
thepower of storytelling to convey concepts and ideas to children.
Imagine you have six different colours of paint. You paint a cube
using a different colour for each of the six faces. How many
different cubes can be painted using the same set of six colours?
Imagine a wheel with different markings painted on it at regular
intervals. Can you predict the colour of the 18th mark? The 100th
Imagine starting with one yellow cube and covering it all over with
a single layer of red cubes, and then covering that cube with a
layer of blue cubes. How many red and blue cubes would you need?
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10
A game for 2 people. Take turns joining two dots, until your opponent is unable to move.
Where can you put the mirror across the square so that you can still "see" the whole square? How many different positions are possible?
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 this shape. How would you describe it?
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 chairs?
Can you fit the tangram pieces into the outline of this telephone?
Imagine you are suspending a cube from one vertex (corner) and
allowing it to hang freely. Now imagine you are lowering it into
water until it is exactly half submerged. What shape does the
surface. . . .
Can you fit the tangram pieces into the outline of Granma T?
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
Can you visualise what shape this piece of paper will make when it is folded?
I found these clocks in the Arts Centre at the University of
Warwick intriguing - do they really need four clocks and what times
would be ambiguous with only two or three of them?
Looking at the picture of this Jomista Mat, can you decribe what
you see? Why not try and make one yourself?
How many different cuboids can you make when you use four CDs or
DVDs? How about using five, then six?
A rectangular field has two posts with a ring on top of each post.
There are two quarrelsome goats and plenty of ropes which you can
tie to their collars. How can you secure them so they can't. . . .
Exchange the positions of the two sets of counters in the least possible number of moves
How many different ways can I lay 10 paving slabs, each 2 foot by 1
foot, to make a path 2 foot wide and 10 foot long from my back door
into my garden, without cutting any of the paving slabs?
On which of these shapes can you trace a path along all of its
edges, without going over any edge twice?
This problem invites you to build 3D shapes using two different
triangles. Can you make the shapes from the pictures?
Can you dissect a square into: 4, 7, 10, 13... other squares? 6, 9,
12, 15... other squares? 8, 11, 14... other squares?
What shape is made when you fold using this crease pattern? Can you make a ring design?
Can you work out what shape is made by folding in this way? Why not create some patterns using this shape but in different sizes?
Use the lines on this figure to show how the square can be divided into 2 halves, 3 thirds, 6 sixths and 9 ninths.
Can you fit the tangram pieces into the outline of Little Ming?
Make a flower design using the same shape made out of different sizes of paper.
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 Wai Ping, Wah Ming and Chi Wing?
Can you arrange the shapes in a chain so that each one shares a
face (or faces) that are the same shape as the one that follows it?
Can you cut a regular hexagon into two pieces to make a
parallelogram? Try cutting it into three pieces to make a rhombus!
Imagine a large cube made from small red cubes being dropped into a pot of yellow paint. How many of the small cubes will have yellow paint on their faces?
Each of the nets of nine solid shapes has been cut into two pieces. Can you see which pieces go together?
This article for teachers describes how modelling number properties
involving multiplication using an array of objects not only allows
children to represent their thinking with concrete materials,. . . .
Reasoning about the number of matches needed to build squares that
share their sides.
An extension of noughts and crosses in which the grid is enlarged
and the length of the winning line can to altered to 3, 4 or 5.
Choose a couple of the sequences. Try to picture how to make the next, and the next, and the next... Can you describe your reasoning?