This article looks at levels of geometric thinking and the types of
activities required to develop this thinking.
One face of a regular tetrahedron is painted blue and each of the
remaining faces are painted using one of the colours red, green or
yellow. How many different possibilities are there?
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 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?
This task depends on groups working collaboratively, discussing and
reasoning to agree a final product.
Investigate the number of paths you can take from one vertex to
another in these 3D shapes. Is it possible to take an odd number
and an even number of paths to the same vertex?
A toy has a regular tetrahedron, a cube and a base with triangular
and square hollows. If you fit a shape into the correct hollow a
bell rings. How many times does the bell ring in a complete game?
You want to make each of the 5 Platonic solids and colour the faces
so that, in every case, no two faces which meet along an edge have
the same colour.
This is the first article in a series which aim to provide some insight into the way spatial thinking develops in children, and draw on a range of reported research. The focus of this article is the. . . .
Each of the nets of nine solid shapes has been cut into two pieces. Can you see which pieces go together?
Try this interactive strategy game for 2
Can you fit the tangram pieces into the outline of this shape. How would you describe it?
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 shape is made when you fold using this crease pattern? Can you make a ring design?
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?
Can you fit the tangram pieces into the outlines of the lobster, yacht and cyclist?
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?
Can you fit the tangram pieces into the outlines of the chairs?
This problem invites you to build 3D shapes using two different
triangles. Can you make the shapes from the pictures?
This problem is about investigating whether it is possible to start at one vertex of a platonic solid and visit every other vertex once only returning to the vertex you started at.
Blue Flibbins are so jealous of their red partners that they will
not leave them on their own with any other bue Flibbin. What is the
quickest way of getting the five pairs of Flibbins safely to. . . .
This article for teachers describes a project which explores
thepower of storytelling to convey concepts and ideas to children.
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?
Can you dissect a square into: 4, 7, 10, 13... other squares? 6, 9,
12, 15... other squares? 8, 11, 14... other squares?
Paint a stripe on a cardboard roll. Can you predict what will
happen when it is rolled across a sheet of paper?
Which of the following cubes can be made from these nets?
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 the child walking home from school?
Can you fit the tangram pieces into the outlines of these clocks?
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?
Can you fit the tangram pieces into the outline of Little Ming?
Exchange the positions of the two sets of counters in the least possible number of moves
On which of these shapes can you trace a path along all of its
edges, without going over any edge twice?
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.
Can you visualise what shape this piece of paper will make when it is folded?
Can you fit the tangram pieces into the outline of this telephone?
Can you fit the tangram pieces into the outline of Little Ming playing the board game?
Can you fit the tangram pieces into the outlines of these people?
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 this brazier for roasting chestnuts?
For this task, you'll need an A4 sheet and two A5 transparent sheets. Decide on a way of arranging the A5 sheets on top of the A4 sheet and explore ...
Can you fit the tangram pieces into the outline of Little Fung at the table?
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
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?
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 fit the tangram pieces into the outline of this sports car?
Can you fit the tangram pieces into the outline of this goat and giraffe?
What happens when you turn these cogs? Investigate the differences
between turning two cogs of different sizes and two cogs which are
Investigate how the four L-shapes fit together to make an enlarged L-shape. You could explore this idea with other shapes too.