What shape is the overlap when you slide one of these shapes half
way across another? Can you picture it in your head? Use the
interactivity to check your visualisation.
Players take it in turns to choose a dot on the grid. The winner is the first to have four dots that can be joined to form a square.
A game for 1 or 2 people. Use the interactive version, or play with friends. Try to round up as many counters as possible.
Here are the six faces of a cube - in no particular order. Here are
three views of the cube. Can you deduce where the faces are in
relation to each other and record them on the net of this cube?
Lyndon Baker describes how the Mobius strip and Euler's law can
introduce pupils to the idea of topology.
A package contains a set of resources designed to develop pupils'
mathematical thinking. This package places a particular emphasis on
“visualising” and is designed to meet the needs. . . .
Find a way to cut a 4 by 4 square into only two pieces, then rejoin the two pieces to make an L shape 6 units high.
A game for 2 players. Given a board of dots in a grid pattern, players take turns drawing a line by connecting 2 adjacent dots. Your goal is to complete more squares than your opponent.
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?
How many balls of modelling clay and how many straws does it take
to make these skeleton shapes?
A group activity using visualisation of squares and triangles.
On which of these shapes can you trace a path along all of its
edges, without going over any edge twice?
Can you cut up a square in the way shown and make the pieces into a
Move four sticks so there are exactly four triangles.
These points all mark the vertices (corners) of ten hidden squares.
Can you find the 10 hidden squares?
If you can post the triangle with either the blue or yellow colour face up, how many ways can it be posted altogether?
A game has a special dice with a colour spot on each face. These
three pictures show different views of the same dice. What colour
is opposite blue?
What is the greatest number of squares you can make by overlapping
Start with a large square, join the midpoints of its sides, you'll see four right angled triangles. Remove these triangles, a second square is left. Repeat the operation. What happens?
A game for 2 people. Take turns joining two dots, until your opponent is unable to move.
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?
What can you see? What do you notice? What questions can you ask?
On the graph there are 28 marked points. These points all mark the
vertices (corners) of eight hidden squares. Can you find the eight
What is the greatest number of counters you can place on the grid
below without four of them lying at the corners of a square?
What is the shape of wrapping paper that you would need to completely wrap this model?
A game for 2 players. Can be played online. One player has 1 red
counter, the other has 4 blue. The red counter needs to reach the
other side, and the blue needs to trap the red.
Investigate how the four L-shapes fit together to make an enlarged
L-shape. You could explore this idea with other shapes too.
Can you find a way of representing these arrangements of balls?
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.
Imagine a 3 by 3 by 3 cube made of 9 small cubes. Each face of the large cube is painted a different colour. How many small cubes will have two painted faces? Where are they?
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?
An activity centred around observations of dots and how we visualise number arrangement patterns.
Each of the nets of nine solid shapes has been cut into two pieces.
Can you see which pieces go together?
What shape has Harry drawn on this clock face? Can you find its
area? What is the largest number of square tiles that could cover
Here are shadows of some 3D shapes. What shapes could have made
Where can you put the mirror across the square so that you can
still "see" the whole square? How many different positions are
Mathematics is the study of patterns. Studying pattern is an
opportunity to observe, hypothesise, experiment, discover and
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.
Imagine a 4 by 4 by 4 cube. If you and a friend drill holes in some of the small cubes in the ways described, how many will not have holes drilled through them?
What is the total area of the four outside triangles which are
outlined in red in this arrangement of squares inside each other?
Can you fit the tangram pieces into the outline of this goat and giraffe?
This article for teachers discusses examples of problems in which
there is no obvious method but in which children can be encouraged
to think deeply about the context and extend their ability to. . . .
Can you fit the tangram pieces into the outline of Little Ming and Little Fung dancing?
Can you fit the tangram pieces into the outlines of the watering can and man in a boat?
Can you fit the tangram pieces into the outline of this sports car?
Billy's class had a robot called Fred who could draw with chalk
held underneath him. What shapes did the pupils make Fred draw?
Can you fit the tangram pieces into the outline of these convex shapes?
The aim of the game is to slide the green square from the top right
hand corner to the bottom left hand corner in the least number of
If you split the square into these two pieces, it is possible to fit the pieces together again to make a new shape. How many new shapes can you make?
This article looks at levels of geometric thinking and the types of
activities required to develop this thinking.