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.
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. . . .
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.
Lyndon Baker describes how the Mobius strip and Euler's law can
introduce pupils to the idea of topology.
On the graph there are 28 marked points. These points all mark the
vertices (corners) of eight hidden squares. Can you find the eight
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.
What can you see? What do you notice? What questions can you ask?
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?
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?
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?
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?
Exchange the positions of the two sets of counters in the least possible number of moves
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?
Mathematics is the study of patterns. Studying pattern is an
opportunity to observe, hypothesise, experiment, discover and
How many balls of modelling clay and how many straws does it take
to make these skeleton shapes?
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?
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
Investigate how the four L-shapes fit together to make an enlarged
L-shape. You could explore this idea with other shapes too.
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?
Each of the nets of nine solid shapes has been cut into two pieces.
Can you see which pieces go together?
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.
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.
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!
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?
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?
Here are shadows of some 3D shapes. What shapes could have made
A game for two players on a large squared space.
Where can you put the mirror across the square so that you can still "see" the whole square? How many different positions are possible?
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.
What is the total area of the four outside triangles which are
outlined in red in this arrangement of squares inside each other?
What is the shape of wrapping paper that you would need to completely wrap this model?
This article looks at levels of geometric thinking and the types of
activities required to develop this thinking.
Can you fit the tangram pieces into the outline of this sports car?
Can you fit the tangram pieces into the outline of these convex shapes?
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 this goat and giraffe?
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 junk?
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 workmen?
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. . . .