What is the total area of the four outside triangles which are
outlined in red in this arrangement of squares inside each other?
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.
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
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.
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?
Investigate how the four L-shapes fit together to make an enlarged
L-shape. You could explore this idea with other shapes too.
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?
A group activity using visualisation of squares and triangles.
A game for 1 or 2 people. Use the interactive version, or play with friends. Try to round up as many counters as possible.
What is the greatest number of squares you can make by overlapping
If you can post the triangle with either the blue or yellow colour face up, how many ways can it be posted altogether?
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?
Choose a box and work out the smallest rectangle of paper needed to
wrap it so that it is completely covered.
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?
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.
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.
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 happens to the area of a square if you double the length of
the sides? Try the same thing with rectangles, diamonds and other
shapes. How do the four smaller ones fit into the larger one?
Exploring and predicting folding, cutting and punching holes and
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's a simple way to make a Tangram without any measuring or
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.
Lyndon Baker describes how the Mobius strip and Euler's law can
introduce pupils to the idea of topology.
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,. . . .
What happens when you turn these cogs? Investigate the differences
between turning two cogs of different sizes and two cogs which are
This article looks at levels of geometric thinking and the types of
activities required to develop this thinking.
Billy's class had a robot called Fred who could draw with chalk
held underneath him. What shapes did the pupils make Fred draw?
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?
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?
Make a cube out of straws and have a go at this practical
Can you find a way of representing these arrangements of balls?
You have been given three shapes made out of sponge: a sphere, a cylinder and a cone. Your challenge is to find out how to cut them to make different shapes for printing.
A hundred square has been printed on both sides of a piece of
paper. What is on the back of 100? 58? 23? 19?
Which of these dice are right-handed and which are left-handed?
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 outlines of Mai Ling and Chi Wing?
Here are shadows of some 3D shapes. What shapes could have made
Can you cut a regular hexagon into two pieces to make a
parallelogram? Try cutting it into three pieces to make a rhombus!
Use the three triangles to fill these outline shapes. Perhaps you can create some of your own shapes for a friend to fill?
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.
Can you fit the tangram pieces into the outlines of the candle and sundial?
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?
Reasoning about the number of matches needed to build squares that
share their sides.
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?
Create a pattern on the left-hand grid. How could you extend your pattern on the right-hand grid?
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?
Each of the nets of nine solid shapes has been cut into two pieces.
Can you see which pieces go together?