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 has Harry drawn on this clock face? Can you find its
area? What is the largest number of square tiles that could cover
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.
Eight children each had a cube made from modelling clay. They cut them into four pieces which were all exactly the same shape and size. Whose pieces are the same? Can you decide who made each set?
Exploring and predicting folding, cutting and punching holes and
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?
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?
Can you work out what shape is made when this piece of paper is folded up using the crease pattern shown?
If you can post the triangle with either the blue or yellow colour face up, how many ways can it be posted altogether?
A group activity using visualisation of squares and triangles.
These points all mark the vertices (corners) of ten hidden squares.
Can you find the 10 hidden squares?
Move four sticks so there are exactly four triangles.
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?
Choose a box and work out the smallest rectangle of paper needed to
wrap it so that it is completely covered.
How many loops of string have been used to make these patterns?
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 greatest number of squares you can make by overlapping
Imagine a 3 by 3 by 3 cube. If you and a friend drill holes in some of the small cubes in the ways described, how many will have holes drilled through them?
How many pieces of string have been used in these patterns? Can you
describe how you know?
Can you fit the tangram pieces into the outline of these convex shapes?
Can you fit the tangram pieces into the outline of Wai Ping, Wah Ming and Chi Wing?
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?
Take it in turns to place a domino on the grid. One to be placed horizontally and the other vertically. Can you make it impossible for your opponent to play?
Can you fit the tangram pieces into the outline of the telescope and microscope?
Can you fit the tangram pieces into the outline of this plaque design?
Can you fit the tangram pieces into the outline of these rabbits?
Can you fit the tangram pieces into the outline of the rocket?
Can you fit the tangram pieces into the outline of this junk?
A game for two players. You'll need some counters.
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10
Imagine a wheel with different markings painted on it at regular
intervals. Can you predict the colour of the 18th mark? The 100th
Here's a simple way to make a Tangram without any measuring or
Here are shadows of some 3D shapes. What shapes could have made
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?
Investigate how the four L-shapes fit together to make an enlarged L-shape. You could explore this idea with other shapes too.
A shape and space game for 2,3 or 4 players. Be the last person to be able to place a pentomino piece on the playing board. Play with card, or on the computer.
Each of the nets of nine solid shapes has been cut into two pieces. Can you see which pieces go together?
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!
Use the three triangles to fill these outline shapes. Perhaps you can create some of your own shapes for a friend to fill?
Can you fit the tangram pieces into the outlines of the candle and sundial?
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.
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,. . . .
Lyndon Baker describes how the Mobius strip and Euler's law can
introduce pupils to the idea of topology.
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.
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.