On the graph there are 28 marked points. These points all mark the
vertices (corners) of eight hidden squares. Can you find the eight
A cheap and simple toy with lots of mathematics. Can you interpret
the images that are produced? Can you predict the pattern that will
be produced using different wheels?
How many moves does it take to swap over some red and blue frogs? Do you have a method?
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?
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 is the total area of the four outside triangles which are
outlined in red in this arrangement of squares inside each other?
Choose a box and work out the smallest rectangle of paper needed to
wrap it so that it is completely covered.
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.
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?
This article looks at levels of geometric thinking and the types of
activities required to develop this thinking.
What happens when you turn these cogs? Investigate the differences
between turning two cogs of different sizes and two cogs which are
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,. . . .
A game for two players. You'll need some counters.
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.
Here's a simple way to make a Tangram without any measuring or
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?
Can you fit the tangram pieces into the outline of this junk?
Can you fit the tangram pieces into the outline of the rocket?
Can you fit the tangram pieces into the outline of this plaque design?
If you can post the triangle with either the blue or yellow colour face up, how many ways can it be posted altogether?
Billy's class had a robot called Fred who could draw with chalk
held underneath him. What shapes did the pupils make Fred draw?
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
These points all mark the vertices (corners) of ten hidden squares.
Can you find the 10 hidden squares?
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 workmen?
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 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.
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 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?
Each of the nets of nine solid shapes has been cut into two pieces.
Can you see which pieces go together?
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.
Reasoning about the number of matches needed to build squares that
share their sides.
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.
Investigate how the four L-shapes fit together to make an enlarged
L-shape. You could explore this idea with other shapes too.
Here are shadows of some 3D shapes. What shapes could have made
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 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 these rabbits?
Can you fit the tangram pieces into the outline of Little Ming and Little Fung dancing?
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.
Can you fit the tangram pieces into the outlines of the candle and sundial?
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?
A hundred square has been printed on both sides of a piece of paper. What is on the back of 100? 58? 23? 19?
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10
Think of a number, square it and subtract your starting number. Is
the number you’re left with odd or even? How do the images
help to explain this?