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?
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 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?
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?
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.
These points all mark the vertices (corners) of ten hidden squares.
Can you find the 10 hidden squares?
A group activity using visualisation of squares and triangles.
We start with one yellow cube and build around it to make a 3x3x3 cube with red cubes. Then we build around that red cube with blue cubes and so on. How many cubes of each colour have we used?
Choose a box and work out the smallest rectangle of paper needed to
wrap it so that it is completely covered.
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?
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?
What is the greatest number of squares you can make by overlapping
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 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.
Can you work out what shape is made when this piece of paper is folded up using the crease pattern shown?
Have a go at this 3D extension to the Pebbles problem.
What can you see? What do you notice? What questions can you ask?
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?
Square It game for an adult and child. Can you come up with a way of always winning this game?
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?
How many pieces of string have been used in these patterns? Can you
describe how you know?
How many moves does it take to swap over some red and blue frogs? Do you have a method?
Can you fit the tangram pieces into the outline of this plaque design?
Here are shadows of some 3D shapes. What shapes could have made
Imagine a wheel with different markings painted on it at regular
intervals. Can you predict the colour of the 18th mark? The 100th
A game for 2 people. Take turns joining two dots, until your opponent is unable to move.
Can you fit the tangram pieces into the outline of the rocket?
A game for two players. You'll need some counters.
Which of these dice are right-handed and which are left-handed?
Can you fit the tangram pieces into the outline of these rabbits?
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 Wai Ping, Wah Ming and Chi Wing?
Can you fit the tangram pieces into the outline of this junk?
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 fit the tangram pieces into the outline of the telescope and microscope?
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10
Can you fit the tangram pieces into the outline of these convex shapes?
Lyndon Baker describes how the Mobius strip and Euler's law can
introduce pupils to the idea of topology.
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?
Here's a simple way to make a Tangram without any measuring or
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 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. . . .
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 hundred square has been printed on both sides of a piece of paper. What is on the back of 100? 58? 23? 19?
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
Can you fit the tangram pieces into the outlines of the workmen?
This article looks at levels of geometric thinking and the types of
activities required to develop this thinking.
Can you work out what is wrong with the cogs on a UK 2 pound coin?