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
What can you see? What do you notice? What questions can you ask?
If you can post the triangle with either the blue or yellow colour face up, how many ways can it be posted altogether?
Can you work out what shape is made when this piece of paper is folded up using the crease pattern shown?
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?
I found these clocks in the Arts Centre at the University of
Warwick intriguing - do they really need four clocks and what times
would be ambiguous with only two or three of them?
These points all mark the vertices (corners) of ten hidden squares.
Can you find the 10 hidden squares?
How many pieces of string have been used in these patterns? Can you
describe how you know?
On the graph there are 28 marked points. These points all mark the
vertices (corners) of eight hidden squares. Can you find the eight
Choose a box and work out the smallest rectangle of paper needed to
wrap it so that it is completely covered.
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?
Move four sticks so there are exactly four triangles.
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?
A game for 2 people. Take turns joining two dots, until your opponent is unable to move.
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
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?
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?
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?
A group activity using visualisation of squares and triangles.
Square It game for an adult and child. Can you come up with a way of always winning this game?
We're excited about this new program for drawing beautiful mathematical designs. Can you work out how we made our first few pictures and, even better, share your most elegant solutions with us?
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?
Exploring and predicting folding, cutting and punching holes and
How many loops of string have been used to make these patterns?
Can you fit the tangram pieces into the outline of these convex shapes?
Can you fit the tangram pieces into the outline of the rocket?
Can you fit the tangram pieces into the outline of this junk?
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 outlines of the watering can and man in a boat?
Use the three triangles to fill these outline shapes. Perhaps you can create some of your own shapes for a friend to fill?
Which of these dice are right-handed and which are left-handed?
Here are shadows of some 3D shapes. What shapes could have made
Can you fit the tangram pieces into the outline of these rabbits?
Can you fit the tangram pieces into the outline of the telescope and microscope?
A game for two players. You'll need some counters.
Can you fit the tangram pieces into the outlines of Mai Ling and Chi Wing?
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.
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 this plaque design?
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.
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 Wai Ping, Wah Ming and Chi Wing?
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 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.
Can you fit the tangram pieces into the outline of Little Ming and Little Fung dancing?
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