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 can you see? What do you notice? What questions can you ask?
Move four sticks so there are exactly four triangles.
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.
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?
What is the greatest number of squares you can make by overlapping
Choose a box and work out the smallest rectangle of paper needed to
wrap it so that it is completely covered.
A game for 1 or 2 people. Use the interactive version, or play with friends. Try to round up as many counters as possible.
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.
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 package contains a set of resources designed to develop pupils'
mathematical thinking. This package places a particular emphasis on
“visualising” and is designed to meet the needs. . . .
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?
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?
If you can post the triangle with either the blue or yellow colour face up, how many ways can it be posted altogether?
How can the same pieces of the tangram make this bowl before and after it was chipped? Use the interactivity to try and work out what is going on!
Mathematics is the study of patterns. Studying pattern is an
opportunity to observe, hypothesise, experiment, discover and
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 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.
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.
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.
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.
Exchange the positions of the two sets of counters in the least possible number of moves
These points all mark the vertices (corners) of ten hidden squares.
Can you find the 10 hidden squares?
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?
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?
Lyndon Baker describes how the Mobius strip and Euler's law can
introduce pupils to the idea of topology.
A group activity using visualisation of squares and triangles.
A game for 2 people. Take turns joining two dots, until your opponent is unable to move.
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 shape of wrapping paper that you would need to completely wrap this model?
Can you find a way of representing these arrangements of balls?
Exploring and predicting folding, cutting and punching holes and
A game for two players on a large squared space.
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 is the greatest number of counters you can place on the grid below without four of them lying at the corners of a square?
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?
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?
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,. . . .
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
This article looks at levels of geometric thinking and the types of
activities required to develop this thinking.
This challenge involves eight three-cube models made from
interlocking cubes. Investigate different ways of putting the
models together then compare your constructions.
Billy's class had a robot called Fred who could draw with chalk
held underneath him. What shapes did the pupils make Fred draw?
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?
What happens when you turn these cogs? Investigate the differences
between turning two cogs of different sizes and two cogs which are
A hundred square has been printed on both sides of a piece of
paper. What is on the back of 100? 58? 23? 19?
Here's a simple way to make a Tangram without any measuring or
Can you fit the tangram pieces into the outlines of the workmen?
Which of these dice are right-handed and which are left-handed?