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?
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 is the greatest number of squares you can make by overlapping
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 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.
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?
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. . . .
Move four sticks so there are exactly four triangles.
A game for 1 or 2 people. Use the interactive version, or play with friends. Try to round up as many counters as possible.
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 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.
Mathematics is the study of patterns. Studying pattern is an
opportunity to observe, hypothesise, experiment, discover and
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.
Lyndon Baker describes how the Mobius strip and Euler's law can
introduce pupils to the idea of topology.
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?
If you can post the triangle with either the blue or yellow colour face up, how many ways can it be posted altogether?
These points all mark the vertices (corners) of ten hidden squares.
Can you find the 10 hidden squares?
Exchange the positions of the two sets of counters in the least possible number of moves
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?
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.
A game for two players on a large squared space.
Exploring and predicting folding, cutting and punching holes and
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?
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?
Can you find a way of representing these arrangements of balls?
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?
What is the shape of wrapping paper that you would need to completely wrap this model?
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?
This article introduces the idea of generic proof for younger children and illustrates how one example can offer a proof of a general result through unpacking its underlying structure.
Create a pattern on the left-hand grid. How could you extend your pattern on the right-hand grid?
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,. . . .
Here's a simple way to make a Tangram without any measuring or
Can you fit the tangram pieces into the outline of this goat and giraffe?
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?
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.
What happens when you turn these cogs? Investigate the differences
between turning two cogs of different sizes and two cogs which are
Can you fit the tangram pieces into the outlines of the workmen?
Here are shadows of some 3D shapes. What shapes could have made
Which of these dice are right-handed and which are left-handed?
Investigate how the four L-shapes fit together to make an enlarged
L-shape. You could explore this idea with other shapes too.