Mathematics is the study of patterns. Studying pattern is an
opportunity to observe, hypothesise, experiment, discover and
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?
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. . . .
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. . . .
On the graph there are 28 marked points. These points all mark the
vertices (corners) of eight hidden squares. Can you find the eight
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?
Have a go at this 3D extension to the Pebbles problem.
What is the shape of wrapping paper that you would need to completely wrap this model?
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 find a way of representing these arrangements of balls?
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.
In each of the pictures the invitation is for you to: Count what you see. Identify how you think the pattern would continue.
The image in this problem is part of a piece of equipment found in the playground of a school. How would you describe it to someone over the phone?
This practical problem challenges you to make quadrilaterals with a loop of string. You'll need some friends to help!
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
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.
These points all mark the vertices (corners) of ten hidden squares.
Can you find the 10 hidden squares?
What is the greatest number of squares you can make by overlapping
Here are some arrangements of circles. How many circles would I need to make the next size up for each? Can you create your own arrangement and investigate the number of circles it needs?
Can you picture where this letter "F" will be on the grid if you
flip it in these different ways?
What can you see? What do you notice? What questions can you ask?
Can you work out what kind of rotation produced this pattern of
pegs in our pegboard?
Can you fit the tangram pieces into the outlines of Mai Ling and Chi Wing?
Can you fit the tangram pieces into the outlines of the watering can and man in a boat?
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?
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 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?
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!
Can you fit the tangram pieces into the outline of this shape. How would you describe it?
Where can you put the mirror across the square so that you can still "see" the whole square? How many different positions are possible?
Can you fit the tangram pieces into the outlines of the chairs?
Can you fit the tangram pieces into the outlines of the lobster, yacht and cyclist?
Can you fit the tangram pieces into the outlines of these clocks?
Can you fit the tangram pieces into the outline of the child walking home from school?
Which of the following cubes can be made from these nets?
Make a cube out of straws and have a go at this practical
Can you cut a regular hexagon into two pieces to make a
parallelogram? Try cutting it into three pieces to make a rhombus!
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 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?
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.
What happens when you turn these cogs? Investigate the differences
between turning two cogs of different sizes and two cogs which are
Which of these dice are right-handed and which are left-handed?
Can you fit the tangram pieces into the outline of the rocket?
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?
For this task, you'll need an A4 sheet and two A5 transparent sheets. Decide on a way of arranging the A5 sheets on top of the A4 sheet and explore ...