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?
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
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?
Mathematics is the study of patterns. Studying pattern is an
opportunity to observe, hypothesise, experiment, discover and
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. . . .
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.
A group activity using visualisation of squares and triangles.
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. . . .
What is the greatest number of squares you can make by overlapping
What is the total area of the four outside triangles which are
outlined in red in this arrangement of squares inside each other?
Lyndon Baker describes how the Mobius strip and Euler's law can
introduce pupils to the idea of topology.
These points all mark the vertices (corners) of ten hidden squares.
Can you find the 10 hidden squares?
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?
Can you find a way of representing these arrangements of balls?
What is the shape of wrapping paper that you would need to completely wrap this model?
Choose a box and work out the smallest rectangle of paper needed to
wrap it so that it is completely covered.
Have a go at this 3D extension to the Pebbles problem.
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?
Can you fit the tangram pieces into the outlines of the candle and sundial?
Here's a simple way to make a Tangram without any measuring or
Which of these dice are right-handed and which are left-handed?
Can you fit the tangram pieces into the outline of Little Ming and Little Fung dancing?
Can you fit the tangram pieces into the outlines of the workmen?
What happens when you turn these cogs? Investigate the differences
between turning two cogs of different sizes and two cogs which are
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.
Make a cube out of straws and have a go at this practical
Can you fit the tangram pieces into the outlines of the chairs?
Can you fit the tangram pieces into the outline of this shape. How would you describe it?
Can you fit the tangram pieces into the outlines of the lobster, yacht and cyclist?
Can you fit the tangram pieces into the outline of the child walking home from school?
Can you fit the tangram pieces into the outlines of these people?
Can you fit the tangram pieces into the outlines of these clocks?
Where can you put the mirror across the square so that you can still "see" the whole square? How many different positions are possible?
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?
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?
Can you cut a regular hexagon into two pieces to make a
parallelogram? Try cutting it into three pieces to make a rhombus!
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.
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!
Which of the following cubes can be made from these nets?
This article looks at levels of geometric thinking and the types of
activities required to develop this thinking.
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 these convex shapes?
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 ...
Paint a stripe on a cardboard roll. Can you predict what will
happen when it is rolled across a sheet of paper?
This practical problem challenges you to make quadrilaterals with a loop of string. You'll need some friends to help!
Can you work out what shape is made when this piece of paper is folded up using the crease pattern shown?
Can you visualise what shape this piece of paper will make when it is folded?
Can you fit the tangram pieces into the outline of Little Ming?