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.
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?
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 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.
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 work out what shape is made when this piece of paper is folded up using the crease pattern shown?
What can you see? What do you notice? What questions can you ask?
A group activity using visualisation of squares and triangles.
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. . . .
What is the greatest number of squares you can make by overlapping
Move four sticks so there are exactly four triangles.
Lyndon Baker describes how the Mobius strip and Euler's law can
introduce pupils to the idea of topology.
Mathematics is the study of patterns. Studying pattern is an
opportunity to observe, hypothesise, experiment, discover and
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. . . .
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?
These points all mark the vertices (corners) of ten hidden squares.
Can you find the 10 hidden squares?
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?
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?
If you can post the triangle with either the blue or yellow colour face up, how many ways can it be posted altogether?
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?
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?
Can you find a way of representing these arrangements of balls?
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?
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?
How many pieces of string have been used in these patterns? Can you
describe how you know?
How many loops of string have been used to make these patterns?
Square It game for an adult and child. Can you come up with a way of always winning this game?
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?
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?
Exploring and predicting folding, cutting and punching holes and
Which of these dice are right-handed and which are left-handed?
Design an arrangement of display boards in the school hall which fits the requirements of different people.
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 outlines of the watering can and man in a boat?
Can you fit the tangram pieces into the outline of this goat and giraffe?
Can you fit the tangram pieces into the outline of these convex shapes?
Can you fit the tangram pieces into the outline of this junk?
A game for two players. You'll need some counters.
Can you fit the tangram pieces into the outline of these rabbits?
Can you fit the tangram pieces into the outline of this plaque design?
Can you fit the tangram pieces into the outline of the rocket?
Here are shadows of some 3D shapes. What shapes could have made
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 outlines of Mai Ling and Chi Wing?
This article looks at levels of geometric thinking and the types of
activities required to develop this thinking.