See if you can anticipate successive 'generations' of the two
animals shown here.
Can you recreate these designs? What are the basic units? What
movement is required between each unit? Some elegant use of
procedures will help - variables not essential.
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?
How can you make an angle of 60 degrees by folding a sheet of paper
The second in a series of articles on visualising and modelling shapes in the history of astronomy.
Can you cut up a square in the way shown and make the pieces into a
This article explores ths history of theories about the shape of our planet. It is the first in a series of articles looking at the significance of geometric shapes in the history of astronomy.
A train leaves on time. After it has gone 8 miles (at 33mph) the driver looks at his watch and sees that the hour hand is exactly over the minute hand. When did the train leave the station?
A bus route has a total duration of 40 minutes. Every 10 minutes,
two buses set out, one from each end. How many buses will one bus
meet on its way from one end to the other end?
Here's a simple way to make a Tangram without any measuring or
You have 27 small cubes, 3 each of nine colours. Use the small cubes to make a 3 by 3 by 3 cube so that each face of the bigger cube contains one of every colour.
Every day at noon a boat leaves Le Havre for New York while another
boat leaves New York for Le Havre. The ocean crossing takes seven
days. How many boats will each boat cross during their journey?
Paint a stripe on a cardboard roll. Can you predict what will
happen when it is rolled across a sheet of paper?
Have a look at what happens when you pull a reef knot and a granny
knot tight. Which do you think is best for securing things
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?
Which of the following cubes can be made from these nets?
What shape is made when you fold using this crease pattern? Can you make a ring design?
Make a flower design using the same shape made out of different sizes of paper.
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 outline of this shape. How would you describe it?
Can you fit the tangram pieces into the outline of Granma T?
Can you predict when you'll be clapping and when you'll be clicking
if you start this rhythm? How about when a friend begins a new
rhythm at the same time?
Can you fit the tangram pieces into the outline of Little Ming?
A magician took a suit of thirteen cards and held them in his hand
face down. Every card he revealed had the same value as the one he
had just finished spelling. How did this work?
Use the interactivity to play two of the bells in a pattern. How do
you know when it is your turn to ring, and how do you know which
bell to ring?
In how many ways can you fit two of these yellow triangles
together? Can you predict the number of ways two blue triangles can
be fitted together?
Investigate the number of paths you can take from one vertex to
another in these 3D shapes. Is it possible to take an odd number
and an even number of paths to the same vertex?
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!
This article for teachers describes a project which explores
thepower of storytelling to convey concepts and ideas to children.
Can you visualise what shape this piece of paper will make when it is folded?
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?
Cut four triangles from a square as shown in the picture. How many
different shapes can you make by fitting the four triangles back
This problem invites you to build 3D shapes using two different
triangles. Can you make the shapes from the pictures?
Can you fit the tangram pieces into the outlines of the chairs?
Use the interactivity to listen to the bells ringing a pattern. Now
it's your turn! Play one of the bells yourself. How do you know
when it is your turn to ring?
On which of these shapes can you trace a path along all of its
edges, without going over any edge twice?
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 ...
Draw three straight lines to separate these shapes into four groups
- each group must contain one of each shape.
Exchange the positions of the two sets of counters in the least possible number of moves
Use the lines on this figure to show how the square can be divided into 2 halves, 3 thirds, 6 sixths and 9 ninths.
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?
How many DIFFERENT quadrilaterals can be made by joining the dots
on the 8-point circle?
Can you fit the tangram pieces into the outline of this telephone?
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?
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 people?
Can you fit the tangram pieces into the outline of this brazier for roasting chestnuts?
Can you fit the tangram pieces into the outline of Little Ming playing the board game?