A circle rolls around the outside edge of a square so that its circumference always touches the edge of the square. Can you describe the locus of the centre of the circle?
Choose a box and work out the smallest rectangle of paper needed to
wrap it so that it is completely covered.
What is the total area of the four outside triangles which are
outlined in red in this arrangement of squares inside each other?
See if you can anticipate successive 'generations' of the two
animals shown here.
It is possible to dissect any square into smaller squares. What is
the minimum number of squares a 13 by 13 square can be dissected
Can you maximise the area available to a grazing goat?
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
Three circles have a maximum of six intersections with each other.
What is the maximum number of intersections that a hundred circles
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.
Looking at the picture of this Jomista Mat, can you decribe what
you see? Why not try and make one yourself?
In a right angled triangular field, three animals are tethered to posts at the midpoint of each side. Each rope is just long enough to allow the animal to reach two adjacent vertices. Only one animal. . . .
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?
You can move the 4 pieces of the jigsaw and fit them into both
outlines. Explain what has happened to the missing one unit of
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.
Points P, Q, R and S each divide the sides AB, BC, CD and DA respectively in the ratio of 2 : 1. Join the points. What is the area of the parallelogram PQRS in relation to the original rectangle?
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?
Seven small rectangular pictures have one inch wide frames. The
frames are removed and the pictures are fitted together like a
jigsaw to make a rectangle of length 12 inches. Find the dimensions
of. . . .
Is it possible to remove ten unit cubes from a 3 by 3 by 3 cube made from 27 unit cubes so that the surface area of the remaining solid is the same as the surface area of the original 3 by 3 by 3. . . .
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?
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.
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 work out what shape is made by folding in this way? Why not create some patterns using this shape but in different sizes?
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?
This article for teachers describes a project which explores
thepower of storytelling to convey concepts and ideas to children.
This problem invites you to build 3D shapes using two different
triangles. Can you make the shapes from the pictures?
Which of the following cubes can be made from these nets?
Can you work out what is wrong with the cogs on a UK 2 pound coin?
Can you fit the tangram pieces into the outline of this shape. How would you describe it?
What shape is made when you fold using this crease pattern? Can you make a ring design?
Can you fit the tangram pieces into the outline of Little Ming?
On which of these shapes can you trace a path along all of its
edges, without going over any edge twice?
Can you visualise what shape this piece of paper will make when it is folded?
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?
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?
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?
Take a rectangle of paper and fold it in half, and half again, to
make four smaller rectangles. How many different ways can you fold
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.
Can you fit the tangram pieces into the outline of Little Ming playing the board game?
Can you fit the tangram pieces into the outline of Little Fung at the table?
Can you fit the tangram pieces into the outlines of the lobster, yacht and cyclist?
Imagine a wheel with different markings painted on it at regular
intervals. Can you predict the colour of the 18th mark? The 100th
Can you fit the tangram pieces into the outlines of the chairs?
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 clocks?
Can you fit the tangram pieces into the outline of this brazier for roasting chestnuts?
Can you fit the tangram pieces into the outlines of these people?
Can you fit the tangram pieces into the outline of Granma T?
Make a flower design using the same shape made out of different sizes of paper.