What is the total area of the four outside triangles which are
outlined in red in this arrangement of squares inside each other?
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. . . .
Four rods, two of length a and two of length b, are linked to form
a kite. The linkage is moveable so that the angles change. What is
the maximum area of the kite?
A group activity using visualisation of squares and triangles.
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?
Billy's class had a robot called Fred who could draw with chalk
held underneath him. What shapes did the pupils make Fred draw?
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
How many different triangles can you make on a circular pegboard that has nine pegs?
Draw three straight lines to separate these shapes into four groups
- each group must contain one of each shape.
ABCDEFGH is a 3 by 3 by 3 cube. Point P is 1/3 along AB (that is AP
: PB = 1 : 2), point Q is 1/3 along GH and point R is 1/3 along ED.
What is the area of the triangle PQR?
How many DIFFERENT quadrilaterals can be made by joining the dots
on the 8-point circle?
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 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?
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?
Can you visualise what shape this piece of paper will make when it is folded?
If you have only 40 metres of fencing available, what is the maximum area of land you can fence off?
Can you fit the tangram pieces into the outline of this telephone?
Can you fit the tangram pieces into the outline of these rabbits?
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?
Can you fit the tangram pieces into the outline of the telescope and microscope?
The whole set of tiles is used to make a square. This has a green and blue border. There are no green or blue tiles anywhere in the square except on this border. How many tiles are there in the set?
Can you fit the tangram pieces into the outline of the rocket?
Can you fit the tangram pieces into the outline of this junk?
Can you fit the tangram pieces into the outline of this plaque design?
Here you see the front and back views of a dodecahedron. Each
vertex has been numbered so that the numbers around each pentagonal
face add up to 65. Can you find all the missing numbers?
Can you cut up a square in the way shown and make the pieces into a
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?
Make a flower design using the same shape made out of different sizes of paper.
ABC is an equilateral triangle and P is a point in the interior of
the triangle. We know that AP = 3cm and BP = 4cm. Prove that CP
must be less than 10 cm.
Can you fit the tangram pieces into the outline of Granma T?
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?
Which hexagons tessellate?
Can you fit the tangram pieces into the outline of Wai Ping, Wah Ming and Chi Wing?
Draw some isosceles triangles with an area of $9$cm$^2$ and a vertex at (20,20). If all the vertices must have whole number coordinates, how many is it possible to draw?
Can you fit the tangram pieces into the outline of Little Ming playing the board game?
This problem invites you to build 3D shapes using two different
triangles. Can you make the shapes from the pictures?
Can you cut a regular hexagon into two pieces to make a
parallelogram? Try cutting it into three pieces to make a rhombus!
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
Can you fit the tangram pieces into the outline of these convex shapes?
Can you fit the tangram pieces into the outlines of the workmen?
Here are four tiles. They can be arranged in a 2 by 2 square so that this large square has a green edge. If the tiles are moved around, we can make a 2 by 2 square with a blue edge... Now try to. . . .
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?
Can you fit the tangram pieces into the outline of Little Ming and Little Fung dancing?
Rectangles are considered different if they vary in size or have different locations. How many different rectangles can be drawn on a chessboard?
Players take it in turns to choose a dot on the grid. The winner is the first to have four dots that can be joined to form a square.
ABCD is a regular tetrahedron and the points P, Q, R and S are the midpoints of the edges AB, BD, CD and CA. Prove that PQRS is a square.
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. . . .
Can you fit the tangram pieces into the outlines of the watering can and man in a boat?
An irregular tetrahedron is composed of four different triangles.
Can such a tetrahedron be constructed where the side lengths are 4,
5, 6, 7, 8 and 9 units of length?
Can you fit the tangram pieces into the outlines of Mai Ling and Chi Wing?