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?
A tilted square is a square with no horizontal sides. Can you
devise a general instruction for the construction of a square when
you are given just one of its sides?
Semi-regular tessellations combine two or more different regular polygons to fill the plane. Can you find all the semi-regular tessellations?
How many moves does it take to swap over some red and blue frogs? Do you have a method?
In a three-dimensional version of noughts and crosses, how many winning lines can you make?
Starting with four different triangles, imagine you have an
unlimited number of each type. How many different tetrahedra can
you make? Convince us you have found them all.
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. . . .
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.
How could Penny, Tom and Matthew work out how many chocolates there
are in different sized boxes?
On the graph there are 28 marked points. These points all mark the
vertices (corners) of eight hidden squares. Can you find the eight
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10
Charlie and Alison have been drawing patterns on coordinate grids. Can you picture where the patterns lead?
A 2 by 3 rectangle contains 8 squares and a 3 by 4 rectangle
contains 20 squares. What size rectangle(s) contain(s) exactly 100
squares? Can you find them all?
How many different symmetrical shapes can you make by shading triangles or squares?
Can you mark 4 points on a flat surface so that there are only two
different distances between them?
Billy's class had a robot called Fred who could draw with chalk
held underneath him. What shapes did the pupils make Fred draw?
Slide the pieces to move Khun Phaen past all the guards into the position on the right from which he can escape to freedom.
Exchange the positions of the two sets of counters in the least possible number of moves
Can you fit the tangram pieces into the outline of this goat and giraffe?
Can you fit the tangram pieces into the outline of this sports car?
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?
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?
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. . . .
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?
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?
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?
Imagine you are suspending a cube from one vertex (corner) and
allowing it to hang freely. Now imagine you are lowering it into
water until it is exactly half submerged. What shape does the
surface. . . .
How many different triangles can you make on a circular pegboard that has nine pegs?
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?
Can you make a 3x3 cube with these shapes made from small cubes?
A huge wheel is rolling past your window. What do you see?
Can you maximise the area available to a grazing goat?
Can you discover whether this is a fair game?
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?
Try this interactive strategy game for 2
What happens when you turn these cogs? Investigate the differences
between turning two cogs of different sizes and two cogs which are
Can you fit the tangram pieces into the outline of Granma T?
Can you fit the tangram pieces into the outline of Little Ming?
Bilbo goes on an adventure, before arriving back home. Using the
information given about his journey, can you work out where Bilbo
A rectangular field has two posts with a ring on top of each post.
There are two quarrelsome goats and plenty of ropes which you can
tie to their collars. How can you secure them so they can't. . . .
Given the nets of 4 cubes with the faces coloured in 4 colours, build a tower so that on each vertical wall no colour is repeated, that is all 4 colours appear.
Can you fit the tangram pieces into the outline of this telephone?
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 these rabbits?
In how many ways can you fit all three pieces together to make
shapes with line symmetry?
Can you fit the tangram pieces into the outline of the telescope and microscope?
Can you fit the tangram pieces into the outline of Wai Ping, Wah Ming and Chi Wing?
These points all mark the vertices (corners) of ten hidden squares.
Can you find the 10 hidden squares?
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