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?
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?
How can you make an angle of 60 degrees by folding a sheet of paper
The triangle ABC is equilateral. The arc AB has centre C, the arc
BC has centre A and the arc CA has centre B. Explain how and why
this shape can roll along between two parallel tracks.
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?
What is the shape of wrapping paper that you would need to completely wrap this model?
Here is a solitaire type environment for you to experiment with. Which targets can you reach?
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?
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?
Is it possible to rearrange the numbers 1,2......12 around a clock
face in such a way that every two numbers in adjacent positions
differ by any of 3, 4 or 5 hours?
Slide the pieces to move Khun Phaen past all the guards into the position on the right from which he can escape to freedom.
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. . . .
The aim of the game is to slide the green square from the top right
hand corner to the bottom left hand corner in the least number of
Which hexagons tessellate?
The image in this problem is part of a piece of equipment found in the playground of a school. How would you describe it to someone over the phone?
Lyndon Baker describes how the Mobius strip and Euler's law can
introduce pupils to the idea of topology.
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.
Anne completes a circuit around a circular track in 40 seconds.
Brenda runs in the opposite direction and meets Anne every 15
seconds. How long does it take Brenda to run around the track?
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?
A half-cube is cut into two pieces by a plane through the long diagonal and at right angles to it. Can you draw a net of these pieces? Are they identical?
The diagram shows a very heavy kitchen cabinet. It cannot be lifted but it can be pivoted around a corner. The task is to move it, without sliding, in a series of turns about the corners so that it. . . .
Charlie and Alison have been drawing patterns on coordinate grids. Can you picture where the patterns lead?
Choose a couple of the sequences. Try to picture how to make the next, and the next, and the next... Can you describe your reasoning?
Draw a pentagon with all the diagonals. This is called a pentagram.
How many diagonals are there? How many diagonals are there in a
hexagram, heptagram, ... Does any pattern occur when looking at. . . .
Mathematics is the study of patterns. Studying pattern is an
opportunity to observe, hypothesise, experiment, discover and
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. . . .
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.
Triangle numbers can be represented by a triangular array of squares. What do you notice about the sum of identical triangle numbers?
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?
Show that among the interior angles of a convex polygon there
cannot be more than three acute angles.
A standard die has the numbers 1, 2 and 3 are opposite 6, 5 and 4 respectively so that opposite faces add to 7? If you make standard dice by writing 1, 2, 3, 4, 5, 6 on blank cubes you will find. . . .
At the time of writing the hour and minute hands of my clock are at
right angles. How long will it be before they are at right angles
If you can copy a network without lifting your pen off the paper and without drawing any line twice, then it is traversable.
Decide which of these diagrams are traversable.
A game for 2 players
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. . . .
A 3x3x3 cube may be reduced to unit cubes in six saw cuts. If after
every cut you can rearrange the pieces before cutting straight
through, can you do it in fewer?
Given a 2 by 2 by 2 skeletal cube with one route `down' the cube.
How many routes are there from A to B?
A Hamiltonian circuit is a continuous path in a graph that passes through each of the vertices exactly once and returns to the start.
How many Hamiltonian circuits can you find in these graphs?
A huge wheel is rolling past your window. What do you see?
Blue Flibbins are so jealous of their red partners that they will
not leave them on their own with any other bue Flibbin. What is the
quickest way of getting the five pairs of Flibbins safely to. . . .
Use the animation to help you work out how many lines are needed to draw mystic roses of different sizes.
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
What would be the smallest number of moves needed to move a Knight
from a chess set from one corner to the opposite corner of a 99 by
99 square board?
In the game of Noughts and Crosses there are 8 distinct winning
lines. How many distinct winning lines are there in a game played
on a 3 by 3 by 3 board, with 27 cells?
On the graph there are 28 marked points. These points all mark the
vertices (corners) of eight hidden squares. Can you find the eight
Bilbo goes on an adventure, before arriving back home. Using the
information given about his journey, can you work out where Bilbo
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?
How could Penny, Tom and Matthew work out how many chocolates there
are in different sized boxes?
Have a go at this 3D extension to the Pebbles problem.