On the 3D grid a strange (and deadly) animal is lurking. Using the tracking system can you locate this creature as quickly as possible?
There are 27 small cubes in a 3 x 3 x 3 cube, 54 faces being
visible at any one time. Is it possible to reorganise these cubes
so that by dipping the large cube into a pot of paint three times
you. . . .
This is an interactive net of a Rubik's cube. Twists of the 3D cube become mixes of the squares on the 2D net. Have a play and see how many scrambles you can undo!
The opposite vertices of a square have coordinates (a,b) and (c,d). What are the coordinates of the other vertices?
P is a point on the circumference of a circle radius r which rolls,
without slipping, inside a circle of radius 2r. What is the locus
To avoid losing think of another very well known game where the
patterns of play are similar.
Place a red counter in the top left corner of a 4x4 array, which is
covered by 14 other smaller counters, leaving a gap in the bottom
right hand corner (HOME). What is the smallest number of moves. . . .
A right-angled isosceles triangle is rotated about the centre point
of a square. What can you say about the area of the part of the
square covered by the triangle as it rotates?
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
Square It game for an adult and child. Can you come up with a way of always winning this game?
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.
A square of area 3 square units cannot be drawn on a 2D grid so that each of its vertices have integer coordinates, but can it be drawn on a 3D grid? Investigate squares that can be drawn.
A game for 2 players
Can you find a rule which connects consecutive triangular numbers?
Can you find a rule which relates triangular numbers to square numbers?
Show that all pentagonal numbers are one third of a triangular number.
Watch these videos to see how Phoebe, Alice and Luke chose to draw 7 squares. How would they draw 100?
Charlie and Alison have been drawing patterns on coordinate grids. Can you picture where the patterns lead?
Two boats travel up and down a lake. Can you picture where they
will cross if you know how fast each boat is travelling?
A game for 2 people. Take turns joining two dots, until your opponent is unable to move.
Find the point whose sum of distances from the vertices (corners)
of a given triangle is a minimum.
Bilbo goes on an adventure, before arriving back home. Using the
information given about his journey, can you work out where Bilbo
Can you discover whether this is a fair game?
Simple additions can lead to intriguing results...
Glarsynost lives on a planet whose shape is that of a perfect
regular dodecahedron. Can you describe the shortest journey she can
make to ensure that she will see every part of the planet?
A 10x10x10 cube is made from 27 2x2 cubes with corridors between
them. Find the shortest route from one corner to the opposite
The triangle OMN has vertices on the axes with whole number co-ordinates. How many points with whole number coordinates are there on the hypotenuse MN?
A and C are the opposite vertices of a square ABCD, and have
coordinates (a,b) and (c,d), respectively. What are the coordinates
of the vertices B and D? What is the area of the square?
Some students have been working out the number of strands needed for different sizes of cable. Can you make sense of their solutions?
Can you make sense of the charts and diagrams that are created and used by sports competitors, trainers and statisticians?
Can you describe this route to infinity? Where will the arrows take you next?
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?
Build gnomons that are related to the Fibonacci sequence and try to
explain why this is possible.
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 reader is invited to investigate changes (or permutations) in the ringing of church bells, illustrated by braid diagrams showing the order in which the bells are rung.
This is a simple version of an ancient game played all over the world. It is also called Mancala. What tactics will increase your chances of winning?
Two intersecting circles have a common chord AB. The point C moves
on the circumference of the circle C1. The straight lines CA and CB
meet the circle C2 at E and F respectively. As the point C. . . .
Can you cross each of the seven bridges that join the north and south of the river to the two islands, once and once only, without retracing your steps?
A cyclist and a runner start off simultaneously around a race track each going at a constant speed. The cyclist goes all the way around and then catches up with the runner. He then instantly turns. . . .
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.
A package contains a set of resources designed to develop pupils'
mathematical thinking. This package places a particular emphasis on
“visualising” and is designed to meet the needs. . . .
Show that among the interior angles of a convex polygon there
cannot be more than three acute angles.
How efficiently can you pack together disks?
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.
Mathematics is the study of patterns. Studying pattern is an
opportunity to observe, hypothesise, experiment, discover and
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?
Can you mark 4 points on a flat surface so that there are only two
different distances between them?
In how many ways can you fit all three pieces together to make
shapes with line symmetry?
See if you can anticipate successive 'generations' of the two
animals shown here.