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?
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!
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.
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. . . .
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
The opposite vertices of a square have coordinates (a,b) and (c,d). What are the coordinates of the other vertices?
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. . . .
To avoid losing think of another very well known game where the
patterns of play are similar.
On the 3D grid a strange (and deadly) animal is lurking. Using the tracking system can you locate this creature as quickly as possible?
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
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 mathematically themed crossword.
Can you discover whether this is a fair game?
Match pairs of cards so that they have equivalent ratios.
Re-arrange the pieces of the puzzle to form a rectangle and then to
form an equilateral triangle. Calculate the angles and lengths.
in how many ways can you place the numbers 1, 2, 3 … 9 in the
nine regions of the Olympic Emblem (5 overlapping circles) so that
the amount in each ring is the same?
Start with any number of counters in any number of piles. 2 players
take it in turns to remove any number of counters from a single
pile. The winner is the player to take the last counter.
Match the cards of the same value.
A metal puzzle which led to some mathematical questions.
How good are you at estimating angles?
Can you beat the computer in the challenging strategy game?
There are thirteen axes of rotational symmetry of a unit cube. Describe them all. What is the average length of the parts of the axes of symmetry which lie inside the cube?
Show that for any triangle it is always possible to construct 3
touching circles with centres at the vertices. Is it possible to
construct touching circles centred at the vertices of any polygon?
Can you beat Piggy in this simple dice game? Can you figure out
Piggy's strategy, and is there a better one?
Use Excel to explore multiplication of fractions.
Can you put the 25 coloured tiles into the 5 x 5 square so that no column, no row and no diagonal line have tiles of the same colour in them?
Use an Excel to investigate division. Explore the relationships
between the process elements using an interactive spreadsheet.
Use an interactive Excel spreadsheet to investigate factors and
A simple file for the Interactive whiteboard or PC screen,
demonstrating equivalent fractions.
Use an interactive Excel spreadsheet to explore number in this
Use Excel to investigate the effect of translations around a number
Help the bee to build a stack of blocks far enough to save his
friend trapped in the tower.
Use an Excel spreadsheet to explore long multiplication.
Use Excel to practise adding and subtracting fractions.
An Excel spreadsheet with an investigation.
A spherical balloon lies inside a wire frame. How much do you need
to deflate it to remove it from the frame if it remains a sphere?
A weekly challenge concerning prime numbers.
It is possible to identify a particular card out of a pack of 15
with the use of some mathematical reasoning. What is this reasoning
and can it be applied to other numbers of cards?
Have you seen this way of doing multiplication ?
With red and blue beads on a circular wire; 'put a red bead between
any two of the same colour and a blue between different colours
then remove the original beads'. Keep repeating this. What happens?
Six circles around a central circle make a flower. Watch the flower
as you change the radii in this circle packing. Prove that with the
given ratios of the radii the petals touch and fit perfectly.
Overlaying pentominoes can produce some effective patterns. Why not
use LOGO to try out some of the ideas suggested here?
Make and prove a conjecture about the cyclic quadrilateral
inscribed in a circle of radius r that has the maximum perimeter and the maximum area.
This set of resources for teachers offers interactive environments
to support work on graphical interpretation at Key Stage 4.
An environment that simulates a protractor carrying a right- angled
triangle of unit hypotenuse.
Can you set the logic gates so that the number of bulbs which are on is the same as the number of switches which are on?
A tool for generating random integers.
A collection of our favourite pictorial problems, one for each day
Here is a chance to play a fractions version of the classic
This game challenges you to locate hidden triangles in The White
Box by firing rays and observing where the rays exit the Box.