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
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.
Try ringing hand bells for yourself with interactive versions of
Diagram 2 (Plain Hunt Minimus) and Diagram 3 described in the
article 'Ding Dong Bell'.
Can you discover whether this is a fair game?
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?
To avoid losing think of another very well known game where the
patterns of play are similar.
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.
Can you be the first to complete a row of three?
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.
The opposite vertices of a square have coordinates (a,b) and (c,d). What are the coordinates of the other vertices?
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?
Find all the ways of placing the numbers 1 to 9 on a W shape, with
3 numbers on each leg, so that each set of 3 numbers has the same
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. . . .
On the 3D grid a strange (and deadly) animal is lurking. Using the tracking system can you locate this creature as quickly as possible?
Match pairs of cards so that they have equivalent ratios.
This resources contains a series of interactivities designed to
support work on transformations at Key Stage 4.
A mathematically themed crossword.
Charlie likes tablecloths that use as many colours as possible, but insists that his tablecloths have some symmetry. Can you work out how many colours he needs for different tablecloth designs?
Find the vertices of a pentagon given the midpoints of its sides.
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.
Match the cards of the same value.
Here is a chance to play a fractions version of the classic
Can you beat the computer in the challenging strategy game?
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. . . .
Can you beat Piggy in this simple dice game? Can you figure out
Piggy's strategy, and is there a better one?
A point P is selected anywhere inside an equilateral triangle. What
can you say about the sum of the perpendicular distances from P to
the sides of the triangle? Can you prove your conjecture?
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
A counter is placed in the bottom right hand corner of a grid. You
toss a coin and move the star according to the following rules: ...
What is the probability that you end up in the top left-hand. . . .
Help the bee to build a stack of blocks far enough to save his
friend trapped in the tower.
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!
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?
This set of resources for teachers offers interactive environments
to support work on loci at Key Stage 4.
Use Excel to practise adding and subtracting fractions.
An Excel spreadsheet with an investigation.
Investigate how logic gates work in circuits.
This resource contains interactive problems to support work on
number sequences at Key Stage 4.
Is this a fair game? How many ways are there of creating a fair
game by adding odd and even numbers?
How good are you at finding the formula for a number pattern ?
Use an interactive Excel spreadsheet to investigate factors and
A metal puzzle which led to some mathematical questions.
Take any parallelogram and draw squares on the sides of the
parallelogram. What can you prove about the quadrilateral formed by
joining the centres of these squares?
Use an Excel spreadsheet to explore long multiplication.
Overlaying pentominoes can produce some effective patterns. Why not
use LOGO to try out some of the ideas suggested here?
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.
When number pyramids have a sequence on the bottom layer, some interesting patterns emerge...
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?
Balancing interactivity with springs and weights.
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?
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?