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?
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.
What are the areas of these triangles? What do you notice? Can you generalise to other "families" of triangles?
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
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?
To avoid losing think of another very well known game where the
patterns of play are similar.
This resource contains a range of problems and interactivities on
the theme of coordinates in two and three dimensions.
The interactive diagram has two labelled points, A and B. It is
designed to be used with the problem "Cushion Ball"
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?
Match pairs of cards so that they have equivalent ratios.
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 discover whether this is a fair game?
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!
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?
This resources contains a series of interactivities designed to
support work on transformations at Key Stage 4.
Discover a handy way to describe reorderings and solve our anagram
in the process.
Do you know how to find the area of a triangle? You can count the
squares. What happens if we turn the triangle on end? Press the
button and see. Try counting the number of units in the triangle
now. . . .
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.
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
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?
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. . . .
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?
Can you give the coordinates of the vertices of the fifth point in
the patterm on this 3D grid?
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 collection of resources to support work on Factors and Multiples at Secondary level.
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. . . .
Can you make a right-angled triangle on this peg-board by joining
up three points round the edge?
On the 3D grid a strange (and deadly) animal is lurking. Using the tracking system can you locate this creature as quickly as possible?
An environment that enables you to investigate tessellations of
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 good are you at finding the formula for a number pattern ?
A java applet that takes you through the steps needed to solve a
Diophantine equation of the form Px+Qy=1 using Euclid's algorithm.
An Excel spreadsheet with an investigation.
Use Excel to practise adding and subtracting fractions.
Find the vertices of a pentagon given the midpoints of its sides.
Use this animation to experiment with lotteries. Choose how many
balls to match, how many are in the carousel, and how many draws to
make at once.
This set of resources for teachers offers interactive environments
to support work on graphical interpretation at Key Stage 4.
This game challenges you to locate hidden triangles in The White
Box by firing rays and observing where the rays exit the Box.
Practise your skills of proportional reasoning with this interactive haemocytometer.
A collection of our favourite pictorial problems, one for each day
A tool for generating random integers.
An environment that simulates a protractor carrying a right- angled
triangle of unit hypotenuse.
This resource contains interactive problems to support work on
number sequences at Key Stage 4.
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
Here is a chance to play a fractions version of the classic
The classic vector racing game brought to a screen near you.
A group of interactive resources to support work on percentages Key