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.
A metal puzzle which led to some mathematical questions.
Can you make a right-angled triangle on this peg-board by joining
up three points round the edge?
Can you beat the computer in the challenging strategy game?
Find the vertices of a pentagon given the midpoints of its sides.
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. . . .
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.
If you continue the pattern, can you predict what each of the following areas will be? Try to explain your prediction.
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. . . .
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 opposite vertices of a square have coordinates (a,b) and (c,d). What are the coordinates of the other vertices?
Can you give the coordinates of the vertices of the fifth point in
the patterm on this 3D grid?
This resource contains a range of problems and interactivities on
the theme of coordinates in two and three dimensions.
Can you discover whether this is a fair game?
Match pairs of cards so that they have equivalent ratios.
The interactive diagram has two labelled points, A and B. It is
designed to be used with the problem "Cushion Ball"
Discover a handy way to describe reorderings and solve our anagram
in the process.
An environment that enables you to investigate tessellations of
Use Excel to explore multiplication of fractions.
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?
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.
The classic vector racing game brought to a screen near you.
Square It game for an adult and child. Can you come up with a way of always winning this game?
A simple spinner that is equally likely to land on Red or Black. Useful if tossing a coin, dropping it, and rummaging about on the floor have lost their appeal. Needs a modern browser; if IE then at. . . .
This resource contains interactive problems to support work on
number sequences at Key Stage 4.
This set of resources for teachers offers interactive environments
to support work on loci at Key Stage 4.
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. . . .
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
What are the areas of these triangles? What do you notice? Can you generalise to other "families" of triangles?
When number pyramids have a sequence on the bottom layer, some interesting patterns emerge...
Match the cards of the same value.
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.
This is an interactivity in which you have to sort the steps in the
completion of the square into the correct order to prove the
formula for the solutions of quadratic equations.
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 collection of resources to support work on Factors and Multiples at Secondary level.
Help the bee to build a stack of blocks far enough to save his
friend trapped in the tower.
A group of interactive resources to support work on percentages Key
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.
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
An environment that simulates a protractor carrying a right- angled
triangle of unit hypotenuse.
Use an interactive Excel spreadsheet to investigate factors and
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?
A simple file for the Interactive whiteboard or PC screen,
demonstrating equivalent fractions.
Use an interactive Excel spreadsheet to explore number in this