A and B are two interlocking cogwheels having p teeth and q teeth respectively. One tooth on B is painted red. Find the values of p and q for which the red tooth on B contacts every gap on the. . . .
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.
Slide the pieces to move Khun Phaen past all the guards into the position on the right from which he can escape to freedom.
Ask a friend to choose a number between 1 and 63. By identifying which of the six cards contains the number they are thinking of it is easy to tell them what the number is.
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 game for 2 players. Can be played online. One player has 1 red
counter, the other has 4 blue. The red counter needs to reach the
other side, and the blue needs to trap the red.
If you continue the pattern, can you predict what each of the following areas will be? Try to explain your prediction.
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?
An environment that enables you to investigate tessellations of
What can you say about the values of n that make $7^n + 3^n$ a multiple of 10? Are there other pairs of integers between 1 and 10 which have similar properties?
The opposite vertices of a square have coordinates (a,b) and (c,d). What are the coordinates of the other vertices?
This resource contains interactive problems to support work on
number sequences at Key Stage 4.
Triangle ABC has equilateral triangles drawn on its edges. Points
P, Q and R are the centres of the equilateral triangles. What can
you prove about the triangle PQR?
Here is a solitaire type environment for you to experiment with. Which targets can you reach?
Here is a chance to play a fractions version of the classic
Have you seen this way of doing multiplication ?
A tool for generating random integers.
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?
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. . . .
This game challenges you to locate hidden triangles in The White
Box by firing rays and observing where the rays exit the Box.
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.
Can you beat Piggy in this simple dice game? Can you figure out
Piggy's strategy, and is there a better one?
Four cards are shuffled and placed into two piles of two. Starting with the first pile of cards - turn a card over...
You win if all your cards end up in the trays before you run out of cards in. . . .
Can you give the coordinates of the vertices of the fifth point in
the patterm on this 3D grid?
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.
A collection of our favourite pictorial problems, one for each day
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?
Work out how to light up the single light. What's the rule?
The classic vector racing game brought to a screen near you.
These formulae are often quoted, but rarely proved. In this article, we derive the formulae for the volumes of a square-based pyramid and a cone, using relatively simple mathematical concepts.
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. . . .
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
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
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.
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?
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. . . .
Use Excel to explore multiplication of fractions.
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?
To avoid losing think of another very well known game where the
patterns of play are similar.
Can you find all the 4-ball shuffles?
Can you beat the computer in the challenging strategy game?
Practise your skills of proportional reasoning with this interactive haemocytometer.
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?
Match the cards of the same value.
This set of resources for teachers offers interactive environments
to support work on loci at Key Stage 4.
Balancing interactivity with springs and weights.
Investigate how logic gates work in circuits.
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?