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
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 the frequency distribution for ordinary English, and use it to help you crack the code.
The opposite vertices of a square have coordinates (a,b) and (c,d). What are the coordinates of the other vertices?
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?
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.
Try entering different sets of numbers in the number pyramids. How does the total at the top change?
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
A game for 2 players that can be played online. Players take it in turns to select a word from the 9 words given. The aim is to select all the occurrences of the same letter.
Euler discussed whether or not it was possible to stroll around Koenigsberg crossing each of its seven bridges exactly once. Experiment with different numbers of islands and bridges.
The number of plants in Mr McGregor's magic potting shed increases
overnight. He'd like to put the same number of plants in each of
his gardens, planting one garden each day. How can he do it?
Triangle numbers can be represented by a triangular array of
squares. What do you notice about the sum of identical triangle
Can you find all the 4-ball shuffles?
Match the cards of the same value.
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.
How good are you at finding the formula for a number pattern ?
A game for two people, or play online. Given a target number, say 23, and a range of numbers to choose from, say 1-4, players take it in turns to add to the running total to hit their target.
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.
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
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.
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?
The interactive diagram has two labelled points, A and B. It is
designed to be used with the problem "Cushion Ball"
Can you make a right-angled triangle on this peg-board by joining
up three points round the edge?
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. . . .
Can you beat Piggy in this simple dice game? Can you figure out
Piggy's strategy, and is there a better one?
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. . . .
Can you give the coordinates of the vertices of the fifth point in
the patterm on this 3D grid?
Use Excel to explore multiplication of fractions.
On the 3D grid a strange (and deadly) animal is lurking. Using the tracking system can you locate this creature as quickly as possible?
Discover a handy way to describe reorderings and solve our anagram
in the process.
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. . . .
A collection of our favourite pictorial problems, one for each day
Here is a chance to play a fractions version of the classic
Practise your skills of proportional reasoning with this interactive haemocytometer.
This resource contains interactive problems to support work on
number sequences at Key Stage 4.
A tool for generating random integers.
This game challenges you to locate hidden triangles in The White
Box by firing rays and observing where the rays exit the Box.
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. . . .
The classic vector racing game brought to a screen near you.
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.
Is this a fair game? How many ways are there of creating a fair
game by adding odd and even numbers?
A metal puzzle which led to some mathematical questions.
Match pairs of cards so that they have equivalent ratios.
We can show that (x + 1)² = x² + 2x + 1 by considering
the area of an (x + 1) by (x + 1) square. Show in a similar way
that (x + 2)² = x² + 4x + 4
To avoid losing think of another very well known game where the
patterns of play are similar.
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...
This set of resources for teachers offers interactive environments
to support work on loci at Key Stage 4.
Can you beat the computer in the challenging strategy game?