What is the shape and dimensions of a box that will contain six cups and have as small a surface area as possible.
Chris is enjoying a swim but needs to get back for lunch. If she can swim at 3 m/s and run at 7m/sec, how far along the bank should she land in order to get back as quickly as possible?
The builders have dug a hole in the ground to be filled with concrete for the foundations of our garage. How many cubic metres of ready-mix concrete should the builders order to fill this hole to. . . .
Sometime during every hour the minute hand lies directly above the
hour hand. At what time between 4 and 5 o'clock does this happen?
Christmas trees are planted in a rectangular array of 10 rows and
12 columns. The farmer chooses the shortest tree in each of the
columns... the tallest tree from each of the rows ... Which is. . . .
This month there is a Friday the thirteenth and this year there are
three. Can you explain why every year must contain at least one
Friday the thirteenth?
Is this eco-system sustainable?
The second in a series of articles on visualising and modelling shapes in the history of astronomy.
The King showed the Princess a map of the maze and the Princess was
allowed to decide which room she would wait in. She was not allowed
to send a copy to her lover who would have to guess which path. . . .
In a league of 5 football teams which play in a round robin
tournament show that it is possible for all five teams to be league
A manager of a forestry company has to decide which trees to plant.
What strategy for planting and felling would you recommend to the
manager in order to maximise the profit?
This article for students gives some instructions about how to make some different braids.
Basic strategy games are particularly suitable as starting points
for investigations. Players instinctively try to discover a winning
strategy, and usually the best way to do this is to analyse. . . .
If it takes four men one day to build a wall, how long does it take
60,000 men to build a similar wall?
This article for pupils gives an introduction to Celtic knotwork
patterns and a feel for how you can draw them.
How do you write a computer program that creates the illusion of stretching elastic bands between pegs of a Geoboard? The answer contains some surprising mathematics.
Explore the transformations and comment on what you find.
Use the computer to model an epidemic. Try out public health policies to control the spread of the epidemic, to minimise the number of sick days and deaths.
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?
A bus route has a total duration of 40 minutes. Every 10 minutes,
two buses set out, one from each end. How many buses will one bus
meet on its way from one end to the other end?
Mike and Monisha meet at the race track, which is 400m round. Just to make a point, Mike runs anticlockwise whilst Monisha runs clockwise. Where will they meet on their way around and will they ever. . . .
A ladder 3m long rests against a wall with one end a short distance from its base. Between the wall and the base of a ladder is a garden storage box 1m tall and 1m high. What is the maximum. . . .
This article for students introduces the idea of naming knots using numbers. You'll need some paper and something to write with handy!
bioNRICH is the area of the stemNRICH site devoted to the
mathematics underlying the study of the biological sciences,
designed to help develop the mathematics required to get the most
from your. . . .
PhysNRICH is the area of the StemNRICH site devoted to the mathematics underlying the study of physics
Formulate and investigate a simple mathematical model for the design of a table mat.
What shapes should Elly cut out to make a witch's hat? How can she make a taller hat?
Build a scaffold out of drinking-straws to support a cup of water
Simple models which help us to investigate how epidemics grow and die out.
Your school has been left a million pounds in the will of an ex-
pupil. What model of investment and spending would you use in order
to ensure the best return on the money?
Investigate circuits and record your findings in this simple introduction to truth tables and logic.
Fancy a game of cricket? Here is a mathematical version you can play indoors without breaking any windows.
Can you suggest a curve to fit some experimental data? Can you work out where the data might have come from?
In this article for teachers, Alan Parr looks at ways that
mathematics teaching and learning can start from the useful and
interesting things can we do with the subject, including. . . .
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.
32 x 38 = 30 x 40 + 2 x 8; 34 x 36 = 30 x 40 + 4 x 6; 56 x 54 = 50
x 60 + 6 x 4; 73 x 77 = 70 x 80 + 3 x 7 Verify and generalise if
Suppose you are a bellringer. Can you find the changes so that,
starting and ending with a round, all the 24 possible permutations
are rung once each and only once?
The third installment in our series on the shape of astronomical systems, this article explores galaxies and the universe beyond our solar system.
Learn about the link between logical arguments and electronic circuits. Investigate the logical connectives by making and testing your own circuits and fill in the blanks in truth tables to record. . . .
Problem solving is at the heart of the NRICH site. All the problems
give learners opportunities to learn, develop or use mathematical
concepts and skills. Read here for more information.
A car is travelling along a dual carriageway at constant speed. Every 3 minutes a bus passes going in the opposite direction, while every 6 minutes a bus passes the car travelling in the same. . . .
This article explores ths history of theories about the shape of our planet. It is the first in a series of articles looking at the significance of geometric shapes in the history of astronomy.
To win on a scratch card you have to uncover three numbers that add
up to more than fifteen. What is the probability of winning a
A brief video explaining the idea of a mathematical knot.
At Holborn underground station there is a very long escalator. Two
people are in a hurry and so climb the escalator as it is moving
upwards, thus adding their speed to that of the moving steps. . . .
Every day at noon a boat leaves Le Havre for New York while another
boat leaves New York for Le Havre. The ocean crossing takes seven
days. How many boats will each boat cross during their journey?
How does the time of dawn and dusk vary? What about the Moon, how does that change from night to night? Is the Sun always the same? Gather data to help you explore these questions.
Blue Flibbins are so jealous of their red partners that they will
not leave them on their own with any other bue Flibbin. What is the
quickest way of getting the five pairs of Flibbins safely to. . . .
You have two bags, four red balls and four white balls. You must
put all the balls in the bags although you are allowed to have one
bag empty. How should you distribute the balls between the two. . . .
The triathlon is a physically gruelling challenge. Can you work out which athlete burnt the most calories?