Explain why, when moving heavy objects on rollers, the object moves twice as fast as the rollers. Try a similar experiment yourself.

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.

The shortest path between any two points on a snooker table is the straight line between them but what if the ball must bounce off one wall, or 2 walls, or 3 walls?

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.

Edward Wallace based his A Level Statistics Project on The Mean Game. Each picks 2 numbers. The winner is the player who picks a number closest to the mean of all the numbers picked.

Investigate circuits and record your findings in this simple introduction to truth tables and logic.

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. . . .

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.

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. . . .

The second in a series of articles on visualising and modelling shapes in the history of astronomy.

How do scores on dice and factors of polynomials relate to each other?

Simple models which help us to investigate how epidemics grow and die out.

See how differential equations might be used to make a realistic model of a system containing predators and their prey.

How do these modelling assumption affect the solutions?

First of all, pick the number of times a week that you would like to eat chocolate. Multiply this number by 2...

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 distance. . . .

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?

How is the length of time between the birth of an animal and the birth of its great great ... great grandparent distributed?

This article for students introduces the idea of naming knots using numbers. You'll need some paper and something to write with handy!

If a is the radius of the axle, b the radius of each ball-bearing, and c the radius of the hub, why does the number of ball bearings n determine the ratio c/a? Find a formula for c/a in terms of n.

Learn about the link between logical arguments and electronic circuits. Investigate the logical connectives by making and testing your own circuits and record your findings in truth tables.

A brief video explaining the idea of a mathematical knot.

PhysNRICH is the area of the StemNRICH site devoted to the mathematics underlying the study of physics

Fancy a game of cricket? Here is a mathematical version you can play indoors without breaking any windows.

See how the motion of the simple pendulum is not-so-simple after all.

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. . . .

engNRICH is the area of the stemNRICH Advanced site devoted to the mathematics underlying the study of engineering

chemNRICH is the area of the stemNRICH site devoted to the mathematics underlying the study of chemistry, designed to help develop the mathematics required to get the most from your study. . . .

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

Invent scenarios which would give rise to these probability density functions.

Work in groups to try to create the best approximations to these physical quantities.

An advanced mathematical exploration supporting our series of articles on population dynamics for advanced students.

An advanced mathematical exploration supporting our series of articles on population dynamics for advanced students.

Sixth in our series of problems on population dynamics for advanced students.

This is our collection of tasks on the mathematical theme of 'Population Dynamics' for advanced students and those interested in mathematical modelling.

Can you suggest a curve to fit some experimental data? Can you work out where the data might have come from?

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?

Fifth in our series of problems on population dynamics for advanced students.

Fourth in our series of problems on population dynamics for advanced students.

Look at the calculus behind the simple act of a car going over a step.

First in our series of problems on population dynamics for advanced students.

Second in our series of problems on population dynamics for advanced students.

Third in our series of problems on population dynamics for advanced students.

This problem opens a major sequence of activities on the mathematics of population dynamics for advanced students.

This is the section of stemNRICH devoted to the advanced applied mathematics underlying the study of the sciences at higher levels

The probability that a passenger books a flight and does not turn up is 0.05. For an aeroplane with 400 seats how many tickets can be sold so that only 1% of flights are over-booked?

Can you make sense of information about trees in order to maximise the profits of a forestry company?

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. . . .

Given the graph of a supply network and the maximum capacity for flow in each section find the maximum flow across the network.