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.
Explain why, when moving heavy objects on rollers, the object moves
twice as fast as the rollers. Try a similar experiment yourself.
First of all, pick the number of times a week that you would like
to eat chocolate. Multiply this number by 2...
Sixth in our series of problems on population dynamics for advanced students.
Fifth in our series of problems on population dynamics for advanced students.
An advanced mathematical exploration supporting our series of articles on population dynamics for advanced students.
This is about a fiendishly difficult jigsaw and how to solve it
using a computer program.
Two cyclists, practising on a track, pass each other at the starting line and go at constant speeds... Can you find lap times that are such that the cyclists will meet exactly half way round the. . . .
Fourth in our series of problems on population dynamics for advanced students.
Invent scenarios which would give rise to these probability density functions.
Third in our series of problems on population dynamics for advanced students.
See how differential equations might be used to make a realistic
model of a system containing predators and their prey.
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.
First in our series of problems on population dynamics for advanced students.
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. . . .
Second in our series of problems on population dynamics for advanced students.
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?
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 record your findings in truth tables.
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.
Look at the calculus behind the simple act of a car going over a
This problem opens a major sequence of activities on the mathematics of population dynamics for advanced students.
A brief video explaining the idea of a mathematical knot.
Why MUST these statistical statements probably be at least a little
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. . . .
This is the section of stemNRICH devoted to the advanced applied
mathematics underlying the study of the sciences at higher levels
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. . . .
This article for students introduces the idea of naming knots using numbers. You'll need some paper and something to write with handy!
How many eggs should a bird lay to maximise the number of chicks
that will hatch? An introduction to optimisation.
See how the motion of the simple pendulum is not-so-simple after
Work in groups to try to create the best approximations to these
How do these modelling assumption affect the solutions?
engNRICH is the area of the stemNRICH Advanced site devoted to the mathematics underlying the study of engineering
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. . . .
A player has probability 0.4 of winning a single game. What is his
probability of winning a 'best of 15 games' tournament?
Can you suggest a curve to fit some experimental data? Can you work out where the data might have come from?
The third installment in our series on the shape of astronomical systems, this article explores galaxies and the universe beyond our solar system.
This is our collection of tasks on the mathematical theme of 'Population Dynamics' for advanced students and those interested in mathematical modelling.
At what positions and speeds can the bomb be dropped to destroy the
An account of how mathematics is used in computer games including
geometry, vectors, transformations, 3D graphics, graph theory and
Bricks are 20cm long and 10cm high. How high could an arch be built
without mortar on a flat horizontal surface, to overhang by 1
metre? How big an overhang is it possible to make like this?
Given the graph of a supply network and the maximum capacity for
flow in each section find the maximum flow across the network.
In four years 2001 to 2004 Arsenal have been drawn against Chelsea
in the FA cup and have beaten Chelsea every time. What was the
probability of this? Lots of fractions in the calculations!
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. . . .
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.
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. . . .