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Visualising. Biology. Physics. Optimisation. Differentiation. Sine, cosine, tangent. Real world. Maths Supporting SET. Engineering. Mathematical modelling.There are 69 results
Broad Topics > Using, Applying and Reasoning about Mathematics > Mathematical modelling
Maximum Flow
Age 16 to 18 Challenge Level:
Given the graph of a supply network and the maximum capacity for flow in each section find the maximum flow across the network.
Ramping it Up
Age 16 to 18 Challenge Level:
Look at the calculus behind the simple act of a car going over a step.
Population Dynamics
Age 16 to 18 Challenge Level:
This problem opens a major sequence of activities on the mathematics of population dynamics for advanced students.
In Constantly Passing
Age 14 to 16 Challenge Level:
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. . . .
Rocking Chairs, Railway Games and Rayboxes
Age 5 to 18
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. . . .
Model Solutions
Age 16 to 18 Challenge Level:
How do these modelling assumption affect the solutions?
The Wrong Stats
Age 16 to 18 Challenge Level:
Why MUST these statistical statements probably be at least a little bit wrong?
Predator - Prey Systems
Age 16 to 18 Challenge Level:
See how differential equations might be used to make a realistic model of a system containing predators and their prey.
Advanced Scientific Mathematics
Age 16 to 18 Challenge Level:
This is the section of stemNRICH devoted to the advanced applied mathematics underlying the study of the sciences at higher levels
Chemnrich
Age 14 to 18 Challenge Level:
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
Age 14 to 18 Challenge Level:
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
Age 14 to 18 Challenge Level:
PhysNRICH is the area of the StemNRICH site devoted to the mathematics underlying the study of physics
Engnrich
Age 16 to 18 Challenge Level:
engNRICH is the area of the stemNRICH Advanced site devoted to the mathematics underlying the study of engineering
Big and Small Numbers in Physics - Group Task
Age 16 to 18 Challenge Level:
Work in groups to try to create the best approximations to these physical quantities.
The Not-so-simple Pendulum 1
Age 16 to 18 Challenge Level:
See how the motion of the simple pendulum is not-so-simple after all.
Stemnrich - the Physical World
Age 11 to 16 Challenge Level:
PhysNRICH is the area of the StemNRICH site devoted to the mathematics underlying the study of physics
Where to Land
Age 14 to 16 Challenge Level:
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?
Twenty20
Age 7 to 16 Challenge Level:
Fancy a game of cricket? Here is a mathematical version you can play indoors without breaking any windows.
Pdf Stories
Age 16 to 18 Challenge Level:
Invent scenarios which would give rise to these probability density functions.
Branching Processes and Extinction
Age 16 to 18 Challenge Level:
An advanced mathematical exploration supporting our series of articles on population dynamics for advanced students.
Population Dynamics - Part 1
Age 16 to 18 Challenge Level:
First in our series of problems on population dynamics for advanced students.
Population Dynamics - Part 2
Age 16 to 18 Challenge Level:
Second in our series of problems on population dynamics for advanced students.
Population Dynamics - Part 3
Age 16 to 18 Challenge Level:
Third in our series of problems on population dynamics for advanced students.
Population Dynamics - Part 4
Age 16 to 18 Challenge Level:
Fourth in our series of problems on population dynamics for advanced students.
Population Dynamics - Part 5
Age 16 to 18 Challenge Level:
Fifth in our series of problems on population dynamics for advanced students.
Population Dynamics - Part 6
Age 16 to 18 Challenge Level:
Sixth in our series of problems on population dynamics for advanced students.
Population Ecology Using Probability
Age 16 to 18 Challenge Level:
An advanced mathematical exploration supporting our series of articles on population dynamics for advanced students.
Population Dynamics Collection
Age 16 to 18 Challenge Level:
This is our collection of tasks on the mathematical theme of 'Population Dynamics' for advanced students and those interested in mathematical modelling.
Guessing the Graph
Age 14 to 16 Challenge Level:
Can you suggest a curve to fit some experimental data? Can you work out where the data might have come from?
The Legacy
Age 14 to 16 Challenge Level:
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?
Elastic Maths
Age 14 to 18
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.
The Use of Mathematics in Computer Games
Age 16 to 18
An account of how mathematics is used in computer games including geometry, vectors, transformations, 3D graphics, graph theory and simulations.
Chocolate 2010
Age 14 to 16 Challenge Level:
First of all, pick the number of times a week that you would like to eat chocolate. Multiply this number by 2...
Drawing Doodles and Naming Knots
Age 7 to 18
This article for students introduces the idea of naming knots using numbers. You'll need some paper and something to write with handy!
Dam Busters 1
Age 16 to 18 Challenge Level:
At what positions and speeds can the bomb be dropped to destroy the dam?
Shaping the Universe III - to Infinity and Beyond
Age 11 to 16
The third installment in our series on the shape of astronomical systems, this article explores galaxies and the universe beyond our solar system.
Over-booking
Age 16 to 18 Challenge Level:
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?
Shaping the Universe II - the Solar System
Age 11 to 16
The second in a series of articles on visualising and modelling shapes in the history of astronomy.
Shaping the Universe I - Planet Earth
Age 11 to 16
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.
Concrete Calculation
Age 14 to 16 Challenge Level:
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. . . .
Truth Tables and Electronic Circuits
Age 11 to 18
Investigate circuits and record your findings in this simple introduction to truth tables and logic.
FA Cup
Age 16 to 18 Challenge Level:
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!
Escalator
Age 14 to 16 Challenge Level:
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. . . .
What's a Knot?
Age 7 to 16 Challenge Level:
A brief video explaining the idea of a mathematical knot.
Stonehenge
Age 16 to 18 Challenge Level:
Explain why, when moving heavy objects on rollers, the object moves twice as fast as the rollers. Try a similar experiment yourself.
The Mean Game
Age 16 to 18
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.
Time to Evolve 2
Age 16 to 18 Challenge Level:
How is the length of time between the birth of an animal and the birth of its great great ... great grandparent distributed?
Bird-brained
Age 16 to 18 Challenge Level:
How many eggs should a bird lay to maximise the number of chicks that will hatch? An introduction to optimisation.
Circuit Training
Age 14 to 16 Challenge Level:
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. . . .
Overarch 2
Age 16 to 18 Challenge Level:
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?
NRICH is part of the family of activities in the Millennium Mathematics Project.