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Broad Topics > Using, Applying and Reasoning about Mathematics > Mathematical modelling

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Time to Evolve 2

Stage: 5 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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

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The Not-so-simple Pendulum 1

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2

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

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The Legacy

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

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?

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Dam Busters 1

Stage: 5 Challenge Level: Challenge Level:1

At what positions and speeds can the bomb be dropped to destroy the dam?

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Over-booking

Stage: 5 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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?

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Epidemic Modelling

Stage: 4 and 5 Challenge Level: Challenge Level:1

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.

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Spinners

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2

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

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Where to Land

Stage: 4 Challenge Level: Challenge Level:1

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?

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FA Cup

Stage: 5 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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!

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Buses

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

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?

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Tree Tops

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

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?

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Rule of Three

Stage: 3 Challenge Level: Challenge Level:1

If it takes four men one day to build a wall, how long does it take 60,000 men to build a similar wall?

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Straw Scaffold

Stage: 3 Challenge Level: Challenge Level:1

Build a scaffold out of drinking-straws to support a cup of water

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Witch's Hat

Stage: 3 and 4 Challenge Level: Challenge Level:1

What shapes should Elly cut out to make a witch's hat? How can she make a taller hat?

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Investigating Epidemics

Stage: 3 and 4 Challenge Level: Challenge Level:1

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

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Designing Table Mats

Stage: 3 and 4 Challenge Level: Challenge Level:1

Formulate and investigate a simple mathematical model for the design of a table mat.

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Troublesome Triangles

Stage: 2 and 3 Challenge Level: Challenge Level:1

Many natural systems appear to be in equilibrium until suddenly a critical point is reached, setting up a mudslide or an avalanche or an earthquake. In this project, students will use a simple. . . .

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Observing the Sun and the Moon

Stage: 2 and 3 Challenge Level: Challenge Level:1

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.

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Population Dynamics Collection

Stage: 5 Challenge Level: Challenge Level:1

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

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Population Dynamics - Part 1

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2

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

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More Realistic Electric Kettle

Stage: 4 and 5 Challenge Level: Challenge Level:2 Challenge Level:2

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Food Web

Stage: 3 Challenge Level: Challenge Level:1

Is this eco-system sustainable?

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Triathlon and Fitness

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

The triathlon is a physically gruelling challenge. Can you work out which athlete burnt the most calories?

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Pdf Stories

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2

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

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Twenty20

Stage: 2, 3 and 4 Challenge Level: Challenge Level:1

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

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Bird-brained

Stage: 5 Challenge Level: Challenge Level:1

How many eggs should a bird lay to maximise the number of chicks that will hatch? An introduction to optimisation.

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Population Ecology Using Probability

Stage: 5 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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

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Population Dynamics - Part 5

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2

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

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Population Dynamics - Part 6

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2

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

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Stemnrich - the Physical World

Stage: 3 and 4 Challenge Level: Challenge Level:1

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

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Branching Processes and Extinction

Stage: 5 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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

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Population Dynamics - Part 4

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2

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

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Population Dynamics

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2

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

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Population Dynamics - Part 2

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2

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

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Rocking Chairs, Railway Games and Rayboxes

Stage: 1, 2, 3, 4 and 5

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. . . .

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Population Dynamics - Part 3

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2

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

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Guessing the Graph

Stage: 4 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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

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An Introduction to Computer Programming and Mathematics

Stage: 5

This article explains the concepts involved in scientific mathematical computing. It will be very useful and interesting to anyone interested in computer programming or mathematics.

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Ramping it Up

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2

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

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Modelling Assumptions in Mechanics

Stage: 5

An article demonstrating mathematically how various physical modelling assumptions affect the solution to the seemingly simple problem of the projectile.

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Model Solutions

Stage: 5 Challenge Level: Challenge Level:1

How do these modelling assumption affect the solutions?

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Poiseuille's Equation

Challenge Level: Challenge Level:1

Look at the flow of fluids down circular pipes.

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Predator - Prey Systems

Stage: 5 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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

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The Wrong Stats

Stage: 5 Challenge Level: Challenge Level:1

Why MUST these statistical statements probably be at least a little bit wrong?

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Advanced Scientific Mathematics

Stage: 5 Challenge Level: Challenge Level:1

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

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Engnrich

Stage: 5 Challenge Level: Challenge Level:1

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

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Physnrich

Stage: 4 and 5 Challenge Level: Challenge Level:1

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

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Chemnrich

Stage: 4 and 5 Challenge Level: Challenge Level:1

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. . . .

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Bionrich

Stage: 4 and 5 Challenge Level: Challenge Level:1

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. . . .

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Truth Tables and Electronic Circuits

Stage: 2, 3 and 4

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