# Resources tagged with: Mathematical modelling

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### There are 67 results

Broad Topics > Thinking Mathematically > Mathematical modelling

### Fixing the Odds

##### Age 14 to 16Challenge Level

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. . . .

### Snooker

##### Age 16 to 18Challenge Level

A player has probability 0.4 of winning a single game. What is his probability of winning a 'best of 15 games' tournament?

### Scratch Cards

##### Age 14 to 16Challenge Level

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 prize?

### 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.

### FA Cup

##### Age 16 to 18Challenge 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!

### Time to Evolve 2

##### Age 16 to 18Challenge Level

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

### Investigating Epidemics

##### Age 11 to 16Challenge Level

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

### Twenty20

##### Age 7 to 16Challenge Level

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

### The Wrong Stats

##### Age 16 to 18Challenge Level

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

### 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 Legacy

##### Age 14 to 16Challenge 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?

### Population Dynamics

##### Age 16 to 18Challenge Level

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

### Model Solutions

##### Age 16 to 18Challenge Level

How do these modelling assumption affect the solutions?

### Modelling Assumptions in Mechanics

##### Age 16 to 18

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

### Predator - Prey Systems

##### Age 16 to 18Challenge Level

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

##### Age 16 to 18Challenge Level

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

### Spinners

##### Age 16 to 18Challenge Level

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

### An Introduction to Computer Programming and Mathematics

##### Age 16 to 18

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.

### Ramping it Up

##### Age 16 to 18Challenge Level

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

### Population Dynamics - Part 1

##### Age 16 to 18Challenge Level

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

### Chemnrich

##### Age 14 to 18Challenge 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 18Challenge 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 18Challenge Level

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

### Engnrich

##### Age 16 to 18Challenge 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 18Challenge Level

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

### The Not-so-simple Pendulum 1

##### Age 16 to 18Challenge Level

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

### 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. . . .

### Pdf Stories

##### Age 16 to 18Challenge Level

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

### Branching Processes and Extinction

##### Age 16 to 18Challenge Level

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

### Maximum Flow

##### Age 16 to 18Challenge Level

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

### Population Dynamics - Part 2

##### Age 16 to 18Challenge Level

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

### Population Dynamics - Part 3

##### Age 16 to 18Challenge Level

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

### 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!

### Ball Bearings

##### Age 16 to 18Challenge Level

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.

### Cushion Ball

##### Age 16 to 18Challenge Level

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?

### Stonehenge

##### Age 16 to 18Challenge Level

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

### Problem Solving, Using and Applying and Functional Mathematics

##### Age 5 to 18Challenge Level

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.

### Over-booking

##### Age 16 to 18Challenge 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?

### Overarch 2

##### Age 16 to 18Challenge 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?

### Population Dynamics Collection

##### Age 16 to 18Challenge Level

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

### 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.

### Impuzzable

##### Age 16 to 18

This is about a fiendishly difficult jigsaw and how to solve it using a computer program.

### Population Ecology Using Probability

##### Age 16 to 18Challenge Level

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

### Tree Tops

##### Age 14 to 16Challenge Level

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

### Population Dynamics - Part 6

##### Age 16 to 18Challenge Level

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

### Population Dynamics - Part 5

##### Age 16 to 18Challenge Level

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

### Truth Tables and Electronic Circuits

##### Age 11 to 18

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

### Population Dynamics - Part 4

##### Age 16 to 18Challenge Level

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

### Bird-brained

##### Age 16 to 18Challenge Level

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

### Guessing the Graph

##### Age 14 to 16Challenge Level

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