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Resources tagged with Mathematical modelling similar to Calculus Countdown:

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

Chocolate 2010

Stage: 4 Challenge Level:

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

Ball Bearings

Stage: 5 Challenge 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.

Problem Solving, Using and Applying and Functional Mathematics

Stage: 1, 2, 3, 4 and 5 Challenge 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.

Ramping it Up

Stage: 5 Challenge Level:

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

Stonehenge

Stage: 5 Challenge Level:

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

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.

Lap Times

Stage: 4 Challenge Level:

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. . . .

Logic, Truth Tables and Switching Circuits Challenge

Stage: 3, 4 and 5

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. . . .

Bionrich

Stage: 4 and 5 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. . . .

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. . . .

Spot the Card

Stage: 4 Challenge Level:

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?

Stemnrich - the Physical World

Stage: 3 and 4 Challenge Level:

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

Predator - Prey Systems

Stage: 5 Challenge Level:

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

In Constantly Passing

Stage: 4 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. . . .

Model Solutions

Stage: 5 Challenge Level:

How do these modelling assumption affect the solutions?

The Wrong Stats

Stage: 5 Challenge Level:

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

Stringing it Out

Stage: 4 Challenge Level:

Explore the transformations and comment on what you find.

Stage: 5 Challenge Level:

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

Twenty20

Stage: 2, 3 and 4 Challenge Level:

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

Population Dynamics - Part 5

Stage: 5 Challenge Level:

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

Population Dynamics - Part 4

Stage: 5 Challenge Level:

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

Population Dynamics - Part 6

Stage: 5 Challenge Level:

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

Population Ecology Using Probability

Stage: 5 Challenge Level:

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

Population Dynamics Collection

Stage: 5 Challenge Level:

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

Population Dynamics - Part 3

Stage: 5 Challenge Level:

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

Population Dynamics - Part 2

Stage: 5 Challenge Level:

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

Pdf Stories

Stage: 5 Challenge Level:

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

Where to Land

Stage: 4 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?

Population Dynamics

Stage: 5 Challenge Level:

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

Branching Processes and Extinction

Stage: 5 Challenge Level:

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

Population Dynamics - Part 1

Stage: 5 Challenge Level:

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

Bird-brained

Stage: 5 Challenge Level:

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

Spinners

Stage: 5 Challenge Level:

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

Shaping the Universe III - to Infinity and Beyond

Stage: 3 and 4

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

Stage: 5 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?

Scratch Cards

Stage: 4 Challenge 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?

Overarch 2

Stage: 5 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?

The Mean Game

Stage: 5

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.

Concrete Calculation

Stage: 4 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. . . .

Escalator

Stage: 4 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. . . .

Drawing Doodles and Naming Knots

Stage: 2, 3 and 5

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

The Legacy

Stage: 4 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?

What's a Knot?

Stage: 2, 3 and 4 Challenge Level:

A brief video explaining the idea of a mathematical knot.

Cushion Ball

Stage: 5 Challenge 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?

Fixing the Odds

Stage: 4 Challenge 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. . . .

Impuzzable

Stage: 5

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

The Use of Mathematics in Computer Games

Stage: 5

An account of how mathematics is used in computer games including geometry, vectors, transformations, 3D graphics, graph theory and simulations.

Circuit Training

Stage: 4 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. . . .

Shaping the Universe II - the Solar System

Stage: 3 and 4

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

Maximum Flow

Stage: 5 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.