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Resources tagged with Mathematical modelling similar to Circular Circuitry:

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

Impuzzable

Stage: 5

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

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.

Pdf Stories

Stage: 5 Challenge Level:

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

Dam Busters 1

Stage: 5 Challenge Level:

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

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.

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.

Engnrich

Stage: 5 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

Stage: 5 Challenge Level:

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

Physnrich

Stage: 4 and 5 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.

The Wrong Stats

Stage: 5 Challenge Level:

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

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.

The Not-so-simple Pendulum 1

Stage: 5 Challenge Level:

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

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.

Ramping it Up

Stage: 5 Challenge Level:

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

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 4

Stage: 5 Challenge Level:

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

Population Dynamics - Part 5

Stage: 5 Challenge Level:

Fifth 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 - 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.

Model Solutions

Stage: 5 Challenge Level:

How do these modelling assumption affect the solutions?

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.

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

Elastic Maths

Stage: 4 and 5

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.

Drawing Doodles and Naming Knots

Stage: 2, 3, 4 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!

What's a Knot?

Stage: 2, 3 and 4 Challenge Level:

A brief video explaining the idea of a mathematical knot.

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?

Logic, Truth Tables and Switching Circuits

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 record your findings in truth tables.

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. . . .

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.

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. . . .

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?

Truth Tables and Electronic Circuits

Stage: 3, 4 and 5

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

Population Dynamics

Stage: 5 Challenge Level:

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

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. . . .

Guessing the Graph

Stage: 4 Challenge Level:

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

Witch's Hat

Stage: 3 and 4 Challenge Level:

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

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?

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.

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...

Snooker

Stage: 5 Challenge Level:

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

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. . . .

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?

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. . . .

Shaping the Universe I - Planet Earth

Stage: 3 and 4

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.

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?