Resources tagged with: Mathematical modelling

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There are 67 results

Broad Topics > Thinking Mathematically > Mathematical modelling

Spinners

Age 16 to 18
Challenge Level

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

Ball Bearings

Age 16 to 18
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.

Population Dynamics - Part 5

Age 16 to 18
Challenge Level

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

Pdf Stories

Age 16 to 18
Challenge Level

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

Truth Tables and Electronic Circuits

Age 11 to 18

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

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 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 1

Age 16 to 18
Challenge Level

First 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.

Problem Solving, Using and Applying and Functional Mathematics

Age 5 to 18
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

Age 16 to 18
Challenge Level

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

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

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.

The Wrong Stats

Age 16 to 18
Challenge Level

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

Model Solutions

Age 16 to 18
Challenge Level

How do these modelling assumption affect the solutions?

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. . . .

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.

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.

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?

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!

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. . . .

Bus Stop

Age 14 to 16
Challenge Level

Two buses leave at the same time from two towns Shipton and Veston on the same long road, travelling towards each other. At each mile along the road are milestones. The buses' speeds are constant. . . .

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!

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.

Cushion Ball

Age 16 to 18
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?

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.

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.

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. . . .

Lap Times

Age 14 to 16
Challenge Level

Can you find the lap times of the two cyclists travelling at constant speeds?

Impuzzable

Age 16 to 18

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

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.

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.

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...

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?

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.

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.

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?

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.

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

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. . . .

Physnrich

Age 14 to 18
Challenge Level

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

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. . . .

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.

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?

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. . . .

Slippage

Age 14 to 16
Challenge Level

A ladder 3m long rests against a wall with one end a short distance from its base. Between the wall and the base of a ladder is a garden storage box 1m tall and 1m high. What is the maximum distance. . . .