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Resources tagged with Mathematical modelling similar to Stonehenge:

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

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.

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...

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. . . .

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.

Truth Tables and Electronic Circuits

Age 11 to 18

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

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.

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. . . .

Spot the Card

Age 14 to 16 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?

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?

Population Dynamics - Part 3

Age 16 to 18 Challenge Level:

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

Stringing it Out

Age 14 to 16 Challenge Level:

Explore the transformations and comment on what you find.

Model Solutions

Age 16 to 18 Challenge Level:

How do these modelling assumption affect the solutions?

The Wrong Stats

Age 16 to 18 Challenge Level:

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

Population Dynamics - Part 2

Age 16 to 18 Challenge Level:

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

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.

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

Ramping it Up

Age 16 to 18 Challenge Level:

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

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 4

Age 16 to 18 Challenge Level:

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

Chemnrich

Age 14 to 18 Challenge 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 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. . . .

Physnrich

Age 14 to 18 Challenge Level:

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

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

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.

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.

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. . . .

Stemnrich - the Physical World

Age 11 to 16 Challenge Level:

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

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.

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.

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?

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.

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. . . .

Population Dynamics - Part 5

Age 16 to 18 Challenge Level:

Fifth 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!

What's a Knot?

Age 7 to 16 Challenge Level:

A brief video explaining the idea of a mathematical knot.

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.

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?

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?

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. . . .

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?

Shaping the Universe III - to Infinity and Beyond

Age 11 to 16

The third installment in our series on the shape of astronomical systems, this article explores galaxies and the universe beyond our solar system.

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.

Overarch 2

Age 16 to 18 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

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.

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.

Impuzzable

Age 16 to 18

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

Lap Times

Age 14 to 16 Challenge Level:

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

Dam Busters 1

Age 16 to 18 Challenge Level:

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

Population Dynamics - Part 6

Age 16 to 18 Challenge Level:

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

Shaping the Universe II - the Solar System

Age 11 to 16

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