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Spreadsheets. Conditional probability. Theoretical probability. Combining probabilities. Biology. Mathematical modelling. Experimental probability. Tree diagrams. Random variables. Probability.There are 69 results
Broad Topics > Using, Applying and Reasoning about Mathematics > Mathematical modelling
Fixing the Odds
Age 14 to 16 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. . . .
Snooker
Age 16 to 18 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?
Time to Evolve 2
Age 16 to 18 Challenge Level:
How is the length of time between the birth of an animal and the birth of its great great ... great grandparent distributed?
Scratch Cards
Age 14 to 16 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?
Investigating Epidemics
Age 11 to 16 Challenge Level:
Simple models which help us to investigate how epidemics grow and die out.
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 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!
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 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?
The Wrong Stats
Age 16 to 18 Challenge Level:
Why MUST these statistical statements probably be at least a little bit wrong?
Tree Tops
Age 14 to 16 Challenge Level:
Can you make sense of information about trees in order to maximise the profits of a forestry company?
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. . . .
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.
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.
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. . . .
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
Physnrich
Age 14 to 18 Challenge Level:
PhysNRICH is the area of the StemNRICH site devoted to the mathematics underlying the study of physics
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. . . .
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. . . .
Ramping it Up
Age 16 to 18 Challenge Level:
Look at the calculus behind the simple act of a car going over a step.
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.
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
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
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.
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.
Pdf Stories
Age 16 to 18 Challenge Level:
Invent scenarios which would give rise to these probability density functions.
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 1
Age 16 to 18 Challenge Level:
First in our series of problems 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 5
Age 16 to 18 Challenge Level:
Fifth 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.
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?
Designing Table Mats
Age 11 to 16 Challenge Level:
Formulate and investigate a simple mathematical model for the design of a table mat.
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.
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.
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.
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.
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?
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.
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. . . .
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?
NRICH is part of the family of activities in the Millennium Mathematics Project.