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Summation of series. Conditional probability. Combining probabilities. Mathematical modelling. Spreadsheets. Biology. Equally likely outcomes. Probability. Experimental probability. Tree diagrams. Theoretical probability.There are 67 results
Broad Topics > Mathematical Thinking > 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?
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?
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!
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?
Investigating Epidemics
Age 11 to 16 Challenge Level:
Simple models which help us to investigate how epidemics grow and die out.
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 Wrong Stats
Age 16 to 18 Challenge Level:
Why MUST these statistical statements probably be at least a little bit wrong?
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.
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
Age 16 to 18 Challenge Level:
This problem opens a major sequence of activities on the mathematics of population dynamics for advanced students.
Model Solutions
Age 16 to 18 Challenge Level:
How do these modelling assumption affect the solutions?
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.
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.
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
Spinners
Age 16 to 18 Challenge Level:
How do scores on dice and factors of polynomials relate to each other?
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.
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.
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. . . .
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.
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.
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.
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!
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.
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?
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?
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.
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.
Impuzzable
Age 16 to 18
This is about a fiendishly difficult jigsaw and how to solve it using a computer program.
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.
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?
Population Dynamics - Part 6
Age 16 to 18 Challenge Level:
Sixth 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.
Truth Tables and Electronic Circuits
Age 11 to 18
Investigate circuits and record your findings in this simple introduction to truth tables and logic.
Population Dynamics - Part 4
Age 16 to 18 Challenge Level:
Fourth in our series of problems on 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.
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?
NRICH is part of the family of activities in the Millennium Mathematics Project.