Resources tagged with: Mathematical modelling

Filter by: Content type:
Age range:
Challenge level:

There are 53 results

Broad Topics > Thinking Mathematically > Mathematical modelling

Fixing the Odds

Age 14 to 16Challenge 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. . . .

Scratch Cards

Age 14 to 16Challenge 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?

Master Minding

Age 11 to 14Challenge Level

Your partner chooses two beads and places them side by side behind a screen. What is the minimum number of guesses you would need to be sure of guessing the two beads and their positions?

Investigating Epidemics

Age 11 to 16Challenge Level

Simple models which help us to investigate how epidemics grow and die out.

On Time

Age 11 to 14Challenge Level

On a clock the three hands - the second, minute and hour hands - are on the same axis. How often in a 24 hour day will the second hand be parallel to either of the two other hands?

Flight of the Flibbins

Age 11 to 14Challenge Level

Blue Flibbins are so jealous of their red partners that they will not leave them on their own with any other bue Flibbin. What is the quickest way of getting the five pairs of Flibbins safely to. . . .

Twenty20

Age 7 to 16Challenge Level

Fancy a game of cricket? Here is a mathematical version you can play indoors without breaking any windows.

Spot the Card

Age 14 to 16Challenge 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?

Buses

Age 11 to 14Challenge Level

A bus route has a total duration of 40 minutes. Every 10 minutes, two buses set out, one from each end. How many buses will one bus meet on its way from one end to the other end?

Circuit Training

Age 14 to 16Challenge 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. . . .

The Bridges of Konigsberg

Age 11 to 18Challenge Level

Investigate how networks can be used to solve a problem for the 18th Century inhabitants of Konigsberg.

The Legacy

Age 14 to 16Challenge 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?

KÃ¶nigsberg

Age 11 to 14Challenge Level

Can you cross each of the seven bridges that join the north and south of the river to the two islands, once and once only, without retracing your steps?

Tree Tops

Age 14 to 16Challenge Level

Can you make sense of information about trees in order to maximise the profits of a forestry company?

Pattern of Islands

Age 11 to 14Challenge Level

In how many distinct ways can six islands be joined by bridges so that each island can be reached from every other island...

Bell Ringing

Age 11 to 14Challenge Level

Suppose you are a bellringer. Can you find the changes so that, starting and ending with a round, all the 24 possible permutations are rung once each and only once?

Chocolate 2010

Age 14 to 16Challenge Level

First of all, pick the number of times a week that you would like to eat chocolate. Multiply this number by 2...

Crossing the Atlantic

Age 11 to 14Challenge Level

Every day at noon a boat leaves Le Havre for New York while another boat leaves New York for Le Havre. The ocean crossing takes seven days. How many boats will each boat cross during their journey?

Age 11 to 14Challenge Level

In a league of 5 football teams which play in a round robin tournament show that it is possible for all five teams to be league leaders.

Learning Mathematics Through Games Series: 4. from Strategy Games

Age 5 to 14

Basic strategy games are particularly suitable as starting points for investigations. Players instinctively try to discover a winning strategy, and usually the best way to do this is to analyse. . . .

Stemnrich - the Physical World

Age 11 to 16Challenge Level

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

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. . . .

Observing the Sun and the Moon

Age 7 to 14Challenge Level

How does the time of dawn and dusk vary? What about the Moon, how does that change from night to night? Is the Sun always the same? Gather data to help you explore these questions.

Troublesome Triangles

Age 7 to 14Challenge Level

Many natural systems appear to be in equilibrium until suddenly a critical point is reached, setting up a mudslide or an avalanche or an earthquake. In this project, students will use a simple. . . .

Guessing the Graph

Age 14 to 16Challenge Level

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

Food Web

Age 11 to 14Challenge Level

Is this eco-system sustainable?

Triathlon and Fitness

Age 11 to 14Challenge Level

The triathlon is a physically gruelling challenge. Can you work out which athlete burnt the most calories?

Physnrich

Age 14 to 18Challenge Level

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

Bionrich

Age 14 to 18Challenge 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. . . .

Designing Table Mats

Age 11 to 16Challenge Level

Formulate and investigate a simple mathematical model for the design of a table mat.

Chemnrich

Age 14 to 18Challenge 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. . . .

Witch's Hat

Age 11 to 16Challenge Level

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

Stringing it Out

Age 14 to 16Challenge Level

Explore the transformations and comment on what you find.

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.

In Constantly Passing

Age 14 to 16Challenge 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 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.

Where to Land

Age 14 to 16Challenge 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?

Concrete Calculation

Age 14 to 16Challenge 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. . . .

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!

Celtic Knotwork Patterns

Age 7 to 14

This article for pupils gives an introduction to Celtic knotwork patterns and a feel for how you can draw them.

Problem Solving, Using and Applying and Functional Mathematics

Age 5 to 18Challenge 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.

Rule of Three

Age 11 to 14Challenge Level

If it takes four men one day to build a wall, how long does it take 60,000 men to build a similar wall?

Escalator

Age 14 to 16Challenge 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. . . .

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.

Slippage

Age 14 to 16Challenge 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. . . .

Friday 13th

Age 11 to 14Challenge Level

Can you explain why every year must contain at least one Friday the thirteenth?

Quick Times

Age 11 to 14Challenge Level

32 x 38 = 30 x 40 + 2 x 8; 34 x 36 = 30 x 40 + 4 x 6; 56 x 54 = 50 x 60 + 6 x 4; 73 x 77 = 70 x 80 + 3 x 7 Verify and generalise if possible.

Lap Times

Age 14 to 16Challenge Level

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

Shaping the Universe I - Planet Earth

Age 11 to 16

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.