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Resources tagged with Mathematical modelling similar to The Four Colour Theorem:

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

Königsberg

Stage: 3 Challenge 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?

Konigsberg Plus

Stage: 3 Challenge Level:

Euler discussed whether or not it was possible to stroll around Koenigsberg crossing each of its seven bridges exactly once. Experiment with different numbers of islands and bridges.

Bell Ringing

Stage: 3 Challenge 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?

Buses

Stage: 3 Challenge 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?

Crossing the Atlantic

Stage: 3 Challenge 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?

Pattern of Islands

Stage: 3 Challenge Level:

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

Flight of the Flibbins

Stage: 3 Challenge 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. . . .

Master Minding

Stage: 3 Challenge 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?

Tree Tops

Stage: 3 Challenge Level:

A manager of a forestry company has to decide which trees to plant. What strategy for planting and felling would you recommend to the manager in order to maximise the profit?

Stage: 3 Challenge 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.

Troublesome Triangles

Stage: 2 and 3 Challenge 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. . . .

Problem Solving, Using and Applying and Functional Mathematics

Stage: 1, 2, 3, 4 and 5 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.

Learning Mathematics Through Games Series: 4. from Strategy Games

Stage: 1, 2 and 3

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. . . .

What's a Knot?

Stage: 2, 3 and 4 Challenge Level:

A brief video explaining the idea of a mathematical knot.

Lap Times

Stage: 4 Challenge Level:

Two cyclists, practising on a track, pass each other at the starting line and go at constant speeds... Can you find lap times that are such that the cyclists will meet exactly half way round the. . . .

Logic, Truth Tables and Switching Circuits Challenge

Stage: 3, 4 and 5

Learn about the link between logical arguments and electronic circuits. Investigate the logical connectives by making and testing your own circuits and fill in the blanks in truth tables to record. . . .

Celtic Knotwork Patterns

Stage: 2 and 3

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

Shaping the Universe I - Planet Earth

Stage: 3 and 4

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.

Twenty20

Stage: 2, 3 and 4 Challenge Level:

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

Food Web

Stage: 3 Challenge Level:

Is this eco-system sustainable?

Stemnrich - the Physical World

Stage: 3 and 4 Challenge Level:

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

Spot the Card

Stage: 4 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?

Truth Tables and Electronic Circuits

Stage: 3, 4 and 5

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

Drawing Doodles and Naming Knots

Stage: 2, 3, 4 and 5

This article for students introduces the idea of naming knots using numbers. You'll need some paper and something to write with handy!

Quick Times

Stage: 3 Challenge 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.

Shaping the Universe II - the Solar System

Stage: 3 and 4

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

Concrete Calculation

Stage: 4 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. . . .

Hands Together

Stage: 3 Challenge Level:

Sometime during every hour the minute hand lies directly above the hour hand. At what time between 4 and 5 o'clock does this happen?

Friday 13th

Stage: 3 Challenge Level:

This month there is a Friday the thirteenth and this year there are three. Can you explain why every year must contain at least one Friday the thirteenth?

Christmas Trees

Stage: 3 Challenge Level:

Christmas trees are planted in a rectangular array of 10 rows and 12 columns. The farmer chooses the shortest tree in each of the columns... the tallest tree from each of the rows ... Which is. . . .

On Time

Stage: 3 Challenge 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?

Stage: 3 Challenge Level:

The King showed the Princess a map of the maze and the Princess was allowed to decide which room she would wait in. She was not allowed to send a copy to her lover who would have to guess which path. . . .

Chocolate 2010

Stage: 4 Challenge Level:

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

Logic, Truth Tables and Switching Circuits

Stage: 3, 4 and 5

Learn about the link between logical arguments and electronic circuits. Investigate the logical connectives by making and testing your own circuits and record your findings in truth tables.

Scratch Cards

Stage: 4 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?

Observing the Sun and the Moon

Stage: 2 and 3 Challenge 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.

Rocking Chairs, Railway Games and Rayboxes

Stage: 1, 2, 3, 4 and 5

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. . . .

Triathlon and Fitness

Stage: 3 Challenge Level:

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

Fixing the Odds

Stage: 4 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. . . .

Investigating Epidemics

Stage: 3 and 4 Challenge Level:

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

Witch's Hat

Stage: 3 and 4 Challenge Level:

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

Straw Scaffold

Stage: 3 Challenge Level:

Build a scaffold out of drinking-straws to support a cup of water

Designing Table Mats

Stage: 3 and 4 Challenge Level:

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

Physnrich

Stage: 4 and 5 Challenge Level:

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

Rule of Three

Stage: 3 Challenge 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?

Guessing the Graph

Stage: 4 Challenge Level:

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

Elastic Maths

Stage: 4 and 5

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.

Escalator

Stage: 4 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. . . .