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Resources tagged with Mathematical modelling similar to Magic Squares:

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

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Chocolate 2010

Stage: 4 Challenge Level: Challenge Level:1

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

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Problem Solving, Using and Applying and Functional Mathematics

Stage: 1, 2, 3, 4 and 5 Challenge Level: Challenge Level:1

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.

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Quick Times

Stage: 3 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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.

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Pattern of Islands

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

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

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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. . . .

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Buses

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

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?

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Truth Tables and Electronic Circuits

Stage: 2, 3 and 4

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

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Königsberg

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

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?

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On Time

Stage: 3 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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?

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Konigsberg Plus

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

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.

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Master Minding

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

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?

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Lap Times

Stage: 4 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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. . . .

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Twenty20

Stage: 2, 3 and 4 Challenge Level: Challenge Level:1

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

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Crossing the Atlantic

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

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?

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Flight of the Flibbins

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

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. . . .

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Bell Ringing

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

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?

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Where to Land

Stage: 4 Challenge Level: Challenge Level:1

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?

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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. . . .

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Stemnrich - the Physical World

Stage: 3 and 4 Challenge Level: Challenge Level:1

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

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Food Web

Stage: 3 Challenge Level: Challenge Level:1

Is this eco-system sustainable?

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Bionrich

Stage: 4 and 5 Challenge Level: Challenge Level:1

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. . . .

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Stringing it Out

Stage: 4 Challenge Level: Challenge Level:1

Explore the transformations and comment on what you find.

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Spot the Card

Stage: 4 Challenge Level: Challenge Level:1

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?

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Epidemic Modelling

Stage: 4 and 5 Challenge Level: Challenge Level:1

Use the computer to model an epidemic. Try out public health policies to control the spread of the epidemic, to minimise the number of sick days and deaths.

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In Constantly Passing

Stage: 4 Challenge Level: Challenge Level:1

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. . . .

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Tree Tops

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

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?

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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. . . .

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Friday 13th

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

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?

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Fixing the Odds

Stage: 4 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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. . . .

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Plaiting and Braiding

Stage: 2 and 3

This article for students gives some instructions about how to make some different braids.

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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.

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The Legacy

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

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?

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Drawing Doodles and Naming Knots

Stage: 2, 3 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!

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What's a Knot?

Stage: 2, 3 and 4 Challenge Level: Challenge Level:1

A brief video explaining the idea of a mathematical knot.

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Christmas Trees

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

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. . . .

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Rule of Three

Stage: 3 Challenge Level: Challenge Level:1

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

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Scratch Cards

Stage: 4 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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?

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Hands Together

Stage: 3 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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?

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Escalator

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

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. . . .

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Football Crazy Hockey Mad

Stage: 3 Challenge Level: Challenge Level:1

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.

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Shaping the Universe III - to Infinity and Beyond

Stage: 3 and 4

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

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Concrete Calculation

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

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. . . .

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Observing the Sun and the Moon

Stage: 2 and 3 Challenge Level: Challenge Level:1

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.

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Guessing the Graph

Stage: 4 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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

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Troublesome Triangles

Stage: 2 and 3 Challenge Level: Challenge Level:1

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. . . .

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More Realistic Electric Kettle

Stage: 4 and 5 Challenge Level: Challenge Level:2 Challenge Level:2

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Straw Scaffold

Stage: 3 Challenge Level: Challenge Level:1

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

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Witch's Hat

Stage: 3 and 4 Challenge Level: Challenge Level:1

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

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Designing Table Mats

Stage: 3 and 4 Challenge Level: Challenge Level:1

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

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Investigating Epidemics

Stage: 3 and 4 Challenge Level: Challenge Level:1

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