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There are **100** NRICH Mathematical resources connected to **Mathematical modelling**, you may find related items under Thinking mathematically.

Problem
Primary curriculum
Secondary curriculum
### Triathlon and Fitness

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

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### What's That Graph?

Can you work out which processes are represented by the graphs?

Age 14 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Place Your Orders

Can you rank these sets of quantities in order, from smallest to largest? Can you provide convincing evidence for your rankings?

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Speed-time Problems at the Olympics

Have you ever wondered what it would be like to race against Usain Bolt?

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Dangerous Driver?

Was it possible that this dangerous driving penalty was issued in error?

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Cuboid Challenge

What's the largest volume of box you can make from a square of paper?

Age 11 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Time to Evolve 2

How is the length of time between the birth of an animal and the birth of its great great ... great grandparent distributed?

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### The Not-so-simple Pendulum 1

See how the motion of the simple pendulum is not-so-simple after all.

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### The Legacy

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?

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Over-booking

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?

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Spinners

How do scores on dice and factors of polynomials relate to each other?

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Where to Land

Chris is enjoying a swim but needs to get back for lunch. How far along the bank should she land?

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### FA Cup

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!

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Buses

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?

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Tree Tops

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

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Rule of Three

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

Age 11 to 14

Challenge Level

Article
Primary curriculum
Secondary curriculum
### Elastic Maths

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.

Age 14 to 18

Problem
Primary curriculum
Secondary curriculum
### Spot the Card

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?

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Slippage

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 up the wall which the ladder can reach?

Age 14 to 16

Challenge Level

Article
Primary curriculum
Secondary curriculum
### Learning Mathematics Through Games Series: 4. from Strategy Games

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 the outcomes of series of 'moves'. With a little encouragement from the teacher, a mathematical investigation is born.

Age 5 to 14

Problem
Primary curriculum
Secondary curriculum
### Circuit Training

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 meet at the start again? If so, after how many circuits?

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Bus Stop

Two buses leave at the same time from two towns Shipton and Veston on the same long road, travelling towards each other. At each mile along the road are milestones. The buses' speeds are constant and in the ratio 5 to 4. The buses travel to and fro between the towns. What milestones are at Shipton and Veston?

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Maximum Flow

Given the graph of a supply network and the maximum capacity for flow in each section find the maximum flow across the network.

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### The Bridges of Konigsberg

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

Age 11 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Chocolate 2010

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

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Bell Ringing

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?

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### In Constantly Passing

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 direction. Buses leave the depot at regular intervals; they travel along the dual carriageway and back to the depot at a constant speed. At what interval do the buses leave the depot?

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### KÃ¶nigsberg

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?

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Stringing it Out

Explore the transformations and comment on what you find.

Age 14 to 16

Challenge Level

Article
Primary curriculum
Secondary curriculum
### Impuzzable

This is about a fiendishly difficult jigsaw and how to solve it using a computer program.

Age 16 to 18

Article
Primary curriculum
Secondary curriculum
### The Use of Mathematics in Computer Games

An account of how mathematics is used in computer games including geometry, vectors, transformations, 3D graphics, graph theory and simulations.

Age 16 to 18

Article
Primary curriculum
Secondary curriculum
### The Mean Game

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.

Age 16 to 18

Problem
Primary curriculum
Secondary curriculum
### Football Crazy Hockey Mad

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.

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Flight of the Flibbins

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 the new planet?

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Pattern of Islands

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

Age 11 to 14

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Problem
Primary curriculum
Secondary curriculum
### Master Minding

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?

Age 11 to 14

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Problem
Primary curriculum
Secondary curriculum
### Lap Times

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

Age 14 to 16

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Problem
Primary curriculum
Secondary curriculum
### Concrete Calculation

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 make the concrete raft for the foundations?

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Quick Times

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.

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Escalator

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. ... How many steps are there on the escalator?

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Friday 13th

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

Age 11 to 14

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Problem
Primary curriculum
Secondary curriculum
### On Time

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?

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Scratch Cards

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?

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Fixing the Odds

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 bags so as to make the probability of choosing a red ball as small as possible and what will the probability be in that case?

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Crossing the Atlantic

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 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Snooker

A player has probability 0.4 of winning a single game. What is his probability of winning a 'best of 15 games' tournament?

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Stonehenge

Explain why, when moving heavy objects on rollers, the object moves twice as fast as the rollers. Try a similar experiment yourself.

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Cushion Ball

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?

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Overarch 2

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?

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Ball Bearings

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.

Age 16 to 18

Challenge Level