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### There are 41 results

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

### Buses

##### Age 11 to 14 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?

### Rule of Three

##### Age 11 to 14 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?

### Straw Scaffold

##### Age 11 to 14 Challenge Level:

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

### Witch's Hat

##### Age 11 to 16 Challenge Level:

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

### Investigating Epidemics

##### Age 11 to 16 Challenge Level:

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

### Designing Table Mats

##### Age 11 to 16 Challenge Level:

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

### Troublesome Triangles

##### Age 7 to 14 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. . . .

### Observing the Sun and the Moon

##### Age 7 to 14 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.

### Food Web

##### Age 11 to 14 Challenge Level:

Is this eco-system sustainable?

### Triathlon and Fitness

##### Age 11 to 14 Challenge Level:

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

### 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.

### Stemnrich - the Physical World

##### Age 11 to 16 Challenge 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. . . .

### Truth Tables and Electronic Circuits

##### Age 11 to 18

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

### Logic, Truth Tables and Switching Circuits Challenge

##### Age 11 to 18

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. . . .

### Logic, Truth Tables and Switching Circuits

##### Age 11 to 18

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.

### Turning Granny

##### Age 7 to 11 Challenge Level:

A brief video looking at how you can sometimes use symmetry to distinguish knots. Can you use this idea to investigate the differences between the granny knot and the reef knot?

### What's a Knot?

##### Age 7 to 16 Challenge Level:

A brief video explaining the idea of a mathematical knot.

### Simple Train Journeys

##### Age 5 to 11 Challenge Level:

How many different journeys could you make if you were going to visit four stations in this network? How about if there were five stations? Can you predict the number of journeys for seven stations?

### 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.

### 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.

### 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.

### 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.

### 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.

### 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. . . .

### Konigsberg Plus

##### Age 11 to 14 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

##### Age 11 to 14 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?

### Königsberg

##### Age 11 to 14 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?

### Hands Together

##### Age 11 to 14 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?

##### Age 11 to 14 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.

### Flight of the Flibbins

##### Age 11 to 14 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. . . .

### Pattern of Islands

##### Age 11 to 14 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...

### Master Minding

##### Age 11 to 14 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?

### Quick Times

##### Age 11 to 14 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.

### Christmas Trees

##### Age 11 to 14 Challenge Level:

Christmas trees are planted in a rectangular array. Which is the taller tree, A or B?

### Friday 13th

##### Age 11 to 14 Challenge Level:

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

### The Lady or the Lions

##### Age 11 to 14 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. . . .

### On Time

##### Age 11 to 14 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?

### Crossing the Atlantic

##### Age 11 to 14 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?