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Broad Topics > Using, Applying and Reasoning about Mathematics > Real world

### Olympic Turns

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

This task looks at the different turns involved in different Olympic sports as a way of exploring the mathematics of turns and angles.

### The Animals' Sports Day

##### Age 5 to 7 Challenge Level:

One day five small animals in my garden were going to have a sports day. They decided to have a swimming race, a running race, a high jump and a long jump.

### Performing Beyond Expectations - Using Sport to Motivate Students in Mathematics Lessons

##### Age 7 to 16

In this article, Alan Parr shares his experiences of the motivating effect sport can have on the learning of mathematics.

### Olympic Records

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

Can you deduce which Olympic athletics events are represented by the graphs?

### Discuss and Choose

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

This activity challenges you to decide on the 'best' number to use in each statement. You may need to do some estimating, some calculating and some research.

### What Is the Time?

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

Can you put these times on the clocks in order? You might like to arrange them in a circle.

### Over-booking

##### Age 16 to 18 Challenge Level:

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?

### Epidemic Modelling

##### Age 14 to 18 Challenge Level:

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.

### FA Cup

##### Age 16 to 18 Challenge Level:

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!

### Far Horizon

##### Age 14 to 16 Challenge Level:

An observer is on top of a lighthouse. How far from the foot of the lighthouse is the horizon that the observer can see?

### Cool as Ice

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

Design and construct a prototype intercooler which will satisfy agreed quality control constraints.

### Straw Scaffold

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

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

### Gym Bag

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

Can Jo make a gym bag for her trainers from the piece of fabric she has?

### Decathlon: the Art of Scoring Points

##### Age 14 to 18

How do decisions about scoring affect who wins a combined event such as the decathlon?

### Make Your Own Pencil Case

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

What shape would fit your pens and pencils best? How can you make it?

### Olympic Cards

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

Design your own scoring system and play Trumps with these Olympic Sport cards.

### Curve Spotting

##### Age 5 to 7 Challenge Level:

Can you spot circles, spirals and other types of curves in these photos?

### 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.

### May the Best Person Win

##### Age 5 to 16

How can people be divided into groups fairly for events in the Paralympics, for school sports days, or for subject sets?

### Population Dynamics Collection

##### Age 16 to 18 Challenge Level:

This is our collection of tasks on the mathematical theme of 'Population Dynamics' for advanced students and those interested in mathematical modelling.

### Food Web

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

Is this eco-system sustainable?

### Fill Me Up

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

Can you sketch graphs to show how the height of water changes in different containers as they are filled?

### Bird-brained

##### Age 16 to 18 Challenge Level:

How many eggs should a bird lay to maximise the number of chicks that will hatch? An introduction to optimisation.

### Bent Out of Shape

##### Age 14 to 18 Challenge Level:

An introduction to bond angle geometry.

### Population Dynamics

##### Age 16 to 18 Challenge Level:

This problem opens a major sequence of activities on the mathematics of population dynamics for advanced students.

### Guessing the Graph

##### Age 14 to 16 Challenge Level:

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

### Turning the Place Over

##### Age 11 to 18 Challenge Level:

As part of Liverpool08 European Capital of Culture there were a huge number of events and displays. One of the art installations was called "Turning the Place Over". Can you find our how it works?

### Moving Stonehenge

##### Age 16 to 18 Challenge Level:

A look at the fluid mechanics questions that are raised by the Stonehenge 'bluestones'.

### Spectrometry Detective

##### Age 16 to 18 Challenge Level:

From the atomic masses recorded in a mass spectrometry analysis can you deduce the possible form of these compounds?

### Predator - Prey Systems

##### Age 16 to 18 Challenge Level:

See how differential equations might be used to make a realistic model of a system containing predators and their prey.

### Carbon Footprints

##### Age 14 to 16 Challenge Level:

Is it really greener to go on the bus, or to buy local?

### Engnrich

##### Age 16 to 18 Challenge Level:

engNRICH is the area of the stemNRICH Advanced site devoted to the mathematics underlying the study of engineering

### Physnrich

##### Age 14 to 18 Challenge Level:

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

### Chemnrich

##### Age 14 to 18 Challenge 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. . . .

### The Mathematical Problems Faced by Advanced STEM Students

##### Age 16 to 18

STEM students at university often encounter mathematical difficulties. This articles highlights the various content problems and the 7 key process problems encountered by STEM students.

### Tiles in a Public Building

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

What is the same and what is different about these tiling patterns and how do they contribute to the floor as a whole?

### Where Am I?

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

From the information you are asked to work out where the picture was taken. Is there too much information? How accurate can your answer be?

### Fitting Flat Shapes

##### Age 16 to 18 Challenge Level:

How efficiently can various flat shapes be fitted together?

### Bionrich

##### Age 14 to 18 Challenge 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. . . .

### Randomness and Brownian Motion

##### Age 16 to 18

In Classical times the Pythagorean philosophers believed that all things were made up from a specific number of tiny indivisible particles called ‘monads’. Each object contained. . . .

### A Brief History of Time Measurement

##### Age 11 to 18

Noticing the regular movement of the Sun and the stars has led to a desire to measure time. This article for teachers and learners looks at the history of man's need to measure things.

### Big and Small Numbers in Physics - Group Task

##### Age 16 to 18 Challenge Level:

Work in groups to try to create the best approximations to these physical quantities.

### There and Back Again

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

Bilbo goes on an adventure, before arriving back home. Using the information given about his journey, can you work out where Bilbo lives?

### Production Equation

##### Age 16 to 18 Challenge Level:

Each week a company produces X units and sells p per cent of its stock. How should the company plan its warehouse space?

### 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.

### Mathematical Patchwork

##### Age 7 to 14

Jenny Murray describes the mathematical processes behind making patchwork in this article for students.

### Path to Where?

##### Age 5 to 7 Challenge Level:

Can you imagine where I could have walked for my path to look like this?

### Parallel Parking

##### Age 14 to 16

Scientist Bryan Rickett has a vision of the future - and it is one in which self-parking cars prowl the tarmac plains, hunting down suitable parking spots and manoeuvring elegantly into them.

### Classic Cube

##### Age 16 to 18 Challenge Level:

The net of a cube is to be cut from a sheet of card 100 cm square. What is the maximum volume cube that can be made from a single piece of card?