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

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.

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

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

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.

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

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?

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.

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!

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

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

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

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

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

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

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

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

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.

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

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

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

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

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

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

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?

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

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

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

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

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

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

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. . . .

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.

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

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?

How efficiently can various flat shapes be fitted together?

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. . . .

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. . . .

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.

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

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

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 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.

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

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

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.