Index of Teacher Packages

How do you judge the risks and benefits of a new medical treatments, or of lifestyle choices? With a finite health care budget, how do you decide which treatments should be made freely available on the NHS? Historically, decisions like these have been made on the basis of doctors' individual experiences with how these treatments perform, but over recent decades the approach to answering these questions has become increasingly rational. Statistics and maths are used not just to test new treatments, but also to measure such fuzzy terms as quality of life, and to figure out which treatments provide most "health for money".

While the decisions of health authorities affect all our lives, the underlying calculations are rarely discussed in the media. To explore these difficult decisions and the role of maths in evidence-based medicine, we have put together a package of 6 articles, 3 podcasts, a career interview and a classroom activity.

The notion of proof lies at the very heart of maths: it's when it comes to proving things that mathematicians let lose their genius and creativity, and in the process often discover unexpected surprises or deep philosophical issues. But proofs can also be daunting. So to help you and your students along, we've brought together a range of Plus articles on proofs.

Infectious diseases hardly ever disappear from the headlines. If it's not the disease itself that hits the news, then it's the vaccines with their potential side effects. It can be hard to tell the difference between scare mongering and responsible reporting, because media coverage rarely provides a look behind the scenes. How do scientists reach the conclusions they do? How do they predict how a particular disease will spread, and whether it is likely to mutate into a more dangerous strand? And how do they assess the impact of an intervention like vaccination, and make sure that a vaccine is safe?

Two answer these questions, we have put together a package of five articles, a podcast, and a classroom activity.

This teacher package brings together all Plus articles on graph and network theory. Graphs and networks turn up in many real-life problems, from neuroscience to telecommunications. In the UK curriculum, they make a frequent appearance in the area known as decision maths. Our articles explore a wide range of related topics, from simple algorithms to complex network topologies.

In this issue's teacher package we look at some of the maths and science behind a recent expedition to the Arctic. The aim of the Catlin Arctic Survey was to gather data on ice thickness that will help to predict when the North Pole sea ice cover will melt, an event that will have dramatic consequence for the Arctic ecosystem and the Earth's climate as a whole. Plus was commissioned by Catlin Arctic Survey Education to produce mathematics and science enrichment material for ages 14 to 19 (key stages 4 and 5). The toolkits look at climate and sea ice models, GPS and cartography, how to predict future climate trends, and how to present statistical evidence.

From the geometry of Euclid to the shape of the Universe — geometry is a vast field. We've got plenty of articles exploring geometry from all angles, so have a look and take your pick.

So basic, yet so tricky: prime numbers are the atoms among natural numbers and lie at the centre of some of the most difficult open problems in maths. This package brings together all material we have on primes, from prime number algorithms to new discoveries. And you will find out what all that's got to do with David Beckham.

This issue's teacher package brings together all Plus articles on group theory, exploring its applications and recent breakthroughs, and giving explicit definitions and examples of groups. It also has some handy links to related problems on our sister site NRICH.

This issue's teacher package brings together all Plus articles on vectors and matrices, exploring anything from the maths of computer movies to climate change. It also has some handy links to related problems on our sister site NRICH.

This issue's teacher package brings together all Plus articles on probability and statistics, exploring anything from maths in the dock to games of chance. It also has some handy links to related problems on our sister site NRICH.

Complex numbers — what are they, how do they work and what do they have to do with computer-generated movies, fractals and chaos? This teacher package brings together all Plus articles on complex numbers and gives some handy links to related problems on our sister site NRICH.

The flocking behaviour of birds, the spread of diseases and the Cuban missile crisis — all of these and much more can be modelled mathematically. In our second teacher package we bring together all Plus articles on mathematical modelling, ready for use in classroom discussions or students projects.

One thing that will never change is the fact that the world is constantly changing, and differential equations are the way we mathematically describe the changing world around us. In our first Teacher package we bring together all the material on Plus that deals with differential equations, including applications in biology, physics, finance, and even football!