# teacher package

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.

Whether it's the planets moving around the Sun or building the perfect cycling track, the key to many questions in our lives lies in classical mechanics. This teacher package brings together all our content on mechanics.

This teacher package is devoted to the number line and the two major classes of numbers it's divided into: rational numbers, which can be written as fractions, and irrational numbers, which are everything else.

Game theory is a great way of sneaking up on maths. You can start off playing an actual game, then start thinking about strategies, and before you know it you're doing proper maths, either conceptually or using equations and formulae. In this teacher package you'll find all our articles on game theory.

One of the first bits of school maths that gives us a real glimpse of infinity are infinite series: those never-ending sums that may nevertheless add up to a finite number. For this teacher package we've brought together all our articles on these beautiful objects.

In some sense, all of maths should come under the label "logic", but mathematical logic has shown that mathematics isn't entirely logical. Makes sense? If not, then this teacher package may help.

This teacher package brings together all our articles that have to do with sport, from cricket to football and from the sport itself to sporting architecture and infrastructure.

This teacher package brings together our material on trigonometry, from problems about simple triangles to the wavy behaviour of trig functions.

Maths is all about patterns and rhythms, so it's no surprise that there's plenty of maths in art. Whether it's the visual or the performing arts, maths can be a tool, an inspiration, or simply something that's naturally contained within the structures and patterns.
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.
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.
• Want facts and want them fast? Our Maths in a minute series explores key mathematical concepts in just a few words.