BASIC MATHEMATICS
An Introduction
Alan Graham
Contents
Meet the author
Welcome to Basic Mathematics !
If you found that maths was something of a closed book at school, please dont feel intimidated or frightened by the prospect of opening up and reading through this book now. Having spent most of my adult life teaching adults at the Open University, I have come to realize that 90% of peoples problems with the subject stem from fear fear of failure, fear of showing yourself up in front of others, fear of feeling lost and confused. All of these negative feelings combine to bring the shutters down on your learning to the point where you are no longer able to listen or even think.
You may be wondering what has changed to enable you to succeed now where you didnt before. The answer is, everything! You may not fully realize it, but as a functioning adult who has survived in the world beyond school, you have actually picked up a lot of useful skills on the way:
You have a much better understanding of how the world works something that will be invaluable when it comes to understanding, selecting and using mathematical skills.
You have greatly developed your thinking skills in the course of tackling the many decisions and problems of your everyday life.
Most importantly, you almost certainly now have a confidence and a desire to learn that you didnt possess at the age of 15.
All of these factors will combine to raise the shutters of your mind, so that it is truly open to the clear thinking needed to understand and master mathematical skills.
And finally, remember that there is nothing that succeeds like success. The more you find yourself getting the exercises right, the more youll want to tackle the next one, and gradually you will really start to believe that, yes, Im becoming a mathematician!
Acknowledgements
Many thanks to Wendy Austen, Carrie Graham, James Griffin and Sally Kenny for their help in the preparation of this book.
Introduction
Mathematics is about numbers. But, more than that, it is about describing and explaining patterns that includes number patterns (arithmetic ) but also patterns in shape and space (geometry ). Increasingly, our digital world bombards us with numerical information and an essential life skill is being able to generate, collect, observe and explain patterns when handling data (statistics ). Finally, mathematics is about responding to an inner human need to pose and solve problems, be they everyday problems or those of the inventively curious mind.
There are four main strands of basic mathematics:
In the main part of the book you will cover these four themes; you will also learn what algebra is about and discover how to use a spreadsheet.
You will have the chance to try a variety of puzzles such as the one below:
What are the next two letters in this sequence:
O, T, T, F, F, S, S, E,,?
Finally, at the end of this book, you will find 14 case studies showing you how mathematics can help to solve everyday problems and provide insights that would not otherwise have been obvious.
The next two letters in this sequence are N and T (the letters are the initials of One, Two, Three,
Numbers and calculations
For most people, the topics numbers and calculations represent the core of the mathematics that they learnt at school; some basic ideas about numbers are explained in will also help you to become more familiar with a simple four-function calculator.
Fractions, decimals and percentages
Moving beyond whole numbers raises the question of what lies in-between them. These broken bits of numbers can be written using fractions, decimals and percentages. These each require their own special notation and include numbers like three point seven, four and three quarters, twenty-five per cent, and so on. In , you will get a straightforward explanation of what fractions, decimals and percentages are, how they are written (e.g. 3.7, 4
and 25%, respectively), why they are written that way and how to perform calculations with them.
Measuring
How many times would you say you perform some measurement task during the course of an average day? The answer is probably much more often than you think. Sometimes the measurement you do is formal perhaps reading the time on a watch or clock, checking the temperature on a thermostat, reading the dial (in litres or in money) as you fill the car up with petrol, checking your weight on the bathroom scales and so on.
There may be even more occasions where you are engaging in informal measurement and this often involves making judgements based on using estimation skills like working out whether the armchair will fit into the gap between the sideboard and the door, or choosing how many potatoes to cook for a family of four. Informal measurement often involves the use of some everyday template or benchmark against which to make comparisons. For example, when estimating, say, 100 metres, I tend to think about the length of a football pitch or when estimating weights I think of a bag of sugar (1 kilo).
It is worth remembering that numbers which arise in the everyday world have had to come from somewhere and the chances are that they are the result of some measuring process. But in order to handle these numbers sensibly and with understanding, you need to know how they were measured and in which measuring units. These are some of the issues explored in .
Statistical graphs and charts
It is claimed that about 80% of all the data in the world today has been created in the past two years. According to computer company IBM, 2.5 exabytes that is 2.5 billion gigabytes of data was generated every day in 2012. This is not a static figure estimates suggest that it is growing by roughly 30% each year. It is hard to avoid the conclusion that we are drowning in statistical data. And unfortunately, for most people, the sight of a page full of figures gives them the heeby-jeebies.
There are two main ways of seeking out helpful patterns in data. One is to use summaries, like reducing the many numbers to a simple average. The other is to depict the data visually, using a statistical chart. It is the second approach that is explored here. A number of such charts are explained in , including barcharts, piecharts, scattergraphs and line graphs. You will also learn some of the tricks and dodges used by advertisers and others to deliberately mislead the gullible public. You have been warned!
Algebra
And then theres algebra. I have often heard students observe when thinking back to their school days, that, just when they were getting to grips with doing calculations involving numbers, along came letters like x and y , and a and
