Chapters

Mathematics! The discipline that sends many a student into a cold sweat, from primary school to sixth form; from passing GCSE maths to A-levels. Some students brave it and venture into maths in higher education, at degree level or beyond. **Maths is everywhere**. Whether you aspire to study sociology, psychology, physics, biology or even economics, maths is held in high regard, and you will be called on solve various maths problems, as part of your work. Maths is relevant to a wide variety of **academic subjects on the GCSE course and **A Level curriculum, which not only means that a poor understanding of maths can cause students to struggle in many other subjects but also that it could **limit their further studies options** as well as their **employability** when they come to think about career options.

Many classes school involve counting, estimating, measuring, weighing, drafting, working out formulas, using statistics and analyzing data, all of which have their roots firmly in the field of Mathematics.

If you don't believe us, just take a look at **how Maths crosses over into other subjects** below, and we don't just mean Science and Technology! *Science and Technology* You are probably already aware that **science and math are closely connected**, particularly the topics of chemistry, astronomy and physics. This is why students who can't master basic arithmetic skills will have a hard time reading scientific charts and graphs and risk not being accepted on a scientific course in their higher education. Geometry, algebra, and calculus can help students solve chemistry problems but practical sciences, such as engineering and computer science, also **benefit from maths**. For example, pupils may have to use complex equations and algorithms when designing and writing computer programs. On the opposite spectrum, nurses deal with science and maths as they carry out their everyday duties, needing to know how to precisely calculate dosages and to identify abnormal results in patients' tests. *Literature and Writing* Literature, one of the subjects you might think of as the furthest away from maths and science, is actually **full of mathematical theories**. Poetry is a great example, with its meter and particular rhythms. All of these are based on maths calculations don't you know! But that's not where it begins and ends, Math can help students to plan reading assignments by enabling them to work out roughly how many pages they can read in a half hour and thus estimating how long it will take them to read a particular work. The same goes for their planning of any written assignments. This is because **Maths teaches us to think logically and solve problems**. This ability to reason can also have an effect on the way that literature pupils tackle their answers clearly. *Humanities* Classes like history and other social sciences sometimes require students to review charts and graphs containing historical data or information on ethnic groups. They also ask them to look at events in the context of when they took place, which naturally causes pupils to think back from now and work out how many years ago these would have taken place and just how much has changed in society over that number of decades. In geography classes, students might need to consider how the force of the sea can erode our coasts and at what rate, whilst also understanding how the elevation of an area can affect its population or the average lifespan of individuals living in them. **Knowledge of basic mathematical terms and formulae **makes statistical information more accessible and therefore easier to apply in order to back up findings and theories. *The Arts* Once again, though not obviously related to maths, drama, music, dance or art pupils can benefit from **basic mathematical knowledge** due to the way it informs rhythm and the basic beats of dances used in all types of performances. Art itself relies heavily on geometry, particularly some modern masterpieces, as well as social statistics so students who understand basic geometric formulas and can identify patterns in stats can usually craft impressive and influential art pieces. Photographers, on the other hand, **use math to calculate** things like shutter speed, lighting, angles, exposure time, and focal length.

#### What Elements of Maths can be found in Other Academic Areas?

See here the elements of Maths that crop up in other subjects at GCSE or A Level.

Science and Technology | Literature | Humanities | The Arts |
---|---|---|---|

Basic arithmetic | Meter in poetry | Working with statistics | Rhythm and beat |

Reading charts and graphs | Time management | Thinking about time in context | Understanding statistics |

Understanding equations and algorithms | Logical thinking | Using formulas | Calculation |

^{st}lesson free!

^{st}lesson free!

^{st}lesson free!

^{st}lesson free!

^{st}lesson free!

^{st}lesson free!

^{st}lesson free!

^{st}lesson free!

## Math In Real Life Is Endless

As you can see, Maths is ever-present in many of our other academic subjects, and just as visible in our general day-to-day lives.

Many students and adults never think to use the maths they have learnt, or are still learning in their everyday lives. In this, they are wrong for many reasons!

First of all, as we will see, mathematics is present in **many aspects of your daily life**, from a trip to the bank, to cooking and even doing DIY. Another point, not to be taken lightly, is that learning maths, and more broadly all the 'hard' sciences, trains your mind and conditions you to think and **analyse problems** (not necessarily mathematical ones) more effectively. In addition to the purely technical elements, **mathematics also teaches you methods of reasoning** and a certain rigour in how you approach your work. Why do you think it is that the highest A-level pass rates are found in the scientific disciplines? It's because these students have learned intellectual rigour, and have developed **analytical skills** well beyond the sphere of maths. Search for math tutoring now. It is time to recognise the importance of maths, and to get over your reservations about the topic!

## Real Life Maths: An Essential Part of our Lives

You may well have already asked yourself questions such as:- "How will trigonometry help me in the future?"
- "How, and why, should I draw up variation table?"
- "Why should I learn to calculate with negative numbers if this will have no use in my work?"
- "What is the use of working out a vector, a differential maths equation, Pythagoras' theorem, confidence intervals, algebra questions, or the graphical analysis of a function?"

Pupils and students often ask such questions, and as a maths teacher or maths tutor, it can be hard to give a convincing answer without drawing on **practical everyday examples**. Search for maths tutor Brisbane or maths tutor Sydney now. To avoid resorting to retorts like "actually, square roots are very useful: To pass your exam and succeed in maths!" or "I'm sure the Minister for Education would find your point of view very interesting!" let's look further than simple exam success, and explore some concrete examples. Did you know that about **1 person in 10 is at a disadvantage in their daily lives** **thanks to their poor knowledge of maths?** Let's not leave them behind!

^{st}lesson free!

^{st}lesson free!

^{st}lesson free!

^{st}lesson free!

^{st}lesson free!

^{st}lesson free!

^{st}lesson free!

^{st}lesson free!

## Maths in the Real World

Here are some examples which show that **maths is essential** in our lives and serves us in many important ways.

**Maths and Shopping**

Maths surrounds you the minute you step through the doors of your favourite supermarket! Indeed, the automatic doors and security scanner you pass through are composed of electronic systems that could never have been designed without maths. Then, when you start shopping, you fill your trolley with products labelled with **barcodes**, which reference the manufacturer and the specific identity of each product. The products, thanks to the barcode, are scanned at the checkout with a **laser**. All you have to do is pay for your purchases by** check, credit card or cash**: All of which, again, are possible thanks to mathematics!

All these steps and operations use mathematical concepts, like those taught in the classroom.

Another example would be if, while shopping, you realise that the store has a 30% off promotional discount, and that this reduction increases if you purchase 2 items. You understand, however, that a 10% off the first product and 20% off the second do not make a total discount of 30%! The value of knowing some basic mental calculation can be** very useful when out shopping.**

**Cooking**

The use of maths in cooking is almost inevitable, and it is often the **famous rule of 3**that is applied, when you have to convert the proportions of a recipe for 6 people to a different number.

It's important to calculate and adjust the quantities for the recipe to turn out well.

Similarly, you should know the basic rules for converting weights (grammes to pounds and vice versa), temperature (between Celsius and Fahrenheit, depending on where you get your recipes from) or simply **to add or divide ingredients. **For example: "Mix 2/3 of 500 g flour, add 2 eggs, and milk, then add the remaining 1/3."

**Buying a House or an Apartment**

Buying property is among **the most significant and practical examples of using maths in your everyday life**. Given the importance of such a purchase, it's better to pay attention to all the details, to be sure of a favourable transaction. In fact, when you borrow money, you are offered a repayment plan that accounts for **interest rates**, sometimes fixed, sometimes variable, but different depending on the length of your loan: **The rate differs whether you borrow for 2, 10, 25 or 30 years**. To know how much you're going to pay overall, what you need to save and what you have to repay, **interest rate calculations** prove to very important. If you're going to build a house, then besides the loan you're going to take out, you'll need to draw up plans. For this, you should know how to use a ladder, measure angles and provide for furniture to scale, to finalise your plans. Here as well, the use of maths, and more precisely of geometry, is paramount.

**Do-It-Yourself**

Whether for small or large jobs, maths will be one of your best friends when doing DIY!

Whether you want to calculate the angles necessary to erect a partition or work out the number of tiles needed to decorate a bathroom, you need to know how to use the **rule of three**, how to calculate angles and the hypotenuse of a triangle, and be at ease calculating **surfaces in square meters and volumes in cubic meters**. Examples like these are so familiar that it's easy to forget that maths comes into play so often when **redesigning or transforming the interior of your home**!

**Travel**

Nowadays, GPS receivers are found in so many cars and smartphones. There, too, maths is at work! Before all this technology came along, we had **the compass, protractor, sextant and the **astrolabe: It's with **triangulation** that we can determine our distance from a fixed point, and direction of movement. Triangulation (today greatly improved with satellites) with its calculations of angles and distances has always been a mainstay of cartography and navigation.

Just ask someone sailing around the world, how they would manage if they were not able to identify their location on a map!

**Maths and Gambling**

Although chance does play a role in card games, mathematics gives the best poker and bridge players an advantage over average players, who don't use probability or calculate odds to give themselves an advantage. In poker, if you can grasp a few statistical notions and keep in mind some other factors, like the hand you hold or the pot size, you will be able to **play more consistently**. Moreover, for any great card player, the expectation of gain is not calculated in the short term, but in the long term. While it may not be possible to win systematically, it's important to be systematic in the long term.

As such, good poker players are all familiar with the law of large numbers, even if only implicitly.

The law of large numbers tells us that the more frequently you toss a coin, for example, the more the observed result will approach the theoretical mean, in this case 50% heads and 50% tails. This helps to explain the legendary calm shown by some players when losing large sums: **Because they know that in the long run, they will.**

**Music and Videogames**

On an audio compact disc, the sounds you hear are coded by a mathematical sequence into a string of 1s and 0s, which are grouped into 8-bit words. So that the recorded sound is more resilient to damage to the medium, duplicate packets of data are added to the disc, so that the decoding device (a CD player) can** detect and correct the sequence**, if dust or scratches obscure some of the data on the disc.

This branch of mathematics has a name:

theory of error correcting codesand is found in many other applications such as data transmission via satellite, and even theInternet:

Without you even knowing it, maths makes it easy for you to access your favourite websites!

**Telling the Time**

Once you've learned how to tell the time as a child, you rarely give it a second thought and can look at a clock and instantly know what the time is. However, when you break it down, **the concept of time** isn't all that straightforward. There are a lot of things you need to understand, all at once, in order to know **how to tell time**. For example, you need to be aware that there are 24 hours in a day, that each day is then split into two 12-hour halves, that each hour lasts 60 minutes, and that each minute is 60 seconds-long... plus 60 isn't the easiest number to work with! Don't you just hate it when you read that a film is 93 mins long and you have to try to work out in your head **what this equates to** in hours and minutes?! Fractions also come into play, when we say it’s “a quarter-to six,” we're actually telling them that a *quarter *of an hour remains until it becomes six o’clock. Digital clocks can involve maths too, though. When you read a digital display that says 11.35, you don't simply take it as "eleven thirty-five" do you? When asked, you would probably say to someone that it is "twenty-five to twelve", meaning that you are subconsciously picturing a clock with its longest hand just west of the bottom. You are **automatically working out in your head** that an hour is divided up into sections of five minutes, quarters and halves and are applying this theory all at once. Furthermore, if you read 16:20 on your digital clock display, don't you instantly read this as "4:22"? If so, then you have just gone through** yet another mathematical process**, taking into consideration that there are 12 hours in each half of the 24 hour day.

**Driving**

Operating any type of machinery is down to **a series of calculations**, and many of us sit in our cars for hours in a day. Not only do we work out before we set out on a journey how many miles there are to the destination, how long it will take to drive, will the time of day mean an increase in traffic, how much petrol do we have, etc... but also, when actually driving, we think about what the speed limit is, how long it would take us to slow down for a junction or to stop in an emergency, which numerical gear to be in (or manuals), and so on. Though most of these questions come down to our **time management**, many are directly linked with maths equations.

## Maths in the Real World of Work

Beyond universal applications that touch everyone's lives, mathematics is very much a part of our **professional lives**. Much more so if you are an accountant than a literary critic, granted, but applications abound in many spheres of work. Here are some examples.

**Mathematics and Sales**

Whether calculating prices in Excel, working out sales percentages, commissions, a discount or converting currencies,Having at least a basic understanding of maths while working in sales is an indispensable asset.

**maths is a central part of the daily life of all who are involved in sales.**However, you won't have your maths teacher alongside you, so be sure to practice properly!

**Maths and Accounting**

You don't need a maths degree to become an accountant or a secretary, or even to plan your monthly household budget, however, you need at least some knowledge of maths to successfully navigate your day's work. To manipulate an Excel table, do basic statistical analyses, evaluate a forecast budget, balance your books or determine management thresholds to assess the health of an organisation: **Maths is everywhere**!

**Geometry and Architecture**

Maths, with its formulas for area and volume, is widely used in architecture to **represent buildings in three dimensions** and to create perspective views of a plan.

Maths can even be found in video and animated film design, throughThales' theorem also allows us to calculate hard-to-measure distances, such as the height of a pyramid.

**3D special effects**and image morphing software. In fact, it's impossible to manipulate 3D images in space, create representations of surfaces or curves, or

**distort images**without a minimum knowledge of maths.

**Maths and Economics**

Most economic models use mathematics. Broadly, economists are interested in **production, productivity and the distribution of wealth** in a given country. The range of applications of mathematics is **as broad as the economy itself,** from simple calculations like the aggregation of a company's payroll, to more technical notions such as share price updates and concepts found in macro- and microeconomics. However, one of the most interesting aspects of maths in economics, though far from the easiest, is their use in** predictive economic models**. Maths allows us to store data that will allow us to anticipate, to some extent, the future fluctuations of a phenomenon we are attempting to explain. There are other subjects closely related to both economics and the application of mathematics which fulfil other roles. One such sub-discipline is econometrics, which seeks to demonstrate mathematically whether variables are relevant in explaining phenomena. It could be used, for example, to attempt to determine whether and how the number of years of education that a person has acquired is related to his or her salary.

**Maths: The Lingua Franca of Science**

Just as English is the international language of areas like business and geopolitics, **mathematics enjoys the same prestige in the realm of science**. From economics, as we have just seen, to physics, biology, health or neuroscience, **the application of maths in the sciences is omnipresent**. If you are keen to embark on a career in any of these areas, and many more, you should be aware that your maths abilities will be closely scrutinised by recruiters: Just one more proof that maths is present in many professions.

**Maths and its Effects On Health**

Mathematics is an application of matter and contributes to all of our **methodical and systematic behaviours**, which in turn help us to survive. It is Maths, for instance, that has brought order to the communities across this planet and helped prevent chaos and catastrophes. We have learned to live together as humans and evolve as a species using the materials we have at our disposal. Not only are our survival skills** led by maths**, but many of our inherited human qualities are also nurtured and developed by Maths theories, like our spatial awareness, our problem-solving skills, our power to reason (which involves calculated thinking) and even our creativity and communication. This means Maths not only allows us to live, but it also allows us to live a rich life where we can be unique beings. Things that you wouldn't expect to bear any relation to Maths do in fact come down to **an underlying need for mathematics** and the structure it brings to our everyday lives. So how does Maths continue to benefit our wellbeing? Brain training is equally good for your body and brain as it nurtures both **physical and psychological** aspects of our bodies. The NHS itself states that "keeping the mind active may have various benefits, including a reduced risk of dementia. In general, it would seem sensible to keep the mind as well as the body active." There are various things that keeping your mind active with cognitive training can do for you, such as:

- Increase your ability to memorise
- Cut down on the risk, and slow the decline, of mental illnesses such as Dementia
- Improve your brain processing speed
- Prevent boredom
- Enhance concentration

Also, have you ever considered the fact that **everything changes your brain** so it's continuously evolving and growing? Each new person you meet, each new story you read, each new flower you smell... there are so many 'firsts' that continue to take place throughout our lives that we probably don't even give a second thought to. However, when you sit back and think about it, your brain is constantly developing and being influenced by surroundings.

## Real Life Maths Problems: Changing your World View?

**Learning Intellectual Rigour through Maths**

Beyond the practical applications of mathematics in your everyday life, it's worth mentioning some of the discipline's more rarified benefits. In fact, when you practice maths a regular basis, you train and hone your mind in a number of ways. The holistic benefits of mathematics, unlike its practical, everyday applications**, are skills that can be exercised in all kinds of situations.** Indeed, if you are able to reason more effectively and remain consistent and rigorous in your thinking, it is a good bet that you will be able to **make better decisions** than someone with little or no mathematical rigour. Just like studying philosophy, argumentation and rhetoric, mathematics is a tremendous tool for **structuring your thinking**. Superprof maths tutors can, therefore, enhance your logical mind. Look up maths tutor Perth and start taking lessons. To then declare that mathematics makes you more intelligent, as one sometimes hears, is for us a step too far, however, it's true to say that you will likely be more comfortable with the "consistency" and "logic" components of reasoning.

**Maths in Learning Patience**

To put it bluntly, it would be quite difficult to be effective in mathematics

without a minimum level of patience!

Through practice, you will realise that this discipline is a **true therapy for patience**. At times you will need five or six steps of reasoning to answer a single question or solve a puzzle formulated of only a few words. Over time, you will learn how to formulate your reasoning, make your own shortcuts and, above all, stay focused from beginning to end, on an exercise, problem or puzzle.

## Other Places where you find Maths in Action

**In psychology and sociology:**Data are analysed and compared using mathematical or statistical methods**In fitness classes, such as aquagym:**You need to keep count to stay in synch with the sequence of movements.**In biology:**Maths has numerous applications, for example in finding the number of molecules produced in a chemical reaction**In sewing:**Maths is applied when using axial symmetry, to calculate angles and make the correct cuts to create an accurate pattern.**At the theatre:**Maths helps you to locate your seat, to predict the duration of a spectacle, or to calculate light intensity.**Chess:**To anticipate your opponent's moves and calculate the displacement of your own on the board.**In scuba diving:**To stay safe underwater, to evaluate depth, the amount of air remaining, the surface interval (time between dives), you must have a logical approach and a grasp of some of the basics of maths.**Playing your favourite sport:**To evaluate a distance, to make a play, to calculate an angle.**In love:**Maths and seduction are intricately linked!**To organise yourself day-to-day:**To count days and months, or evaluate the time needed to perform a task.**To****calculate****your****taxes****For your household budget:**To give pocket money to your children, to make a monthly budget for family expenses. or plan for major purchases like a new house, car, holiday, etc.**Getting from A to B:**To estimate the distance and time involved in getting to a destination.**Playing billiards:**The application of symmetry.**Painting and drawing:**Knowing how to create given shades of colour by correctly mixing different pigments.**Browsing Facebook and other social media:**Have you ever noticed that thanks to your friends and interests, social networks and the website you surf provide an experience ever more closely aligned with your tastes over time? Behind this "phenomenon" lies a raft of**algorithms**that would not be possible without advanced maths.- And finally, to solve
**puzzles and other mental maths games**!

### S**ummary**

- As you can see,
**mathematics has many real, practical applications in our everyday lives:**Whether in relation to cooking, shopping or buying a house. - Whether you or not you aspire to become a mathematician, this discipline is a science in its own right, and one that has a great importance for everyone. Without maths, a great many
**technological innovations and inventions**would never have been born. - Maths is also an
**essential part of your professional life**, even if yours is a non-scientific job! An administrator needs to know how to use Excel, a salesperson; to do mental calculations, and an architect; to calculate angles. - Finally, maths can teach you to be more
**patient and rigorous**. Give it a try, you might be pleasantly surprised!

Perhaps even without knowing it, you are already using mathematics on a daily basis! It just might be time to rethink your relationship with the topic!

Find a tutor for GCSE maths revision in your local area or an online maths tutor with Superprof.