Topic 1: Concept of Mathematics – Mathematics Form One
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ABOUT THE TOPIC
Mathematics is all around us. Almost everything we do involves Mathematics. It is applied in various fields such as science, engineering, technology, social studies, economics and many others.
Numerous devices such as mobile phones, computers, television sets, and satellites are designed and manufactured on the basis of mathematical knowledge. In this lesson, you will learn about the meaning of Mathematics, branches of Mathematics, relationship between Mathematics and other subjects, and the importance of studying Mathematics.
The competencies developed will enable you to apply Mathematics knowledge and skills to solve daily life problems in different fields such as Agriculture, Entrepreneurship, Botany, Zoology, Music, History, Business, and many other fields.
THE MEANING OF MATHEMATICS
The word ‘Mathematics’ comes from the Greek word ‘mathema’, meaning ‘which is learnt’ or ‘science, knowledge or learning’. Numbers, measurements, shapes of physical objects, and equations form a small part of it.
Mathematics can be thought of as the science of the structures, orders, patterns, and relations that have evolved from elementary practices of counting, measuring, and describing the shapes of objects.
It can also be thought of as a language of science because by using mathematical reasoning, one can develop an understanding and be able to predict nature. Mathematics has the ability to provide precise expression for every concept that can be formulated using mathematical symbols and structures.
The knowledge and skills of Mathematics play a crucial role in understanding the concepts of other subjects, both in sciences and arts.
Branches of Mathematics
Mathematics can be categorized into different branches such as Arithmetic, Algebra, and Geometry.
Arithmetic
Arithmetic is a branch of Mathematics that deals with properties and manipulations of numbers. Manipulation of numbers is achieved through the use of basic mathematical operations namely: addition, subtraction, multiplication, and division. Examples:-
Algebra
Algebra is a branch of Mathematics in which arithmetic operations are applied to symbols rather than specific numbers. The symbols or letters in algebra are called variables which represent quantities with no fixed values. Example:-
Geometry
The word geometry was derived from the Greek word ‘Geo’, which means ‘earth’ and ‘metry’, which means ‘measurement’. Therefore, Geometry is a branch of Mathematics which deals with the study of the sizes, shapes, positions, angles, and dimensions of different physical objects.
Moreover, properties of points, lines, planes, similarities, congruence, and shapes of different regular objects are also studied in Geometry. Example:-
Relationship between Mathematics and other subjects
Every aspect of our life makes use of Mathematics in one way or another. Mathematics plays a major role as a tool for effective understanding of other subjects. Numerous concepts in other subjects and fields are described precisely using Mathematics.
Learning Mathematics can also benefit students through developing their problem solving and critical thinking skills. Note that, Mathematics formulas which are used to represent and describe concepts and scenarios in other fields are commonly referred to as mathematical models.
1. Mathematics and Agriculture
Agriculture is closely related to Mathematics. For instance, when farmers want to buy seeds, they need to understand the ratio of seeds that is sufficient per piece of land. Similarly, the determination of the number of bags of fertilizers needed per acre requires some calculations.
In these two examples, Mathematics enables farmers to avoid the wastage of financial resources by purchasing only the required amount of inputs. Mathematics is also used in Agriculture to determine suitable amount of water to be used in irrigation and the spacing between seedlings.
Similarly, Mathematics is used to determine the investment, expenditure, and savings in cultivating a specific crop, dividing a piece of land, calculating the cost of labour, and so forth.
2. Mathematics and Biology
There is a direct relationship between Mathematics and Biology. For example, normal animal weights, rate of respiration, nutritive values of food, and transpiration are a few quantities in Biology that can be calculated using mathematical concepts.
Mathematics can also be used to estimate the number of blood cells present in the body, measurement of blood pressure, and counting sex chromosomes, among many others.
3. Mathematics and Chemistry
Mathematics is widely applied in Chemistry to represent and solve various problems. Some Chemistry activities involve measurement of masses, volumes, lengths, temperatures and densities of matter.
Mathematics is also used to measure the constituents of mixtures, balancing chemical equations, among many other applications.
4. Mathematics and Physics
Physics involves the study of laws, principles, and theorems which governs how matter works. Most of the quantities in Physics are expressed mathematically through formulas. In order to understand how to apply the formulas to solve some physics challenges, knowledge of Mathematics is needed.
All the quantities in physics are expressed in numbers and units which have to be manipulated using the concepts and skills of Mathematics. For example, to determine the speed of a moving object, one has to find a ratio between the distance covered and the time taken.
5. Mathematics and Information and Communications Technology
Mathematics plays a big role in the field of Information and Communications Technology (ICT). Computer programs, applications, software, and computer languages make use of mathematical concepts.
A common example of the application of numbers is in defining colours in web development languages. For instance, the HTML (hypertext markup language) and CSS (cascading style sheets) uses colour notations such as #000000 which represent Black, #008000 for Green and #800000 for Maroon. Furthermore, the digits 0 and 1 are commonly used in computing systems in computers.
6. Mathematics and Business Studies
Mathematics is widely applied in daily life activities related to Business Studies. For example, if one wants to determine profit or loss in business, a difference between the selling and buying prices is to be calculated. If the buying price is less than the selling price, the business makes profit.
If the buying price is higher than the selling price, the business makes loss. Mathematics is also applied in other areas such as in loan borrowing, determining prices of items, among many other applications.
7. Mathematics and Geography
Geographers require mathematical calculations to find the distance from one place to another, finding gradients, altitudes of hills and mountains. Through mathematical calculations, geographical locations of different places are determined using latitudes and longitudes, and real-life objects such as buildings are represented on a map through the use of scales.
8. Mathematics and History
Mathematics helps in describing various historical activities such as duration of events and expressing historical events which happened at different points in time. For example, a simple mathematical operation is used to determine duration of historical events such as World Wars, colonial periods and time spent by leaders in positions, determining dates and ages of fossils by using some mathematical principles such as carbon-14 among many other applications.
9. Mathematics and Literature
Mastering basic concepts of arithmetic can enable a person to understand better and manage literary works. A kind of writing which can draw attention to readers depend on several factors such as number of words per sentence, the number of sentences per paragraph, and the number of paragraphs per page.
For example, 20 words in a sentence are considered as average. Thus, in analysing writing style, one need to find an average number of words in each sentence, which requires Mathematics concepts.
10. Mathematics and Music
The knowledge of Mathematics plays a vital role in music. For instance, playing one note in piano has a different sound as when three harmonic notes are played together. Music notes are distinguished mathematically by their different values.
A semibreve has four beats, a minim has two beats, crotchet has one beat, quaver has 1/2 a bit, semi quaver has 1/4 a bit, and so on. Reading and playing music represented by notes in a music sheet depends on the mathematical ability to understand these values.
11. Mathematics in Sports and Games
Mathematics is important in all forms of sports and games. For example, in many sports and games, winners are those who have accumulated highest number of points. Furthermore, in most of the sports and games, there are specific number of players in the playing ground.
For instance, a football team has 11 players while a netball team has 7 players. Moreover, players in some games such as football are given names in terms of numbers. In football, a goalkeeper is normally assigned number 1. In addition, all playing grounds are prepared with specific standards of measurements.
Importance of Mathematics
Learning Mathematics and using mathematical skills in daily life enhances problem solving, critical thinking, effective time management among many other importances.
Financial Management
Financial management requires mathematical skills during the preparation of budgets. Calculations are done to ensure the budget prepared correlates with the funds collected.
Problem-solving skills
Problem-solving is one of the most important skills in life. Mathematics is one of the most effective ways to increase analytical and logical thinking, which helps us to become better problem solvers.
Time management
Time management is a key to success for everyone. Therefore, time must be carefully managed. Mathematics helps to determine the time spent on every activity so as to maximize its efficiency.
