Math

Imagine a world without mathematics. Sounds chaotic right? Math is about numbers, shapes, logic, patterns, and so on. It deals with quantities, operations, and how those operations are making our lives easier. So, let's see why math is important.

 

Mathematics is the study of numbers, shapes, formulas, data, and arrangement. Math plays a major role in many fields like engineering, science, medicine, economics, finance, etc. So it is significant to understand math concepts. And we even use math in our daily life for checking time, date, calculation, shopping, cooking, etc.
 

 

Math is the science of numbers and their operations, properties, and relations. It also deals with data, measurements, quality, angles, and change. Now let’s discuss more about the concepts of math. The basic operations of numbers are addition, subtraction, multiplication, and division. 

Math and numbers have been a part of history since ancient times. In all these years math has developed from simple counting, calculation, and measuring to advanced math and online math.

Archimedes introduced the formula to calculate the volume and surface area of solids. So he is known as the father of mathematics. Aryabhatta, the father of Indian mathematics, introduced zero (0) to the world.

Euclid, Pythagoras, Bhaskaracharya, Hipparchus, etc., are some famous mathematicians in the history of math. The tally marks on bones and caves show evidence of the usage of math during the Paleolithic age. Traces of math are also found in civilizations like Egypt, Mesopotamia, and Greece. With time, the need to count more things increased, leading to the development of numbering systems by the Greeks, Hebrews, and Egyptians. For a standardized number system by the ninth century, Arabic numerals (0-9) were introduced, making calculation easier.

 

Then came a need to calculate the motion, change, and do advanced physics. As a solution, by the 17th century, Calculus was developed by Sir Isaac Newton and Gottfried Wilhelm Leibniz. It is used in different fields of physics and engineering. By the 20th century, cryptography, computational complexity theory, and coding theory saw the applications of mathematics. Mathematics has developed a lot and is developing daily.
 

Why is math important in academics?

Mathematics plays an essential role in developing cognitive skills and problem-solving skills. So, math is a part of academics from grade K. It has topics and concepts relevant to daily life. Math is applied in fields like engineering, medicine, physics, and so on. Applied math and pure math are the branches of mathematics.
 

Aren’t we using math from the time we wake up till we sleep? Math is the base for many of our daily activities. Math for kids is structured in such a way that it can help them develop decision-making and problem-solving skills. Now let’s discuss the importance of mathematics:

 

• Math is an integral part of our daily life. We use it in many ways like checking time, date, measurements, calculations, and many more.

 

• We schedule our day with the help of math. We know it is easier for us to manage our day by calculating the difference between two or more time periods.

 

• We use math in finance as budgeting is part of our life. As a kid, when you get pocket money, you need to calculate it and plan your expenditure. So you all need to know about math. 

 

• Math offers a wide range of career options.

 

• Solving math requires critical thinking. We need to remember the formulas and concepts to solve math equations.

 

• Helps in cognitive development; after getting familiar with the basic math concepts, kids can solve them using mental math. This increases their cognitive skills.
   

Why do kids consider math as a complex subject? To solve math equations, we must have the knowledge of different concepts. Also, solving math problems requires a lot of patience and practice. For a better understanding of basic math concepts, kids should be aware of the fundamentals of math. Let’s check out some fundamentals of math:

 

1.Number: Numbers are a part of basic math concepts, and numbers are the basic arithmetic values used to represent quantity. There are various types of numbers like integers, rational numbers, irrational numbers, prime numbers, even numbers, odd numbers, etc. Example: Integers: -5, -4, 0, 1, 2

Rational numbers: 12, 57, 0.35
Irrational numbers: √15, √6, π
Prime numbers: 2, 3, 5, 7
Even numbers: 2, 4, 6, 8
Odd numbers: 1, 3, 5, 7

2.Operations: The basic math operations are addition, subtraction, multiplication, and division. These operations are for real numbers. Each operation is represented using different signs like + (plus) for addition, — (minus) for subtraction, × (time sign) for multiplication, and ÷ (division sign) for division. 

Addition: Here, two or more numbers are added together to get a new sum. The numbers added together are called addends.
Example: 2 + 5 = 7

Subtraction: Here, the difference of two or more numbers is calculated.
Example: 5 - 3 = 2

Multiplication: In multiplication, numbers are multiplied together to get a product. Multiplication is the repetitive addition of the same numbers.
Example: 5 × 6 = 30

Division: Here, a larger number is broken down into smaller numbers. 
Example: 8 ÷ 2 = 4

 

3.Geometry: Geometry is all about the shapes, structures, angles, and dimensions of different objects. The type of geometry is plane geometry, three-dimension geometry, solid geometry, etc.

 

4.Algebra: The relationship between the things that change is expressed using mathematical statements. The variables like x, y, and z are used.

 

5.Calculus: Calculus deals with the study of changes and motion. Derivatives and integrals are used in calculus. 

 

6.Trigonometry: Trigonometry is the study of the relationship between angles, length, height, and distance. The basic functions are cosine, tangent, cotangent, secant, and cosecant.
 

From all we read till, do you think math has branches? Yes, math is not into one but has a lot of branches. Branches of mathematics are the interlinked topics which overlap each other. The common two branches of mathematics are - 

• Pure mathematics: It is the math for math’s sake. It is more into math and discovering new realms of math by, here the focus is on abstract and theoretical concepts in math and proving them

 

• Applied mathematics: It is the practical form of math. It is the practical application of math in the field of engineering, science, physics, etc. 

 

Pure mathematics Vs. Applied mathematics

 

• Online math learning: Online math learning is the way of learning math using the internet. Here, the teacher can directly interact with the students and teach them, so it offers personalized learning. It makes students understand the concept well and increases the focus. Nowadays, there are many online math courses according to the needs of the students.

Math is all about the formulas and how we use them. One of the best practices to learn math is remembering formulas. In this section, we can learn some basic math formulas

 

• Geometry formulas: 

Some examples of 2-D formulas

Triangle-

Area of a triangle = 1/2bh
Here, ‘b’ is the base and ‘h’ is the height of the triangle

 

Circle -

Circumference of a circle = 2πr
Area of a circle = πr²
Here ‘r’ is the radius of the circle 

 

Square -

Area of a square = a²
Perimeter of a square = 4a
Here, ‘a’ refers to the length of a side

 

Rectangle -

Area of a rectangle = l × b
Perimeter of a rectangle = 2(l + b)
Here ‘l’ is the length and ‘b’ is the breadth of the rectangle 

 

• Quadratic formula: ax² + bx + c = 0

It is a polynomial equation of the second degree. Here, the variable is ‘x’, the real numbers are ‘a’, ‘b’, and ‘c’. Here, a ≠ 0

 

 

• Pythagorean theorem: c =  √a² + b² 

The Pythagorean theorem is applicable to a right-angle triangle. This equation is applicable to find the length of the longest side. Here, the length of the longest side is ‘c’, and ‘a’ and ‘b’ are the lengths of the other side.

 

• Algebra formulas:

(a + b)² = a² + 2ab + b²
(a - b)² = a² - 2ab + b²
a2 - b² = (a - b) (a + b)
a² + b² = (a + b)² - 2ab

 

 

• Percentage formula:

 

Percentage is the representation of a number as a fraction of 100.

Percentage = given value / total value × 100
 

In math, for representing operations, relations, concepts, and so on we use symbols. Each function has a unique symbol, let’s learn some of them.
 

• Plus symbol: + used in addition

 

• Minus symbol: - used in subtraction

 

• Times sign: × used in multiplication

 

• Division sign: ÷ used in division 

 

• Equal to: =

 

• Not equal to: ≠

 

• Greater than and less than: >, <

 

• Plus or minus sign: ±

 

• Exponent: a²

 

• Square root: √

 

• Cube root: 3√a

 

• Percentage: %

 

• Set: {}

 

• Pi: π
   

The characteristics of a number that follow when doing operation are the properties in mathematics. 
 

The four properties of math are:

 

• Commutative property
• Associative property
• Distributive property
• Identity property

 

Commutative property:

 

Commutative property is applicable for addition and multiplication. When you add or multiply two numbers in any order, the result will be the same.  

In addition: a + b = b + a
Example: 2 + 5 = 7
5 + 2 = 7

In multiplication: a × b = b × a
 Example:  2 × 5 = 10
5 × 2 = 10
 

Associative property:

 

Grouping the numbers differently won't affect the result. However, it can be applicable only for multiplication and addition.

(a + b) + c = a + (b + c), example (2 + 5) + 3 = 2 + (5 + 3) = 10
(a × b) × c = a × (b × c), example (2 × 2) × 5 = 2 × (2 × 5) = 20
 

 

Distributive property:

 

Distributive property states that a × (b + c) = (a × b) + (a × c). When you multiply a number ‘d’ with the sum of two other numbers, ‘a’ and ‘b’, the resultant will be equal to the sum of two products. Here, the products will be (d × a) and (d × b).

For example, 2 × (4 + 3) = (2 × 4) + (2 × 3) = 14
 

Identity property:

 

The numbers are identities in certain operations:

In addition: when adding 0 to a number, the sum is the number itself.
24 + 0 = 24

In multiplication: The product of multiplying a number with 1 is the number. 
24 × 1 = 24

 

The devices which help us to perform math calculations are the math calculators. It is available as both devices and software. Some of them are basic calculators, scientific calculators, online calculators, graphing calculators, and so on. 

Nowadays, children use web-based tools like online calculators for easy calculation. These are easily accessible and free to use. We can use it to perform various calculations from basic math concepts to advanced math applications. Here are the list of online math calculators:
 

Math is always considered a difficult subject, isn’t it? To improve math skills, let’s check out some tips. Here are some easy math tricks and tips. 

 

 

• Memorizing - One of the easiest math tricks is to memorize. Try to memorize multiplication, values of pi, and formulas. For memorizing, kids can use flashcards. 

 

• Regular practice - Regular practice can help you master math. So, you need to practice regularly to understand math concepts. For practice, kids can use math worksheets, work on different problem-solving techniques, and math practice online.

 

• Remembering Formulas - For Geometry, Trigonometry, remembering formulas is an effective way to imply them in calculations.

 

• Rechecking Answer Sheets - In examinations, children make silly mistakes in calculations, they should spend a quality amount of time to revise the answer sheets.

 

• Proper Writing of Symbols and Numbers - In many cases, children may get confused with symbols, it is advisable to check those symbols with apt attention.

 

• Online Mock Tests - For lower grades, usually online mock tests or online math practice is also helpful to overcome the mistakes. 
   

From all we learn, we know that Math has an impact on the real world. So there are ample career opportunities for a person with a strong foundation in mathematics. Let's see some interesting career opportunities in mathematics. Mathematics teacher, accountant, computer programmer, financial analyst, finance planner, engineer, auditor, statistician, economist, etc.