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Math Education Math for Grownups

What, Where and How to do Mathematics

What, Where and How to do Mathematics

What and Where is Mathematics….?

Everyone is aware with the word math. But no one try to define what math is. If you are thinking that what the rubbish question is it, everyone knows what math is, then you are wrong.

If we ask someone what math is? He probably said addition, subtraction, multiplication of numbers etc. or someone said solving algebra is mathematics. A few people can tell us exactly what mathematics is. It is not their fault. There is a fault of our systems, who do not develop the books properly. Some of teachers try to clear concept of mathematics but some of them not.

That is why many of us dislike the subject mathematics and suppose it to be hard or tough subject, but it is not. Mathematics is very easy subject if we found a teacher who try developing our concept. I taught by a teacher who never try to answer my question whether he always give me these questions as assignment from home. So, I never try to make question in front of him. But every time it is not the fault of our teachers, we are also wrong many times, we never give the proper time to mathematics, even not try to find something new. So today we try to understand definition of mathematics.

Every word has proper definition like Physics (Study of energy and motion), chemistry (study of molecules and chemicals), and biology (study of human and living things). But mathematics has not proper definition. Many philosophers try to introduce definition of mathematics. Some of said math is abstract science of numbers, some of said math is mother of sciences.

The math is too huge and cannot summarize in few words. Many philosophers claim that mathematics is a language of science which help each science branch to speak. Without mathematics every science field is mute. Like medical tell us about blood pressure but it cannot measure without the help of mathematics. Physics tells us about speed, but it cannot be measured without the help of mathematics.

Mean in every field you must use mathematics, even you cannot but a bus ticket without using mathematics. You cannot cock delicious food without using mathematics, you always put salt according to taste and quantity of food.

That is why philosophers said mathematics is a language, without it we cannot make conversation like other English French etc.

Imagine you are on the grocery shop and you are asked to buy 1 kg rice. How you tell the shopkeeper that you want to buy 1 kg rice? You look like a deaf. You have not any other way to tell him without using mathematics.

You can never think to live without mathematics. Mathematics is a necessary tool of life.

Once I was reading the history of mathematics, that how numbers were introduced? I read the story of Egyptians who invent the numbers first time 5000 BC. A herdsman compared sheep of his herd with a pile of stones when the herd left for grazing and again on its return for missing animals. In the earliest system probably the vertical strokes or bars such as I, II, III, IIII etc. were used for numbers 1, 2, 3, ….

After reading this story I come to know the exact meaning of “Necessity is the mother of invention”. But the mathematics is the mother of sciences said by mathematicians. But now a day mathematics is growing up as a language.

If we talk about painting, even mathematics is here. Exact amount of two colors makes a new color.

How to do Mathematics….?

We always listen from our math teacher if you want to perfection in mathematics then do practice, practice, and practice. Are you ever think that how to do practice? Many of us think practice mean do one question again and again. No…. Its not mean this. Its mean does practice of your concept.

How to practice of your question? When ever you learn a new question then first make question on it with teacher. Ask the teacher,

what is the purpose of this?

Why we are doing it?

At each step ask why we do as and why not?

We have a typically question with the math teacher to repeat the question. This is not a way to improve your math skills.

After getting the answers to your question,

open your note book any start solving this question

According to your thought and complete it in any cost

Even you are doing wrong

When you finish it then match your solution with the correct solution

Match the step where you did wrong

After pointing out each mistake in your solution go to math teacher

Asked him why we cannot do as I do

He will explain your mistake

Now start again a new question

Now at each wrong step your mind jerks you that it Is not write because you have taught by your math teacher that it is wrong.

When we made mistake by own hand and then get explanation of mistake, and then whenever try to make same mistake again, our mind never with us. Which is the sign of our mistake.

That is called practice. When each time you do new question by yourself by understanding each step, that why I am doing it or why not. Never hesitate to ask question by your teacher, if you are feeling hesitation you are not going to learn new things. Develop your habit to ask questions and always try that your question start with why, which, how etc. never say repeat it.

The last thing always sees the solution after the completion of your question. If you see solution at each point where you stuck, you are not going to learn new thing. When you make mistake, it will be resolved and you learn it, when you start copy paste you never get confidence to learn.

We always learn by our mistake.

Categories
Math Education Math for Grownups Math Secrets

An Easy Approach to Mathematical Modeling

In daily life we use mathematics to estimate our budget, calculate price, profit, loss etc. Doing this work is known as mathematical modeling. Basically, mathematical modeling is the part of our real life. Many of us know by the word “word problems”. In mathematics when a problem described by words it called word problem.

If we make mathematical model of our daily routine then it is very easy to maintain the time in work, game and for family. In this era of busy life, time management is a big deal. If we draw the mathematical model of time and spend time according to this, we can mange time easily.  

Not just the time, even we make a mathematical model of daily expenses we can also save a lot of money. Many of us are willing to take load from the bank but unable to calculate the mortgage of credit. If they are expert in solving word problems, then they can calculate their budget to know that are they able to return loan on time. How they can save money by paying installment in how many times?

I remember when I was kid, my mom gives me $15 pocket money for a month and asked, “How much you have to spent daily for covering the whole month?” Because I always spent the whole money before the end of the month. Now I understand that mathematics is too useful even for a kid. That time if I able to make equation of my expenditure then now I have too much money.

If mathematician does not develop the mathematical modeling, then physics was a theoretical subject, suppose how physicists find out the velocity with out modeling the definition into mathematical formula?

Many students have issue in solving word problem, but it is not a big deal. Just focus on some points in the statement and you will become expert in solving word problem. The way to write a statement in mathematical expression is called “Mathematical Modeling”.

Before solving any word problem, you must well verse in Mathematical modeling, draw your attention on the following points to make model of any word problem.

Focus on the following points in any statement:

  • What do you know?
  • What do you want to know?
  • What is the proper operation?

Example: Biden bought 2 kg tomatoes, 1 kg potatoes, 5 kg carrots and 3 kg apples from a market. How much weight he carries from the market?

Now according to above points find out the useful information. First see what we have given in the statement:

Biden bought 2 kg tomatoes, 1 kg potatoes, 5 kg carrots and 3 kg apples from a market. How much weight he carries from the market?

What do we know?

Weight of tomatoes= 2 kg

Weight of potatoes= 1 kg

Weight of carrots= 5 kg

Weight of apples= 3 kg

Now see in the statement what we must calculate or evaluate?

Biden bought 2 kg tomatoes, 1 kg potatoes, 5 kg carrots and 3 kg apples from a market. How much weight he carries from the market?

What do we want to know?

Total weight he carries?

The last thing we have to see, how to do? Which operation have to use? Since we want to know total weight so, total amount always calculated by addition.

What is the proper operation?

By adding weight of all.

Total weight=2+1+5+3=11 kg

Hence, Biden carries 11 kg.

If the word problems including more then one operation, then you have to focus on the following points:

  • Find out number of objects / people used in statement
  • Give name to each object / person
  • Breakout the statement into pieces according to object / person
  • Step by step write them with the given relation

Just do some examples to understand:

Example: If the sum of two numbers is 12 and difference is 2. Find the numbers.

According to our points, first see how many objects / persons are discussed?

If the sum of two number is 12 and difference is 2. Find the numbers.

Number of objects is two.

Now give name to both numbers. Let x and y are two numbers.

Now break into pieces:

If the sum of two numbers is 12 and difference is 2. Find the numbers.

The first when saying sum is 12:

So relation becomes

And second one saying difference is 2:

You can list this relation as you want, mean

or

Both are correct.

I take

So, we have two equations:

Both can solve simultaneously to get answer.

Adding both equation

Cancel the opposite terms and do simplification:

We get,

Put this one in any equation, I am putting in the first one

So, the numbers are 5 and 7.

Now what you think? It is easy now to solve word problems.

Consider if a problem consists of a single object / number and relating this object / number by itself then focus on the following points:

  • Name that object / number
  • Find out the relation between object / number
  • Write them in equal

Example:  If a number exceeds its square root by 56. Find the number.

According to our points, first see how many objects / persons are discussed?

If a number exceeds its square root by 56. Find the number.

Let x is that number.

Now break into pieces:

If a number exceeds its square root by 56. Find the number

As we know square root of 4 is 2. Number always greater by its square root so, in the above statement number is greater by its square root and according to statement number exceed by 56.

It can be solved now easily.

Rewrite the above equation:

Taking the square on both side of the equation:

By solving above quadratic equation, we get x=64 and x=49.