Sunday, March 13, 2011

Mental math

Has math always seemed difficult? 
Do you feared math? Do the Reading numbers having more digits, fractions, decimals, addition of decimals, addition of fractions etc blurred? Do you fear terror of making mistakes? Beatings, scolding’s created a type of allergy towards math? Is your progress report is very consistent with red mark? You don’t know ’how to learn math.’
Don’t worry; I will give you ultimate solution.
Most of the students are struggling in academic Math, just because of their Parents,
 ‘Academic Math Teacher’ and ‘Tutor’. It is just like a blind who shows and explains about elephant. Most of the parents themselves are don’t know what is real education is !  They are running after the grades / marks given by the teachers. They believe what it is their in monthly progress statement. Unfortunately the truth of the day is less salaried people are into teaching field.
So called our professional teacher who are inside the concrete premises are cemented their brain in such a way that no new idea should enter into it.
My first question is
Who can maintain a car efficiently?
 Owner    OR
Owner cum driver   OR
A  mechanic
What do you say?
A driver knows how to operate , mechanic knows how to replace different parts of the car.  Owner may handle his car with utmost care. Here affection/love/emotion etc doesn’t make big difference while maintaining a car. The correct answer is ‘ The designer of the car’  means one who knows internal structure of the car, who knows functions of each parts of  a car , principle behind that engine, logic behind each arrangement , can maintain each parts in a better way.
What do I mean is, one who knows internal structure of Math can teach Math in a Easy way . OR One should teach internal structure of Math, then only both Teacher and students can enjoy the process of Teaching – Learning.
Math is having internal structure, it has to be understand by the teacher as well as learner otherwise it is as same as  blind fellow describing another blind about elephant. 
For example if I write 2 x 5 = 10  it is information, it is right , but If someone asked himself or others why it is 10 Why not 11?    then one who answer should know its internal structure.
2 X 5 = 10 has internal structure.
We should understand that math evolved along with men. Initially they were adding like 2+2+2 +2+2 = 10
Then they thought it is better to stop doing donkey work, they wrote multiplication table.  2 x 5=10
Addition of repeated digits is nothing but multiplication.
So multiplication is shortest version of addition.      
  I am not of the opinion that this is not understood by our teacher. Can they explain same way subtraction? Or division?  Just check it out. Better you check with simple questions like this, then decide from whom you/your child should learn math.
Each and every concept of math has its own internal structure. Now you may ask, how this makes a difference while learning math. How it create a difference in performance/speed/comfort/confidence /easiness/curiosity/etc
Let us take one example.
How do you multiply any given number by  5 ?
 Say  48 x 5
Without knowing internal structure
Multiply 5 by 8:     5 X 8 = 40
Keep o in unit place :                   0
Then take 4 as carry
Then Multiply 5 by 4:     5 x 4 = 20
Add carry 4 to 20:    20 +4  =  24
Write 24 before 0 :            240

By  knowing internal structure
Example 1:   48 x 5
First Divide 48 by 2   :  48 2 = 24
Place zero in front of it. 240

Take any other example  360 x 5
First Divide 360  by 2   :  360 2  = 180
place zero in front of it----1800

Take one more example 6624 x 5
First Divide 6624  by 2   :  6624 2  = 3312
place zero in front of it----33120

Take one more example   37x 5
First Divide 37 by 2:  37 =18.5
18.5Multiply by 10 (multiplying with 10 is a if placing zero----185) =185
Here I am not doing any magic, it is just a common sense used after understanding internal structure of addition.  As we know multiplication is addition of repeated digits. In Example 1 48 x 5  , actually 48 should be added 5 times. But when we divide 48 by 2 it becomes its half). So instead of adding 48 by 5 times we are adding its half (24) , 10 times ,  nothing but  24 X 10 =240.  Multiplying with 10 is as simple as placing zero in unit place. Isn’t it?
Trick No 2:
How do you multiply any given number by 4?
SAY    27 x 4
                      27 x 4
Multiply 4 by 7 :  4 X 7 =28
Multiply 2by 4:   2 X 4 = 8
Add 8and 2 : 8 +2 =10
Place 10 before unit digit 8
          THEN  ANSWER IS  108
1. To multiply any number by 4 : All we do is double it, then double it again
First Double the 27:   27 x 2 = 54
Then Doble the 54 : 54  x 2 = 108

Take any example32 x 4
First Double the 32:   32 x 2 =64
Then Doble the 64 : 64  x 2 = 128
I will teach you hundreds of such amazing shortcuts right from addition, division, multiplication,  algebra, geometry  till calculus .
Thousands of shortcuts are already existed; lacs of tricks can be created only by understanding internal structure of math. If you check online materials available in the name of easy math, it is bullshit. The websites created to learn math are software in which you need to enter the numbers, it will display answers. Even in offline, books which are written in the name of easy math are exemplary in nature.
(It is unique effort to teach math in easy understandable way along with clarifications of doubt so raised. ………………………………..)