Thursday, June 5, 2008

Magic of Numbers

Mathematics/Maths is the most wonderful subject I had ever known. Nothing amuses me as solving problems in maths. I feel that the subject explains the essence of life wonderfully. There is no problem without a solution and all you need to do is to apply right logic at the right time to arrive at solution.

When It comes to learning maths, many cultivate an aversion towards the subject. Imagine it a game of numbers, then you will relish the act of problem solving.

When I was a kid I had kept a technique to deal with maths problems. I would imagine every problem to be a small treasure hunt. I would like to share few techniques which I followed and eventually ended up making it my favorite subject.

Problem Solving Technique

1.When you are given a problem, just read through it, look between the statements, you will end up finding hints which help to understand it better.
2.Split the problem to pieces and list down information available and what is to be arrived at.
3.Categorize the problem. I mean Classify which subject is it related to say Algebra,Trignometry.

I had this habit of imagining that I was flipping through pages of my textbook. Once I categorize the problem, and I find it to fit into chapter 5, I imagine that I am flipping though pages of that chapter.This may sound weird but it really helped me to track down the best fit.

4.Categorize it further to match it to a theorem/formulae.
5.List down the formulae you find related to it.
If you have followed perfectly till step 5 , Congrats you are almost there :).
6.Now place the information you have obtained from step 2 to the formulae you have.
7.With little of practice you made prior to exams and using common application knowledge you will end up finding solution to the problem.
8.Congratulate yourself for arriving at the destination(Hey you started it as finding a Treasure right..here you are!! )

Tips to Enjoy learning maths

1.Take a piece of paper and list down the chapters you have and pin it above your desk.
2.Once a chapter is complete list down all possible formulaes in a paper and file it. Take quick glances every day. You will end up memorizing them easily.
3.Practice maths problems never attempt to read them like reading a story book. Practice makes a man perfect :)! This will help you to face problems with courage in exams. During practicing problem, We tend to get stuck mid way and we try to solve them. If you face similar situation in exam, you can go over the hurdle with ease.
4.Attempt to solve problems using different approaches. Enables you to adopt new ideas. who knows you may end being a B-School grad "Thinking Out of Box" in future ;)
5.Discuss with peers and help out friends who struggle to solve problems. You will gain a lot.

I used to think myself as a teacher and practice as if I am teaching a student ;)


Learning Made Simpler

Would you like to be called a "Super Computer" calculating at random rates? Welcome to the world of "VEDIC MATHEMATICS".
For literature about it read here .

I am presenting few simpler techniques I learnt.

Multiplication of a two digit number with 11

What is 11 * 12 ? Oh don’t start multiplying, here is a simple method.

11 * 12 = 1 (1+2) 2 = 132

11 * 13 = 1 (1+3) 3 = 143

11 * 24 = 2 (2+4) 4 = 264

11 * 38 = 3 (3+8) 8 = 418 (Carry on from addition to be added to 3)

Square of a two digit number which is a multiple of 5

35 * 35 = (3*4) (5*5) = 1225

1.Seperate the ten's place and one's place.
2.For Ten's place multiply the ten's place number with its immediate successor .
Example: In above illustration, we have to find square of 35 so multiplying 3 with its immediate successor 4 will give the
result

65 * 65 = (6*7) (5*5) = 4225

55 * 55 = (5*6) (5*5) = 3025 Bingo!

Doesn't it look simpler and easy ? Of course you will relish the magic of numbers once you start using these techniques :)

We do have so many tutorials and books on this vast subject which cannot be discussed in one go. We will discuss some more Simpler techniques in next part.

22 comments:

  1. Divya said...

    Very good Post Ramya:))

    Great job!!

  2. Divya said...

    \\What is 11 * 12 ? Oh don’t start multiplying, here is a simple method.

    11 * 12 = 1 (1+2) 2 = 132

    11 * 13 = 1 (1+3) 3 = 143

    11 * 24 = 2 (2+4) 4 = 264

    11 * 38 = 3 (3+8) 8 = 418 (Carry on from addition to be added to 3)\\

    Simple & Intresting:))

  3. Divya said...

    \\We will discuss some more Simpler techniques in next part.\\

    Looking fwd for the next part .........to learn more techniques.

  4. ஜி said...

    Saringa Teacher...

    Will forward this page to school going friends...

    Nice Informative post...

    aana namakku antha alavukku arivellaam illeenga :)))

  5. GURU said...

    Good Morning Teacher!!!!
    hey its gud.... namakku dhan sutu potalaum kanaku varamatengudhu....

  6. ILA said...

    shh
    padicha maths maranthu poyirum pola irukee :(

  7. Priya Murthi said...

    Ramya... edho namma range ku musical wishes... namma ooru seemati appudinu potutu irrundhe... dhidirenu rangeeee maathitiyeee.... kalaku...

    Maths pathi oru nalla write up... school la irrukumbodhu blog illama pochu... irundhrundha indha technique ellam use panni mark adhigama vaangi irrukalam...:)...

    informative post and clearly reflects your passion for Maths... Keep going...

  8. விஜய் said...

    I too have love for numbers. If you want to figure out what x to the power 2 would be, I figure out the number, whose square root would be x.
    I shall give you more amazing facts with numbers:
    13 x 13 = 169
    31 x 31 = 961
    103 x 103 = 10609
    301 x 301 = 90601
    1003 x 1003 = 1006009
    3001 x 3001 = 9006001
    10003 x 10003 = 100060009
    30001 x 300001 = 900060001

    Actually I found this interesting analogy by myself. Not sure, anybody has already found this.

    About Maths, you should read this post of mine. My father teaching me mathematics
    http://vettivambu.blogspot.com/2005/07/blog-post_20.html

    anbudan,
    Vijay

  9. Usha said...

    divya-oda pic dhan ennoda comment :)

  10. Srinivas said...

    Hello,
    Nice Blog...Keep Going.
    I like the pictures...and also post.
    You must check this blog,if u got free time..don't forget...
    www.pgkut.co.cc

  11. மோகன் கந்தசாமி said...

    ///Welcome to the world of "VEDIC MATHEMATICS".////

    Vedic?,….MATHEMATICS?,….

    Ha ha, how do you explain that? The so called MATHEMATICS in Veda are merely tricks, there is no proof. Math is a science which needs proof even for the obvious like one plus one equals two.

    Else, we can say it algorithms. Of course, algorithm needs to be proved, but not rigorously as long as it works fine. Example, Knuth-Morris-Pratt algorithm.

    Another blabber I use to listen to my mother, a math teacher, is “Siddha Sayings” proved Pythagorean theorem.

    “Hypotenuse of a right angled triangle is the sum of seven eighth of larger side and half of smaller side”

    My question was “Is it consistent with law of cosines?” If no, then it’s, again, merely one of many tricks.

    But, we must appreciate these tricks are really useful for school goers. Thanks, this post is worth reading.

  12. gils said...

    wow..maths is my fav suj too..mite sound weird but 11th 12th apolam bore adicha maths poatu pathitrupen...avlo pudikum... :) neenga CBSE style schoolla padicheengala? AMTInu oru magazine varum theriyuma? Association of maths teachers (india) nenakren..it had all sorts of shortcuts like u've mentioned here

  13. தமிழன்... said...

    நாங்களும் கணிதம் தான் படிச்சோம் ஒரு காலத்துல...ஆனா இப்ப அப்படின்னா என்னான்னு கேக்குற அளவுல இருக்கு அறிவு..:(

    உண்மையாவே கணக்கு பத்தி பேச ஆரம்பிச்சாலே எனக்கு நிறைய பழைய நினைவுகள் மனதை நிறைத்து விடுகிறது...

  14. Ramki said...

    No problem without a solution ?

    http://en.wikipedia.org/wiki/Unsolved_problems_in_mathematics

    http://www.claymath.org/millennium/

    I guess one of the charms of math or any science is the fact that we'll never know if we'll be able to solve all the problems. If we do, it is just a matter of working out the details ( remember the the clockwork universe ). Thanks to Kurt Godel and Heisenberg, we now that certain problems will eternally remain unsolved, thus adding to the appeal of science

  15. Ramya Ramani said...

    @divya

    Thanks Divya.Will surely share the other techniques i know :)

    @Geeya
    Ok sir Sureah School pora kozhandaigalukku sollunga usefulah irukkum :))

    @Guru
    Inda techniques usepanna easyahvum interestingahvum irukkum sir

    @ILA
    Ada enna sir ippadi solliteenga!!

  16. Ramya Ramani said...

    @Priya

    Yeah maths fascinated and continues to do so till date :))

    @Vijay
    Good gracious!! Your analogy s simple and good...btw ur post was good :) Reminded me of learning Tamil from Amma..may be the ways she thought me had inspired me to blog in tamil as well occassionally ;)

  17. Ramya Ramani said...

    @Usha
    :))

    @Srinivas
    Thanks for dropping in.Will surely visit urs :)

    @Mohan Kandaswamy
    \\Ha ha, how do you explain that? The so called MATHEMATICS in Veda are merely tricks, there is no proof. Math is a science which needs proof even for the obvious like one plus one equals two.\\

    I do understand that Maths need proof
    Still My 2 Cents
    Any Kid who finds it quite difficult to learn maths must be taught in a method such that he/she gains interest in the subject..As the post topic goes..if u could teach them such simpler methods I bet they wud develop interest :))

    \\But, we must appreciate these tricks are really useful for school goers. Thanks, this post is worth reading. \\

    Ade Ade..Thanks for comments too :))

  18. Ramya Ramani said...

    @gils
    \\wow..maths is my fav suj too..mite sound weird but 11th 12th apolam bore adicha maths poatu
    pathitrupen...avlo pudikum... :)\\

    Cool! Enga veetla ellam paperla formulas,chemistry equationsah irukkum..pazhaya paper karan kitta ammava maths notebooks mattum poda vidamatten..innum paranla irukkanum all my maths notebooks from 2 std hopefully :P

    \\neenga CBSE style schoolla padicheengala? AMTInu oru magazine varum theriyuma? Association of maths teachers (india) nenakren..it had all sorts of shortcuts like u've mentioned here\\

    Aha kandupidichuteengala..yeah CBSE school dhan padichen..neenga solradhu nyabagam irukku..moreover enga schoola oru miss VEDIC MATHEMATICSla research ellam pannituirundhanga so she use to tell this everyday in assembly..we learnt maths as if it was a daily activity :)) Tortoise sutha vechiteeenga ;))

  19. Ramya Ramani said...

    @Thamizhan

    Adade Maths padicheengala nalladu..thanks for comments :)

    @Ramki

    Yeah I do agree to your point but these tricks would fascinate school goers and who feel that maths is subject of problems alone:)
    BTW thanks for the links would definitely look into them. Thanks for comments too :))

  20. Anonymous said...

    //pazhaya paper karan kitta ammava maths notebooks mattum poda vidamatten..//

    avvvvvv...same blud :) aana recenta veeta ozhikaren pervazhinu enaku theriyma enga amma bookslam edaiku potutaanga :(

    //moreover enga schoola oru miss VEDIC MATHEMATICSla research ellam pannituirundhanga so she use to tell this everyday in assembly//

    ithu suber..i used to subsrcibe to that mag. till i was in that school..ipolam varuthanu therila..

    ~gils

  21. Shwetha Robert said...

    First visit to your page from your comments in Divya's blog,

    your post has planted a passion for Mathametics in me:-)

    Pls,share on the other techniques you know Ramya.

  22. Sireesha said...

    The blog on "Magic of Numbers" is very good.