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The Gaddha, Ghhorra and the Haathi concept: for teaching Addition and Subtraction of fractions

Posted by Dhiren Achtani under

Stories from School[2009-11],

Teach For India,

Teaching Mathematics
[2] Comments
My students – most of the grade-8 students found it difficult to add and subtract fractions. Though it was easy to make them understand addition and subtraction of simple fractions using the pie diagrams, it became difficult to do the same when the denominator was a large number and/or there was more than one pie involved (in case of improper fraction). Also, the concept of why we should find the LCM of the denominators and then add/subtract fractions became difficult for them to grasp. At this juncture of their age, it is important that the students first get the concept for their operational use and are confident to apply it rather than understanding the concept from first principle method. So i first made them get the concept operationally through a method I call the Gaddha(Donkey),Ghhorra (Horse) and Haathi (Elephant) method.

So let us say that we have to solve the following question –

3/4 – 4/6 = ? —> Change this to 3 gaddhas – 4 ghhorras = ?

Symbol for Gaddha = **/4** —> so this is how you identify gaddhas; All gaddhas have denominator as number 4.

Symbol for Ghhorra = **/6 **—> so this is how you identify ghhorras; All ghhorras have denominator as number 6.

Now, i ask the students – if they can take out 4 ghhorras from 3 gaddhas — the answer is a resounding ‘No’. So, i tell them that now we need to make them same so that we can solve this question.

How we do it is to USE ONLY the multiplication operation on the gaddha and the ghhorra respectively and find ONE resulting number that will make the gaddha and ghhorra into a haathi.

Easiest way to do it is by multiplying gaddha and ghhorra with each other.

Therefore, **/4** **X 6** = **/24 —> Haathi **

** ****/6** X 4 = **/24 —> Haathi**

One thing we need to remember is that whatever we multiply in the denominator, we must multiply the same number in the numerator of this fraction (otherwise the value of the fraction will change).

So, we finally get our new baby elephants (resulting numbers) through cross-breeding horse with a donkey.

3/4 becomes equal to 18/24 (18 haathis or elephants)

4/6 becomes equal to 16/24 (16 haathis or elephants)

=> 3/4 – 4/6 = 18/24 – 16/24 = 18 elephants – 16 elephants = 2 elephants = 2/24.

I have tried this method couple of times with my students and it works wonders.

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February 16, 2012 at 7:25 AM

Bhaiya I am your student Kshitija.I am not anyone to comment on your things,but yes I miss you a lot.Please visit us once.Bye!

February 20, 2012 at 9:40 PM

Bhaiya,today I read all your posts or blogs or whatever they are called and god promise they are fab.First I thought you were only good at math and brain stuff.But you seem:-Psorry are an all-rounder!Bye!