Hello friends,

I did not know that I will be back with the new post so soon... But then, this summer has given me a wonderful opportunity to work with the children Daily. And hence, I am so lucky to be a part of (learn from) such stories daily.

If some of you have been unable to read the earlier post, where Poonam is intentionally allowed to make a spate of mistakes in the multiplication and division algorithms, how she arrives at a (erroneous) conjecture by observing / analyzing some patterns in these mistakes, and finally how she spots her mistake to counter/ discard her own conjecture. A beautiful cycle of discovery that probably mathematicians and scientists would go through.

This is the link to this story:

__http://rupeshgesota.blogspot.in/2015/06/we-can-divide-product-only-with-first.html__
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It all started with just a casual inquiry to one of my students - "what do you feel how much does my bag weigh?"

From which the discussion gradually navigated to the fact that how some shopkeepers cheat the consumers by fixing the std. weights. Sachin claimed that he has seen the 'hole' on the other side of the standard 1kg weight so that no one can spot it. To which Sushma responded that in such cases, the vendor would earn more money. This as seem did not at first augur well with Sachin because his opinion was stationed on the fact that consumer would get any quantity lesser than the weight on the other side of the balance.

It was interesting for me to learn that what is sometimes so obvious for one student (& the teacher) may not be so obvious for the other student. I allowed Sushma to explain her view and this quickly brought a smile on Sachin's face.

Sushma had already brought into this discussion her experience of purchasing 1-kg rice from the vendor. So I thought to just built upon it. I did not know that my next question would help me learn something so interesting from my students.

"If we assume that the vendor has removed the piece of weight worth 50 gms from the std. weight of 1 kg, then how much will he earn from the transaction of 1 kg of rice, sold at Rs.24 per kg?"

Of course, both the above values -- 50 gms and Rs.24 per kg were arrived at with the help of "students", they were not my (the teacher's) enforcement! It was equally interesting to study their estimation sense and even help that develop using this real-life example) But I am not going deeper into those conversations this time. Why? Well, Because I hardly get any acknowledgement from the readers for this effort :-)

Yes, coming back to the problem and how my students saw this and solved this.... Again, here too I am going very quick this time i.e I am not mentioning all the (beautiful) conversations that Really happened.

Sachin finally could settle down with this argument that if 1 kg costs Rs.24, then half kg would cost Rs.12. So 50 grams would be worth Rs.2.20

It was interesting for me to see him arrive at the cost of 50 grams directly from half kg. I would suggest you to pause for a while and answer this question. (of course, I will be much happier if you even reply to me with your answer) - 'What according to you must be the way that Sachin would have devised to arrive at Rs.2.20?' I hope you will honestly pause and think before reading further :)