I often consider myself luckier -- to have at least one child near my seat during the long distance train travels..It not only kind-of shortens my journey but often such encounters / interactions have turned out to be enriching / interesting ones, and in many ways :-)
One such happened again recently. It was 13th Dec 2024, I was travelling by train to Ahmadabad from Mumbai. Just few minutes after I occupied my (window) seat, I saw a lady coming with an 8-9 yr old girl and occupying the seats in front of mine. I felt the Aha! within me, however 'controlled' my emotions for the time being :-)
After couple of hours, a girl, of age similar to that of the former one, came in our compartment to sell some key-chains. Soon she came to me and kept the tray full of key-chains on my lap suggesting me to take something. I thought for a while and then took one of those & put it in my pocket, giving her a smile. She kept looking at me with wonder for some time and then said, "Give me Rs.10"
"What for?"
"You took the key-chain."
"You gave me the tray and told me to take some.So I took."
"Give me Rs.10"
"Okay.. I will give. Tell me how much is this?" - while showing her 4 fingers,
"Four"
'Now?" - while showing 6 fingers,
"Six"
"Now?" - while showing 9 fingers,
"Seven.....No, Eight"
"Its not Eight."
She started counting one by one now... arriving at the correct answer 9.
"Good. Was there any other way?"
She thought for a while.. and then resorted to,"Give me Rs.10"
I removed the Rs.10 note from my wallet and while giving it to her asked her to show me her 10 fingers and she did so... Now, I just closed one of her fingers and asked her to tell this number.... And she said, "Nine"
"So was there another method?"
She shook her head (implying yes) and left with a smile and the 10 rupee note...
And I saw that this game (between me and this girl) had drawn the attention of some passengers around, including that of the girl sitting in front of me. I smiled at her and she shyfully pushed herself into her mom trying to hide her face :-)
Later, I noticed that her mother was telling her to sleep but she didn't want to.
"May be she has already slept for 20 hours!" I said this while looking at her.
She shook her head (implying no) with a smile...
"Oh.. you don't sleep much? How many hours do you sleep then --- 2 hrs, 3 hrs?"
"More than that..".
Phew!! finally she spoke! ;-)
"Oh okay... What time do you sleep?"
She looked at her mom for the answer who told her "around 11 o' clock"
"And you get up at?"
Again she looked at her mom for the answer -- "6 o' clock"
"Hmm... So how long do you sleep then?"
I see her thinking and then it comes from her -- "Seven hours"
"Yes...correct.. so then how many hours are you awake?"
She gave me a puzzled look...
"Why? Is it difficult to find?"
No response for few seconds..
"Do you know how many hours in a day?"
"24 hrs."
"So can you find now?"
I see a smile on her face and her fingers start moving in the air now.. :-)
"18 hrs." she said.
"What???" her mother reacted loudly to this (wrong answer!)..And I had to request her to hold / hide her reactions for a while..... Luckily, she understood and kindly stayed away from the rest of the game, though she paid attention to our conversations probably to learn something from this....
I asked the girl how did she calculate 18 hrs... Her explanation implied the vertical orientation of numbers - (standard) subtraction algorithm.
"No"
The passenger next to me who was listening to all this kindly & immediately offered his pen and one of the old train tickets from my wallet became our note-pad.
"Can you plz show your work on this paper?"
And this is what she did (check image)
She was surprised with this answer, as it was different than the one she had said.She gave the paper back to me with a shy smile.
"So how many hours do you sleep?" :-)
I decide to play devil now... "I think there is some mistake in this work. . Let me show you where.".... And I scribble the numbers on paper while trying to explain that 4 minus 7 equals 3 and then 2 comes down as it is. . So the answer is 23. (check image)
And then she gave me a strange look while shouting -- "No, its wrong""Whats wrong? Isn't 7-4 equals 3?"
"It is.. but here it is 4-7"
"So?"
"That's not possible... So we borrow from 2."
"Oh okay.. I got it..."
She looks relieved now :)
"But you know what? you said that 4-7 is not possible... But actually, its possible!"
Again a strange look :-)
"You want to see?"
Curiosity is high by now!!
"Take your mom's phone.. Do you know calculator?"
She takes her phone, starts the App and waits for me.
"See what happens when you type 4-7 in it"
And guess what -- it happened what was expected -- puzzled look on her face again! And I could see her mother hiding her laughter :-)
"What's the answer?"
She said "3"
"Ummm.. its not 3.... Plz read properly"
She looked down and with little hesitation came..... "Minus 3"
"Yes,. 4 - 7 is minus 3....So its possible or not?"
She was smiling but I could also see some dissatisfaction on her face.
"What do you think 8-10 is possible?"
"No"
I was surprised by this. But then told her "Lets check on the calculator."
And soon came "Minus 2" with a surprised smile from her...
"So now what do you think, will 10-40 be possible?"
She was about to plug these symbols on the calci and I stopped her!!
"Wait... I want you to guess first now.. What would be the answer?"
And within couple of seconds she said "Minus 30"
"lets check this on calci now"
And when HER Answer appeared on calci, Joy too appeared on her face!
I saw there was a smile on mother's face too :)
We played this game with few more pairs, like 40-90, 30-25, etc in the Same order - first Guess & then Check. It was a delight to see her play & enjoy this (new) math!
Well, if you think that the game was over... then the answer is NO! . Something more was simmering in the teacher's mind... in fact, the real game was about to begin :-)
And you might wonder what's that? This adventurous journey is shared in the Part-2 of this post... Link below :-)
https://rupeshgesota.blogspot.com/2025/01/math-journey-in-train-journey-part-2.html
Thanks and Regards
Rupesh Gesota
https://rupeshgesota.weebly.com
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