Playing Maths: "Hundred and Hundred and Hundred and Hundred and....."

If you remember, my previous story was about my visit to my sister's place where I face the ‘adventurous encounter’ with negative numbers with my 6-yr old nephew (Jash) and his 9-yr old cousin (my ‘new niece’ ;-)  

For those, who haven’t read that story, may find it here: 
http://rupeshgesota.blogspot.in/2014/09/it-was-day-of-rakhi.html

Soon I had to visit my sister’s place again, but this time for Ganpati darshan. And I had no idea that I will again collide with these two young mathematicians, so soon.  It was only after few minutes, that the same voice (but it was loud and insisting this time) fell into my ears --

“Maamaaa, today you have to teach me 7^th standard Maths!” And I was like........Bowled!

No doubt, as a Math teacher I am always alert, looking for such natural opportune moments to start theMath-talk, however to her, I gave a pat response – “What? Do I come here to teach you Maths?”

“Mama, plz teach na.....plzzzzzz...plzzzzzzzzzzzzzz...”

I was so much enjoying this desperation and was, in fact now, more desperate than her to kick off, but --- I again wore the devil’s hat -- “No, I am not going to teach you this time. I am sure you would have forgotten the 6^th std. Maths that I taught you last time.”

“No...No.. I remember everything.”

“Oh, Really?”

“Yes, you can ask me.”

“Theek hai, Tell me what is 50-20?”

After a pause, “You did not teach me this way. We did smaller minus bigger.”

With this proud feeling of achievement, I forge ahead – “Ok. I am happy you remember. So then tell me what is 20-50?”

“It’s Minus 30.... Simple!”

“Hmmm...That was easy. Now let me give you a difficult one. What is 17-30?”

She started moving her fingers and lips and watching this disappointed me a bit. You know, we had done a bit of Mental Math too that day, before signing off... But soon, I also found myself pacifying ‘how unjust of me to expect a 9-yr old to ‘remember, recall and use’ the strategies showed orally/casually to her in ‘just 10-15 minutes’, and that too after a gap of 20 days'. And while I was stoned into this looking-for-justification, a confident and loud voice brought me back into the moment.

“Minus 13.”

“Oh, good. And how did you do that?”

“30-17=13...... So 17-30= -13.”

“Hmm... I get it. But how did you get 30-17? I saw you counting fingers. Remember, we did something interesting last time – Mental Math?”

‘Oh, Yes...Wait...Wait.... I will do by that method now.”

And soon, after speaking to the wall and air for few seconds, she spoke to me and even reasoned out beautifully and stole my heart “We want to remove 17 from 30. So, we first remove 10 from 30. This leaves 20. And 20-7 = 13.”

“But why 20-7?”

“Arrey, we have to remove 17 na? Not 10. So I removed 7 more.”

“Oh, ok...ok... I got it. Shall I give you one more problem?”

“No... No... I gave you the right answers. Plz teach me 7^th std. Maths now!”

I was trapped now and started wondering as to what do I do with her now? I was just thinking to remove the gadget (calculator) again, but we were yelled for the lunch and  hence, I was saved (or sad?)

But if I (and even you) felt that I had an escape, then I am (& you are) grossly incorrect J  She finished off the lunch before me and was now, smiling at me with her inviting expressions as if she was just waiting for me to finish, so as to pounce upon the mouse like a hungry cat... I pondered over this thought  -- Maths if dealt well can excite the child to such phenomenal levels!

Not giving her time would be injustice now. So I got back into our ‘maths room’ with no clue about what to do... Meanwhile, I saw my hero - Jash - playing video game on someone’s handset and I could not control, but tickled him – “Jash, do you know, she remembers everything what we did last time?”

No reply! (He was completely engrossed into the gadget.)

“Hmmm....Means, you have forgotten.”

And like a flash came the scream – “No... I do not forget anything. I remember everything.”

“Ok... Then can you tell me something what we did last time?”

“We did Minus on Calculator.” He said this in a super speed without moving his eyes from the game.

And before I could take this ahead, my senior pupil intervened – “Ok, then tell us what 5-10 is ?”

“I don’t want to do that now.... I am playing video game.”

This, as if gave an opportunity to the girl to tease him (But why blame her?  Who was the real culprit?  J

“See, you don’t remember.... You have forgotten....”  She repeated this couple of times, to tease him further and then to no surprise, the volcano erupted!

“Maaamaaa, tell her not to trouble me....” And while saying this he turns to her, “I know one lakh times more than you!”

YES!! What a beautiful word he has thrown out.  I finally got my lesson-plan J 

“Jash, do you know how many zeroes are there in one lakh?”

“Yes,.... three zeroes!” came the confident-instant answer.

Hearing this, the girl starts laughing aloud..... But then, I am so glad that our eyes itself did the job this time (perhaps, she could recollect the BIG Lessons we had talked about Mistakes and Struggle and she stopped laughing/teasing)

“Jash, can you verify -- if one lakh has 3 zeroes?”

“Yes!” And he immediately closes the game app and opens up the calculator app while quickly rolling his tiny fingers on the numbers. (Again, Maths wins!! :-) He types 1000 and shows us with confidence.

“Arrey, this is one thousand!” the older one argues with the younger one.

But Jash turns to me for the confirmation and I tell him that I completely agree with her. I also realize that the symbolic notation of 1000 was yet 'too big' for his eyes and mind to grasp and, probably that's why it was one 'lakh' for him. I ask him –

“What comes after one hundred?”

No response.

“Ok, what comes after 90?”

“Ninety-one”

“After that?”

“Ninety-two.”

And we went this way till ninety-nine. 

“After that?”

“Hundred.” He says this along with a big beautiful smile that generally appears on all children’s faces after reaching this first 3 digit figure. (I sometimes wonder what's so special about hundred that makes them like so much J

“Good.  And what comes after hundred?”

The girl could not tolerate his silence again and she guided him – “Hundred and one.”

He repeats after her... And I continue... “So what after that?”

He says with reluctance, “Hundred and two.” It was very clear that he was not so sure and was just following his instincts/ some kind of pattern/logic that he had seen some where back.

“Good.... And after that?”

“Hundred and three.....Hundred and four... Hundred and five...” And soon, I found that the train had speeded up.

“Ok...Ok... Wait Jash..... This will go on till what?”

He thought for a while and said “........Hundred and ten.”

(And I expected ---- Two Hundred.... What about you?)

“Ok... So what comes after hundred and ten then?”

Brakes on the Car... And the girl (the assistant teacher :-) guided him again – “Hundred and eleven.”

“After that..?”

“Hundred and twelve.”... And the car was back on acceleration.... :)

“Wait....Wait.... I don’t want you to tell me everything... Just tell me what will be the number at the end?”

 But this time without stepping on the brakes – “Hundred and Twenty!”

(Oh! It still did not come out...... But then now, I had learned something very interesting, as to how he saw ‘the last number or the number at the end.’ Can you all recollect how we  and our students generally are instructed to write numbers from 1-100 in their note-book? It is in columns of ten. J  So now, with this awakening, I plan to strategize our road ahead.

“So,what after hundred and twenty?”

“Hundred and twenty one...... hundred and twenty two.....”

“Wait.... Number at the end?”

“............Hundred and thirty.”

And this way, by just finding and speaking out the first 2-3 numbers and the last number of every decade, we finally reach the climax....  And more importantly, as a bonus, it was so heartening to watch my senior pupil too enjoying the learning process of the younger one. Or was it a reflection of elder sister’s love and care for her younger brother?  J I feel it was more to do with the enthusiasm levels of Jash and mine that were affecting her too J

So he reaches Hundred and Ninety...

“What after that?”

“Hundred and ninety-one.... hundred and ninety-two....”

“And this will go on till?”

Silence....

I could gauge the reason for this... But obviously, my little assistant was too anxious and was almost about to utter... but this time I ‘instructed’ her to say nothing and let him figure out on his own... She obeyed (perhaps, understood).

Seeing him unable to figure out after 3-4 seconds, I chipped in. “Ok, tell me what comes after hundred and ninety-five?”

“Hundred and ninety-six”

“Go ahead...” I say this while acknowledging his every response with my head and hand and SMILE.

“Hundred and ninety-seven....... ..Hundred and ninety-eight............Hundred and ninety-nine..........Hundred and........ Hundred and...............”

And now... after noticing this, I was almost sure of what is going to come out of his mouth/mind...

“Yes, go ahead Jash. Hundred and ........?”

“Hundred and....hundred!”

“Oh wow! You could figure it out... Good.. What after this number?”

“Hundred and Hundred and one.”

“Go ahead...”

“Hundred and hundred and two.....hundred and hundred and three.....”

“Wait... Wait.... Tell me what will be the number in the extreme end. I ensured that I was focusing highly on the word ‘extreme’ this time.  With a bit of explanation of what I meant/ wanted, he finally uttered out –

“Hundred and hundred and hundred!”

“Good...... This will also go on for long.... and where will it end?”

“Hundred and hundred and hundred and hundred.”

And by this, all three of us, and especially his ‘9-year old teacher’ too was completely into giggles,.. rolling on the floor, almost similar to what some of you must be mentally going through while reading the past few lines....

His imagination by now was unstoppable, running at top speed....  And he had started reciting these words like a rhyming poem – “Hundred and hundred and hundred and hundred and hundred and ...... “  And while doing this, he hopped off the bed and zoomed out of the room with Joy...... Was this Joy of Discovery? :-)