Wednesday, March 30, 2016

Masti with Multiplication -- Part - 2

Hello friends, 

As promised.. I am back, with the part-2  :-)

I wanted to write and share the part-2, the next day itself. However some day-long assignments used to drain me out completely - making difficult for me to sit and type the (long) conversation after reaching home in the night... However, I had made up my mind to complete this task today.... You know what motivated me to do this?

It is the honest appreciation (and even confessions) from some of you who could see the 'value' in the patience demonstrated during the previous conversation... Thank you so much for these acknowledgements,.. It tells me that I am on the right track...

By the way, could any of you try out that problem (32 x 8 using 22 x 8) with your children/ students? If yes, then please share your experiences....

If you have not yet read my previous post i.e part-1, then I would suggest you to first read that before you scroll down.. Here is the link:

Hmmm... So where did we stop last time?

The students could (surprisingly and beautifully and confidently) think of and even communicate four different strategies for computing 32x8...  But as my student Poonam had (rightly) pointed out in the end, they were still far from the approach that I was specifically looking for....

Considering this scenario, I decided to walk along the same path that was traced out by them.... .of pattern recognition.

"Hmm.... I see, you have seen a pattern in the previous two problems and their solutions to the solve this third (similar) problem... Interesting.... So then, can you go ahead further?  I mean, can you predict what would be 42 x 8 ?"

"Yes sir....I am already working on this....", said Rajesh

And immediately, Saif shouted out the product - "Sir, it will be 336."

"And how did you do that? Can you please explain to us on board?"

He said that he had simply extended the pattern that he had seen in the former products. 

12 x 8 =  96
22 x 8 = 176
32 x 8 = 256.....  So,
42 x 8 = 336

" the one's place will have 6..... ten's place decreases by 2...... and hundred's place increases by 1...... You see, 12 x 8 = 96.... i.e. it also has '0' in the hundred's place...."

All fine, but his last observation about being able to see the invisible zero really delighted me! Mathematician at work !!

Saturday, March 26, 2016

Masti with Multiplication -- Part - 1

They were eagerly waiting for me. I had not visited them or worked with them since long...Their teacher had told me the day before that students were complaining about my absence. "Sir, does not teach us now. He just goes to other school." This shook me & so I decided to meet them today....& make our Friday, really a Good Friday :)

As I was about to enter, I could hear their non-stop recitation of multiplication tables. The moment I entered, the tape-recorder stopped with a delightful surprise on their eyes. 

"Please continue." I suggest this to him while greeting their teacher who was managing this show.

And he started telling the table of 12, but with little hesitation this time. He completed it well and as was about to sit, 

"Hey, wait. How much did you say 12x8?"

Students generally (and unfortunately) get scared when their maths teacher responds to their solution with a question. 

"Don't worry... You were correct. I am just telling you to say again."

"12 x 8 = 96"

"True. Can you tell me how much would be 22 x 8 then? "    (I had no idea or plan to do this to them today.... but somehow, this happened :)

I could see some of them quickly resorting to pen and paper. I instruct them not to do so. Within 10-15 seconds, the same boy replied -

"It's 176"

"Okay.... and how did you do this?"

"Sir, I knew the table of 22."

Gosh!! My plan flopped. However, I didn't give up.

"Good, What if I ask you 32 x 8 now?"

"I don't know the table of 32."

"Yes, that's why I asked you so. You don't even need to know the table of 32... I was surprised when you said that you knew the table of 22. Though this pleased me, but I think, you don't need to memorize even till that."

His blank expression worried me. So I thought to reiterate the question.

"If 22x8 = 176, then what would be 32x8 ?  We need to find the product without directly multiplying 32 and 8."

To ensure that everyone understood the question, I asked one of them to share what they understood from the question.

Realizing that the entire class was still not with me, I asked the other student to write the question on the board.

And then, almost instantly, a hand went up.

"Sir, 32 x 10 = 320. Hence 32 x 8 = 320 - 64 = 256."