Sunday, October 19, 2014

Playing Maths - "But these problems need brains! And our text-books have easy ones!"

Hello friends,

Firstly thanks a lot for taking out time in reading my long emails -- Math conversations. And more importantly, even sending your feedback/comments. I had requested this earlier too and I request/ repeat again, Plz share your reply with the group so that everyone can benefit and learn from your views/opinions and may even comment on the same, which can probably lead to an interesting discussion thread. After all, that's why we have created a group right? :-)

Secondly,I have also received requests to re-send the group invitation because the system generated emails had slipped into other folders like Promotion/Social etc and by the time you read it -- the invitation had expired. So here is the link that you can simply hit and your request to join the group will straightaway come to my inbox, which I will approve much before it expires.

Thirdly, I am so happy that within such a short span of time, more than 100 (116 till now) Mathsteachers of various schools and educators/ educationists have become part of this google-group. Hope to see more constructive discussions in the near future. If you know any Maths teachers who would like to be part of this Learners group, plz share this idea with them, and by this way, you get an opportunity to touch the lives of even their students! :)

New members/ recipients may plz visit our group page (above link) to get updated about/ learn from/ comment on any of  the previous stories/ posts/ documents shared in the group.

And yes, finally the main part --- I am glad to share with you all one of the Math conversations that I had with a student couple of weeks back. Hope you will see some value in this. And I would wait for/ love to listen to your feedback :-)

It was 9 and I had just reached home, when the door-bell rang again and I could hear the voice of my mom, “Yes, you may go inside!”

And I saw a boy dragging his feet towards me while carrying a wide smile and raised eye-brows. What was more surprising that he also carried a book in his hand! It’s been over 3 years I stay with them, but nothing such has ever happened. I mean, the only thing that the children of our building ask/expect from me, whenever they see me, is a ‘Game or Puzzle.’ But today – a Book! My childhood memories came alive and I saw myself in him. I was pretty sure that he had come for some clarification or guidance. I was happy to see these changes, but more than that – was Excited J

“I don’t understand this problem”, he says with a shy tone, handing over the book to me.

“Ok, what is in it that you don’t’ understand?”

“How to find the value of Circle minus Triangle? Which option is correct?”

“What do you feel, which option is correct?”

“I don’t know. Everything is given as addition”

“Ok. What information is given in the problem?”

He converted the written symbolic language into speech and then stopped for me.  I felt I figured out the cause and so tore out a page from my book and copied on it, the diagrams same as above, but with different numbers.

“Tell me, what do you feel what could be the values of Circle and Triangle here?”

“I don’t know.”

“Give a try. What can be their possible values?”


“Ok, Can Circle be 5 and Triangle be 3?”

After a while ---”No!”

“Why not?”

“Because then, they add up to 8”

“So what?”

“Arrey, they should add up to 10 na?”, he says while pointing at the first equation.

“Oh, ok. Then why don’t you give a try now?”

Though I am travelling the path of learning the right math teaching-learning practices, the conventional teacher within me could not withstand the student’s silence for more than 10-15 seconds and so it sprang out its ugly head.

“What’s going on?” I asked.

“I am thinking.”

“Oh, sorry.”

Within 4-5 seconds, he shouted out the correct answer.  “Circle is 6 and Triangle is 4.”

“Good. And how did you get that?”

“First I took the combination of 8 and 2. But it did not work in the second statement. So then I tried (7,3) and so on.”

“Ok. So you were trying to ensure that the pair of values satisfied both the equations.”


“Did you get the correct values in the 1st try?”

“No... As I said, I had to try for various values.”

“Ok. Do you feel there can be another method?”

He started thinking. Honestly, I felt he would need some guidance here. But I am so happy that he proved me wrong! He picked up on his own.

“Yes, we know that the Circle and Triangle add up to 10, so we can use this in the second equation to get the triangle’s value.” While saying this he also highlighted this pair with a box in the second equation. (Check the image)

“Good. And what value will we get through this method?”

“We will get the same answer.”

“Is it? Did you verify?”

“No...... Wait!” 

After a while – “Yes! I am getting the same answer.” 

Excitement was evident. I have observed that children love guessing and estimating and more importantly, they super-enjoy the verification process – irrespective of the outcome.  This hardly takes any time and effort. But yet, one may find out the amount of such exploration opportunities given to our students.

“So, can we go back to the original problem now?”

He snatched the book from my hand and was about to solve it.

“Wait. Can we discuss first?”

“It is same as the problem that we solved now.”

“You mean to say – It is Similar.”

“Yes, Similar.”

“How will you go ahead with this then?”

He straightaway went to the solution. “Triangle is 6871- 4882

“Ohk. How come so fast? I did not see you trying out different values?”

“That method will be very difficult here.”

“Oh! I am glad that you have done some analysis. Now then, can you tell me the two methods that we have learned?”

And we enlisted these two methods on the paper while discussing the pros/cons of each.  (As shown in the image above)

“So can you select the correct option now?”

He looked at the problem for a while and said, “No, here we need to find the difference of the values of square and triangle.”

“Good.  But how do you get the square’s value?”

“Arrey, we can substitute the triangle’s value in the 1st equation.”

It was as if music to listen to the sophisticated mathematical vocabulary flowing out of him, Finally J

He started scribbling to find the right option but I interrupted, “You feel you can do this at home?”


I was about to get up, but he held me back.

“Wait. There is one more problem.”

“What? Solve that independently now. “

“I tried, but I couldn’t. Plz plz help me solve this.” and while he was saying this, he had already opened up the page and handed over the book, back to me.

I read the problem and asked him. “What’s difficult in this?”

“I don’t understand how to solve this.”

“Ok. Can you read it?”

He began but soon paused at the symbol of ‘club’.

“What picture is that?”

“It’s a tree.”

“Fine, go ahead.”

And soon, he was stuck at the symbol of ‘spade’.

“Now what does this symbol look like?”


“Go ahead then.”

He went on till the end. But I was not sure about the comprehension (inadequate fluency). So I asked him to read the entire question again.

“So what is the data and what’s the question?”

He identified the first line as data and second line as question.

“So? What do you do now?”


“How will you express the data in mathematical form?”


I threw this question aside, gave him a note-book on one hand and a folder-file on another and asked him, “What can you say about their weights?”

I had to help him to recall the word ‘heavy’ but then he made the correct statement.  “File is heavier than the book”

“Ok, can you estimate their weights?”

This was little difficult for him, but after some guidance – “Book would be around 100 grams and File would be around 400-500 grams.”

“Let’s assume it is 400 grams. Now can you write these statements on paper?”

“Now write a mathematical statement that shows this relation?”

And he wrote: File = 4 x Notebook

“Good. Can we go back to our original question now?”

And he immediately wrote:  t = 6 x L

“Fine! Now what?”


“What’s the question?”

And he read the complete thing:  ‘What is the value of Tree if Leaf-28=59?

“Hmm... So now?”


“Can you recollect our last problem? How did we solve it?”

“There were two equations. We found the value of one variable and then using the second equation, calculated the value of another.”

“Yes, so what’s the problem here?”


“How many variables are there in this problem?”


“And equations?”



“So how will you go ahead?”


“Is it possible to break the last line into two parts?”

And I finally heaved a sigh of relief. He broke it this way:

What is the value of Tree?
Leaf – 28 = 59

“Hmm....Good... So now, was the entire line a question or some data could be extracted from it?”

And getting this clue, he finally penned down the 2nd equation as well as question in algebraic form. (check the image)

I now thought that the show was about to end, but alas! he got freezed at the equation L – 28 = 59. I pulled off a paper and scribbled this equation: 

L – 3 = 5   And asked him what is the value of L?


I wrote this in small font near the variable and asked him -- “Did you check it?”

“Sorry, sorry... It is 8.”

I was compelled to throw another similar question:   L – 10 = 17    What is the value of L now?



“So can you go back to the original problem now?”

He looked at me with a smile! Perhaps, he had sensed the rhythm J

You may also learn something from his calculation in the image above. But finally he said 87, with a smile again! J   Kids are really smart and in such cases, they don’t need our words to signal what we mean.

“So, is the job done?”

“No. We need to get the value of Tree.”

This was easy for him. (And I too took a deep breath; No game of here-and-there this time  J



“Anything else?”

“No, Thank you.”

I closed the book and was surprised looking at the cover page of the book. The book was meant to practice for some competitive exam for grade-7.

I inquired, “This is not your text book.”

“No. I am in 9th std. My mother was unable to solve these problems. She has to teach her students. So she told me to ask you.”

I knew his mother takes tuitions. I see at least two dozens of pairs of chappals outside their house, while going down the stairs – be it morning, afternoon or evening, sometimes even on Sundays! It’s also usual for me now to face the pick-and-drop doing parents, holding the little fingers of their 5-8 year olds. Yes, I feel like crying, shouting and yelling! But I stay mum – I leave the site silently, just exchanging smiles with the kids.

So I ask this chap now --- “Oh! You have already solved such problems earlier. You should be able to help your mom.”

“No, such problems are not there in our book.”

“What? Don’t you have linear equations, simultaneous equations?”

“We have... But yeh sab problems dimaaag-waalaaa hai.... hamaare book mein sab easy hai!”

“Oh really? Were they difficult? Who has solved these problems now? You or Me?”

“Yes,I have solved it.” and while saying this he zoomed out with a big smile. I was wondering if I could succeed in some way to improve his approach towards Math! If vibes are to be believed, I could feel the emanation of confidence from him. Further, I felt more relaxed & as fresh as in the morning!  :-)

1 comment:

  1. On Wed, Nov 5, 2014 at 4:36 PM, hemangini bansod wrote:

    Rupeshji, I appreciate your patience with kids and the enjoyment it brings to you and students surely a great feeling. Regards HRB


    Yours sincerely,

    Hemangini R. Bansod