Saturday, June 27, 2015

ABCDE x 4 = EDCBA


The video below is only first (Part-1) of the two videos. It captures the process that students go through while solving the following logical puzzle:

PROBLEM:  Students were given this problem a day before.... They have to find out a non-zero 5-digit number ABCDE such that its fourth multiple is the reverse of itself i.e. EDCBA.... 



To check Both the videos of this problem, click on this link:
https://www.youtube.com/playlist?list=PLZBBZFls_2nG-hl3pxr7jK3FotkPGMBNv


Fractions Laddoos Problem


The video below is only first (Part-1) of the three videos. It captures the process that students go through while solving the following problem:

PROBLEM:  Four friends take away the laddoos from the basket, but only one by one (i.e. one after the another). The 1st person takes one fourth of the total quantity and leaves. The 2nd person takes one-third of the remaining quantity and leaves. The 3rd person takes half of what was left and the 4th person takes away the remaining 2 laddoos, thus emptying the basket. The question is to figure out the total number of laddoos and the amount each friend takes.




To check All the Three videos of this problem, click on this link:
https://www.youtube.com/playlist?list=PLZBBZFls_2nE6opV47C367_aV_SDi5z5Y


ABCD x 4 = BEEB


The video below is only first (Part-1) of the five videos. It captures the process that students go through while solving the following problem:

PROBLEM: This problem was given to them a day before so that they can work on this at home... They need to find out a Four digit number ABCD such that when it is added to itself 4 times, the answer is BEEB..... 





To check All the five videos of this problem, click on this link:
https://www.youtube.com/playlist?list=PLZBBZFls_2nH4ET0kvN8ENwlek7LkMoeD

Chocolates problem


The video below is only first (Part-1) of the two videos. It captures the process that students go through while solving the following problem:

PROBLEM: Its a problem involving two types of chocolates. An Eclair costs one rupee while a mango bite toffee costs 50 paise... If 10 chocolates are purchased in all using Rs.6, then figure out the quantity of each of these chocolates purchased... 



To check both the videos of this problem, click on this link:
https://www.youtube.com/playlist?list=PLZBBZFls_2nGhGIc6lnL23IsTXFQNK4HI


Sum of the Numbers Trick


The video below is only first (Part-1) of the 12 videos. It captures the process that students go through while solving the following problem:

PROBLEM:  The number trick was performed before them a day before.. They were supposed to work out the reason at home... While Poonam starts sharing her views (video- part-1), Shreya claims that she has figured out something and takes over...   

TRICK: I claim that I can predict the sum of 5 numbers without knowing all the numbers, and hence I write this sum on a piece of paper.. I then write the first number on the board... Students tell me the 2nd number. I write the 3rd number. Students tell me the 4th number. I write the 5th number. And very smartly and Instantly, I also write the sum of these numbers as written on that piece of paper....Students take time to add up all these numbers and after 2 minutes get shocked as to how I could predict this sum before-hand.... I do this trick twice... i.e. with two sets of numbers... You can see these problems unerased on the white board....One has the sum 22466 and other has the answer 22541



To check all the twelve videos of this problem, click on this link:
https://www.youtube.com/playlist?list=PLZBBZFls_2nGBmbOh-0HmU5qVSNxu18Ym

Thank You...

3 Hats Logical Puzzle


The video below is only first (Part-1) of the four videos. It captures the process that students go through while solving the following logical puzzle:

The problem was given to them and  they were given 10 minutes to think independently..

PROBLEM: 






To check All the four videos of this problem, click on this link:
https://www.youtube.com/playlist?list=PLZBBZFls_2nFsth0xMJRYpSYQVkuz_UOx

Thank You...

Tuesday, June 2, 2015

"We can divide the product only with the first factor"

Hello friends, 

Our First "Maths Teachers Study Group" meet on 18th May was fantastic. I will soon share its proceedings. Thanks to all the teachers who participated in this initiative :)

Yesterday night, I saw the video of Deborah Ball where she shares some interesting insights about the competency required by the maths teachers to spot the error in their students’ work. I don’t want to spoil your excitement by narrating her video and hence would recommend you to first watch this video and then resume your reading. https://www.youtube.com/watch?v=nrwDM4ejNqs

Who is Deborah Ball?

Deborah shows three multiplication problems to the committee members and asks them if they can figure out the errors made by the three students. You may call me crazy but, something drove me next day to pose the same challenge to my class-7 students J I wrote these 3 problems as it is on the board. Believe me, it was a real pleasure and a rich learning experience to watch and hear them analyze these problems - hunt for others’ mistakes and base reason on their arguments. I strongly felt the need to video record these conversations. We will discuss about this process at length during our next ‘Maths Teachers Study Group’ scheduled on Sunday, 31st May.

But in this email, I want to share with you some equally (if not more) interesting observations that came out as a by-product of the discussions on the above problem.

The students were very happy (and even surprised) to come across one of the new ways of doing multiplication.  I leave this up to you now to figure out (and tell me) the reason for their excitement. You will have to watch the video for this. 

In fact Poonam was so thrilled by this experience that she wanted to test/ apply this method (‘new’ method - according to her) on a different problem now. This is how she did it.




She asked me to check if it’s correct. (Hold on - What do you feel about her way of doing multiplication this way?) 

Now, they have heard enough from me that it is not the teacher’s business to check if the student’s work is correct. But my experiences have taught me that the Undoing and Unlearning effect takes some time J

She got the message. “I can cross-check this answer by using division. Shall I?”

“Go ahead.”

And this is how she did.

I noticed that she has erred.



“Sir, how come the quotient is 154? Shouldn’t I get 198?”

“How do I know dear?” I see to it that my pretended innocence is not caught J

Perplexed, she thought for a while, and decides to solve the same problem using the ‘old’ multiplication method now.



She errs again and gets the product (3770) which is different than the one she had got in the former one (4950)

“Oh sir, it means I have some done some mistake in the first multiplication process. Or, is it that the ‘new’ method doesn’t work?”

“What do you feel?”

“But we had seen earlier that we get the same and correct answers using both the methods....because they are actually similar methods.”

(We had already discussed about the use of commutative property in these two methods.)

“Hmm....So what do we do now?”

She thinks for a while.... And I was so happy to hear her say, “Shall I cross-check the product that I have got using division?”

(Of course, there were other smarter ways for verifying the correctness of product, but talking about all that at this juncture had the potential danger of disturbing her present flow. Hence I choose to just let her go - her way(struggle)).

So this is how she did it.




“Oh my god! Sir, I am getting a remainder of 20 now!”

I also noticed that her process of division was not complete. Look at the quotient. (In fact, it’s one of the most common mistakes made by most of the students (why so?) However, I choose to ignore this error as of now. And I will surely bring this to her notice, but later, and with the help of this snap :-)  ...To continue to read, click on 'Read More' below...