How an interesting date can help a Maths teacher?

Yes, I am aware that I need to write the Part-3 of the series of posts on Solving Simultaneous equations Their way.... I will do that soon... But now I am more excited to share with you what happened in our class today --- 

Most of you must be aware of another interesting date we had couple of days back....  

For those who failed to notice -- So would you like to Discover it Now?

Well then, you need to honestly follow these directions (without scrolling down :)

1)  What was the date on first Thursday of August 2016?  
2)  Now write this date in the form DD-MM-YY format. 

Hmm.... Could you see something interesting pattern?

.....

No..?

Try again..... 

Give a closer look.... I am sure, you will....  !!    :-)

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Could you spot this beautiful sequence in the date 4-8-16 ?

Well, to be honest -- I too had failed to observe this remarkable date.   :(

I came to know about this only late in the evening via WhatsApp (& then Fb) - thanks to couple of maths teachers and maths lovers who keep me posted about such events  :)

So sadly, I missed talking about this with my students in the noon.... However luckily, something struck me and I could throw this ball the next day with my another group of students... 

"You know, there was something interesting yesterday and none of you have pointed that to me till now", in a complaining tone. I did not want to hint them by using the word 'date'

And I was so so so happy when most of them instantly shouted ---

"Sir, yes - yesterday was 4 - 8 - 16"

"Oh wow!  I am glad you had noticed it... So what's interesting in it?"

One of them -- "Sir, double of 4 is 8.... and double of 8 is 16...."

The other chap -- " All are powers of 2"

Third one --- "Sir, these are consecutive powers of 2"

"Fantastic !!  Good observation!   Did you share this with your school teachers?"

"Yes, we did... Even she was very happy to know this!  In fact, we saw this when she wrote the date on the board and we immediately pointed it out."

"Hmm.... Good... Well, can you tell me something more interesting in this date?"

---

---

after few seconds 

---

--- "all are multiples of 4..."

--- " all are even"

"Well, aren't the above facts 'obvious' when these are consecutive powers of 2?"

(laughter)

"Let me help you a bit"  and I write this on the board -- (complete year)

4 - 8 - 2016

And soon, some voices filled up the room --

"Again all of them 4,8,16 and 20 are multiples of 4...."

"But 2016 is not a power of 2..... ", Raju follows the former guy.

"And how do you know this?", I ask him.

".....16, 32, 64,.......128......256......512......1024...... 2048..... We should have the year as 2048 for all to be powers of 2"

"True.... Anything more?"

------ silence ------

"Ok.... let me help you further....Because this demands a much sharper observation... I too missed it.... I came to know about this because of a message sent by my friend.."

"Sir, if YOU could not notice it, then how can WE notice?"

"Why do you feel so?  You need not compare your abilities with me... Many of the times, you have made better and more observations than me.... Further, I have also learnt many new problem solving approaches from you....", While I continue to confess, some look at each other with wonder as to what am I saying, while others are still glued to the date.  :-)

"Lets focus on the factors of 2016"  I continue... "What do you think of 4 and 8 then?"

"Sir, both are factors of 2016"

"Explain"

"We applied divisibility tests for 4 and 8...  For 4, we checked the last 2 digits, and for 8, we checked the last 3 digits."

(Please note that these students also know the reasons behind these tests...

What about you and your students?)

"Ok.... What about 4 + 8 now?"

"That's 12..."

"I know it's 12 Sahil.... Can you now check if 12 too divides 2016 evenly?"

"Yes sir...even 12 divides 2016....."

"And how do you know this?"

"Because 2016 is divisible by 3 as well as 4..."

"Good... That's not all.... what do you feel I will ask you now...?"   

Silence...

I write this on the board...   ( 4, 8, 4 + 8, 4 x 8, 48)

"Oh Sir,.... do you mean 4 x 8 and 48 also divide 2016 evenly?"

"Why don't you check?"

Some mur-mur and......

"Yes, its divisible by 32...."

"Explain"

"32 is fifth power of 2..... So we need to check the last 5 digits....  So we appended 2016 with a leading 0... which is 2016 itself.... and we divided 2016 by 32.... we got remainder=0"

"Okay.... Lets go ahead...."

.....

.....

I was very curious now -- What will they do to figure out if 2016 is divisible by 48....?

What will you do at this juncture ? What will your child / students do ?

....

"Sir, it's divisible by 48 also..."

"Don't tell me you have actually done the division"

"No sir... we have used the divisibility test for 48..."

I was so satisfied and relieved to hear this response --    :)

" 16 and 3 are co-primes of 48.... 2016 is divisible by 32, so it has to be divisible by 16.... and we have already checked that 2016 is divisible by 3.... So, 2016 has to be divisible by 48...."

Listening to such a Math from a student would be like a Music for a Maths teacher, isn't it? :)

And I was waiting for them to wonder at this fact that -- 

2016 is divisible by 4, 8, 4 + 8, 4 x 8 and even 48.....   But it seems their car was still in motion....

"Sir... even 8 / 4  and 8 - 4 divides 2016", Rohit points out to me.

I look at the students for their comments... and all roared happily with "Yes Sir!"

(Laughter)

Wait... Wait.... There is more they had...  :)

"Sir, do you know we have another interesting date next month?" Sania asks me with confidence. 

And.... I am puzzled... calculating the number corresponding to September.....!!  And while I am still engrossed, Sidharth makes an entry !!!

" Yes, I know Sir.... The date is 4 - 9 - 16.... "

Rohit too joins him soon --- "Yes, and we even have our class on that day... It's Sunday!"

While many of them, and including me, were still wondering about the theater around....

But we could soon decode the code in this date...

See if you can decipher the code?   :-)  :-)

As usual, we even discussed more - relating to such types of dates...

Can you/ your children/ students make some observations?  

And as if this was not enough.... Pandurang had meanwhile scribbled something on the board. He asked us "Can you all now find out what's interesting in this next year's date?"  :-)

Incidentally, we had some engaging conversations few days back on some other interesting category of dates...  You may check out this post here:

Mathy Date (Square root day)

http://rupeshgesota.blogspot.in/2016/04/mathy-date-square-root-day.html

Mathy Date.. Extended....

http://rupeshgesota.blogspot.in/2016/04/mathy-date-extended.html

"Sir, tomorrow is a Happy Date"

http://rupeshgesota.blogspot.in/2016/07/sir-tomorrow-is-happy-date.html

I am waiting ......to hear from you ---- the answers to the questions I asked you in this post   :-)

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(1) If you liked this post Or if you have similar class-room stories to share, then I would love to know.. It will be great if you post your reply, stories and views, in the comments section of my blog itself, instead of replying over email.only to me.. Why? Because these could possible trigger some interesting conversations, thus helping (motivating) many other readers (teachers and parents), now & even later...

Here is the link: http://rupeshgesota.blogspot.in/2016/08/how-interesting-date-can-help-maths.html

(2) You may even subscribe to my blogs via email. There is a text box on the left hand side of the blog, where you can enter your email-id.

(3) The conversation above happened not in English, but in Marathi, because the students belong to marathi-medium municipal school with whom I work regularly. Check the website: www.supportmentor.weebly.com to know more about this program. There's a short video-clip on its homepage.

Thanks and Regards

Rupesh Gesota