04/27/06: Division with ‘mental’ paper and the trick with 3’s
During the drop off today, I challenged Alexa to do a 3-digit number divided by a 1-digit.
“But I need paper for THAT”, she declared as all of my students do when they are first challenged for such task.
“Let’s try without one. You’d be surprised how big of mental paper you have in your mind.”
“I do?”
“We all do. Some of us use it more often than others and the ones use it more often have a bigger piece of ‘mental paper’.”
“Okay, let’s try one.”
“90 divide by 3”
“Oh, but I can’t do it without paper!”
“Let’s just try it!”
“Okay,” she hesitantly started. “90 is inside the house, 3 says ‘knock, knock’ and 9 says ‘I can give you 3’ and 3 asked, ‘why 3?’” from there, she quickly realized that the answer is 3-0.
“Great job! You mental paper just double in size! Wanna try another one?”
“Sure!”
“123 divide by 3”
“Oh, that’s too hard!”
“Just give it a try, you’d be surprised at how powerful your mind is.”
“ 123 is inside the house, and 3 is out. 3 says ‘knock, knock’, and 1 inside the house says “uh, I don’t have enough to cover 3, so I’m going to bring a friend down.” Now it’s 12, so 12 says, ‘I can give you 4’.” From there she got it that answer is 4-1.
Sensing that she still had room for more, I asked her “ what about 513 divided by 3”
“Would there be a remainder?”
“That’s a great question, Alexa! The answer is no, no remainder and I’ll share you the secret after you get the answer.”
“Okay, so 3 says ‘knock, knock’ and 5 says, ‘I can give you 1’, and with 5 minus 3 is 2 and bring down a friend, so 21 says “I can give you 7’. So it’s 1-7-1’
“Great!”
So how did you know that there wouldn’t be any remainder?”
“The trick is that if you add all the digit together, if the sum is a multiple of 3, then you won’t have a remainder.”
“So, with 5-1-3, I have 6 plus 3 which is 9. I see!” (Good thing that she could see the big grin I had on my face or she’d be embarrassed!)
“Where do you get all those tricks?”
“Moms are special, aren’t they?”
By then, we got to the school, and she disappeared into her classroom as if I were never there in the first place. Well, I’m back to be the chuffer as all the other chuffers signing in for their kids — just another day, another joy of motherhood.
Happy Zen Math!!
(c) Feenix Pan, 2007. All rights reserved.