Door-2-Math Blog

“What does Fraction really mean?” Alexa asked today while I was dropping her off to her school.Thus far, I’ve covered 2-digits multiplications (26 x 32 on paper), divisions (321 divided by 3 mentally; and 4225 divided by 65 on paper) with her and she was ready to move on.

“What do you think it’s about?”  (I wanted to see where her understanding was and go from there)

“It’s about how much you have in a group?”  (This is how most school textbooks introduces fraction — though not entirely untrue, it is not the clearest way to introduce Fraction — in my opinion any way).

“hm…well, remember that big chocolate cookie daddy makes in the big pot?”

“yeah”

“well, if all four of us spilt the whole cookie evenly, how much cookie do each of us get?

“a quarter!”

“Right!  so in fraction we say it like this ‘ we each get 1 over 4′, which is exactly like you said, ‘a quarter’”

“so fraction means splits cookies?” (only if she knew how close she was to the essence of fraction!)

“Right on!  Fraction means ‘A part of a whole’.  Now can you tell me when splitting cookies, do you want more people splitting it or less?”

“Less of course!  I’ll have more splitting an olive with me” (she does not like olive as you might’ve guessed).

“So if we bring a cookie made of olive to your school, and all the kids there splitting it evenly, how big of chunk do you get?”

“hm…1 over 32″ (there are 32 kids in her combined 1st and 2nd grades).

“Right!”

“Now going back to the cookies with chocolate, if I didn’t want mine and give my share to you, how much would you have?”

“Two quarters of course!”

“Right again.  So we say ’2 over 4′.  Now do you know how we write 2 over 4?”

“2 with a line and then 4.”

“Good!  Can you tell me which number is on the top? The 2 or the 4?”

“2.”

“So when you want eat more, do you have the bottom number big or top number big?’

“The bottom number is how many people splitting it, so I want the bottom number small and the top number big, since the top number is how many slices I get to have.”

“Very good!”

“Okay, Mommy, my head had enough math now.”

That was a good start on fractions.

Happy Zen Math!

(c) Feenix Pan, 2007.  All rights reserved.

Today during the drop off, Byron announced that he is tired to adding with 9’s. I promptly asked him ‘oh, yeah, what’s the trick with adding 9’s?”

“Borrow 1, make ten and add ‘teen’.’ (Not bad for a 4-yr old, I thought).

“Cool! Do you want to know what to do with adding 8?”

“ Then, we are done?” (Boy, he really didn’t want math today).

“Yep.” (I’m a firm believer that there is absolutely no point in dragging a non-thirsty horse to the riverbank!)

“All do you with adding 8 is ‘Borrow 2, make ten and add ‘teen’.”

“that’s it?” (Kids are always amazed that math can be so simple!)

“That’s it with 8. wanna do some tomorrow?”

“of course!” We then moved onto who is doing what at his pre-k grade at the Montessori Schoolhouse.

Happy Zen Math!!

(c) Feenix Pan, 2007.  All rights reserved.

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.