A little Mommy Brag

[Condessa]

I was teaching my youngest long division yesterday.  He just turned seven, and has missed about half of his first grade year due to his surgery and cancer treatments.

He thought it was hilarious to blurt out the quotient and remainder as I wrote down the question for him, rather than writing the work out.  I started going to bigger numbers to find something he would need to practice writing out the format on, instead of just doing it in his head.  I had to go up to 4-digit dividends and 2-digit divisors to get the cheeky little guy to actually practice writing out the process.

[Not_a_Number]

23 minutes ago, Condessa said:

I was teaching my youngest long division yesterday.  He just turned seven, and has missed about half of his first grade year due to his surgery and cancer treatments.

He thought it was hilarious to blurt out the quotient and remainder as I wrote down the question for him, rather than writing the work out.  I started going to bigger numbers to find something he would need to practice writing out the format on, instead of just doing it in his head.  I had to go up to 4-digit dividends and 2-digit divisors to get the cheeky little guy to actually practice writing out the process.

Hah! Nice. Any idea how he’s doing it?

[Condessa]

14 minutes ago, Not_a_Number said:

Hah! Nice. Any idea how he’s doing it?

I probed a little, and it sounds like for small numbers, he doesn’t know how he does it.  It’s like it’s just intuitive for him.  But with the medium-sized numbers, he was actually using long division, but picturing the numbers and format in his head.

ETA: long division the BA way, which is a bit different than how I learned it.

Edited May 14, 2021 by Condessa

[Not_a_Number]

5 hours ago, Condessa said:

I probed a little, and it sounds like for small numbers, he doesn’t know how he does it.  It’s like it’s just intuitive for him.  But with the medium-sized numbers, he was actually using long division, but picturing the numbers and format in his head.

ETA: long division the BA way, which is a bit different than how I learned it.

Hmmm. Interesting. As in, he’s splitting the number? I’d personally prod because I tend to want explanations 🙂 .

Did he learn long division already?

Edited May 14, 2021 by Not_a_Number

[Condessa]

19 minutes ago, Not_a_Number said:

Hmmm. Interesting. As in, he’s splitting the number? I’d personally prod because I tend to want explanations 🙂 .

Did he learn long division already?

It sounds honestly like he can see it in his head as though he were writing it on a whiteboard.  It went something like this:

Me: How did you find that answer? (To 973 divided by 8 )

Him:  Well, I could give a hundred to each, and there was a hundred left over, so that’s seventeen tens, so they use up sixteen by getting two tens, and then there’s thirteen leftovers so that’s a remainder of five after one more, so one hundred twenty-one plus the extra five of course!

When he was solving 3-digits divided by 2-digits, I saw him gesturing as though he were moving numbers around in the air in front of him.

 

He has understood division in general as the opposite of multiplication/ dividing things into equal pieces for a long time.  He often listens in on his older siblings’ math and watches BA videos for fun, so he may be familiar with long division from before I introduced it to him, but I first talked to him about it and demonstrated a problem earlier this week, and had him do a problem for the first time yesterday.  As far as I can tell, he completely grasps it and can apply it to any size number.  

[Condessa]

When he gets really excited about a math question, he hops around the room in circles on his good leg while talking through the problem out loud.  So if you picture him delivering the above explanation at top volume while bouncing up and down on one foot in a circle and clapping his hands in time with every other hop, then leaping bodily into my arms on the “of course!”, you will get an idea of math time at our house.

Edited May 14, 2021 by Condessa

[Not_a_Number]

27 minutes ago, Condessa said:

It sounds honestly like he can see it in his head as though he were writing it on a whiteboard.  It went something like this:

Me: How did you find that answer? (To 973 divided by 8 )

Him:  Well, I could give a hundred to each, and there was a hundred left over, so that’s seventeen tens, so they use up sixteen by getting two tens, and then there’s thirteen leftovers so that’s a remainder of five after one more, so one hundred twenty-one plus the extra five of course!

When he was solving 3-digits divided by 2-digits, I saw him gesturing as though he were moving numbers around in the air in front of him.

 

He has understood division in general as the opposite of multiplication/ dividing things into equal pieces for a long time.  He often listens in on his older siblings’ math and watches BA videos for fun, so he may be familiar with long division from before I introduced it to him, but I first talked to him about it and demonstrated a problem earlier this week, and had him do a problem for the first time yesterday.  As far as I can tell, he completely grasps it and can apply it to any size number.  

Ah-ha. Right, he's obviously splitting into groups via splitting the powers of 10. Makes sense! That's what DD8 did before she learned the written algorithm, too. 

Sounds like he's very enthusiastic about it!! 😄 

Edited May 14, 2021 by Not_a_Number

[gstharr]

Your explanation of how he does it reminded me of Dr, Arthur Benjamin- the Mathemagician,  He is local for us. We see him perform around once a year. it never gets old. Your little guy might get a kick.  https://www.youtube.com/watch?v=baxOXLN23GI

[Condessa]

1 minute ago, Not_a_Number said:

Ah-ha. Right, he's obviously splitting into groups via splitting the powers of 10. Makes sense! That's what DD8 did before she learned the written algorithm, too. 

Sounds like he's very enthusiastic about it!! 😄 

When he was doing 2-digit divisors, he didn’t always use powers of ten.  I’m not remembering the specific numbers, but at one point he came up with something like 17 and 4 and one more makes 22, instead of so many hundreds, tens, and ones.

[Not_a_Number]

2 minutes ago, Condessa said:

When he was doing 2-digit divisors, he didn’t always use powers of ten.  I’m not remembering the specific numbers, but at one point he came up with something like 17 and 4 and one more makes 22, instead of so many hundreds, tens, and ones.

Ah yeah, we had that stage, too. I think we started here and it took me some work to move into restricting to powers of 10 times a digit 😛 . She wanted to do unconstrained partial quotients for the longest time! 

ETA: I was happy with her doing it however she wanted, of course, but I wanted her to see that it could work to always restrict so we could do long division... And she was quite resistant! 

Edited May 14, 2021 by Not_a_Number