My oldest ( 8yrs ) is curerntly in 8th grade has been working furiously with his white board doing math and has been doing algebraic equations

Today, he just gets out of bed ( 6:30 am ) and says there is another way to do multi-digit multiplication. he says it works best when the numbers are in the same 10s group [ ie 14 x 19, or 145 x 142 or 1567 x 1562 )

He gives this example :

211 x 215

You take the one's place digit.

211 = 210 + 1
215 = 210 + 5

210 = z
1 = a
5 = b

211 x 215 = ( z+a) (z+b)

(z+a)(z+b) = z^2 + zb + za + ab

z^2 + zb + za + ab = z(z+b) + a(z+b)

I told him that could be done with 2 digit problems as well, he said it was just quicker to do it the regular way than this way

So when faced with a multi-diigit multiplication problem with numbers in the same 10s group just use z(z+b) + a(z+b)

I smiled at him and said good job, and I sent him off to figure out how to make this equation work for multi-digit division ...

This is not the first time he has done this ....

Before he showed me this a couple weeks ago.

( b√x )^(b-1) = x ÷ b√x

I asked him where in the book that he was reading that was stated ... he said it isn't .. he just looked at the numbers and figured it out. I read the book he was reading .. it was not stated anywhere.

So we did 3 examples to prove this and it does work

So now it seems I need to start reading some math books ... and refresh my knowledge from that math I took in high school and college.

That's one for the brag thread.

That is totally cool!! Also great that you're supporting him.

Since you're on this board, I assume you know about this stuff already, but maybe he would enjoy AoPS or (our local option) IMACS or EPGY? Our DD isn't anywhere near as advanced as your DS, but it still is hard for me to keep up and without some kind of program I would have a really hard time keeping ahead of her enough to teach her anything. Probably you don't have that issue but it might be useful to look into.

I hope he continues to enjoy it.

Unbelievably amazing, Cawdor. I remember doing this sort of thing myself when I was 14 or 15, not when I was 8! This is AWESOME! A cool thing that I discovered was that the sum of the digits of a product of two numbers is the same as product of the sum of the digits of the numbers. So, take 392 x 4978. Write that as (3+9+2)x(4+9+7+8) or ((1+4) x (2+8)) or 5 x 1 = 5. Now take their actual product which is 1951376. Add the digits to get 32 or 3 +2 = 5.
Thought your DS would like that!