

Elegant visual way to multiply numbers by hand - RiderOfGiraffes
http://www.youtube.com/watch?v=gwaAAEYIW_8 [video]

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Avshalom
Cute but it does kind of predictably fall down when you're doing 9s and 8s
instead of 2s and 3s.

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klochner
This method essentially converts the typical tabular calculations into a
lattice, where the x-axis is the 10's coefficient.

Cool way to think about it, but I doubt it would give any extra insight to
someone learning how to multiply.

It also loses a lot of the "elegance" when you have to carry over sums > 10.

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Avshalom
Maybe not insight but it gives you an approach to multi-digit multiplication
that you can use even if you're still sketchy on single digit.

I know as a kid I'd occasionally resort to just adding a number up the
appropriate number of times. and while that works for 67 * 5 it's super error
prone for a 6 year old if that 5 is a 9 or worse a 30. This might (might) give
6 year old me an approach to that, sure it doesn't change the need to be able
to count and do a little addition but it's a way to break the problem down
that I sure wouldn't have thought of.

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bitwize
That's like saying it gives you an approach to running that you can use even
if you're still sketchy on walking.

There's only one proven way to teach arithmetic, and that's drill and
repetition of the basic number facts and the standard algorithms. It's worked
for centuries.

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Avshalom
Just because somebody hasn't mastered step A yet doesn't mean they won't
occasionally need/want step B.

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Avshalom
So playing around with this it also works for multiplication with decimals
using say a dashed line between the appropriate digits. The location can be
read off by finding the intersection of the dashed lines and putting it in
front of that column's digit. It's significantly less elegant, particularly
when that column yields a multi-digit count but it does work visually.

I'm sure I'm not the first person to realize this, but it's cool that decimals
can be integrated into the method while keeping vaguely in the spirit of the
idea.

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eru
It also works with binary numbers.

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nato1138
how does one work this out if there is a zero in one or in both numbers... I
played around with this on a napkin at a bar and couldn't figure it out...

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fairlyodd
Imagine (or draw) a dotted line where the zeroes are..Count the dotted
intersections as contributing zero to the diagonal addition step.

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yardie
123 * 312

Using the first example I would have thought it would be 371376, but no using
some math "voodoo" 7 is added to 1 making it 38376.

How are we supposed to know where these numbers are merged? Gotta buy the
book, I guess.

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RiderOfGiraffes
I'm wondering if you are serious or not - it's hard to tell. It's really
pretty obvous why the "1" from one column goes into the next column over to
the left, isn't it?

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yardie
If you have to use the same rules as the standard multiplication method then
how is this anymore elegant than doing it the old fashioned way. So instead if
counting numbers now you count dots, how revolutionary

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Avshalom
because to perform 312 * 123 you draw 12 lines, count a total of 36
intersections and perform a single addition.

you did not have to actually know any multiplication. and the rules for are
hung on a visual framework instead of just being "the rules."

No one said it was revolutionary (well maybe some youtube commenters..)

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bitwize
No, fuck you. The rules aren't just "the rules". They are directly derivable
from the property of distributivity of multiplication over addition. E.g., 12
* 39 = 12 * (30 + 9) by the property of place value, and hence 12 * 39 = (12 *
30) + (12 * 9) by distributivity. Then you do the same thing again with the
12s to get the two subresults, and... well, you get the idea. This is the
basis of the standard algorithm, and it is derived directly from the
properties of multiplication itself.

But this line thing... this is a trick. And, might I add, a trick that may
actually cause more work and use up more scratch-paper space for the figurer.
Using a "visual framework" without _meaning_ is no way to teach math. The
point is that the standard algorithm is _the shortest_ path from point A to
point B, and that is why it should be taught first and foremost.

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Avshalom
Wow, I'm sorry, did cross hatching molest you as a child or something?

But please explain to a child the difference between abstract rules and
directly derivable properties of distributivity of multiplication over
addition. See how much of a difference there is to a first grader between
"It's a fundamental property of mathematics" and "Because I said so."

>But this line thing... this is a trick.

Yes, yes it is. And seeing as all any one has said is it's a elegant (under
certain circumstances) trick, why are you so hostile. No one here has proposed
replacing the k-12 math curriculum with happy fun line counting time.

EDIT: okay the sibling post may have said something that could possibly be
construed as supporting the addition of this to the standard curriculum. Still
not advocating replacement.

