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Lattice Method for Multiplication

 
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Mkat
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Joined: 10 Apr 2009
Posts: 23
Location: Missouri

PostPosted: Thu Dec 17, 2009 2:13 pm    Post subject: Lattice Method for Multiplication Reply with quote

My 9th grade son went through Everyday Math in elementary school and when he hit a different school for middle grades, he was told that his techniques were "wrong." The main problem was that he was taught the Lattice Method for multiplication.

Here's how you do it:
http://mathforum.org/library/drmath/view/52468.html

Since we've been homeschooling using Math-U-See (after Saxon not working for him very well), I've not let him use the lattice method because he knew it worked, but he never knew why, and I worried because of all the criticism against it and obviously wanted the best foundation for him for higher math. He's really behind in math (we're doing the end of Gamma MUS) and my goal is to plug up holes in his understanding that he's lost along the way. He's moving fairly quickly but I started him at the beginning to make sure things lost were patched up.

Well, turns out he doesn't get why the standard way works either. And you know what? Neither do I. At least, not why it works any "better" than other methods. With Lattice (also called Napier's Method)or the Box Method,

http://www.cimt.plymouth.ac.uk/projects/mepres/book7/bk7i6/bk7_6i2.htm

the numbers are handled exponentially and broken down into tens and ones. I can see why it works and so can my son now that we've dug into it a bit. Numbers are their sums of tens and ones (and hundreds, etc).

So, now I'm questioning the criticism I've read and thinking it's just because it's different than people are used to. The Lattice is 800 years old, it's not new. I think I'll be exploring these methods with him over the next several months.

What do you guys think? Any experience with these methods?
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Theodore
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Joined: 06 Oct 2005
Posts: 2122
Location: Missouri, US

PostPosted: Tue Dec 22, 2009 1:43 am    Post subject: Reply with quote

Fascinating, but I don't use any of those methods.

Code:

  42
  37
----
 294
126
----
1554

Basically, you multiply 7 x 42 (one place at a time, carry over in your head). Then you move one place to the left and multiply 3 x 42. Etc. When you're done you just add everything up. Seems an intuitive method to me.
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Mkat
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Joined: 10 Apr 2009
Posts: 23
Location: Missouri

PostPosted: Tue Dec 22, 2009 1:49 pm    Post subject: Reply with quote

Yep, this is the standard method that I think most people use. It's intuitive to you, and to me, but not to my son. This may simply be because he was taught differently than I was and from what I gather, most people, or maybe it's the way his brain works.

I just wondered if anyone has any experience with the other methods.
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Theodore
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PostPosted: Wed Dec 23, 2009 1:22 am    Post subject: Reply with quote

The lattice method obviously works, but it's done more on paper and less in your head than the regular method, so it's probably going to be a bit slower and require more space. I'm guessing that's why nobody uses it.
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Mkat
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PostPosted: Wed Dec 23, 2009 10:44 pm    Post subject: Reply with quote

That's the criticism I've read for it, that it's on paper and harder to transfer into a brain-only activity. I'm not convinced of it...since it's still ones, tens, etc. but we'll see how the different methods translate for him. I really want success for him, and with his low motivation, the standard method is just frustrating him so far.
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