Whoa two blog posts in one week. I figured I’d use this one to post a cool math trick I saw a while back, that’s really simple (and pretty cool because it’s so simple). Start by watching this video.

http://www.youtube.com/watch?v=pOYuEUkE06I&NR=1

First things first, this is cool right? It’s also clear that it works for numbers of any size, albeit it’s probably messy after 3 digits. Second thing, why does this work? As far as I can gather, the method is this. Each line represents one of the digits, but they’re configured in such as way as to take into account place values. It’s kind of a method of foiling, if you look at the 21 and 13 example, you can see that the lines are drawn so that the 1 intersects with the 2 on the far left, and the 3 with the 1 on the far right, and the two in the middle. This delineates the far left as the most weighted, aka the intersection of the two numbers holding the greatest place values, etc, etc. The geometric representation of the place values allows you to add them vertically. Hmm, not the best explanation I’ve ever given, but I think it intuitively makes sense as to why this would work, though I can’t say I’d ever come up with it myself.

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In the second one, do you know why they added the one to the 8 and how you would know when to do that?

By:

jschon November 6, 2008at 4:12 pm

They add the one to the 8 because the one was really an 11, and just like when you add 7+4, you add a 1 to the 10’s place. So basically whenever it goes over 10, or 20 etc, you add it to the place directly to the left.

By:

dschneid2010on November 6, 2008at 4:22 pm

That was a really great video. Thanks for showing it, my students are going to love this little trick. My 8th graders are constantly drawing anyway, this might give them something else to draw (if only for a minute).

By:

Lindaon November 7, 2008at 9:52 pm

Yeah, it’s a wonderful way to visualise multiplication and decimal notation. Thanks!

By:

Prof. Kateon November 8, 2008at 3:49 pm