One thing that I have found to be extraordinarily interesting is the topic of multiplication. I got to thinking about what it really is and why we do it the way we do. It seems like everyone that I have every met has learned to do it the same way. There are, of course differences in terminology and sometime the order that things are done, but for the most part it's the same. You take your numbers and stack them up like a cake and then slowly work your way across, devouring each place value until you you get the very end (or beginning). What you find yourself with then is an empty plate...or a number, depending on what we are still talking about. Anyhow, I got to wondering if we all do multiplication that way because that's the only way to do it...that didn't seem logical, so there must be another way. Then it came to me! A calculator...that's how most people do multiplication these days. I include myself in that blanket statement. It honestly wasn't until my teacher assisting in a second grade class this past semester that I really had to retrain my brain to do multiplication like I learned at that age.

I couldn't possibly be building up this whole "how to do multiplication" thing, just to say that people use calculators, surely not. So what then? Well it turns out that there is another way, a pretty cool way, in fact, that doesn't involve writing numbers at all. At least in the way that we are used to. From my understanding, this multiplication has it's origins in China. So how do you do it?

Well basically it's like writing tallies. Lets say you wanted to multiply 14 and 12, you would start by writing one tally and then four tallies, representing 14. Then you would do the same thing for the 12 except crossing the lines horizontally over the 14 like this:

You then count up the intersections like the illustration below. The red indicates the hundreds place, the blue added up represents the tens place and the green represents the ones place. Of course you can do this same process with larger numbers, but then there is "carrying" involved. But! I thought this was a really cool, visual way to teach students how to do multiplication differently.

Sorry I've been missing your posts somehow.

ReplyDeleteInteresting topic for a post. Content wise: this would be stronger if you either addressed why the line crossing works, or the pedagogical side, what would be the advantage of showing this to students. For consolidation, you can summarize (what), consider the importance (so what) or the context (now what).