I lurve the idea of teaching students lots of methods for solving math problems because I just plain love math problems and I can’t help but think that there has got to be a better way of teaching concepts than the humorless, awful, dry, disempowering way I was taught. Follow the blue box. OR ELSE. You will be WRONG. WRONGITY WRONG WRONG WRONG. Oh, don’t fret, dear, girls aren’t good at math anyway. Yeah, maybe because boys in my childhood were the only people raised with the kind of self-esteem and security that lets you face that kind of instruction.
ANYHOO, I will watch “new math” tutorials online until my eyeballs bleed because they are so fun and I am so curious. I decided over the weekend to take a whack at the visual line-factoring method that is variously referred to as “Japanese multiplication.” I really couldn’t find out whether it was Japanese or not, or who was the originator of it; most websites are focused on teaching you the how and why of it, not the history of it. But whoever made it up, good job.
The method is explained very well here. In sum, you draw out lines for each digit of each number in one direction, and then you draw outline lines for each digit of the multiplier crossing the first, and then you add the intersections of the lines that occur at specific locations: the hundreds, tens, and ones.
I didn’t happen upon this site until I had been noodling around a little bit and gotten myself in a little trouble, and then that site made sense: it’s not an efficient method for numbers with large digits: I got myself in trouble pretty fast getting ambitious with 973 x 819. It’s not that it doesn’t work; it’s that it’s a PITA to draw all those damn lines and count up all the intersections, and it gets messy. AHA. So THAT’S why all the exemplars are things like that 321 x 123.
It’s not an efficient method of calculation, but it is a very good way to understand what is actually happening with multiplication. Using this method, you see how factors work. So you don’t really need to do examples with the larger digits–you can just use the standard algorithm or a ubiquitous calculator if you want to calculate efficiently.