Unfortunately, the way schools teach, and the way we have accepted, is the "standard" (read: good enough for government work). Real math is based on the personal discovery you have made. All basic operations have methods that are better the the awful, rote Junk-Ed we learned in school. Those methods are only considered "tricks" by people who know no valuable mathematics. You discovered a pattern, and a logical way to use it. It's not a trick. You did a great thing.
"Showing the work" is what you did when you explained it. Unfortunately, (again) schools don't want to see good work, they want to see the work they are programmed to see, regardless of its value.
Take your Idea further. To multiply any whole number, no matter how large, tack a zero onto the end of the number, start from the left and divide by two (no, for crapsake don't show work!) Now see if you can use that method to figure out how to multiply 24*84,358 in your head. It's easier than learning the "five-times-table."
Why don't they teach this in school? Are you kidding? What if they taught kids to think, and then graduated them? They'd create a population that wouldn't support the BS that they are fed. What kind of little consumers would we have then?
Keep up the good work!
He also left me a link to his site, Math Mojo. It's a great site with lessons, book recommendations, resources, a blog (look for the post on the Richard Feynman article!), e-books to purchase and a nifty newsletter you can sign up for. Once you sign up for the newsletter you get access to the archives and there's some great stuff in those archives there that any homeschooling parent or math curious person could use.
Seriously, get a cup of coffee and spend a bit of time exploring Brian's site. Make sure you sign up for the newsletter. Math Mojo should find itself on your Favourites list pretty quickly.