My years as an elementary school teacher made it clear to me that if students didn't master multiplication facts at grade level, they would find it all but impossible to do well in math thereafter. That's why I found it unacceptable when certain colleagues suggested we address this gap in education by having the kids compensate using pocket calculators, or even altogether dismissed the problem by saying something such as, "Oh well, they'll get it
eventually."
The fact of the matter is, students do not get it "eventually," as if by magic. Indeed, the only way to solve a problem is to face it head-on. Accordingly, I made it my goal to find an approach that would guarantee 100% of my learners mastered their multiplication tables at grade level—no exceptions!
And after spending thousands and thousands of hours manipulating the multiplication tables, turning them upside down and inside out, I discovered that there are indeed a handful of
extremely simple patterns, formulas and algorithms that, when applied to the multiplication facts, serve as keys for
instantly unlocking
entire tables at a time—in one fell swoop!
These "pseudo theorems" organize the seemingly arbitrary, isolated products within each table into sets of interrelated numbers, empowering students with the means to
automatically generate the answers to virtually
all the multiplication facts in less than a flash (figuratively speaking).
As a result, my students no longer needed to struggle with attempting to memorize individual facts
one at a time, and this made the learning process fun rather than drudgery, for both them and me alike.
This song summarizes the "algorithm" for the nines table, which is a variation on a "trick" already known to quite a number of educators, which is why I'm willing to post it here rather than keeping it exclusive to a book I'm probably going to self-publish by the end of this year. (The only caveat is you need an introduction the the super-simple concept of "partner digits" as applied in my classroom.)
THE NINES SONG
Copyright © 2024 by Fred Duckworth
https://suno.com/song/b667456a-f097-4646-9313-5b6811504d83