There has been a major and on-going back-and-forth about the need for learning (and teaching) single-digit × facts well-enough so that students access/know/recall/[whatever verb you like] them automatically. I think the automaticity is crucially important, but I strongly believe that if automaticity isn’t approached through understanding, then whatever semblance of fluency seems to have achieved is likely to be subject to erosion due to limitations of cognitive load, unthinking obedience, brute-force memorization, post-colonial whatnot, and other factors. (I still have the scars from a traumatic experience with flashcards in 3rd grade. I remember it like it was only yesterday even though it happened about 70 years ago, but I’ll save that story for a future post—or maybe just leave it as one more painful memory.)
Anyway, once I understood multiplication as repeated addition, and knowing that addition facts didn’t change, and having gotten familiar with the commutative property of addition and extending it to multiplication, I realized that to get faster at my times facts all I had to do was practice. With that in mind I made some powerpoint animations of multiples of whole numbers from 3 to 9. I turned those into videos so people could access them more easily. They’re all short: the longest is less than 3 minutes. And they’re in 3 formats (I intend to insert some screenshots here very soon):
Just the facts (products on a 10×10 grid)
nx3, nx4, nx5, nx6, nx7, nx8, nx9
Multiples step-by-step on the number line
nx3, nx4, nx5, nx6, nx7, nx8, nx9
Multiples making tens on a 10×10 grid
nx3, nx4, nx5, nx6, nx7, nx8,
In case you are wondering, I like Holey Cards for the 100-question time tests. I have my students do these every 2 or 3 days and I have them graph their own progress until they achieve something like exit-velocity. The frequency of the time tests and students graphing their own progress seems to desensitize them to any potential anxiety (“Familiarity breeds contempt.”) and make it clear that the goal was to plot and see their own progress towards 100% accuracy in <3 minutes (so that they would become fluent enough in the nuts and bolts of arithmetic), not any kind of high-stakes.