Mathematically challenged.
You're as right as you can be. The metric mass should be 1.05 kg. I'll make that correction. Thank you for pointing it out.
I'm not familiar with the AR500 plate, but I accept your numbers. I think the reason I went with RHS/RHA is that it can be cut to whatever dimensions work best for a particular backpack. I have no idea what size options, if any, I might have with the AR500 plate.
I think you're right about the books having ballistic stop potential, but I ignored it for the sake of coming up with a "worst case" estimation. Just spitballing, I envisioned a 1/4" plate at the "front" of the backpack (closest to the wearer) and another plate the same thickness (but perhaps not the same area) at the "rear" of the backpack. Books sandwiched between would very likely enhance protection. I haven't shot up enough text books to make a guess as to how much. Erring on the side of caution, I arbitrarily set the protection from books to zero.
Curving the plates would also likely enhance its protection. Sloping armour at 60 degrees to the projectile's flight path effectively doubles the protection obtained, but I think that's an unusable angle. I don't know how to extrapolate for more realistic angles so, again, I assumed zero protection from curvature/attack angle.
Unless the theoretical active shooter is using only armour-piercing projectiles, I suspect that the protection would be considerable. I think the mass of 2 steel plates would be portable from classroom to vehicle or classroom to home, if the backpacker is afoot. I wouldn't want to carry that extra weight on a 20-mile march, but I don't think that's a realistic distance for most students to walk.