You don't need vector calculus. My demonstration of the power factor is a children's swing: if you push against your friend as they travel out you do work on them: if you make contact with your friend aas they're coming back, they do work on you.

Kids have a pretty good mechanical model of swing sets.

Do kids actually learn about power factor?

That point aside, while an intuitive understanding is nice, power factor is really a mathematical construct arising from the multiplication of two out-of-phase sinusoids (i.e. voltage and current).

I think to really understand active / reactive power and pf, you need to look at the maths. It's really not that difficult. And you certainly don't need to know vector calculus, merely high school trig.

Fully describing it, yes, but a 6th grader should at least be able to handle Ohm's law >_>

What about pictures and animations of those vectors? They don't have to perform operations on those vectors to start understanding, they just have to see the vectors. In other words, they have to see pictures of arrows.