Triple integrals are a bit too hard for 11th grade, but they are usefull to calculate the speed of a sailing boat. If you admit only one sail form exist however, you can make a simple algorithm for your pupils to apply different lenght/height and calculate the ultimate ratios. Thank you Mr Mason.
Microwaves are dangerous, but the powder inside fluocompacte (don't have the translation :/) bulbs does not react dangerously, and that can be used to who how low-consumption light can change our consumption (it was before LED bulbs became a thing, overall i have a lot of useless knowledge from this, but the method stayed with me).
You don't need to learn italian to translate a fencing treaty from 17th century bologna, but translating historical text is hard. At least you can use some positions and attacks in your saber competition, it's not good but surprising enough to get some points. But well, my history teacher introduced most of us to HEMA
There is multiple francophone theater festival a year, some of them not in France, and surprisingly not many French school attend (We were mostly the only one each of the 3 time). Tulsea is a fine city, Agadir is better and Liege is interesting too (budget cut in my last year i guess, we did not take the plane).
My brother was in a private school however. And i can tell you the difference: in public school the floor is low, sometime very low compared to private school. But the ceiling can be much, much higher when your school have a bit of money (like if it's also a public trade school).
I've also been part of "les petit debrouillards" and i've taught some chemistry and engineering (sometime even electricity!) to kids, at different levels. I've been invited to public school, to homeschooling association, but never to private school. It might be anecdotal, but our group was very well known and liked, we had a lot more invitations than we could respond to/attend to, and never once we were called to a private school. It's not a dig, but in my mind, it is exactly why i couldn't have done everything i've done if i went to the same private school my brother went. I would probably have a lot more money than i do now (not that i really care, i'm still in the top 10% income), but with a lot less skills and experiences.