He points at Mercy. "Awesome, come up here. What's your name?"

"Mercy."

"Great. I would like you to punch me or shove me. It doesn't really matter how hard, because you can't hurt me and because I will act like I was hit really hard even if you barely tap me so we can entertain the crowd here."

She smiles and nods seriously, then punches him as hard as she can.

He takes a very dramatically satisfying tumble and rolls and stands up and talks about some principles for falling safely. "Again, Mercy?"

She does! Mercy enjoys hitting people as hard as she can. She doesn't seem to mind at all if this specific person is in fact entirely unharmed by it.

What a wonderful person! He will take a bunch of entertaining falls and intersperse a safety lecture that is in significant part about falling but also manages to cover a lot of points that are important for safe sparring generally, either because he's deliberately trying to get that lecture across in a interesting format or because he just keeps thinking of related concepts when he's explaining something. 

Eventually he invites the kids to give it a try.

The kids pair off and practice falling. Karen considers asking if Mercy wants to practice and then thinks better of it and decides to pair off with a random girl who is scared of someone punching her too hard. (Karen does not punch her too hard.)

Mercy doesn't punch kids as hard as she can. That would be unfair to the other kids. She does pick the most formidable-looking boy in the class and practice with him.

Dennis spends a little time trying the falling thing and a lot of time watching the teacher for additional signs that he is some kind of horrifying demonic entity. He doesn't exactly know that this is what he's looking for.

Everyone else seems to like Alex; he'll be a very popular teacher by the end of the day.

He seems to be having the time of his life. He corrects kids who are doing dangerous stuff and lets them self-correct if they're just doing counterproductive stuff, unless they look frustrated.  At the end of class he gives everyone cookies. 

Possible signs he's some kind of demonic entity:

- he doesn't exactly move like a human; particularly when he's not paying attention, he's a little too fluid and fast

- he has long braided blond hair that doesn't go with the rest of his presentation at all

- he seems to really like being a gym teacher????

If the cookies are drugged with something that will turn all the students into rats for him to eat, the effects are not immediate.

Medium suspicious. Dennis puts his cookie in a plastic baggie to be consumed later, when enough time has elapsed that he's decided it's not an evil cookie. Or until he gets hungry.

Karen is more excited than usual when she stops by after the journalism club meeting. "You seem like you're very good at this job."

"I don't actually know if it'll be enough. Could make things worse, if they take more chances since they're all sure of themselves. But I guess an hour of their day doesn't suck, that's something. ...I didn't do well with school."

"I can tell. I mean, I couldn't tell for sure that you ever went to school, but you seem like if you did ever go to school then it didn't agree with you very well."

"It was better than something like Sunnydale High would've been, but it was pretty bad for me until someone noticed I'd be much happier out hunting all the time." He drives them off to their usual practicing grounds.

"I don't think people around here can mostly get by just hunting all the time. But I'm glad you found something you were good at."

There was a point at which she would have wondered what she was good at, if anything, but she feels like she maybe doesn't need to figure that out anymore. She has a job; she's going to do her best with it. She works very hard on slayer training for someone who seems to have a very hard time putting any effort into school things at all.

He doesn't really think that not putting in the effort is her problem with school. 

But anyway, school doesn't matter and this does, so it's a good thing she's a hard worker and a quick study.

She is those things! She mostly does not ask to cover new material on her own, but is nearly always excited when Alex decides that it's time for that. And she always does her best, which is consistently really good for someone with no previous training.

The gym classes go well too! The kids are mostly not as quick studies as Karen but he diligently does a lot of research into the best options for surviving something stronger, faster and tougher than you and teaches the kids that, and bakes a lot of cookies, none of which turn anyone into a rat. On Tuesdays they instead do basketball but after sternly telling them all that the curriculum says they're doing basketball, he works on stances and hand-to-hand fighting with anyone who wants.

Karen's books detail the operations of an organization of unclear size and scope which Michael works for, and which has been clearing small towns of vampires by attacking the main nests in force, leaving blood brothels and blood bank operations alone, instituting new procedures at the coroner's office, and then making it widely known that any vampire who kills a human will die the same day. This takes a lot of legwork to enforce but vampires do learn from examples. The book includes comparisons of the number of deaths caused by doing it this way (usually some vampires test the rule) to the expected casualties of an operation more singlemindedly focused on killing all the vampires. Which one is better kind of depends on how bad you think it is to kill a not-currently-murderous vampire. 

The case study for Cleveland is instead vastly more complicated, because Cleveland apparently was simultaneously near a hellmouth, ground zero of a turf war between two species of demons with a many-thousand-year history of racial hatred, the core port of entry for a dozen smuggling gangs, and home to some very old vampires and some dangerously powerful magicians. 

The books describe every species known to Michael and Alex except, apparently, the species Michael and Alex are. In the background of one picture of a crowd of demons there's another being like the two of them, though.

Karen studiously takes notes on all of this and commits as much of the information to memory as possible. (She has also been taking notes on whatever kind of thing Michael and Alex are, and on every Weird Thing that appears at the school, because she might be probably-going-to-die but it seems like Weird Things are a field where additional notes could someday leave future people more prepared to spend more time not-dying.) 

Whenever she runs out of books, she returns them to Father Michael and asks if he has anything else for her. She continues doing research online, and spends most of her allowance ordering more books from the internet, whenever she runs into one that looks like it might have additional useful information about Weird Stuff. She develops a habit of watching this one cryptid-hunting show on Saturdays, just in case any of the things they're hunting are examples of legitimate Weird Stuff. Also cryptids are fun. She writes up a bunch of perfectly respectable articles for the school paper.

She kind of doesn't push on when they should start properly hunting vampires, because she kind of doesn't know what their game plan there should be, but she does feel like this is maybe a failing on her part and she should maybe be figuring this out faster.

He wanders the streets of Sunnydale at night killing things if they're vampires and aren't Karen's friend Zeke. He's not opposed to bringing Karen along for this but there hasn't yet been an occasion that seems like it'd teach her something useful, and she's not quick enough on her feet yet that he'd be comfortable sending her off outside his hearing.  

And it seems like this is good enough.

Until two kids don't make it to school one day.

"Missing since yesterday," he tells her after class is over. He has pictures. "Do you know either of them?"

"This one's Willow Rosenberg. I don't remember the other one's name, but he's friends with her. She's honors track for everything. Sort of shy and nervous about everything, but super smart. You think something got them?"

"It seems pretty likely." He makes an unhappy sound under his breath, a little bit of a growl. "I didn't hear anything but I can't pick out everyone in the city at the same time."