Dauntless
The training in Dauntless is considerably harder and stranger than his demigod training, but he manages. He learns how to aim and shoot low caliber, handheld guns, how to duck and attack the more modern way. He learns to trust his bulletproof vest, and gets a new backpack, black and bulletproof, to store his meager belongings. Somehow, the adults understand why he needs it.
A few of the older kids are jealous and wary, but most of the adults and the kids his age like him, so he has protection if they ever decide to do something. And magic. He has that too.
Most of his days are spent at school, at training, or climbing buildings. He hasn't ever been to a proper school before, but the majority of stuff he's learning right now he's learned already, back at Camp in the Athena cabin. Climbing buildings is new, but he pretends he's climbing the lava wall and breaks the record for climbing in practically all of Dauntless. He's called talented, special, and if it weren't for the fact that he had no idea how to control his powers, he would have chosen to stay in this world. Some people jokingly call him a mock Erudite, who are apparently the smart people in this world. He's not so sure he's really smart. He just knows a lot of stuff.
Instead, he commandeers an empty notebook to use as a journal. His old one, a plain blue spiral bound, 300 page notebook with the icon of Hephaestus (it happened to match the Dauntless insignia, thank the Gods) was already used for any of the classes he attended in the dimensions, and he didn't want to let it run out of paper so soon. He also sneaks into an Erudite lab one day, by hiding himself, and steals 2 pencils. His special sword pen can write, of course, but he has no clue what he's going to do if it runs out of ink.
He learns the motto's, repeating them over and over again until he really, really believes in them. He stands up for himself and gains a new set of scars after another kid accidentally hits him with a three pronged spear. It hurts, and they both learn to be very, very careful around long ranged weapons.
Using things other than his sword, things that aren't balanced and made for him, is difficult, but he manages just fine. Percy's move, the sword twist maneuver that had been taught to all new demigods at one point is especially useful, and he is praised for being creative despite it not being his idea. He doesn't object. The praise is kind of nice.
2 days after his birthday, celebrated by a pair of trainers who give him a Dauntless jacket, a group of Erudites break into the compound and attempt to take it over. He takes this opportunity to slip away, jumping down and disappearing. The faction declares him dead, lost in the wasteland.