First time poster. I apologize if there is an easy/common answer to this question.

I'm the faculty sponsor of my high school's D&D Club. We've got a lot of kids who want to play but they can't play after school because of other sports or activities, so I'm trying to think of ways to play during our school's "open study hall" time which is an hour and a half divided up into 30 minute segments. Does anyone have any ideas or ways to play in 30 minutes?

My initial idea is something like a gladiatorial arena. DM's design and run combat encounters in a closed area with challenging or way-out-there monsters and players just design characters for combat efficiency. Of course anything could happen - someone could walk into the arena with a charisma-boosted Bard and just talk his way out, which would be hilarious - but the point is that it would be a no-story, blood-sport arena designed to be run in 30-minutes or less. Any other ideas or suggestions for my arena idea?

Basically what you want to do is design something of a puzzle challenge with D&D trappings. What you are going to end up doing is short little "scenes" where you sort of setup the encounter in a voice over narrative for the players, and then have them work out the scene for the allotted time. Maybe sometimes there will be monsters, but not always. Unless you are using really easy to kill monsters or letting them gang up on a singe adversary, combat can drag on for a while and eat up a lot of your time.

Treat this like a problem solving game or some kind of series of story questions from a quiz. "You have been contracted by the nearby village to root out a band of goblins that has taken hold of a cave in the hills. Having gone there and already killed a few of the little buggers, you find your progress stymied by what looks like some sort of puzzle left by some ancient peoples for some reason. The door requires some [insert grade appropriate logic puzzle here] to solve. As a group, solve the puzzle to get to the goblins on the other side before your time runs out and they escape down their secret tunnels!" And if they solve the issue with time to spare, then they can combat some goblins or something.

Not sure if this is the kind of advice you're looking for, sorry if I'm off base, but logistically, assuming you get a lot of interest, I'd think you want to group the tables by experience playing, so you don't get experienced players frustrated with new players needing to look up their abilities and spells/new players discouraged because they can't keep up with the kid who has the PHB memorized.

Can they choose to group two or all three of the study halls together? half hour seems really tight for high school students to all come to the table, get all their stuff out, chit-chat, flirt, and actually play. Maybe encourage them to use die rolling apps on their phone (there's a number of free ones) They'll be faster to prep, its one less thing to carry around, and you don't have to worry about losing time chasing an errant die across the room/ die being thrown at people. If a combat runs more than the half hour, they can always take a picture of the battlefield, so they can re-create it the next day.

The arena idea is really good, but maybe don't mandate it. There could be some kids who could manage a campaign in 30-minute bursts. especially if you get a DM with good time management skills. I realize that contradicts what said about the time being tight, but hey, sometimes people surprise you.

I would shy away from blood-sport arena combat as it likely doesn't teach the right message to kids and also doesn't really explore how thought-provoking the game can be. 

We're playing one-shots and campaigns after school sometimes but not everyone can make those sessions, so I'm trying to find something that some kids can do in our study hall period. But I appreciate where you're coming from.

I agree that just throwing someone into a random combat without any RP or exploration is not going to attract the kind of player who could really get interested in the game.

I suggest having really simplified pre-rolled characters specific to the scenarios you are playing, with notes about skills that could be useful. And instead of important places marked out on your map for players to find, treat them as encounters that happen at specific intervals...very railroady, but you only have half an hour.

Just for example: Your party arrives in Willowvale  to find the place in a frenzy.  A murderous barbarian who was sentenced to execution has escaped, and is already killing foresters and farmers on the outskirts of the village in revenge. Knowing of your reputation, the townspeople beg you to track down and capture or kill the murderer for them.

The party includes a Dragonborn ranger, with notes about using Survival checks for tracking, breath weapons

A druid with healing spells and 'talk to animals' preselected among their spells

A wood elf rogue, with notes about surprise attacks and Mask of the Wild

The players set out from the farm where the barbarian last killed someone.  Each square they move, describe any change in terrain and the Ranger has to do a survival check to see if he is still on the track.  If the trail is lost, the whole party can do perception and/or nature checks to discover clues: a discarded apple core from the food he stole at the farmhouse: the mark of an axe savagely chopped into a tree: realizing that there are caves to the north where the barbarian probabaly is hiding out: looking for an animal the druid can question. If all fails, have them move whatever direction they like (and check again, if you want.) After X number of moves, they come across a young dwarf woodcutter who has been hacked to death with an axe. The woodcutter's dog is whining near the body, and will gladly help the party track the murderer if asked. X moves later, dex check: the Barbarian set a trap for pursuers! If the dog is tracking for them, find the barbarian and kill him.  If not, X moves later, they find a bear caught in a trap that was probably meant for them: if they speak to it, release and heal it, it will gladly lead them right to the barbarian's cave, where they can mount an ambush and get a surprise round.  If they do not enlist the dog or bear, have them roll a perception roll, because the barbarian has doubled back and is sneaking up on them! If they fail, the barbarian gets a surprise round. The barbarian is carrying a locked chest which he apparently stole from somewhere: the rogue can try to unlock the chest.

Something like that can be rushed through by newbies and still give them a chance to experience a lot of the options and possibilities.

Something like that should give them a peek at all the basics

Watch Harmonquest for how to do brief 30 minute chapters.  It's edited, of course, but the point is you don't have to sacrifice story completely.   I co-wrote a ten part epic campaign for my nephews D&D school group in 45 minute installments.  Sweeping location changes, puzzles, NPCs, one fight per episode.  It's doable.  My preferred way of doing it is just to gloss over the crunchy parts. Everyone gets to roll dice, and you describe the fight scenes in the most exciting way you can, but keep an eye on the clock and adjust the monster's hp down according to how much left you have to do.  Don't be afraid to have an NPC nudge them if group decision-making paralysis sets in.

If the kids are regular players, and they actually prefer the crunchy parts, an arena might be the way to go.