Playbuzz lets you create a variety of online games and quizzes very easily – for free. You can embed them, too.
The only problem is that anybody can create them and, though I didn’t see any objectionable ones after taking a quick look, I’ve got a suspicion that some District content filters might block the site.
Here’s an example that somebody (I’d link to them, but it just leads to an “unknown” page) create for English Language Learners (it’s possible that their embedding option doesn’t work in WordPress. If that’s the case, go here to view the game):
I’m adding this post to The Best Websites For Creating Online Learning Games.