My first thought is to streamline things. Only use the
D&D 5e Basic Rules. Limit characters to only that PDF (which is free, so you can give them as handouts to your students).
If this is an ongoing class, you could break it down into phases. Character creation, spellcasting, combat, etc, can each be covered in a their own class session. It's like walking a new player through the process. If it's only one class, you'll definitely want pre-generated characters with the basic options.
As for the actual game, I might break up the class into groups. Each group of 3-5 students is one adventuring party, and each party has the same characters and classes. You stand at the front and present a scenario with a problem, and each party will have some time, maybe 5 minutes, to figure out how to solve it. After the time limit, each group offers up their solution; they can roleplay it if they want, or just describe it. You describe the results based on that group's actions.