"Consume" is occasionally used this way. You can "consume electricity" (use up) or the more traditional "consume" meaning to eat.
"Draw out" means to get to something that can't or won't naturally come out. You might "draw out" a pet from hiding, but the way it is used here is fine. Here "draw out" means to get the information out from the students' brains to the surface where they can use it. "Coax" is another word you might see in the same context. You might also "draw out" someone in conversation, meaning to get them to open up or confide.