As a teacher, what passage from The Scarlet Letter would you hand out to your students, if they are supposed to write a timed essay?
I, too, would choose a selection from the couple's meeting in the forest. In a kind of before and after cutting, I would include the paragraphs where Hester "comes to life" with Dimmesdale. Her hair shines and she looks young again, in contrast with the kind of shriveling effect of having to tuck her hair back in and put the "A" back on her bosom which happens at the end of their interlude. It's an opportunity to write about symbolism and connection to theme and setting. If you're looking for something a little more complex, the last lines of chapter 11 when Roger dances with demonic glee at his discovery is full of writing potential, as well.
I would give students a cutting from the chapter with Dimmesdale and Hester in the woods, acting like themselves and free from the weight of all that has happened, but I would include the part where Hester removes the "A" and Pearl gets upset because that connects several different themes in the work: guilt, sin, public vs. private punishment and atonement, innocence vs. experience, etc. The scene serves a thought-provoking surprise to most readers.
There are passages that relate closely with theme. One is in Chapter X as Chillingworth questions Dimmesdale about what he knows as "secret sin.":
"But still, methinks, it must needs be better for the sufferer to be free to show his pain, as this poor woman Hester is, that to cover it up in his heart."
This question can easily be a discussion question about the dangers of secret sin as contrasted to the punishment of Hester.
Another question is the lines from Chapter XX:
No man for any considerable period can wear one face to himself, and another to the multitude without finally getting bewildered as to which may be true.
These lines again relate to theme. The secret sin and visage which one must wear, take away from the truth which is what will redeem a person. Hawthorne states his moral:
Be true! Be true!... .Be True! Show freely to the world, if not your worst, et some trait whereby the worst may be inferred.
Students could discuss how Hawthorne's theme relates to Puritanism, and how the characters suffer because they are not allowed to "be true."
This is a difficult question to answer because, as a teacher, the passage that I would select would depend so much on what particular themes or parts of the novel that we had looked at more than others. It would depend on the level of the class and their ability as well as how far we had progressed in the novel. Even after these questions had been answered, there would be a range of possible passages that you could select.
Personally, quickly thinking about it, I would go for the last few paragraphs of Chapter Ten, which describes the way that Chillingworth discovers what is on Dimmesdale's breast. It is important for a number of reasons. This passage gives us a real insight into the character of Chillingworth and his diabolial nature. You will want to pay attention as to how he is described once he has made his discovery, and what it says about him that he creeps around and looks at Dimmesdale's breast when he is asleep. This passage relates to key themes such as guilt and really helps develop our understanding of the character of Chillingworth.