Snape's purpose in teaching a lesson on werewolves was obvious: he wanted to lead the students to Lupin's true identity.
But he had clearly overestimated the young wizards of Hogwarts. Which of them would take an assignment from their "substitute teacher" seriously?
Even threatening to make them rewrite it if they did a poor job would do little good. In the original timeline, only Hermione had worked out Lupin's true identity ahead of time. Perhaps other good students had figured it out too, but no one had ever come forward to identify him.
As far as Will was concerned, Snape was wasting his effort.
After class, Will returned to the Room of Requirement and opened the door to a small compartment. It was only a few square meters, with a soft bed inside. This was his "Time Travel Room," connected to both the study and the Potion Room. He often used the Time-Turner here.
He used the Time-Turner to travel through time again, this time going back twelve hours. Lately, he had been gradually increasing the span of his trips, from a few minutes at first to several hours, and now to twelve hours.
Unlike ordinary time travel, nothing around him had changed. There was no one or anything else inside the compartment to cause a change.
He arrived at Hogwarts in the early hours of the morning, returned to the study, and began writing the assignment Snape had set. Will had always avoided meeting himself. Even if his other self was asleep at this hour, he still did not want to be in the same room as him.
Candlelight illuminated the desk as his Quill flew across the page. Before long, neat words filled two rolls of parchment. He tossed them into a wooden tray beside him, where a