Don't let's be silly.
When preparing to meet with my managers to ask about working a shorter week (and working from home more often), I made sure to do my homework. I checked my vacation balance to see how many hours I had available, I double-checked the start and end dates of the semester, and I made a list of questions that would need to be answered (by me, by management, by HR) to make the change. I also thought about what I would say in the proposal, and what likely questions or concerns my managers would have. I even went to the extent of writing up a one-page summary of my points, which refined my approach both in my head and eventually in the meeting with management. (I kept it handy during the meeting, but I ended up not passing it out.)
I consulted with other people who have experience with similar situations -- both from my own viewpoint as an employee and from the other side of the table. Friends who had negotiated flexible schedules (and there are many in the tech industry) offered their encouragement and their suggestions. One of my former managers had a great angle on the circumstances, and convinced me that it wasn't necessary to approach my managers "hat in hand". My request was actually quite reasonable, this person told me, and there shouldn't be a reason for my employer to refuse unless they were ready to let me go. As I was a valued employee with a solid history of contribution, that was unlikely. (Good to hear!) On their combined advice, I nailed down a limited timeframe (from ASAP/end of January to end of May), got my proposal in order, and visualized how I would feel once the change had been approved.