As a retired educator and administrator I need to add my two cents. First of all, I am NOT opposed to children missing school for an occasional family vacation. I do think four weeks out of the year (180 days in our state) is excessive, over 10% of the school year. Please realize that checking with the teacher for approval does little other than placing him/her in a difficult spot. Of course they are going to give their blessing, what other choice do they have, other than to risk a positive relationship with the family? Teachers are expected to prepare work in advnce, then catch up the child, if needed (make-up tests, homework, new concepts presented during the absence, etc). These tasks are to be accomplished in their free time, or class time (possibly taking away from the educational time of other students including yours). Teachers do this all with a smile because they are who they are and I thank them abundantly for that. If you think that they have maybe 25 students in their class, and half of those take five days of vacation time, that's 100+ days of extra work to prepare or cover, in addition to the absences for illness. In my previous district, teachers were not required to prepare work in advance of unexcused absences, but would present a packet of missed work upon return. We did classify absences as excused and unexcused. In this age of school accountability and merit pay for teachers, attendance may become a relevant factor in the standardized testing score game. (in fact in some states distrct school attendance is figured in as part of the school ranking).
One can never discount the benefit of life experiences and family time. Of course, your children are your own and you are free to make decisions on their behalf. I hope to just point out that the family vacation impacts the classroom community. It simply wouldn't hurt to send a special thank you to the teacher who takes on the added responsibility and make sure to ask if there's anything you can do to make it easier.
That being off my chest - we take our dear grandchildren out of school for vacations. The only valid reason we can give is because it's less busy during those times