We take our kids out of school. Ironically, just today I was filling out the paperwork to get permission for this "non school extended trip". I've never had them deny us (this will be my oldest DS 3rd time missing school since K for Disney). When it says "educational reasons" for the trip, it's easy to say that they'll be doing educational things in Disney because they do.
What we do is first talk to the teacher way in advance about the trip. Bring her/him on board to the fact that the child will miss X amount of days. We're sure to not go when there is state testing. Our children also don't miss a lot of school for anything else (one of my sons hasn't missed a day yet this year because he hasn't been sick & the other has only missed 2 days). Then, we apply whatever they are doing in school to the trip.
For instance... My Kindergartener will be looking for "sight words" on the trip - could be in the airport, on the plane, at the hotel, at the parks, etc... He'll write about what words he sees and where. We'll apply any math concepts to what we're doing - he's doing simple stuff with money right now and 3D shapes.
My 3rd grader is learning about other countries in social studies, so we'll be doing some research on one of the Epcot pavilions (he hasn't chosen which one yet). We'll do internet research BEFORE we go, then take pictures at the park. He'll then write about what he saw & what he learned. He'll also be applying math concepts - fractions, elapsed time, multiplication, etc... Then, he needs to write in his journal pages about what he's seen - creative writing stuff using proper grammar and good sentence structure.
Sure, is this more work for us, yes it is. Is this more work for me, at the mom, to be sure the work gets done, yes it is. Does this make our trip more interesting in some ways to see what we can apply to our trip from what they are learning, yes it does make it more interesting. My boys seem to actually enjoy it.