When did you start the Delight directed Learning? Did you find it hard to get through a year-long school course when doing it 4 days a week? Did you just tell the kids they could do whatever they wanted on the non-school day, or did they have certain things they always did, like going to a class in a homeschool coop? Did you allow them to watch TV or play video games during the free day?
Yeah, but don't let your enjoyment of a nice day at the park be limited to your "fun day." We've been known to take school to the park.
I like this idea of a 4 day homeschool and a day of delight directed learning. Sometimes that fifth day can be a field trip or a club or a time to get together with other families. I love that homeschooling is flexible enough that we can enjoy a nice day at the park when the weather allows.
We rarely had our "day off" on Friday. In fact, we sometimes took 1/2 day off one day, and another 1/2 day off on a different day. I don't think it matters what day. I think it just matters that we have enough time for little kids to be little kids - and enough time for teenagers to explore career interests, learn how to love learning, and learn what they like through trial-and-error.
The "fun day" (as we call it) doesn't have to be a Friday. If the food bank needs a volunteer on Wednesday and your child wants to do it, then so be it. Homeschool is flexible enough to accommodate that!
There are 5 situations that homeschoolers may face while homeschooling high school that are so challenging, only a parent can effectively handle the ins and out and eccentricities of the situation.