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I have found that if we don't do school year round...My kid's have to relearn! Out of sight, out of mind! We have a Virtual Academy through K12. In the summer we do subjects that they need improvement in! That way we can continue progress and it stays fresh in their minds! Summer's in AZ are so hot! Either we are in the house or at the lake! Certainly don't want them to play video games all the time...
Maybe kids brains do need be shut off--at least from more organized learning. How about taking a walk in the woods or going to a lake. Pick stuff up, see if you can figure out what it is, talk about weather, seasons, foliage, animals. I am all for getting dirty, messy, and a bit bug bitten in the summer.
Definitely keep up the reading. I have our kids read their books while I'm making dinner or during the early evening (their regular homework time during the school year) just to keep up the routine and their minds active. What they haven't experienced during a typical summer day through camps, road trips and interaction with other kids, they can do so with the help of a good book. They don't even fight me on this -- it's a nice time for them to relax/regroup after a long day.
Your Local Library!!!! Most libraries have summer reading programs that are excellent!!! I know my Jr. High students have a summer reading assignment due on the first day of school. It helps keep them focused. Also, my school offers Day Camp for the kids...it costs some...but they are always active and engaged!