This phrase I periodically whip out of my back pocket:
Boredom breeds creativity.
Shut off all the electronics for a week (TV, Videogames, Computer). Put a big smile on your face. And tell them to go play. Be prepared for the first day or two for lots of melodramatic "walking"/ "flopping".
The phrase : 'I'm bored' gets met with a chore that MUST be completed.
A fit (over chore, or boredom) means being banished to a bedroom for an hour or so.
A non fit/whine/boredom phrase equaling some version of "entertain me" gets met with the phrase "You need to turn on your imagination. We've got tons of stuff to do. I'm not gonna find it, or it won't be as much fun for you." :)
It can take a little while for their imaginations to turn back on after a whole durn year of being told what to do all day in school, and then what to do while they're home (because the time is limited, pure and simple).
We do a week long electronics ban periodically in our house (music/ ipods are allowed) whenever I start to notice kiddo going from TV to Computer to xBox to TV to Computer to... And we've also done 1 month long ban (punishment). ((Actually we have graduated punishment for throwing a fit about an electronic thing; either shutting it off, or not wanting to do anything else. Step 1 is ALL of that day and ALL of the next day. Step 2 is a week. Step 3 is 2 weeks. Step 4 is a month. Increased time comes from either continuing to throw fits over the punishment/ sneaking time/ or the same day or two after getting it back, another fit happens).
It's AMAZING how after a day or two their little brains just TURN ON again and they start coming up with stuff to do.