We've been using the Learn at Home series (Grades 1-6)
We tried that
exact same series-- the grade 1 through 4 versions, anyway. I kind of have some PTSD over that series. LOL.

It was maddening, because she would be in the sweet spot, where it felt (to me, anyway) like she was learning and engaged and I'd think;
Great! I finally found the right level!! Yay, me!!But then within a few more weeks (or really, days) things would.... er...
change. She'd begin refusing to do ANY of it. I think I've noted just how superhuman her refusal skills can be. Let's just say that I tried arguing on the basis of "but if you know it, then showing me ought to be simple" and "you just HAVE to" and even restricting pretty much everything else until she gave us compliance... all this did was turn my home into a war zone.
THEN, finally (I'm slow this way) I'd offer the
end of course evaluation to her, which she'd
ace. At light speed.
I don't know HOW she was making those kinds of jumps... but she certainly was. We'd go from fine-fine-fine to "DONE" overnight-- she'd be months ahead of where she had apparently been happy enough doing work.
As far as I've ever been able to tell,
there are no gaps from this practice. Was she skimming ahead in the curriculum? Possible-- she has always read her textbooks cover-to-cover within a few weeks.
Anyway. That's my story with packaged curriculum. It drove my DH nearly round the bend, because about ever 4 months (when you include the month and a half of DD being "punished" for her refusal to cooperate with ANY school-based directives, I mean) we'd be buying "new school stuff" for homeschooling. Rinse and repeat.
Actually, the Learn at Home series was the
best of those experiences. At least these weren't hideously expensive, unlike the Cuisinaire rods and math curriculum that she barely touched...

Any general curriculum was a disaster, because DD's literacy was
so out of synch with her readiness in some areas, and certainly with what curriculum designers intend. You know you're in trouble when your 5yo is reading the directions on the worksheet-- upside down-- before you even hand it over to her, and frostily inquiring about the need to "waste my time coloring that thing when I already KNOW my letter sounds/math facts/parts of speech."
Anyway. Thought I'd add that anecdote since a general curriculum did NOT work for us, ironically, for the same basic reasons that someone else has liked it.
RE:
how to get kids steered into that informal learning process, we've discovered a couple of things that seem to work for my DD, but they may not work for other kids. We've found that for HER, conversation and access to print materials is the key to anything we want her to think/learn about. This is because that is her natural/preferred learning mode. So if we want her to learn about, say, gun control? We
talk about it. Leave TIME on the coffee table, mention a Bill in committee. She'll jump on board in no time... because she loves to participate and she actually loves
contentious/hot issues.Print media like the chart technique Dude's family uses isn't as effective-- for her. Make it funny, make it emotionally charged, make it a current trending topic on SNL/Jon Stewart, though, and she's all over it.
Science topics, we had to be more deliberate about-- but again, that was just sort of the scientific method in action: a) observation, b) curiosity (Why... what... I wonder if...) c) I wonder how I could see if... d) experimental design, and e) reflection/analysis. You can explore a LOT with that process. But be prepared for things to get burned, broken, scuffed, dirty, and basically for your home to turn into the Mythbusters set.
This kind of learning is about knowing your child(ren)'s learning style and playing to those strengths.
