Although our method in our little homeschool can best be described as a blend of Charlotte Mason/"Thomas Jefferson Education"/Unit Study, we also allow a lot of unstructured time, and I like to "strew" for the kids during that time. Strewing is a technique used in some unschooling households, where interesting resources are left out for kids to see and they can either choose to engage with them or not.
I do this by finding interesting books from the library and leaving them in the kids' piles, or by adding a documentary movie to the "list" on our Netflix account. Sometimes the things that are strewn are supplies ... craft supplies, building kits, art supplies. Sometimes it's a game or a new cookbook. It's not random, though, as I'm trying to find things that match up with recent interests for the kids.
For instance, after my son had done all the computer programming lessons on Khan Academy during his "free time", we bought him a book about programming 3D animation. He was engrossed for almost a whole weekend.
Soon after that, he was trying to build "accurate" castles in Minecraft, so I checked out a bunch of books about castles from the library and left them in a pile. He read most of them, and incorporated them into his building. Then he started talking about architecture and "medieval fantasy", and I found a book about drawing fantasy architecture and left that out for him.
He devoured that book, and for a couple weeks everything was about gothic architecture.
But then he discovered the Stephen Hawking documentaries on Netflix, and began watching those with all his spare time. That led to another documentary series "When We Left Earth". He began to talk about building a rocket. I reminded him we had an old kit somewhere in a closet, and he found that and figured out what else he needed to finish it.
He built the rocket, and on a weekend visit to my family I had my brothers help him launch it in my mother's back field (a good open space with no trees).
The interest in rockets and "flying devices" continues, so I once again have checked out a whole pile of books from the library and left them strewn about for him. Now he says "I can't wait to make my own black powder". Hmmm .... that one is going to be interesting. When we were kids I remember my brother building a little black powder pistol from a kit he bought. Maybe? We'll see what I can find.
But you see how it works. This is "independent study". Nothing is forced, so it's always "fun", but as far as he wants to keep going with something, I'll work to help him find the resources, or to bring things he had no idea he even wanted to his attention. The result is that a lot of learning happens during "free" time.
For now, this works better with my son than it does with my daughter. I try strewing things for her, as well, but she doesn't pick them up as often. Different personalities call for different approaches. It won't work for every kid, but give it a try. It might surprise you where you end up when you dance with your child's interests like this.