If you have good readers you should consider homeschool literature curriculum. This literature based approach focuses the study of all subjects or some subjects through the books children read. Emphasis is on reading real "living books".
This method is not an all or nothing type of method. You can use a literature based approach to only some subjects or base your entire studies around reading good books.
It is very similar to unit studies but unit studies tend to be more hands on and project oriented than a literature approach.
IMHO this is a great way to conduct school. It can be highly effective. I am an avid reader and my sons read well too so this fits with us well.
At the high school ages you'd need to evaluate your child. Is this still working? Are they self motivated enough to continue? Do they learn well through reading. If so develop a record keeping system that can be used to record their experiences for future colleges if needed. Then just keep going. Keep book lists. Record what movies and audios were listened to. Go to museums. Do interviews. Journal what you are doing.
The easiest way to begin using a method like this is to use a prepackaged homeschool literature curriculum. There are many out there. Sonlight is one such literature based curriculum that I have used and is very highly recommended.
Learning Language Art Through Literature is a literature based Language Arts Curriculum. This program only covers language arts skills.
For History reading historical fiction as well as non fiction is a great way to learn. At highschool ages I'd suggest choosing a base textbook to use, then add reading assignments on the same subjects as they are encountered. We use Streams of Civilization, and add lots of historical fiction and non fiction, video and audio.