Your daughter is still young, and so what you are doing literature wise is probably fine. I do think there is value, later, in choosing one or two very meaty books and doing them slowly all year long–perhaps even a two literature books, a history, maybe something else. And having several going at once can be good too. I counted one time in college—in one semester I was concurrently reading 32 books. LOL That is a skill to be valued–being able to track and read and remember where you are in many books. Using CM recommended skills is very helpful in this–narration, review before beginning a reading, some prep (writing proper names, looking up a few definitions or historical details) then narration at the end and asking for what you think will happen next time–these are VITAL skills in cementing details from many books in the mind.
If my kids really have a math concept down, we rarely review it. I might “spot quiz” it occasionally, to make sure they are sharp, but doing endless problems over the same thing when you know you can do it is just dull. It’s like torture. LOL Also doing 27 problems on one concept when you only need 5. I do use a mastery based program, so. I’ve never used a spiral.
SCM should work as well as any CM approach, what you need with a gifted kid is a little flexibility. You may need more books, or to go up a level (which will necessitate more books when your child actually REACHES that level later.) SCM is a good example of a CM education, reaching many places in a child’s mind, feeding from all directions. This is very good. Gifted kids can tend to get lopsided. 🙂
Book ideas. Sigh. You are just going to have to mine the lists. Christie has an especially good collection of book lists. I recommend starting there. Ask the librarian. Be willing to preview at least briefly things that are modern. I hesitate to recommend certain things, as families need to make certain decisions on content for themselves. In other words, I don’t want to get flamed because I let my kids read scifi and fantasy. 😉
I can hook you up for logic and puzzle books, though! 🙂
This site will even recommend things by age group: http://www.criticalthinking.com/ They can tend to be VERY workbooky. We like the quirkier offerings best–we love Mind Benders, Language Smarts, Math Analogies,–keep it fun!
Look for chess instruction online. My kids did an online instruction program at first. Some are very, very good!
Math puzzle books—we love this site: https://www.hickorygrovepress.com/index.cfm THis guy came to one of our conventions, we bought a bunch of books then, the kids all raced through them and we’ve since gone back for more. For younger kids, consider Primary Grade Challenge Math, Becoming a Problem Solving Genius, and anything that looks like fun. We are hopelessly geeky so have almost all the math and science for upper grades by now. He has some particularly good chess books as well. Your library will also have some things like this. My boys went through a stage where they all loved Sudoku puzzles. They have grown bored now, but your child is still young. IF the numbers look daunting, there is a product called Colorku that uses colored balls instead of numbers. We have, like, five of these in the house. 🙂 They were hugely popular when my kids were younger. They even got visiting friends doing them.
Also consider foreign language. Gifted minds can be very good at these, even at early ages. If you are not exploring one, consider adding it, even if only online or DVD or something.
There are tons of videos on YOutube that we use a LOT now. Mathy, sciency, geeky, language-y, music-y—yes, there is a lot of preview necessary. But Youtube, on top of being the king of cat videos, is actually a hotbed of slightly subversive educational content for the very bright. Again, I hesitate to recommend anything. My family is weird and, importantly, my youngest is a teenager. I’d really, really hate to hear anyone say “Bookworm said Rhett and Link are great and we watched this one video and I’m never letting my kid in the internet again!!!!!” So. Beware.