I adore Rightstart. But it's a complete curriculum, not a supplement. So is Horizons, I think. It may not be great to attempt to keep two full curricula going at once, that might be too much for your student. I guess if he's flying through Horizons he might not mind?

So to start, since you're sure you're pulling her, why wait for another some weeks? Why not immediately? As to what to start with, you've probably seen a period of deschooling recommended before starting with curriculum. That's probably the best way to start! I'd probably consider getting Story of the World as an audiobook or read aloud, and just listening to it "for fun" as a world history survey over the rest of the year.

Math: Rightstart (grades K-7, roughly.) Writing: WWE Grammar: FLL Spelling: All About Spelling. (And presumably All About Reading for reading, we haven't used it.) Science: Science in the Beginning (Christian worldview.)

What about the World in Ancient Times series by Oxford University Press?

Have him read the fiction out loud to you. Then you know!

Rightstart Math? It aligns with common core so it should cover everything your son would need for the grade. It does use part/while circles, which I think are number bonds, but doesn't use them a ton so he might be okay with it.

I invented this recipe in university, and it's non-curry. Lentil soup: Throw dry red lentils in water, start to heat. Add carrot, onion and butternut squash in 1 inch chunks. Add squashed/chopped garlic. Season with leftover packets from beef or mushroom ramen (like I said, university... Some kind of bouillon would work.)

Actually.... What about not really doing any grammar or spelling instruction right now? Let her delight in writing for her own pleasure for a while. That's brilliant, and many of us only dream of having our children enjoy writing. After a few months, you could consider looking into Bravewriter, which might be a good approach for her. You could also consider the MCT series if she's loving playing with language.

I would have thought that some of the techniques would be similar to Rightstart, given how it focuses on breaking down numbers and manipulating them. Is it not? Partial products, for instance? If you can, it would probably work best to use her techniques and gradually bridge them over to a more traditional notation form; which, presumably, was what the school would have done anyway. The Rightstart materials may work well for that.

That would probably depends on which state or country you're in, and whether the local schools even teach an historical period in grade 3. Ours doesn't. But the real question is, do you need to be bound by what would match the local schools? In most cases, you don't need to be and can feel free to start at whichever book you like. Ancients would be recommended, and progress through in order. Unless you want to start with book three to get on the "correct book" for the rotation to end in grade 12. If you took that route, perhaps you could just do books one and two as read alouds and then move onto book three.

Roof tiles, I would imagine.

I'd probably start with Progressive Phonics (free online) and see how it goes. You could also check your local library for The Ordinary Parent's Guide to Teaching Reading. Mine doesn't have it, alas.

Probably! I haven't tried. And I do know that my mom's friends used to melt then down in a pan on her stovetop and they caught fire once, so... Use caution!

Usually, a period of deschooling is recommended before starting homeschooling. I'm concerned that schooling through the summer might make things harder for you both.

Crayon rocks are amazing for this. They force a tripod grip without reminding because it's really the only way to hold them. They're pricey, but maybe worth it? Or you can make your own by melting crayons and using a mold for soap or candy or something.