We are often asked about the curriculum we use for homeschooling. It changes every now and then but I'll share this year's lineup.
For our humanities and social studies subjects, we had been using whatever was recommended in The Well-Trained Mind: A Guide to Classical Education at Home. I still recommend that book highly for those thinking of homeschooling or supplementing.
After going through one four-year cycle of that, we have now switched to Tapestry of Grace for history, literature, Bible, art, geography, and writing. From their website, they claim to provide "a plan of study that helps parents provide a Christian, classical education using a guided unit study approach, with the history of the world as the core organizational theme." We are just in our third week but love it so far. If I could sum up the curriculum in a word, it would be convergence. We study the same topic through all of the humanities and social studies disciplines, gaining a much clearer and deeper understanding than if we tackled each discipline individually. When I say "we" I include myself in learning with the kids. I am definitely on the journey too.
For math we use Saxon Math, currently at the end of levels 3 and 5/4. Different approaches to math work for different students but we appreciate how Saxon Math's incremental approach and constant review. For 5/4, we use the DIVE instructional CD.
We use Spelling Workout for spelling. I haven't used other spelling books so I can't compare but I am satisfied with the kids' progress. The teachers' books are sometimes hard to find but you can get by without them. If you really want them, you can find them used online.
For grammar, we are using Jessie Wise's First Language Lessons for the Well-Trained Mind, levels 2 and 4. These are great, but they require a lot of teacher time so we might switch to Daily Grams in when we are ready for new books later this year. (Any advice?)
We use Wordly Wise 3000 for vocabulary, but to be honest, the kids don't like it much. I'm trying to decide if we should try something else or just call it good with the vocabulary that the kids pick up from their reading.
The kids also study Japanese through a combination of reading library books, doing kumon worksheets, and working through the public elementary school textbooks.
I'd be happy to take any questions or ideas in the comments. (For the sake of disclosure, most of the links above have affiliate code in them. If you purchase anything through those links, I get a portion of the purchase price. The prices aren't any higher than they would ordinarily be.)
Edit: I forgot to mention our science curriculum. We use Real Science-4-Kids from Gravitas Publications. We are doing chemistry now. The lessons are simple and the experiments make use of commonly available items (except that we can't find purple cabbage in Japan to use an acid-base indicator. Grrrr). The kids look forward to our Friday "lab days."