Saxon Math: Trigonometry and geometry are taught throughout. The final books in the series are calculus and physics. Get the 1st or 2nd edition only. The word problems in later editions are getting kiked up with common core bullshit. https://www.hmhco.com/shop/k12/Saxon-Math-1-Homeschool/9781565770188 Easy Grammar: Effective at teaching the structure of the English language. Try to find a supplemental handbook on sentence diagramming for when students are a bit more advanced. https://www.easygrammar.com/store/c1/Featured_Products.html Teach vocabulary and spelling as distinct classes early on. All you need for that is a dictionary, the older the better. For the rest of the language arts, just read (preferably history) and write. There are tons of good handbooks for composition like The Elements of Style. https://www.amazon.com/Elements-Style-William-Strunk-Jr/dp/194564401X Introductory and Intermediate Logic: Teach logic as a distinct course as early as your kids can retain the concept. Teaching your kids how to think and form arguments didactically is crucial. https://www.thriftbooks.com/w/introductory-logic-student-4th-edition_james-b-nance_douglas-j-wilson/462885/#edition=5284387&idiq=43731070 Exploring Creation with Science: Either find the earliest editions of the series or look up the newer series re-written by the author, Jay Wile, starting with Science in the Beginning. Apologia owns the Exploring Creation with Science series and started common-coring it up in the later editions. Wile re-wrote the series with the new title. These books are paired with supplemental lab kits and cover from middle school up through high school. The series lays an excellent foundation for technical writing. https://www.christianbook.com/page/homeschool/apologia?kw=exploring%20creation%20science&mt=b&dv=c&event=PPCSRC&p=1018818 https://bereanbuilders.com/ecomm/product/science-in-the-beginning/ All these course series end up at a level well above the 1st or 2nd year general courses offered at most universities. When I was growing up, the public schools around me tried to stop letting homeschooled students come and take their PSAT/SAT/ACT at the school because homeschooled kids who followed curriculum similar to this were always the top few percentiles and were getting a large portion of the national merit scholarships. Add in music lessons and religious studies, and other topics of interest like geography, astronomy, philosophy, electronics, mechanics, etc as they come up. It doesn't need to get super complicated. Teach real life skills like gardening, animal husbandry, auto-repair, woodworking, welding and whatnot as much as you are able. I hope that helps someone.