Books & Curriculum
MIDDLE AND HIGH SCHOOL
Middle and high school aged kids are expected to use the AOPS curriculum. It goes into much more depth than more common texts and will require a fairly high level of maturity and motivation to work through. This is a curriculum that is best used by mathematically talented students.
Kids switching from a traditional curriculum should consider starting with AOPS Prealgebra even if they have completed another pre-algebra book, even if they've otherwise had already completed higher levels of mathematics. The AOPS approach is very different, and the books contain a lot of material that is not part of a traditional curriculum. Advanced kids will breeze through what they know, but will learn some very different ways to problem solving that will make this process quite worthwhile - don't consider it a set-back, but rather an opportunity to have a refresher and then an 'in-depth' look at the materiall.
For Prealgebra, the Introduction Number Theory and Counting and Probability, and the first 11 chapters of the Intro to Algebra the books are keyed to free videos on the AOPS website, so they are designed to be used without a lot of adult assistance. This is meant to be a complete curriculum, plus some. You will not need anything else unless your child is particularly attached to a different curriculum and wants to use them in tandem while they transition. This is far and away the best curriculum for mathematically talented kids. But kids who struggle with math may find it too difficult. Suggestions if you need help here.
The AOPS curriculum for elementary is called Beast Academy. Think of the levels like game levels rather than grade levels. Three Beast levels cover five grade levels. Most kids should start with a level below their grade level. If you have multiple children, have the older ones start with whatever you buy for the youngest. There is plenty to learn from them about mathematical thinking, even for adults. There is also an assessment test to help you decide where to start. It is a comic book format, which may be a turn off to some older kids.
I recommend Singapore Math as a less expensive alternative to Beast Academy, or if your child does not like comic books, or to bridge the gap for kids not ready to go from Beast 5C to AOPS Prealgebra. Kids should definitely be ready for AOPS Pre-algebra after Singapore 6.