We HS for a variety of reasons, including instructional individualization, temperament, and worldview. One of the children did experience several years of b&m school, and did well there, due to school flexibility and personal temperament, but was reaching the point where school-based individualization would look rather like independent study or individual tutoring anyway--so why not do that at home?
We have plenty of opportunity for age-heterogeneous and -homogeneous socialization, with HS co-op, athletics/interest activities, neighborhood, and faith community.
We used Singapore Primary Math (Standards Edition) for elementary, and (the same publisher) Marshall Cavendish's middle/upper school series for after (originally Discovering Math, now Dimensions Math). The original Discovering Math takes you from pre-algebra through algebra II in 3.5 years (last half-year is review/test prep for GCSE exams). Discovering Additional Math covers precalculus and univariate calculus.
