Vanguard Education recommends and uses the Saxon Mathematics curriculum. Some of the following information is specific to Saxon Mathematics. Most is wisdom from an experienced classroom and home school mathematics teacher: Mrs. Bryan.
Mrs. Bryan has a teaching degree in high school mathematics education. She taught in private schools prior to home schooling her children. She created the idea of "corrections" (detailed in a link below) from experience she had in a difficult physics class at university.
The information for the mathematics course is detailed on the next several pages. To read all of the material, follow the links in order; they are numbered. On each page, the next page in the sequence is in italics. If you forget where you are, click on the italicized link to go to the next page.