I offer an Honors Option for Algebra I, Algebra II and Geometry. The following is a definition for an Honors Course from the PHEA website.
Honors: Honors courses are advanced courses offered in the core subject areas (science, math, history, English and foreign languages.) The requirements for honors courses are greater than for college prep courses. Textbooks and/or other course materials must be differentiated and more rigorous than those used in college prep courses. An honors course must have a published syllabus that verifies rigor that is sufficiently beyond the college prep or tech prep requirements.
In addition to working at a pace rigorous enough to complete the entire textbook, the Honors Student will meet all of the South Carolina mathematics standards for each course from the State Department of Education using supplemental materials if necessary.
Each Honors Student will also:
To meet these standards, Honors Students should expect to work one to two hours outside of class for each class session.
The "Honors" designation is actually up to the accountability organization such as PHEA that each homeschool family must report to. I have implemented this Honors Options in hopes that some of my advanced students might qualify for an honors credit. I can not guarantee that each organization will accept this criterion.