Are there required subjects that I must teach?
Specific homeschooling requirements may vary from state to state but basic principles apply to all students. Education on the early levels (grades K - 3) has as its goal assisting the child in learning basic skills such as reading, simple writing and arithmetic. Based on a child's developmental level, this will be accomplished to greater or lesser degrees. Things like social studies and science are taught as processes and concepts, not necessarily an accumulation of dates and facts. Upper elementary and middle school students are building on the foundation laid in the primary grades. At this level a child should use reading as a means to gather information and writing as a process to respond to questions and to express his thoughts, therefore reading and writing can and should be taught in the context of information that is being learned about literature, science, history, etc. Mathematics has moved to the use of higher order thinking skills and hopefully connections have been established for the child between concepts taught and real life application. High school students are processing information using all the tools they have acquired through their years of schooling. Reading and writing, speaking and listening should be readily useable skills. A high school student should also be able to take information, consider it in light of his beliefs and respond with an opinion about the information. Basic research skills should also be in place at this time. A high school student should be able to find information independently, process that information and produce a response to that information. Critical thinking skills are developed throughout the years of a student's education, and do not have to be developed formally, but should be used in the context of whatever a child is reading or thinking about.
Most states have guidelines as to what would be considered a minimum standard for completion of each grade. Go to your state's department of education website and look for their standards. Some states have specific requirements for course content for homeschoolers. This will be found in the state's law regarding homeschooling.