Do I have to follow my state's standard course of study?

We decided to try homeschooling our elementary aged kids, and I'm wondering if I have to follow my state's standard course of study, or if we can design our own course of study?

I guess, specifically, do I have to cover every aspect of every subject that is listed year by year, or can I plan so that these subjects are covered by a certain point in the children's education, for example so that they're ready for high school level subjects by the time they're in high school?