That depends on the school. I was doing long division in 1st, fractions by 2nd grade, and sines, cosines, square roots, cube roots, etc. by 4th. That was a public school, and I can guarantee it is every bit as good today as it was then.
Most public schools in my area are every bit as good. If you look at test scores, they really are highly dependent upon economic status of the students more than anything else. More than ethnic background or school funding level. My gut tells me that means that the parents aren't doing their part in the process. The private schools in the area simply aren't any better than the well run public schools.
In the DC area, "well run public school" is an oxymoron. What geographic area are you discussing?