I like this way because
a) It illustrates a particular type of scaling argument that is
super-easy but often under-emphasized.
b) It serves as a good excuse for a riff on "figuring things out"
in general, and its relationship to memorization. http://www.av8n.com/physics/thinking.htm#sec-derive
This issue is commonly referred to as the "Math Wars" but I don't
like to use that term. The warlike aspects are a discredit to
everyone involved. The sensible approach is to use smart, efficient
algorithms *and* to understand the principles involved.
Forum for Physics Educators