Derivation of the equation of motion for the center of mass for a system of particles. The definition of the center of mass arises from this derivation–do not define it first.
Discuss that the concept of center of mass as it arises in the derivation corresponds to students' intuitive notion.
Discuss that geometric meaning of $\Vec R$, the position vector from the origin to the center of mass. Many students are so quick to put the origin at the center of mass, that $\Vec R$ does not represent a concept that they have thought about.
Discussion of the meaning of the center of mass equation of motion.
It is particularly helpful to connect the idea of center of mass position to other weighted averages (esp. if they have just done Spins and Waves).