The distributive property is one of my favorites to think about as a math teacher. I think about how little I understood about the standard multiplication algorithm when I was in grade school. I try to introduce the property with real number examples, before jumping into the more algebraic approach. I also emphasize the distribution of division at the end of the lesson. I think most Algebra teachers would sympathize with my frustration that even high level students will fail to distribute with division, even when they have it down pat with multiplication.