Introduction to functions

Math teachers: When teaching a concept, have you ever tried to improvise an example or analogy and have it go wrong? To the point you're just rambling made-up nonsense that isn't helping anybody? Of course you have - we've all had this happen. But a good math teacher will sense the frustration -- both from students and from themselves -- and try something different. Other math teachers, unfortunately, just repeat that poor example over 500,000 times in 6+ years.