I did the Mile Markers Activity this past Tuesday after teaching the graphing of absolute value functions and before teaching piece-wise function. This was the perfect placement of this activity. It reinforced the absolute value functions and gave students a real-life situation where it is portrayed. I then had the students think about writing a rule without absolute value symbols. Of course, they were insistent that it couldn't be done. When asked for their reasoning, it was because the same rule did not work for all mile marker values. It was an awesome opportunity to transition into the next topic and showed why piece-wise functions are needed.
Another example for piece-wise functions that I used with my students was working an hourly job full-time and the result when you work over-time. It helped them see the relevence of piece-wise functions, making my job of teaching this topic much easier this year.
I will definitley use this activity again!