After a few days of working on absolute value functions, I wanted my students to apply it to something concrete. They had the transformations and graphing down pretty well and had done creative assignments to demonstrate their understanding. I found a "Fire House" problem that seemed like a good fit. http://www.txar.org/training/materials/Algebra_II/10MAPAbsoluteValueStudentLesson03142007.pdf
My mistake: I used the problem after my students knew too much about writing absolute value functions, so going back to linear functions seemed odd to my students.
I did like the problem; they got right into modeling. The biggest discussion was how you count blocks. Culturally, I could have guessed that this would be hard for my kids to get. I live in a rural area and most students don't live in an area where they can walk "a block" to get somewhere. I saw the lightbulbs go off as I explained how houses are numbered by blocks. The 100s, 200s, and 300s are separated by cross streets. Many didn't know this or had never realized it.
We got through parts I and II today. Tomorrow we'll tackle the graphing calculator-heavy extension.
If I use this problem set again, I will reword a few questions to make it more clear what is being asked. I had a few questions come up over and over as I moved from group to group.
What's your favorite way to teach absolute value functions?