Un-structuring Word Problems

This year, I have the opportunity to teach two sections of advanced algebra 2.  My colleague, Todd, teaches the other five sections of advanced algebra 2.  Todd is an excellent educator and someone I have already learned a lot from.

We are both fans of Dan Meyer's TED talk and love the idea of un-structuring our math problems as much as possible.  In an attempt to force our students to think about what information is necessary to solve a problem, we've begun to modify a question or two each assignment in this way.


Here's a question found in a typical systems of equations lesson:

(c) Pearson Education 2015 Algebra 2

We give our students this problem instead:

*1.       You are considering renting a car from two different rental companies.  Write a function that shows the cost of renting from each company.  Which one should you choose?  Explain.

Our students are aware they do not have enough information to complete the task.  Not yet, anyway.
If we assigned this problem on a Monday, students would be expected to think about what information is important and necessary in order to correctly answer the problem.  On Tuesday, to start class, we give students 1 minute to ask anything they want about the problem.   The problem is then part of their homework for Tuesday night and is expected to finished by Wednesday.

It has been interesting to hear some of the questions students ask on problems like this one.  Often times, students ask for the necessary information very quickly and don't ask for anything unnecessary.  There have been times, however, that we get some interesting questions about things that have no effect on the problem.