Rich Math Tasks - What Are They Really?

I'm sitting in a motel room watching "How the Universe Works" and doing Pre-Calc homework, at the end of day 1 of a math training I've been presenting.  What a Monday.
Math has definitely been on my mind lately, and I'm excited about some of the work I've been presenting at this math training.  Ever heard of a rich math task?  It's the new big thing floating around the math world and I've seen a lot of supposed "math task" cards and activities floating around tPt.  It's actually been a bit frustrating for me as I've opened task document after task document, only to find that it's really just a math activity for small groups or a multi-step story problem.  This is not the core of a rich math task and is not what I'm looking for.  So I thought I'd list some characteristics of rich math tasks.

Rich math tasks...

The problem has important, useful mathematics embedded in it.

The problem requires higher-level thinking and problem solving.

The problem contributes to the conceptual development of students.

The problem creates an opportunity for the teacher to assess what his/her students are learning and where they are experiencing difficulty.

The problem can be approached by students in multiple ways using different solution strategies.

The problem has various solutions or allows different decisions or positions to be taken and defended.

The problem encourages student engagement and discourse.

The problem connects to other important mathematical ideas.

The problem promotes the skillful use of mathematics.

The problem provides an opportunity to practice important skills.

(courtesy of "Why Is Teaching With Problem Solving Important to Student Learning?", NCTM April 2010) 


Would you add any other characteristics to the list?  Do you use rich math tasks?

More resources and math task ideas to come!