Give the Most Difficult Math Problems FIRST!

We as math teachers typically give the easiest problems first in our classes.  Then the problems get more and more difficult as we move along in the class.  Then finally we give the most difficult problem.  Sometimes we don't even have time for this problem because we have spent so much time on the easier questions.  Our homework assignments are the same.  We give 20 problems that get more and more difficult.  Then you get to the "Word Problem"  which is usually skipped by the student.  They are thinking that their teacher will go over it the next day. 

I think we should give the most difficult problem FIRST!  Then we use the easy questions to help us get to the solution.  When we do the most difficult problem first we showing students this is what we expect all to accomplish.  We give it PRIORITY!  When we go straight to the hardest question we show how vital all of the easy questions are to help us get to the tough question.  There is a NEED for the easy questions and not just busy work. 

This sounds really easy to implement.  But I'm having a hard time doing it.  My traditional teacher mind takes over and I can't seem to switch.  However, I'm also finding that you must get the right problem(s) to start with so that this can happen effectively. 

What are your thoughts?  Do you buy in?  How can we accomplish this?

Best