Open Ended "Real" Algebra 2 Problems

Do you ever ask yourself, do my students get the big picture?  Could they solve a "real" problem, work with others, and communicate the results in a clear write up with graphics?  Wow, I am asking for a lot.  One of my goals this year, is to get my students to think on their own, and at least attempt these "real" problems.  In my Algebra 2 classes, they get a problem for each unit.  I give the problem early in the unit with a deadline.  That's it!  I don't help them, they can collaborate with other students, research solving methods, use graphics, whatever they want.  But, and here is the catch, they must communicate clearly their answer and justify in words and mathematical work why their answer is the best (or simply correct).

Here is an example of a systems of equations (my unit 3) problem:

Unit 3 Problem

Solutions must be neat, printed in pencil, all work shown, and all variables defined!

                                                                                                                                                                                                                               

Shonda is organizing the printing of tickets for a show her friends are producing.  She has collected prices from several printers and these two seem to be the best.

                                                       SURE PRINT

Ticket printing

25 tickets for $2

                                                       BEST PRINT

                                                    Tickets printed

$10 setting up

plus

$1 for 25 tickets

Shonda wants to go for the best buy.  She doesn’t yet know how many people are going to come.  Show Shonda a couple of ways in which she could make the right decision, whatever the number of tickets.  Illustrate your advice with a couple of examples.

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The student solutions were varied and I was impressed.  Some students will not turn in anything.  They cannot get past the thinking that there is only one way to work a problem (which is NOT true!).  Since they don't know how to start, they won't.  So, I copied an A+, B-, and C paper (without student names), then projected them up and discussed the different methods, and that they only needed to get started to earn the C.  I hope it opened their eyes.  I hope more will try the next problem.

This problem is from the Mathematics Assessment Project (MAP) website:
http://map.mathshell.org/materials/index.php

Here are some quadratic equations problems on The Futures Channel website:
http://www.thefutureschannel.com/algebra/quadratic_equations_functions.php

There are several sites that have problems you may use.  I hope to incorporate more "real" open ended problems as in-class team projects.