Cup Stacking

This week in class we looked at a cup stacking mathematical question.  We were supposed to determine how many cups tall the teacher is.  This was an extremely open ended question and we first had to figure out what information we would need to start the question.  After careful consideration we found out that we needed to have the teacher's height, the height of one cup and the method of stacking.  We found out that the teacher was about 1.78m, the height of one cup was about 11cm and we had to interlock the cups.  From here there could be a multitude of different ways to go about solving this problem.  If this was in a classroom setting, I would leave this problem completely open to students and tell them to try it using any method.  My first initial thought was to physically stack the cups beside the teacher and try to get a rough estimate but we later found out that there was not enough cups to do this.  Eventually, we figured out that if we determined the height of each lid then we could just continue stacking until we reach 1.78m.  But, this was one only method.  Some students used linear relationships, graphing etc. which all can lead to the final result.
I really believe that these open-ended questions are great because they enhance a student's critical thinking skills.  This can also lead to "mathematical discussions" in the classroom in what we studied earlier in the year.  Students can go up in groups and show how they got their final answer and then can compare and contrast with other students creating a mathematical discussion.  These ideas are not only fun but they provide a rich experience for all students.