This group response includes the ideas of Rasheed, Debbie, Dianne, Willie Mae, and Catherine.
PROBLEM:"The Emperor's Banquet"
You have been invited to the emperor's banquet. The emperor is a really strange host. Instead of sitting with his guests at his large round dining table, he walks around the table pouring oats on the head of every other person. He continues this process. pouring oats on the head of everyone who has not had oats until there is only one person left. This last person is then allowed to join the emperor in his grand feast. The question is, where should you sit if you do not want oats poured on your head?
> >What is your answer? How did you get it? Did you all agree?
We are not going to give any of our answers. We feel that the terms of the problem could be defined in so many ways that the possibilities are too numerous to list or show here.
We did work out a number of solutions. First, we tried to solve the problem individually as a brain teaser (mentally). In checking our solutions, we decided that none of us had considered all of the possibilities and that unless we made some decisions about the problem: defining terms and the "King's process" too many solutions were possible. The biggest stumbling block was in defining the "King's process" and in a sense the problem became insoluable, because if one was to determine the best place to sit so that they might then dine with the king, it would be possible to do this only if you read the king's mind or else had attended a number of these banquets and saw that he always proceeded in the same fashion.
YES! > >What are similar problems that you have used in your classroom?
A similar problem (in the sense that they are thought provoking) are: "A person has two coins, one in each hand. If added together, the sum of the two coins is $0.55. One of the coins is not a nickel. What are the two coins?" > >How would you use this problem in your classroom?
We think that we would proceed in class much as we did today: dividing the children into groups and allowing them to define the problem and seek various solutions. > >How would you change this problem if you were going to use it?
If we wanted to reduce the frustration level, we might give more definition to the problem ourselves. > >How does this problem fit in with your current curricular focus or >focuses? (patterns, functions, and problem solving, cooperative >learning, or whatever)
It would fit all these foci. > >After you've done a bit of this writing, take a look at the solutions >submitted by students and talk about them in your group. What do you >see?
There seems to be a correct solution.
Do you hear anything surprising to you?
Yes, there seems to be a correct solution.
Do you see things that you >talked about when you were solving the problem in your group?