Marjorie Ader distributed a handout that she uses as an introductory activity in her Algebra III class. It emphasizes group work and brainstorming multiple strategies for solving a problem:
You may be challenged by this activity, because it is not a five-minute-or-less type of activity. One of the objectives is to help you learn how to work with a group to solve a problem. Your group should try a variety of problem-solving approaches. Brainstorm to generate ideas. Try not to make quick judgments. When a group member proposes a strategy and/or solution, it should be considered and explained carefully, so that everyone in the group can verify whether or not it works.
In this activity and throughout the course, each group member has the following responsibilities:
- Be cooperative and considerate.
- Listen carefully, without interrupting, while another is talking.
- Ask questions of others and ask others for help. If the group is stuck and can't move on, decide as a group to ask for suggestions or help from me.
- Help others in your group when asked.
- Work on the problem until every group member understands it and is ready to describe the solution to the class.
Camel Crossing the Desert
A camel is sitting by a stack of 3000 bananas at the edge of a 1000-mile-wide desert. He is going to travel across the desert, carrying as many bananas as he can to the other side. He can carry up to 1000 bananas at any given time, but he eats one banana every mile. What is the maximum number of bananas the camel can get across the desert? How does the camel do it? Be prepared to present your solution to the class. (Hint: The camel doesn't have to go all the way across the desert in one trip.
Using trial and error, groups independently began to refine strategies to this problem. Marjorie gave some hints, suggesting an incremental approach and pointing out that
Soon participants became involved in sensitivity analysis and in considering extensions of the problem, an analysis of which may be found within the Classic Problems area of the Ask Dr. Math FAQ.
- the camel does not have to go all the way across the desert in one trip, but can cache bananas along the route;
- the answer contains a fraction;
- the camel need not be thought of as traveling one mile, then eating one banana, but rather as continuously eating bananas at the rate of one per mile.
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