Research George Polya’s problem-solving principles and techniques from the AIU Library or on the Internet.

Although the scenarios below are not specific mathematical situations, they will require application of Polya’s principles to obtain a reasonable solution.

Choose 1 of the following scenarios:

• You are on your way to a very important doctor’s appointment and just barely have enough time to get to the appointment. You know that if you do not get to the appointment on time, it will cost you $200 and you will not be able to get another appointment for weeks. In your haste, going through your front door, you accidentally tear a big hole in your dress or pants. What do you do now?
• A recipe for a sheet cake that serves 54 people is:
  • ½ cup butter
  • ¼ cup oil
  • 3 cups of baking flour
  • 1 tablespoon baking powder
  • 6 eggs
  • 1 cup milk
  • 2 cups sugar
  • ½ teaspoon vanilla extract

After everything is mixed into a cake batter, you are supposed to pour it into a floured 12 in. by 18 in. by 1 in. sheet cake pan. However, all you have is a 9 in. by 14 in. by 1 in. pan, an 8 in. square pan 1 in. deep, and two 8 in. diameter round pans 1 in. deep. Your 46 guests will be arriving shortly, so you do not have time to go to the store to get the correct-sized pan. How will you have enough cake for each guest to have a piece without wasting too much batter?

• It is after midnight, and your kitchen sink cold-water supply has sprung a leak. You know you will not be able to get a plumber to fix the sink for several hours. You do not know where the water turn-off is, and you do not have any plumbing experience. What will you do to minimize the damage?

Follow Polya’s principles to solve your problem.
o Explain your interpretation of what the problem really is about and what the consequences are if the problem is not solved (i.e., do you understand the problem?).
o Develop and write down a strategy for solving this problem. What do you need to know or do to solve this problem?
o Use your strategy to attempt to solve your chosen problem; show the steps in the correct order for your attempted solution.
o Did your strategy actually solve the problem? How do you know?
o Suppose that your solution did not solve the problem. What would be your next action?