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Mathematical Problem Solving Math 6320 Summer 2006

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Date Equations How to do them Do today’s date (5/17/06) and your birthdate. Try to come up with multiple equations for each. After the first day in 2000 and 2001, I had to modify the dates due to a pattern that can be used for every date in those years. What is the pattern? Moreover, any date with a 1 followed by a 0 can be solved one way despite the other numbers, what is it?

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About Problem Solving 1.How do you define problem solving? 2.What is your experience with problem solving? 3.Problem solving definition activity

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Problem Solving Defined Engaging in a task for which the solution is not known in advance. In order to find a solution, students must draw on their knowledge and through this process they will often develop new mathematical understandings.

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Course Syllabus

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Problem Solving Steps 1.Understand the Problem 2.Devise a Plan 3.Solve 4.Look Back and Check Explain Each Step

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Understand the Problem Can you state the problem in your own words What are you trying to find or do What are the unknowns What info do you obtain from the problem What info is missing or not needed

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Devise a Plan Choose a strategy

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Problem Solving Heuristics 1.Guess and Check 2.Look for a Pattern 3.Make a table 4.Draw a picture 5.Sketch a graph 6.Do a simplier problem 7.Use a formula 8.Write an equation 9.Use Inductive/Deductive Reasoning 10.Examine related Problems 11.Make a diagram 12.Work Backwards

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Why use certain heuristics? Heuristics activity

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Solve (Carry out the Plan) Implement the strategy or strategies in the second step and perform any necessary actions or computations Check each step of the plan as you proceed (intuitive or formal) Keep an accurate record of your work

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Look Back and Check Check the results in the orginal problem (sometimes a proof is needed) Interpret the solution in terms of the orginal problem Does your answer make sense Is your answer reasonable Does it answer the question asked Determine if another method for finding solution Determine other related or more general problems for which the techniques will work

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Problems The Locker Problem The Statue of Andrew Jackson Problem The Place Mat Problem

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