Mathematical Problem Solving

Math 6320

Summer 2006

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?

About Problem Solving

1. How do you define problem solving?

2. What is your experience with problem solving?

3. Problem solving definition activity

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.

Course Syllabus

Problem Solving Steps

1. Understand the Problem

2. Devise a Plan

3. Solve

4. Look Back and Check

• Explain Each Step

Understand the Problem

Can you state the problem in your own words

What are you trying to find or doWhat are the unknownsWhat info do you obtain from the

problemWhat info is missing or not needed

Devise a Plan

Choose a strategy

Problem Solving Heuristics

1. Guess and Check2. Look for a Pattern3. Make a table4. Draw a picture5. Sketch a graph6. Do a simplier

problem7. Use a formula

8. Write an equation9. Use

Inductive/Deductive Reasoning

10.Examine related Problems

11.Make a diagram12.Work Backwards

Why use certain heuristics?

• Heuristics activity

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

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 reasonableDoes it answer the question askedDetermine if another method for finding solutionDetermine other related or more general

problems for which the techniques will work

Problems

• The Locker Problem

• The Statue of Andrew Jackson Problem

• The Place Mat Problem