## Discussion: Problem Solving Application

Pick a unique real problem and try to solve it using the general problem solving strategies from this module. Present the problem and the solution to the rest of the class. View the problems posted by your classmates and respond to at least two.

## Purpose

This assignment will help you practice applying what you have learned about general problem solving strategies to real problems or situations, and communicating about mathematical ideas with others.

## Directions

### Pick a problem:

Option 1:  Pick a real problem that you need to solve and use the different general problem solving strategies to try to find a solution.  For example, perhaps you need to figure out how to pack an awkward item in your car trunk, or decide what to spend the most time studying for an exam in another class, or plan the assignments and schedule for a charity clean-up project you are organizing.

Option 2:  Pick a real problem that someone else has solved and describe the general strategies they used.  This could be a friend or relative who solved a problem like the ones described in Option 1, or it could be a historical person, like George Washington Carver, who invented peanut butter and many other things, or Mary Anderson, who invented the windshield wiper.

Option 3:  Pick a currently unsolved problem, like curing cancer or finding better energy sources, and analyze how people are using the different problem solving strategies to find a solution.

### Solve the problem or analyze the solution:

If you are solving your own problem, use the different general problem solving strategies that you learned about in this unit to try to solve it.  If you are analyzing a problem someone else solved, or is trying to solve, identify the different general problem solving strategies used.

Present the problem, the general problem solving strategies used, and the solution to the others in the class:

Post a message in the application discussion forum for this unit.  In your message, describe the problem and how you solved it.  Use the equation editor as necessary to show any mathematical operations.  The better you communicate, the more points you will earn.  If you enjoy and know how to use multimedia, such as video, audio, and graphics, you may use those as well, but this is not required.

View and respond to the application problems submitted by your classmates.

Pick two of your classmates’ applications that were particularly helpful to you.  Write a response to each, explaining in a paragraph or two why their applications helped you better understand the mathematics for this unit or better understand how the mathematics for this unit could be used outside of class.

### Example:

Background: This Saturday is the annual chocolate chip cookie bake sale event. At each of the last 2 bake sale events, there were 600 people who attended. Every annual bake sale must receive 600 attendees. Every attendee eats 5 cookies each.

Problem: We must raise $1,500 for our daughter’s team travel expenses. How many cookies must we make and how much money must each cookie sell for in order to raise the appropriate money? Solution: 1) The amount of cookies to make are 600 (attendees) times 5 (cookies eaten per person) equals 3,000 cookies to make. 2) 3,000 (cookies made) divided by$1,500 (money needed) equal 50 cents per cookie.

Other Topics:  shipping textbooks, pattern recognition, MPG, budgeting, transportation, metric/English conversions, lottery, time management, retail sales, volume of dirt on a softball field, tipping at a restaurant, yard sales, auto part manufacturing, room design, rate of change, estimate the square root of 3 to two decimal places with a calculator without square root key

 Grading Criteria Points Possible The problem: Is it a real-life problem? Is it challenging, not trivial? Is it a unique problem instead of a copy of a classmate’s posting? 5 The strategies: Are one or more general problem solving strategies used? Are the strategies correctly identified? 5 The presentation: Is the problem explained well? Are the problem solving strategies explained well? Are the appropriate terms used? 4 Your responses: Did you post at least two responses? Did you explain how the examples helped you better understand the math in this module? Did you ask questions for clarification or make suggestions on how to change or improve the original application posting or any other follow-up postings? 6