Problem-Solving-Strategies mathmathmathmath
- 1. PROBLEM SOLVING AND REASONING– Problem Solving Strategies Core Idea “Mathematics is not just about numbers; much of it is problem solving and reasoning.” CHAPTER 6c.
- 2. learning objectives 1. become familiar of the problem solving heuristics and be able to identify the strategy most appropriate for the problem; 2. use problem-solving strategies to investigate and understand mathematical content; 3. acquire skill in developing and applying a variety of strategies to solve problems; and 4. verify and generalize results with respect to the original problem situation.
- 3. Historical background qGeorge Polya (1887-1985): advocated basic problem- solving strategy which consists of four steps. 1. Understand the problem. 2. Devise a plan. 3. Carry out the plan. 4. Review the solution POLYA’S PROBLEM SOLVING STRATEGY
- 4. ROUTE PROBLEM Example 1a. Consider the map shown. Allison wishes to walk along the streets from point A to point B. How many direct routes can Allison take?
- 5. A simple diagram of the street map. Example 1a. Consider the map shown. Allison wishes to walk along the streets from point A to point B. How many direct routes can Allison take? ROUTE PROBLEM
- 6. Example 1a. Consider the map shown. Allison wishes to walk along the streets from point A to point B. How many direct routes can Allison take? A street diagram with the number of routes to each intersection labeled ROUTE PROBLEM
- 7. Example 1b. Consider the map shown. Allison wishes to walk along the streets from point A to point B (No back tracking). How many direct routes can Allison take? ROUTE PROBLEM
- 8. Example 1c. How many direct routes are there from A to B if Allison wants to pass by Starbucks? ROUTE PROBLEM
- 9. RIVER CROSSING PROBLEM Example 2. Four people on one side of the river need to cross the river in a boat that can carry a maximum load of 180 pounds. The weights of the people are 80, 100, 150, and 170 pounds. a. Explain how the people can use the boat to get everyone to the opposite side of the river. b. What is the minimum number of crossings that must be made by the boat?
- 10. PUZZLE FROM A MOVIE Example 3. In the movie die hard: With a Vengeance, Bruce Willis and Samuel Jackson are given a 5-gallon jug and a 3- gallon jug and they must put exactly 4 gallons of water on a scale to keep a bomb from exploding. Explain how they could accomplish this feat.
- 11. FAKE COIN PROBLEM Example 4. You have eight coins. They all look identical, but one is a fake and slightly lighter than the others. Explain how you can use the balance scale to determine which coin is the fake in exactly a. three weighings b. two weighings
- 12. Example 5. In a basketball league of 12 teams, each team plays each of the other teams exactly three times. How many league games will be played? OTHER PROBLEMS
- 13. OTHER PROBLEMS Example 6. There was a jar of chocolate cookies on the table. After James and Monica returned after playing outside, they ate half of the cookies inside the jar. Then Victor came along and ate one third of the remaining cookies in the jar. Then came Tiffany, the youngest among them, and took one cookie to munch. When Mother looked at the cookie jar, she saw that there were two cookies left. Use the space below to show your process. a. How many cookies were in the jar to begin with? b. b. How many cookies were there just before Victor came?
- 14. OTHER PROBLEMS Example 7. In consecutive turns of a Monopoly game, Stacy first paid $800 for a hotel. She then lost half her money when she landed on Boardwalk. Next, she collected $200 for passing GO. Shen then lost half of her remaining money when she landed on Illinois Avenue. Stacy now has $2500. How much did she have just before she purchased the hotel?