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Problem Solving 1-3

Problem Solving 1-3. February 11 th 2013. Polya’s Problem Solving Strategy. Polya’s strategy can be summed up in four steps Understand the problem Devise a plan Carry out the plan Review the solution. PPSS #1 Understand. Can you restate the problem?

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Problem Solving 1-3

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  1. Problem Solving 1-3 February 11th 2013

  2. Polya’s Problem Solving Strategy Polya’s strategy can be summed up in four steps • Understand the problem • Devise a plan • Carry out the plan • Review the solution

  3. PPSS #1 Understand • Can you restate the problem? • Can you determine what is know about the type of problem? • What information is missing, if known would make the problem easy to solve? • Any extraneous information that is not needed? • What is the goal?

  4. PPSS #2 A plan! • Make a list. • Draw a diagram. • Make a table or chart. • Work backwards. • Solve a similar easier problem. • Try to write an equation Guess and check. • Indirect reasoning.

  5. PPSS #3 Carry out your plan • Work carefully. • Keep and accurate and neat record of all attempts. • Realize you may need to try more than once and be willing to come up with a new plan or modify your existing plan.

  6. PPSS # Review the solution • Ensure that the solution is consistent with the facts of the problem. • Interpret the solution in the context of the problem. • Does your solution generalize?

  7. How many routes?

  8. Basket Ball Tournament At a basketball tournament, there are six teams: Antelopes, Bears, Cubs, Dusters, Eagles, and Foxes . Each team will play 3 other teams. How many games will be played in all?

  9. Basket Ball After the end of the last basketball game the players of the Antelopes and Dusters shake hands. If there are 10 players in all, how many handshakes take place?

  10. Infinite and repeating! Determine the digit 100 places to the right of the decimal point in the decimal representation of .

  11. Big number! Determine the ones digit of .

  12. Gauss’s dilemna While an elementary student Gauss was able to add the number 1 to 100 in a few minutes. How did he do it?

  13. Homework 1.3 3, 7, 9, 10, 11, 15, 19, 23, 33, 41.

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