Polya’s 4-steps in Problem Solving.pptx

This contains a comprehensive discussion about Polya's 4 steps in Problem Solving.

1. Polya’s 4-steps in Problem Solving Kenth Harold R. Endocal

2. PROBLEM A statement requiring a solution, usually by means of a mathematical operation/geometric construction.

3. PROBLEM SOLVING A mathematical task that has the potential to provide intellectual challenges for enhancing students’ mathematical understanding. It is about resolving problems. It is finding solutions and not just answers to problems. It is an important skill not only in dealing with Mathematics, but also in making decisions in life.

4. METHOD The ways or techniques used to get an answer which will usually involve one or more problem solving strategies.

5. ANSWER A number, quantity or some other entity that the problem is asking for.

6. SOLUTION The whole process of solving a problem, including the method of obtaining an answer and the answer itself.

7. GEORGE POLYA One of the mathematicians to make a study of problem solving. He is a Hungarian mathematician. He describes the methods of Problem Solving. Polya’s four steps are deceptively simple.

8. 1. Understand the Problem You must have a clear understanding of the problem. You must have a full grasp of what are known and not known. Then solve as required by the problem. Polya’s 4 Steps in Problem-Solving

9. 2 . Devise a Plan Try using strategies that could help you solve the problem. Here are some frequently used procedures:  Identifying a subgoal.  Make a table or a chart.  Make an organized list that shows all the possibilities. (Tree diagram, Venn Diagram)  Draw a diagram.  Eliminating possibilities.  M ake an illustration/drawing.  Work backwards.  Write an equation. If necessary, define what each variable represents.  Perform an experiment.  Guess at a solution and then check your result. Trial and error. Polya’s 4 Steps in Problem-Solving

10. 3 . Carry Out the Pla n Once you devised a plan, you must carry it out. As soon as you have an idea for the solution of the problem, write it down instantly then carry out your plan of the solution. Keep trying until something works.  Work carefully.  Keep an accurate and neat record of all your attempts.  Realize that some of your initial plans will not work and that you may have to devise another plan or modify your existing plan. Polya’s 4 Steps in Problem-Solving

11. 4. Review the Solution Take time to reflect, examine, and look back at what you have done – think of what worked and what did not; doing this will enable you to predict what strategy to use to solve future problems.  Ensure that the solution is consistent with the facts of the problem.  Interpret the solution in the context of the problem.  Ask yourself whether there are generalizations of the solution that could apply to other problems. Polya’s 4 Steps in Problem-Solving

12. STATEGY: ELIMINATING POSSIBILITIES Wally asked Joy how old she was. Joy said to him that she would give him three clues and see if he could guess her age. Joy wrote down the clues and let Wally make a guess. My age is between 18 and 35. My age is a multiple of 3. My age is an odd number. The digits of my age are repeated. How old is Joy?

13. 1. Understand the Problem The problem is telling us that Wally has to guess Joy’s age and to be able to guess her age he needs to use the different conditions given. Polya’s 4 Steps in Problem-Solving

14. 2 . Devise a Plan The strategy “Eliminating possibilities” will be used because it is the most suitable strategy and it can be used together with the making a table or making an organized list strategy. Polya’s 4 Steps in Problem-Solving

15. 3 . Carry Out the Pla n We need to use the four different clues to solve the problem. Clue 1: Joy’s age is between 18 and 35. (When we say “between” in math, we mean the numbers excluding the boundaries.) Polya’s 4 Steps in Problem-Solving 19 20 21 22 23 24 25 26 27 28 2 9 30 31 32 33 34

16. 3 . Carry Out the Pla n Clue 2: This clue says that Joy’s age is a multiple of 3. Hence we need to remove from the list all those that are not multiples of 3. So we have, Polya’s 4 Steps in Problem-Solving 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 ❌ ❌ ❌ ❌ ❌ ❌ ❌ ❌ ❌ ❌ ❌

17. 3 . Carry Out the Pla n Clue 3: Joy’s age is an odd number. Among the five numbers left, Polya’s 4 Steps in Problem-Solving 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 ❌ ❌ ❌ ❌ ❌ ❌ ❌ ❌ ❌ ❌ ❌ ❌ ❌

18. 3 . Carry Out the Pla n Clue 4: The digits of my age are repeated. Polya’s 4 Steps in Problem-Solving 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 ❌ ❌ ❌ ❌ ❌ ❌ ❌ ❌ ❌ ❌ ❌ ❌ ❌ ❌ ❌

19. 3 . Carry Out the Pla n Clue 4: The digits of my age are repeated. Therefore, the age of Joy is 33. Polya’s 4 Steps in Problem-Solving 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 ❌ ❌ ❌ ❌ ❌ ❌ ❌ ❌ ❌ ❌ ❌ ❌ ❌ ❌ ❌

20. 4. Review the Solution Our answer is correct because 33 satisfy all the given conditions in the problem. ✓ Clue 1: 33 is between 18 and 35. ✓ Clue 2: 33 is a multiple of 3. ✓ Clue 3: 33 is an odd number. ✓ Clue 4: The digits of 33 are repeating. Polya’s 4 Steps in Problem-Solving