1. How to Solve it?

2. How to Solve It? Polya, G. (1957). How to solve it: A new aspect of mathematical method, 2nd ed. Princeton, NJ: Princeton University Press. George Polya’s Four-Step Method 1. Understand the Problem 2. Devise a Plan 3. Carry Out the Plan 4. Look Back

3. Example Alice and Benny have 168 marbles altogether. Benny has 44 more marbles than Alice. How many marbles does Benny have?

4. Alice and Benny have 168 marbles altogether. Benny has 44 more marbles than Alice. How many marbles does Benny have? STEP 1: Understand the Problem (Identifying information) (Identifying information)

5. STEP 1: Understand the Problem READ the problem carefully. What are you given? data, facts or condition ◦D◦Do you have enough information? ◦I◦Is any information unnecessary or contradictory? (Complex) What are you expected to find? unknowns Explain the problem in your own words ◦B◦Break it into parts (Circle, underline and box the clues) ◦H◦Highlight the key words / phrases (Ex. More than, altogether)

6. STEP 2: Devise a Plan Given: There are 2 persons involved, Alice & Benny Benny has 44 more marbles than Alice Total number of marbles is 168 Can I use model drawing strategy for this problem? What model should I use? (Comparison?) What would be the model like? Unknown: Find the number of marbles Benny had

7. STEP 2: Devise a Plan Look at the unknown. ◦ Do you know how to solve problems with this type of unknown? Can you find a connection between the data and the unknown? Have you seen a problem like this before? What strategy should I use? Do you know any similar problems you can use to help you?

8. Alice and Benny have 168 marbles altogether. Benny has 44 more marbles than Alice. How many marbles does Benny have? Alice Benny STEP 3: Carry out the Plan (Using Model Drawing Strategy) (Using Model Drawing Strategy) 168 ? 44

9. Alice and Benny have 168 marbles altogether. Benny has 44 more marbles than Alice. How many marbles does Benny have? 2u  168 – 44 = 124 1u  124  2 = 62 Benny  62 + 44 = 106 ? 1 unit A B 44 168 Using Model Drawing Strategy Using Model Drawing Strategy

10. 2u  168 – 44 = 124 1u  124  2 = 62 Benny  62 + 44 = 106 2u  168 + 44 = 212 1u  212  2 = 106 (Benny) Method 2 (Alternative) Method 1 ? A B 44 168 Model: Solution(s):

11. STEP 3: Carry Out the Plan Which strategy is the most suitable? Follow your plan CHECK EACH STEP Can you see clearly that each step is correct? Have you shown all the necessary workings with appropriate labels? If it doesn’t lead to a solution… ◦ Return to Step 2. Pick another plan!

12. 2u  168 – 44 = 124 1u  124  2 = 62 Benny  62 + 44 = 106 106 – 62 = 44 (difference) Checking Solution 106 62 A B 44 168 62 + 106 = 168   Benny has 106 marbles. STEP 4: Look Back (Check your work)

13. STEP 4: Look Back Can you check your result? Did you answer the question? Is it reasonable? Can you do the problem differently? Can you use your results to help you solve other problems? Have you learned something from this problem?

14. SUMMARY Four-Step Method of Problem Solving 1. Understand the Problem 2. Devise a Plan 3. Carry Out the Plan 4. Look Back

15. THE END