MA201 Dr. Byrne Fall 2011

1. MA201Dr. Byrne Fall 2011

2. Chapter 1:Problem Solving

3. Problem Solving Polya’s 4-step process: • Understand the problem. • Devise a plan. • Carry out the plan. • Look back.

4. Problem Solving Polya’s 4-step process: • Understand the problem. • Devise a plan. • Carry out the plan. • Look back. Understand

5. Problem Solving Polya’s 4-step process: • Understand the problem. • Devise a plan. • Carry out the plan. • Look back. Understand Think

6. Problem Solving Polya’s 4-step process: • Understand the problem. • Devise a plan. • Carry out the plan. • Look back. Understand Think Do

7. Problem Solving Polya’s 4-step process: • Understand the problem. • Devise a plan. • Carry out the plan. • Look back. Understand Think Do Check

8. Problem Solving Polya’s 4-step process: • Understand the problem. • Devise a plan. • Carry out the plan. • Look back. Understand Think Do Check

9. Compare: NCSS Problem Solving Steps • Identify the problem. • Get the facts related to the problem. • Create a plan. • Carry out the plan. • Check your plan and adjust if needed.

10. Polya’s 4-step process: • Understand the problem. • Devise a plan. • Carry out the plan. • Look back. NCSS Problem Solving Steps • Identify the problem. • Get the facts related to the problem. • Create a plan. • Carry out the plan. • Check the plan and adjust if needed.

11. Class Activity for Ch 1:Instructions and Example • For a given word problem: (These instructions will be repeated.) • Solve the problem with your group. • Consider how you applied Polya’s 4 steps. • If ‘trial and error’ was the strategy, is there another way you could have solved the problem? • Include a careful diagram that you would provide to aid elementary students solving this problem. • Compare your group’s solution with that of the other group working on the same question. • Prepare a short 5 minute presentation comparing and contrasting the way groups worked on the problems and whether Polya’s 4 steps were useful for either group.

12. In Class Example

13. HW: Section 1.1 / Problem Set A • a. If the diagonals of a square are drawn in, how many triangles of all sizes are formed? b. Describe how Polya’s four steps were used to solve part a.

14. Step 1: Understand the problem. If the diagonals of a square are drawn in, how many triangles of all sizes are formed? • Draw a picture of a square with the diagonals drawn in. • The question asks, “how many triangles?” • “CLUE”: how many triangles of all sizes ?

15. Step 1: Understand the problem. If the diagonals of a square are drawn in, how many triangles of all sizes are formed? • Draw a picture of a square with the diagonals drawn in. • The question asks, “how many triangles?” • “CLUE”: how many triangles of all sizes ?

16. Step 1: Understand the problem. If the diagonals of a square are drawn in, how many triangles of all sizes are formed? • Draw a picture of a square with the diagonals drawn in. • The question asks, “how many triangles?” • “CLUE”: how many triangles of all sizes ?

17. Step 1: Understand the problem. If the diagonals of a square are drawn in, how many triangles of all sizes are formed? • Draw a picture of a square with the diagonals drawn in. • The question asks, “how many triangles?” • “CLUE”: how many triangles of all sizes ?

18. Step 1: Understand the problem. If the diagonals of a square are drawn in, how many triangles of all sizes are formed? • Draw a picture of a square with the diagonals drawn in. • The question asks, “how many triangles?” • “CLUE”: how many triangles of all sizes ?

19. Step 2: Devise a plan. How to count the # of triangles of all sizes? Plan: Figure out how many sizes there are and count them from smallest to largest.

20. Step 3: Carry out plan. First, how many sizes of triangles are there?

21. Step 3: Carry out plan. First, how many sizes of triangles are there?

22. Step 3: Carry out plan. First, how many sizes of triangles are there? ‘big’ ‘little’

23. Step 3: Carry out plan. Next, count how many of each size: # little? # big?

24. Step 4: Look back. We’ve counted 8 triangles: If the diagonals of a square are drawn in, how many triangles of all sizes are formed? Answer: 8 4 4

25. Step 4: Look back. We’ve counted 8 triangles: If the diagonals of a square are drawn in, how many triangles of all sizes are formed? Answer: 8 4 4

26. Problem Solving – In Class You will be assigned a chapter problem in small working groups. • Small groups: Solve the problem as a group. As a group, consider how you applied Polya’s 4 steps by filling out the sheet. • Individually: When the time is announced, spend one minute individually drawing a diagram, table or manipulative that could be used to explain the problem to a class of elementary students. • Combined groups: Compare your group’s solution with that of the other group working on the same question. Prepare a short 5 minute presentation comparing and contrasting the way groups worked on the problems and whether Polya’s 4 steps were useful for either group. -- pick one person to describe the problem and draw a diagram -- pick one person to describe the solution (1 minute only) -- pick one person to discuss the effectiveness of Polya’s 4 steps

28. Problem Solving – Homework Choose 3 problems from Section 1.1 that were not assigned in class. Solve the problem using Polya’s 4 steps, clearly dividing the steps of your solution and showing all your work. Carefully make a diagram that you could use in a class to aid elementary students that were assigned this problem.