1. MA201 January 15 th, 2010

2. Results of Paragraph: Explain the importance of elementary mathematics. Generalized answer: Needed for everyday life skills. –To function independently. Develops problems solving skills. Foundation for more complex math in high school (algebra and calculus). Young children are receptive to learning. Some specific answers: Math is a language developed to describe relationships between things. Math is needed as the foundation of careers that keep society going (e.g., building houses).

3. Problem Solving Polya’s 4-step process: 1.Understand the problem. 2.Devise a plan. 3.Carry out the plan. 4.Look back.

4. Problem Solving Polya’s 4-step process: 1.Understand the problem. 2.Devise a plan. 3.Carry out the plan. 4.Look back. Understand

5. Problem Solving Polya’s 4-step process: 1.Understand the problem. 2.Devise a plan. 3.Carry out the plan. 4.Look back. Understand Think

6. Problem Solving Polya’s 4-step process: 1.Understand the problem. 2.Devise a plan. 3.Carry out the plan. 4.Look back. Understand Think Do

7. Problem Solving Polya’s 4-step process: 1.Understand the problem. 2.Devise a plan. 3.Carry out the plan. 4.Look back. Understand Think Do Check

8. Problem Solving Polya’s 4-step process: 1.Understand the problem. 2.Devise a plan. 3.Carry out the plan. 4.Look back. Understand Think Do Check

9. Compare: NCSS Problem Solving Steps 1.Identify the problem. 2.Get the facts related to the problem. 3.Create a plan. 4.Carry out the plan. 5.Check your plan and adjust if needed.

10. Polya’s 4-step process: 1.Understand the problem. 2.Devise a plan. 3.Carry out the plan. 4.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. HW: Section 1.1 / Problem Set A 1.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.

12. 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 ?

13. 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 ?

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 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.

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

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

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

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

22. 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

23. 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

24. Problem Solving You will be assigned a homework problem in small working groups. Solve the problem using Polya’s 4 steps, then present your solution to the class.