1. Problem Solving

2. ALGEBRA 2 10/17/14 Learning Target : I can learn different strategies in problem solving so that I can solve more complex problems. Homework : Study very well for Test 2 Constructed Response on Monday. Answer Practice Test. Warm-up: Think about the problem on the right. What strategies can you use to solve this problem?

3. Why Learning Teams?

4. Standards for Mathematical Practices Focus : Standard 1 Make sense of problems and persevere in solving them.

5. What is a Problem?  Definition: A problem is a situation, quantitative or otherwise, that confronts an individual or group of individuals, that requires resolution, and for which the individual sees no apparent or obvious means or path to obtaining the solution.

6. Exercise vs Problem

7. EXERCISE:  a situation that involves drill and practice to reinforce a previously learned algorithm.

8. Problem :  A situation that requires thought and a synthesis* of previously learned knowledge to solve. *synthesis – the combining of separate elements or substances to form a coherent whole.

9. Polya’s 4-Step Method in Problem Solving:  1. THINK  2. PLAN  3. SOLVE  4. LOOK BACK

11. 1. What was his height at the launch? 2. What was his initial velocity? 3. How many seconds after the launch will he reach the maximum height? 4. What is his maximum height? 5. How long before he lands in the safety net, 8 feet above the ground?

13. 1. What was his height at the launch? His height at the launch was 28 feet.

14. 2. What was his initial velocity? His initial velocity was 24 ft/sec.

15. 3. How many seconds after the launch will he reach the maximum height? How will the graph of the parabola defined by this function look like? Will it open up or down? How do you know? Where is Carl’s maximum height located on this parabola? Which part of the vertex will tell you the number of seconds after the launch Carl will reach his maximum height? How do you solve for the x-coordinate of the vertex? He will reach his maximum height 0.75 seconds after the launch.

16. 4. What is his maximum height? Which part of the vertex will you find the maximum height? How will you find the y-coordinate of the vertex? Carl’s maximum height is 37 feet.

17. 5. How long before he lands in the safety net, 8 feet above the ground? What are you asked to find here? What information is given? What can you do to solve for the time it will take him to land in the safety net, which is 8 feet above the ground?

18. 5. How long before he lands in the safety net, 8 feet above the ground?

19. A negative time does not make sense in this problem, so: Carl will land in the safety net after about 2.1 seconds.