1. This is Part 2 of 3 (2 hour training session)

2. BIG IDEA 1 - Analyze and represent linear functions, and solve linear equations and systems of linear equations. Interpret the slope and the x- and y-intercepts when graphing a linear equation for a real-world problem.

3. BIG IDEA 1 - Analyze and represent linear functions, and solve linear equations and systems of linear equations. Compare the graphs of linear and non-linear functions for real-world situations.

4. The Purpose of this Unit is to (1) solve and explore an example of a linear real world problem (2) describe how to distinguish between linear and non-linear functions (3) solve and explore an example of a non-linear real world problem (4) state the range and domain of nonlinear function

5. Solving and exploring an Example of a linear real world problem http://repurposeful.files.wordpress.com/2009/04/tennis.jpg http://illuminations.nctm.org/LessonDetail.aspx?id=L246

6. How Do You to Distinguish between Linear and Non-Linear Functions Numerically? xy 47 510 613 716 + 3 xy 43 59 627 781 + 6 + 18 + 54 With linear functions, you can recursively add the same nonzero number to each output to obtain the next output. Linear Non-linear

7. How Do You Distinguish Between Linear and Non-linear Functions Graphically? The root word for linear is “line”. All lines are linear.

8. Nonlinear graphs have curves. How Do You Distinguish Between Linear and Non-linear Functions Graphically?

9. A relation of the form y = m x +b, Ax + By = C, and y = c is linear. They are also considered “first order” functions. y = 3x -5 2x + 3y = 6 y = -8 How Do You Distinguish Between Linear and Non-linear Functions Algebraically?

10. A relation of the form y = ax² y = x³, and y = 1/x are nonlinear. They are also considered “higher order” functions. How Do You Distinguish Between Linear and Non-linear Functions Algebraically? y = 3x² -5 y³ = -8

11. Watch this video from the “On-line Learning Math” site about How to Distinguish Between Linear and Non-Linear Functions Nonlinear Functions (5 Minutes 47 seconds) http://www.learner.org/courses/learningmath/video/algebra/wmp/alg _07_ch1.html

12. Solving and Exploring an Example of a Non-linear Real World Problem http://images.chron.com/blogs/keepthefaith/pen ny.jpg http://www.freefoto.com/images/04/28/04_28_50---US- Dollar-Bills_web.jpg

13. Suppose you are given two different options for salary, for a 25 weeks temporary job. Plan A:You are offer $2000 for each week, or Plan B:You can get 1 penny for 1 week, 2 pennies for the second week, 4 pennies for the third week, and it will keep doubling like that for the 25 weeks. Which plan do you want; Plan A or Plan B? Please explain why numerically, graphically or algebraically.”

14. PLAN APLAN B Answer: Plan B

15. Now Watch this video from the “On-line Learning Math” site to reinforce the idea of The Salary Problem http://www.learner.org/courses/learningmath/video/algebra/wmp/alg_07_ch2. html The Salary Problem

16. Remember, Glencoe describes the domain and range on Page 101 The domain of a relation is the set of x-coordinates. The range of a relation is the set of y-coordinates.

17. Can you state the Domain and Range of this Nonlinear Function? Answer: The domain is [-3, 3] and the range is [-4, 4].

18. Can you state the Domain and Range of this Nonlinear Function? Answer: The domain is (-∞,0) u (0,∞) and the range is (-∞,0) u (0,∞).

19. The Purpose of this Unit was to (1) solve and explore an example of a linear real world problem (2) describe how to distinguish between linear and non-linear functions (3) solve and explore an example of a non-linear real world problem (4) state the range and domain of nonlinear function

20. In Unit 3,we will reinforce these ideas using GeoGebra, the National Library of Virtual Manipulatives (NLVM), and the Promethean Planet Website. Please consider how you might use this lessons in your seventh and eighth grade mathematics classroom!