1. Everything you need to know about…

2. The Math Model What is a Math Model?  A Mathematical Representation of a situation, scenario, or set of data Or…  A symbolic Representation of a situation, scenario or data set that involves numbers, graphs, tables, variables and operations.

3. Time Height So, if I drop this ball… A Math Model Of A Dropped Ball!

4. Personal Finance  The management of revenue, money, and resources

5. The Wage Game!  We Are Going To Play A Game…  You will be broken up into three groups  Each group will be given a wage-based scenario  You will have to choose a group member to read your scenario in front of the class and then after each scenario is read, within your groups you will have to decide which rate of pay would be best

6. Scenario One Charlie is offered an initial lump sum of $20 per shift, and he is then paid an additional $2 per hour worked.

7. Scenario Two Ryan is offered an hourly wage of $8 an hour.

8. Scenario Three Brent is offered a lump sum of $50 per shift, but isn’t given an hourly wage.

9. So Which is Best?

10. It Depends On The Hours Worked

11. What was not accounted for in the graph?  The Number of Shifts Worked!

12. Personal Finance

14. MBF3C Unit 8 Outline

15. Personal Finance [MBF3C and MEL3E] 1. Earning and Purchasing 2. Saving, Investing, and Borrowing 3. Transportation and Travel

16. Earning and Purchasing  Different remuneration methods and different remuneration schedules  Components of total earnings  Payroll deductions  Estimating costs

17. Saving, Investing, and Borrowing  Services available from financial institutions  Simple and Compound Interest  Pros, Cons, and Cost of Borrowing

18. Example of an Assignment/Activity

20. Transportation and Travel  Procedures, Costs, and Responsibilities of owning a car  Associated costs with various modes of transportation

21. Example: Car Project

25. Public Transit vs. Private Vehicle Debate

26. MAP 4C and MEL 4E Personal Finance  Annuities / Filing Income Tax  Renting vs. Owning Accommodations  Designing Budgets  Earning and Purchasing  Saving, Investing, and Borrowing  Transportation and Travel

27. Mathematical Models

29. Mathematical Models [MBF3C] 1. Connecting Graphs and Equations of Quadratic Relations 2. Connecting Graphs and Equations of Exponential Relations 3. Solving Problems Involving Exponential Relations

30. Example #1 Investigate the graph y = 3(x – h) 2 + 5 for various values of h, using technology, and describe the effects of changing h in terms of a transformations.

31. Example #2 Explain in a variety of ways how you can distinguish exponential growths represented by y = 2 x from quadratic growths represented by y = x 2 and linear growth represented by y = 2x

32. Example #3 The height, h meters, of a ball after n bounces is given by the equation h = 2(0.6) n. Determine the height of the ball after 3 bounces.

33. MAP4C  Solving Exponential Equations  Modeling Graphically  Modeling Algebraically

34. House Prices, Population Growth, and What Happened?

35.  In your existing groups, please answer the following:  Given the following graph, describe the trend in Canadian house prices, population and immigration growth.  Describe some factors that many have influences these trends.  Predict what the graph would look like if it extended to 2010. Provide your explanation.

38. Practicum Experience: Trend Recognition  While teaching a MAP4C course…  Important ‘take home’ elements for the students were based in trend recognition and real world application and connection.

39. Example The Next Few Slides Make Up A Sample Taken From A Lesson That I Taught

40. Linear or Quadratic? XYFirst Differences 00 12 2 424 12 636 12 848 Linear

41. Linear or Quadratic? XYFirst Differences Second Differences 05 1 162 3 292 5 3142 7 421 Quadratic

42. Linear, Quadratic or Other?  Not Linear  Not Quadratic TimePopulationFirst Differences Second Differences 01 1 121 2 242 4 384 8 4168 53216 32 66432 64 7128 Other

43. 5.3 – Exponential Models  Exponential Models – A model that shows the same ratio of change over equal intervals.  The same first quotients across the data set. TimePopulationRatio of Change 01 2 12 2 24 2 38 2 416 2 532 2 664 2 7128 The Ratio of Change: Similar to the First Difference, we divide the data term from the previous data term to find the Ratio of Change (First Quotient)

44. The graph of an exponential model

45. Examples of Models What kind of model would we use to represent someone’s income if they are making a certain wage per hour?  Linear

46. What kind of model would we use to represent the flight path of a football?  Quadratic

47. What kind of model would we use to represent the growth of money in a bank account with interest?  Exponential

48. As Shown, the important elements are trend recognition and understanding what the trend means when relating it to real world applications

49. Questions  Is this relatable to your own practicum experience?  Do you have any questions or concerns?  Share one thing that you learned from this presentation (new, surprising, or interesting).