Everything you need to know about…
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.
Time Height So, if I drop this ball… A Math Model Of A Dropped Ball!
Personal Finance The management of revenue, money, and resources
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
Scenario One Charlie is offered an initial lump sum of $20 per shift, and he is then paid an additional $2 per hour worked.
Scenario Two Ryan is offered an hourly wage of $8 an hour.
Scenario Three Brent is offered a lump sum of $50 per shift, but isn’t given an hourly wage.
So Which is Best?
It Depends On The Hours Worked
What was not accounted for in the graph? The Number of Shifts Worked!
Personal Finance
MBF3C Unit 8 Outline
Personal Finance [MBF3C and MEL3E] 1. Earning and Purchasing 2. Saving, Investing, and Borrowing 3. Transportation and Travel
Earning and Purchasing Different remuneration methods and different remuneration schedules Components of total earnings Payroll deductions Estimating costs
Saving, Investing, and Borrowing Services available from financial institutions Simple and Compound Interest Pros, Cons, and Cost of Borrowing
Example of an Assignment/Activity
Transportation and Travel Procedures, Costs, and Responsibilities of owning a car Associated costs with various modes of transportation
Example: Car Project
Public Transit vs. Private Vehicle Debate
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
Mathematical Models
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
Example #1 Investigate the graph y = 3(x – h) for various values of h, using technology, and describe the effects of changing h in terms of a transformations.
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
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.
MAP4C Solving Exponential Equations Modeling Graphically Modeling Algebraically
House Prices, Population Growth, and What Happened?
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 Provide your explanation.
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.
Example The Next Few Slides Make Up A Sample Taken From A Lesson That I Taught
Linear or Quadratic? XYFirst Differences Linear
Linear or Quadratic? XYFirst Differences Second Differences Quadratic
Linear, Quadratic or Other? Not Linear Not Quadratic TimePopulationFirst Differences Second Differences Other
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 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)
The graph of an exponential model
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
What kind of model would we use to represent the flight path of a football? Quadratic
What kind of model would we use to represent the growth of money in a bank account with interest? Exponential
As Shown, the important elements are trend recognition and understanding what the trend means when relating it to real world applications
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).