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Everything you need to know about…. Math Models and Personal Finance. The Math Model. What is a Math Model? A Mathematical Representation of a situation, scenario, or set of data Or…

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the math model
The Math Model

What is a Math Model?

  • A Mathematical Representation of a situation, scenario, or set of data


  • A symbolic Representation of a situation, scenario or data set that involves numbers, graphs, tables, variables and operations.
so if i drop this ball
So, if I drop this ball…


A Math Model Of A Dropped Ball!


personal finance
Personal Finance
  • The management of revenue, money, and resources
the wage game
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
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
Scenario Two

Ryan is offered an hourly wage of $8 an hour.

scenario three
Scenario Three

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

what was not accounted for in the graph
What was not accounted for in the graph?
  • The Number of Shifts Worked!
personal finance mbf3c and mel3e
Personal Finance [MBF3C and MEL3E]

1. Earning and Purchasing

  • 2. Saving, Investing, and Borrowing
  • 3. Transportation and Travel
earning and purchasing
Earning and Purchasing
  • Different remuneration methods and different remuneration schedules
  • Components of total earnings
  • Payroll deductions
  • Estimating costs
saving investing and borrowing
Saving, Investing, and Borrowing
  • Services available from financial institutions
  • Simple and Compound Interest
  • Pros, Cons, and Cost of Borrowing
transportation and travel
Transportation and Travel
  • Procedures, Costs, and Responsibilities of owning a car
  • Associated costs with various modes of transportation
map 4c and mel 4e personal finance
MAP 4C and MEL 4E Personal Finance
  • Earning and Purchasing
  • Saving, Investing, and Borrowing
  • Transportation and Travel
  • Annuities / Filing Income Tax
  • Renting vs. Owning Accommodations
  • Designing Budgets
mathematical models mbf3c
Mathematical Models [MBF3C]
  • Connecting Graphs and Equations of Quadratic Relations
  • Connecting Graphs and Equations of Exponential Relations
  • Solving Problems Involving Exponential Relations
example 1
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.

example 2
Example #2

Explain in a variety of ways how you can distinguish exponential growths represented by y = 2x from quadratic growths represented by y = x2 and linear growth represented by y = 2x

example 3
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.

  • Solving Exponential Equations
  • Modeling Graphically
  • Modeling Algebraically
house prices population growth and what happened
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 2010. Provide your explanation.
practicum experience trend recognition
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.

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

linear quadratic or other
Linear, Quadratic or Other?
  • Not Linear
  • Not Quadratic


5 3 exponential models
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.

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)

examples of models
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 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
  • 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).