MATH MODELS AND PERSONAL FINANCE
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
Heig
ht
So, if I drop this ball…
A Math
Model O
f A D
ropped 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
0 1 2 3 4 5 6 7 8 9 100
10
20
30
40
50
60
70
80
90
100
Rates of Pay
Hours Worked
Pay
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)2 + 5
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 = 2x from quadratic
growths represented by y = x2 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?
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
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?X Y First
Differences0 0
122 12
124 24
126 36
128 48
Linear
Linear or Quadratic?X Y First
DifferencesSecond
Differences0 5
1
1 6 2
32 9 2
53 14 2
74 21
Quadrati
c
Linear, Quadratic or Other?
Not Linear Not Quadratic
Time Population First Differences
Second Differences0 1
1
1 2 12
2 4 24
3 8 48
4 16 816
5 32 1632
6 64 3264
7 128
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.
Time Population Ratio of Change
0 1
21 22
2 42
3 82
4 162
5 322
6 642
7 128
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
0 1 2 3 4 5 6 7 80
20
40
60
80
100
120
140
Exponential Population Growth
Years
Po
pu
lati
on
Examples of Models
What kind of model would we use to represent someone’s income if they are making a certain wage per hour?
Linear0 2 4 6 8 10 12
0
20
40
60
80
100
120
Weekly Pay
Hours Worked
Pay
($)
What kind
of model would
we use to
represent the
flight path of a
football?
Quadratic
0 2 4 6 8 10 120
5
10
15
20
25
30
Flight Path Of a Football
Distance (Yrd.)
Hei
gh
t (f
t.)
What kind of
model would we
use to represent the
growth of money in
a bank account with
interest?
Exponential
0 2 4 6 8 10 120
200
400
600
800
1000
1200
Account Balance Over Time
Time (months)
Bal
ance
($)
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).