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.
Height
So, if I drop this ball…
Time
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
Rates of Pay
100
90
80
70
Pay
60
50
40
30
20
10
0
0
1
2
3
4
5
Hours Worked
6
7
8
9
10
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
 Earning and Purchasing

Saving, Investing, and Borrowing

Transportation and Travel

Annuities / Filing Income Tax

Renting vs. Owning Accommodations

Designing Budgets
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
0
0
First
Differences
12
2
12
12
4
24
12
6
36
12
8
48
Linear or Quadratic?
X
Y
0
5
First
Differences
Second
Differences
1
1
6
2
3
2
9
2
5
3
14
2
7
4
21
Linear, Quadratic or Other?
Time
Population
0
1
1
2
First
Differences
Second
Differences
1
1
2
2
4
2
4
3
8
4
8
4
16
8
16
5
32
16
32
6
64
32
64
7
128
Not Linear
 Not Quadratic

5.3 – Exponential Models
Time
Population
0
1
Ratio of
Change
2
1
2
2
2
4
2
3
8
2
4
16
2
5
32
6
64
2
2
7
128
Exponential
The Ratio of Change:
Models
– Difference,
A model
Similar
to the First
we divide the data term from
that shows the
the previous data term to find
thesame
Ratio of Change
ratio (First
of
Quotient)
change over equal
intervals.
 The same first
quotients across
the data set.

The graph of an exponential model
Exponential Population Growth
140
120
Population
100
80
60
40
20
0
0
1
2
3
4
Years
5
6
7
8
Examples of Models
Weekly Pay
120
100
80
Pay ($)
What kind of
model would we
use to represent
someone’s
income if they are
making a certain
wage per hour?
60
40
20
0

Linear
0
2
4
6
Hours Worked
8
10
12
What kind of
Flight Path Of a Football
model would
30
25
we use to
flight path of a
football?
Height (ft.)
represent the
20
15
10
5
0
0
-5

Quadratic
2
4
6
Distance (Yrd.)
8
10
12
What kind of
Account Balance Over Time
model would we
1200
1000
use to represent the
growth of money in
a bank account with
interest?
Balance ($)
800
600
400
200
0
0

Exponential
2
4
6
8
Time (months)
10
12
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).