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).