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© 2014 Pacific Crest
187
M
odel(s)
Exemplars and representations
Scenario:
In 2002, a mathematics teacher purchased her home in Fort Wayne, Indiana for
$120,000. The value of her home fell at the same rate each year, and in 2010, the
value of her home was $104,000. If she retired in 2012, what was her home worth?
Step
Watch it Work!
1. Read and
state the
problem
What was the value of her home in 2012?
2.
Inventory the
information
Given
Her home is in Fort Wayne, Indiana.
Home value was $120,000 in 2002.
Home value was $104,000 in 2010.
Missing
Rate of value
decline
Find
Home value in
2012
3.
Eliminate
irrelevant
information
Her home is in Fort Wayne, Indiana.
The value of her home was $120,000 in 2002.
The value of her home was $104,000 in 2010.
4.
Identify
variables,
constants and
assumptions
Variables and Constants
v
= value of the home in dollars
y
years after 2002
y
= the number of years since 2002
r
= the rate at which the value of the home decreased each year
(in dollars/year)
b =
the value of the home in dollars in 2002
Assumptions
The value of the home decreases at the same rate after 2010.
5.
Determine the
form for the
solution
State what the value of her home was in 2012.
6.
Simplify the
problem
1) How much does the value of the home decrease each year?
2) How much is her home worth after a number of years?
7. Model each
sub-problem
1) How much does the value of the home decrease each year?
$120000 $104000
8 years
r
−
=
2) How much is her home worth after a number of years?
v
=
b
–
r
×
y
4.3 Interpreting a Word Problem