Basic HTML Version
Q
uantitative
R
easoning &
P
roblem
S
olving
86
© 2014 Pacific Crest
●
Justifying an answer instead of validating it
Example
:
How much does the gas cost, in dollars, to drive
500 miles in a car that gets 23.4 miles to the
gallon, if gas costs $3.67?
total cost of gas
price for 1 gallon of gas
miles traveled
miles
gallon
T
P
M
mpg
=
=
=
=
Step 1: Identify formula:
(
)
Step 2: (units were identified previously)
Step 3: Substitute units:
500(23.4)(3.67)
. . . .
gallons
$
Step 8: Validate units:
mile
mile gallon
T M mpg P
T
T
=
=
=
Why?
Often we justify the answer we want instead of validating whether it works or not. In
this case, the student set the problem up incorrectly (in Step 1), but instead of using
the correct units (in Step 8) to validate the work, the student flipped mpg so that the
previous mistake was justified. Had the student actually validated the units, it would
have become obvious that there was an error in the formula used, as the correct units
do
not
validate the formula. When you validate, you’re testing to see if an answer is
correct, not trying to make it correct.
A
re You Ready?
Before continuing, you should be able to ...
I can...
OR
Here’s my question...
correctly multiply a fraction by an integer
substitute correctly in a formula
apply the Order of Operations correctly
use unit analysis correctly in a formula
P
lan
How to complete the activity
1. Compare the answers to Your Turn in practicing the use of the methodology.
2. Answer the Critical Thinking Questions.
3. Complete the remainder of this activity (from Demonstrate Your Understanding through Assessing
Your Performance) on your own, or as directed by your instructor.