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© 2014 Pacific Crest
89
H
ardest Problem
How hard
can
it be? Can you still use what you’ve learned?
Based on the Model, the Methodology, and the Demonstrate Your Understanding (DYU) problems in
this activity, create the
hardest
problem you can. Start with the hardest DYU problem in this experience
and by contrasting and comparing it with the other DYU problems, play “What if” with the different
conditions and parameters in the various problems.
Can you still solve the problem? If so, solve it. If not, explain why not. What is it that makes a problem
where you evaluate a formula a difficult problem to solve?
What are the conditions and parameters that make a problem involving evaluating a formula a difficult
problem to solve?
T
roubleshooting
Find the error and correct it!
Saroya was helping a local artist with a new
installation. Her job was to fill a series of glass
cylinders with colored water. She had managed
all the smaller cylinders but was now faced
with a cylinder taller than she was. Because
she was dying the water herself to the artists
exact specifications of “1.5 ounces of dye per
gallon of water,” it was critical that she know
how much water each cylinder would contain.
She got out a tape measure, found a step ladder,
and determined that the last cylinder was 1.5
feet in diameter and 8 feet tall. At right are her
calculations for the volume of the cylinder.
(
)
(
) (
)
2
2
2
2
and
so
2
2
1.5 feet
12 inches
8 feet
2
1 foot
12 inches
0.75 feet 8 feet
1 foot
0.75 feet
d
d
V r h
r
V
h
V
V
V
=
=
=
=
=
=
π
π
π
π
π
(
)
2
8 feet
(
)
12 inches
1 foot
(
)
(
)
(
)
(
)
2
2
3
0.5625 in 96 inches
3.14 0.5625 in 96 inches
169.56 in
V
V
V
=
=
=
π
Once she had the volume, she checked her smart phone and found that 1 gallon = 231 cubic inches.
Suddenly, she knew she’d done something wrong. There was no way THIS cylinder held less than 1
gallon of water.
M
aking it Matter
Solving problems in your life
●
The loyalty program has been pervasive: Thrifty rental car gives a free rental day for every 16 rental
days purchased; Food Warehouse gives a 1% rebate on non-alcohol purchases, Market Foods is
giving cash rebates on all purchases other than liquor and cigarettes. What is the formula for the
refund or savings you get each month for a program that you or a person you know is involved in?
●
What is the formula for the cost of gas you buy at your local gas station? How much will 5.7 gallons
cost?
●
What is the formula for how much you tip at a local restaurant?
●
What is the formula for postage on a letter mailed at a United States Post Office? How much does it
cost to send a 5 oz. letter by First Class mail?
2.3 Evaluating a Formula