Modeling Algebra 11009
Vision Statement: “Educate students
to become exploratory learners for the
future rather than train them for the
past.”
Goals
The student will be able to:
• Extend and refine problem solving skills
• Improve logical reasoning
• Link various mathematical ideas and processes
• Understand and be able to develop, analyze, and apply
mathematical modeling to real situations
• Utilize technology for visualization and computation
• Develop personal confidence in problem solving skills
• Communicate, interpret, validate and present findings in
a variety of mathematical settings(graphical, symbolic,
literal and data)
• Develop skills as a team player and foster decision
making in a group setting.
• Enjoy applying mathematics to meaningful situations
Objectives
• Be able to identify and formulate appropriate algebraic
models to situations.
• Be able to progress from solving simple problems to
more complex problems
• Be able to ascertain properties of types of mathematical
models from real situations and to apply those properties
to the appropriate situation.
• Recognize properties and operations of real numbers
• Be able to recognize types of functions and apply their
properties to real situations
• Use graphing calculators and/or computer software to
visualize, interpret, and arrive at a meaningful solution
for various problems
• Small group?????
Sample Questions
1. A postage stamp for a letter cost 3 cents
in 1961. By 2007 the price had increased
to 41 cents. Find the average rate of
change at which the price of stamps for
letters increased per year during this
period. Write a model for the price of a
postage stamp as a function of time
(years after 1961). Justify your
representation of this as a linear model.
Predict the price of stamps in 2015.
Another Sample Question
2. Average temperature in Saguaro National Park
drops about 3.5 degrees for every 1000 feet in
elevation and precipitation increases about 4
inches. In Tucson (2400 feet) the average
rainfall is 11 inches, what is the rainfall
average in the Ricon Mountains, Mica
Mountain (8800 feet)? On the summer
solstice, the temperature in Tucson reached
107 º F. How warm was it on the top of Mica
Mountain? How would you represent the
change in temperature with respect to
precipitation for both Tucson and the top of
Mica Mountain?
Number 3
•
Sam Hughes is a section supervisor for an electric utility company. The
employees in his section cut down tall trees, climb poles, and splice wires.
Brown recently reported the following information to the management of the
utility in the end of year budget report:
Out of 100 employees in my section
45 can cut tall trees
50 can climb poles
57 can splice wires
28 can cut trees and climb poles
20 can climb poles and splice wires
25 can cut trees and splice wire
11 can do all three
9 can’t do any of the three
Does Hughes’s data support his claim of 100 employees?
Facetious Question
•
Peter Beal, the peanut man, needs a
new suit. If he is 6 feet tall and the
peanuts are sewn onto the suit in rows
that are 2 inches apart, how many rows
of peanuts will his new suit have and if
the peanuts are sewn at a rate of 8 per
every 3 inches horizontally, how many
peanuts will be needed for his new suit if
he has 37 rows of peanuts?
Work in progress
•
Brushing up against a prickly pear
cactus, I received a few barbs…..