Modeling Algebra 11009

Vision Statement: “Educate students to become exploratory learners for the

future rather than train them for the past.”

GoalsThe 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 section45 can cut tall trees50 can climb poles57 can splice wires28 can cut trees and climb poles20 can climb poles and splice wires25 can cut trees and splice wire11 can do all three9 can’t do any of the threeDoes 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…..