Modeling Algebra 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 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…..