Description: A study of the fundamentals of mathematical modeling:  numerical, graphical, and theoretical methods; qualitative and quantitative aspects of functions and graphs; change, rate of change and percent change; proportional relationships; changing scales; finding perfect fits; looking for good fits; and modeling activities.

Objectives: To help students (a) see connections between mathematics and other disciplines, (b) present and analyze real-world phenomena using a variety of mathematical representations, (c) develop strategies and techniques for applying mathematics to solve problems, and (d) explain and justify their reasoning, using appropriate terminology, in both oral and written expression.

Prerequisites: Algebra II or equivalent.  Any college-level lab science course (may be taken concurrently).

Texts:  Kalman, “Elementary Mathematical Models,” Mathematical Association of America.
            Cathcart & Horseman, “Mathematical Models and Modeling for Middle School Teachers,” MCTP
 

	Weeks
The Modeling Process and Model Fitting The process for constructing, analyzing, interpreting, and evaluating mathematical models; Sample modeling problems;  Numerical, graphical, and theoretical approaches in modeling;  Investigating ways to find equations  to fit a data set.	2
Sequences, Differences Equations, Linear and Quadratic Growth Models  Rules for relationships; Difference equations and functional equations; Patterns of arithmetic (linear) and quadratic growth:  Fitting linear and quadratic equations to data sets.	2
Graphing Some "Standard" Functions and Conjecturing Proportionality Relationships  Graphs of standard functions classified as linear/nonlinear, concave up/concave down, increasing/decreasing/constant;  Statements about observed patterns of change and rate of change; Graphical representation of qualitative aspects of various phenomena; Statements about anticipated changes, rates of change, and proportionality relationships.	1
The Basics of Spreadsheets, Qualitative and Quantitative Aspects of Graphs  Graphing and analyzing patterns of change using Excel; Explorations of physical situations; Using graphs and table to explore and express relationships;  Calculation changes,  rates of change, and percent changes in determining which  functions are candidates for modeling the data.	2
Geometric Growth and  Exponential Functions  Exploration of patterns of change typical of geometric or exponential growth in modeling activities.	1
Changing Scales in Graphs, Finding Fits, Testing for “Best Fit”  The effect of semi-log and log-log scales on the shape of a function’s graph.  Intuitive methods and numerical criteria  for determining a “good or best” model.”	2
Modeling Problems, Proportionality Relationships, Logistic Growth, and Power Functions  Case studies in math modeling; Discussion of assumptions; Derivation of a math model: Interpretation,  explanation, justification and validation of  results.	4