Designing the Optimal Soda Can

COLORADO MATH STANDARDS:
Standard 2:  Students use algebraic methods to explore, model and describe pattern and functions involving numbers, shapes, data and graphs in problem-solving situations and communicate the reasoning used in solving these problems.
Benchmark 1:  Model real world phenomena using functions.
Benchmark 2:  Represent functional relationships using written explanations, tables, equations, and graphs and describe the connections among these representations.
Benchmark 3:  Solve problems involving functional relationships using graphing calculators and/or computers as well as appropriate paper-and-pencil techniques.
Benchmark 4:  Analyze and explain the behaviors, transformations, and general properties of functions.

Target Students:  This lesson is designed for students taking a college level calculus class.

Students should have mathematical knowledge of:
Equivalent forms of functions
Volume and surface area formulas
Derivative procedures
Methods for testing minimum and maximum values
Use of tables and graphs to organize data

Students should have technological knowledge of:
Word processing programs
Equation editing programs
Graphing calculator programs
Online graphing programs

Students may need assistance with:
Choosing multiple methods for proving their value of radius is a minimum
Modeling function for volume of metal in the can
Designing online survey for final analysis
Using an equation editor