Ultimately the goal of any extended analysis should be to allow you to see something new about the problem. The following are some strategies that we will use in this class to do this:

• Generalizing the problem (e.g., replacing numbers with variables and solving again, considering a broader class of contexts, adding dimensions, etc.)
  
• Identifying the general mathematical structure of the problem and solution (e.g., as involving harmonic means vs. arithmetic means, coaxing the solution into revealing forms, etc.)
• Exploring and connecting alternative solution methods (e.g., using calculus, only algebra, geometry, a graphing calculator, etc.)
• Considering extreme cases
• Exploring a physical, computer animated, or other analog model of the function
• Changing some aspect(s) of the problem and discerning the resulting effect
• Graphing relationships in multiple ways (e.g., using a parameter as the independent variable, including additional dimensions, comparing graphs for different values of a parameter, etc.)
• Finding some important structure of the problem or solution and identifying the manifestation of that structure across multiple representations (algebraic, numerical, graphical, contextual, etc.)
• Exploring dimensional analysis
• Looking for isomorphic problem situations
• Comparing various important quantities to identify and understand relationships between them
• Identifying new interpretations of expressions appearing throughout the solution to gain insight into the situation
• Exploring rate of change through multiple analyses (constant increments of one quantity, average rates over various intervals, calculus/derivatives, graphical/geometric analysis, etc.)