At some point a math student needs to move from learning algebra to doing algebra. #algebratech 
Many techniques that students learn are designed to facilitate a person’s understanding and remembrance of algebraic processes and are not optimized for efficiency or speed.  Adding a number to both sides of an equation or always using a least common denominator when adding fractional expressions are examples of the conflation of technique and reason for the technique combined into one rule.

But as students move into the next level math courses,precalculus and calculus, algebra becomes a just a tool for exploring new concepts.  At this point a math learner should be thinking about the new ideas not algebraic processes.  The second term of precalculus with its plethora of proportions, equations and identities is the place, I think, to make this jump.  Therefore I will be modeling fast algebra techniques like those in the image below.


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