Unit 5: Exponentials & Logarithms

Students explore the relationship between exponential functions and their inverses, the logarithmic functions, including solving exponential equations using the properties of logarithms.  This is a chance to re-engage with exponential functions from Algebra 1 while extending them to their inverse, logarithmic functions.  Students express & evaluate logarithms, translate between logs in any base, and simplify logarithmic functions.  Depth can be achieved by proving simple laws of algorithms and deriving & using the formula for the sum of a finite geometric series.

Students should be able to access higher levels of “connecting standards” * as they create equations, rewrite equations, solve equations, graph functions & examine key features, and compare like functions to one another and different functions to one another in different representations in the new contexts of exponential and logarithmic functions.  There are opportunities to build new functions and to reengage with material from middle school and Algebra 1 at deeper levels throughout the unit.  Additional depth in this unit is achieved by spending time interpreting expressions specifically, writing explicit & recursive rules from a context, performing operations on functions, many of which could be embedded in first instruction.

Students explore the relationship between exponential functions and their inverses, the logarithmic functions, which is a chance to embed reengagement with exponential functions from Algebra 1.  The difference being students solving exponential equations using the properties of logarithms. 

Please note: the connecting standards in gray are essential standards, perhaps the most essential standards; they are not something previously covered and superfluous.  They are standards revisited throughout the course in new and different contexts.