Unit 4: Radicals & Rationals 

The two big ideas of this unit are rational expression operations  and solving rational & radical equations.  Rewriting rational expressions can be embedded with rational expression operations, and explaining solution steps can be embedded with solving radical & rational equations.  

Students should also 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 radical and rational functions.  There are opportunities to build new functions and to reengage with material from elementary, middle school, and Algebra 1 at deeper levels throughout the unit.  Depth in this unit is achieved by spending time interpreting expressions specifically, writing explicit & recursive rules from a context, performing operations on functions and finding inverse functions, many of which could be embedded in first instruction.

In order to make working with rational expressions more than just an exercise in the proper manipulation of symbols, instruction should focus  on the characteristics of rational functions that can be understood by rewriting them (e.g., rates of growth, approximation, roots, axis intersections, asymtotes, end behavior & so on).

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.