This learning progression will be applied in a high school end of course class, and there will be no textbooks being used however there will some outside material included such as a Khan Academy video to supplement instruction. The common core state standards being aligned with this progression are: HSF.BF.B.3, HSF.BF.B.4, HSF.BF.B.4A, HSF.BF.B.4B, and HSF.BF.B.5. The following standards for mathematical practice are also included in the progression: MP1: Make sense of problems and persevere in solving them, MP2: Reason abstractly and quantitatively, and MP4: Model with mathematics.
In the first lesson, students investigate what effects adding a constant to a function might have, such as f(x) + k, k*f(x) or f(x+k). Students get more familiar with transforming, or building off of given functions. The second lesson will focus the students on trying to work in the opposite direction, finding the inverses of functions, and for our common core state standard we are sticking to simple linear functions. Students will learn how to prove algebraically if two functions are inverses of one another by taking the compositions of the functions. In the final lesson, students will take their new knowledge of inverses and investigate further the inverse property between exponents and logarithms.
There will be a formative assessment at the end of the progression in the form of a short standards-based quiz that covers the cluster of standards. There are also worksheets for each lesson as well that are intended as benchmark assessments throughout the progression.