Background I am working from the New York State Teacher Certification Examinations (NYSTCE) standards, Field 004: Mathematics. This week, we will be discussing a topic from Competency 0004 - Calculus. Within this Competency, I have chosen the following performance indicator: "applies techniques of differentiation and integration (e.g., product rule, chain rule, u-substitution)." There are no NY State Common Core Learning Standards for Mathematics which align with my selected topic. Regardless, I am choosing to focus on the "power rule." This is a common differentiation technique used in all calculus courses. My goal is to create an engaging activity for students to practice using the power rule. For reference, here is the power rule:

Background I am working from the New York State Teacher Certification Examinations (NYSTCE) standards, Field 004: Mathematics. This week, we will be discussing a topic from Competency 0003 - Functions. Within this Competency, I have chosen the following performance indicator: "analyzes arithmetic and geometric sequences both recursively and with an explicit formula, translates between the two forms, and uses them to model situations."  For simplicity, I will only focus on arithmetic sequences, though the activity can easily be modified to focus on geometric sequences as well. Here are the NY State Common Core Learning Standards for Mathematics which align with my selected topic: My goal is to design a creative activity which requires students to create their own arithmetic sequences rather than solving pre-written problems. It will be assumed that students already understand the basics of arithmetic sequences including the recursive and explicit formulas. This activity could ...