Generalizing is a foundational mathematical practice for the algebra classroom. It entails an act of abstraction and forms the core of algebraic thinking. Kinach (2014) describes two kinds of generalization--by analogy and by extension. This article illustrates how exploration of fractals provides ample opportunity for generalizations of both…

Lessons given to a group of mathematically talented eleventh and twelfth graders enrolled in a problem-solving course that provided practice in applying the heuristic strategy of working backward are detailed. Special attention was given to the process of formulating generalizations that represent large problem classes. (MP)

Features activities for advanced second-year algebra students in grades 11 and 12. Introduces three random variables and considers an empirical and theoretical probability for each. Uses coins, regular dice, decahedral dice, and calculators. (ASK)