The algebraic notation we use today allows for the compact representation of complex calculations and problems, however, that compactness can be a barrier to sense making. Teachers must help students reason through this barrier.

Reasoning about and making sense of algebra are essential to students’ future success. This book examines the five key elements (meaningful use of symbols, mindful manipulation, reasoned solving, connection algebra with geometry, and linking expressions and functions) identified in Focus in High School Mathematics: Reasoning and Sense Making in more detail and elaborates on the associated reasoning habits.

This volume is one of a series of books that support NCTM’s Focus in High School Mathematics: Reasoning and Sense Making by providing additional guidance for making reasoning and sense making part of the mathematics experiences of all high school students every day.