The Standards for Mathematical Practice can be used as a foundation to help educators bring some desperately needed mathematical coherence to school algebra. This talk will look at how a small set of general-purpose habits, like abstracting regularity from repeated calculation, can help students see algebra as a web of interconnected results and methods that makes sense. Seeing algebra in this way makes it more understandable, useful, and enjoyable for students. It makes teaching algebra more satisfying and effective for teachers. And, it connects school algebra to algebra as it is practiced outside of school, both as a scientific discipline and as a central tool in every modern field of scientific inquiry. We'll work through some low-threshold, high-ceiling examples that show how seemingly different topics in high school mathematics can be understood more effectively when they are viewed through the lens of mathematical practice.