A Call for Making Sense of Mathematics for Teaching -- Understanding Mathematics for Teaching -- Engaging in the Mathematical Practices -- Emphasizing the TQE Process -- The Structure of Making Sense -- The Challenge -- The Progression -- The Mathematics -- The Classroom -- The Response -- How to Use This Book -- Equations and Functions -- The Challenge -- The Progression -- Grade 7 -- Grade 8 -- High School -- The Mathematics -- Analyzing Functions With Multiple Representations -- Connecting Domain and Range of a Function to Its Graph -- The Classroom -- TQE Process -- The Response -- Structure of Equations -- The Challenge -- The Progression -- Grade 8 -- High School -- The Mathematics -- Modeling Contexts Through Visualization -- Exploring Different Forms of Linear Functions -- Exploring Different Forms of Quadratic Functions -- The Classroom -- TQE Process -- The Response -- Geometry -- The Challenge -- The Progression -- Grade 8 -- High School -- The Mathematics -- Exploring Transformations -- Exploring Congruence Through Proof -- Exploring Similarity Through Constructions -- The Classroom -- TQE Process -- The Response -- Types of Functions -- The Challenge -- The Progression -- High School -- The Mathematics -- Determining the Impact of Parameters on Function Behavior -- Making Connections Through Representations: Graphic and Algebraic -- Connecting Types of Functions Using Symmetry -- Exploring Rational Functions -- The Classroom -- TQE Process -- The Response -- Modeling With Functions -- The Challenge -- The Progression -- High School -- The Mathematics -- Modeling With Quadratic Functions -- Modeling With Exponential Functions -- Modeling With Radical Functions -- Modeling With Piecewise Functions -- Modeling a Bird's Wings in Flight -- The Classroom -- TQE Process -- The Response -- Statistics and Probability -- The Challenge -- The Progression -- Middle School -- High School -- The Mathematics -- Applying the Normal Model -- Comparing Data Sets -- Understanding Sample Surveys, Experiments, and Observational Studies -- Investigating Probability -- Exploring Scatterplots -- The Classroom -- TQE Process -- The Response -- Epilogue -- Next Steps -- Focus on Content -- Select Good Tasks -- Align Instruction With the Progression of Mathematics -- Build Your Mathematics Content Knowledge -- Observe Other Teachers of Mathematics -- Respond Appropriately to Students' Struggles With Mathematics -- Now What?