Teaching school mathematics

This is a systematic exposition of a major part of the mathematics of grades 5 to 8 (excluding statistics), written specifically for Common Core era teachers. It differs from other books for teachers in that the mathematics is correct, in the sense that all the concepts are clearly and correctly defined, and a grade-appropriate explanation (that is, proof) is given for every assertion. For example, it gives a precise definition of percent and explains how to use the definition to do all the standard problems about percent in an entirely routine manner. It also gives a leisurely explanation for 2negative times negative is positive3. Another key feature is an intuitive introduction to plane geometry via rotations, translations, reflections, and dilations that, instead of treating these transformations as merely fun activities, shows how they make sense of the usual geometric topics in middle school, including congruence, similarity, length, area, and volume. In short, the readers will find in this volume a clear explanation of whatever was once puzzling to them in the mathematics of grades 5 to 8.

This is a systematic exposition of introductory school algebra written specifically for Common Core era teachers. The emphasis of the exposition is to give a mathematically correct treatment of introductory algebra. For example, it explains the proper use of symbols, why 2variable3 is not a mathematical concept, what an equation is, what equation-solving means, how to define the slope of a line correctly, why the graph of a linear equation in two variables is a straight line, why every straight line is the graph of a linear equation in two variables, how to use the shape of the graph of a quadratic function as a guide for the study of quadratic functions, how to define a parabola correctly, why the graph of a quadratic function is a parabola, why all parabolas are similar, etc. This exposition of algebra makes full use of the geometric concepts of congruence and similarity, and it justifies why the Common Core Standards on algebra are written the way they are.

V.1: Pre-Algebra -- v.2: Algebra