Wu offers this text for teachers on how to effectively teach pre-algebra with a logical buildup of skills that should allow students to understand without mere memorization of unproven rules. The book takes the approach that rational numbers and fractions as points on the number line are the most fundamental principles in beginning to build algebraic skills, and that emphasizing geometry first, particularly the concept of slope, is critical to true understanding of algebra. The book proffers precise definitions and proofs for teachers to master, while also offering informal discussions of the approach and perspectives on what students often have trouble grasping. The first of five chapters discusses fractions in terms of the number line and defines arithmetic with fractions from this basis and extends fractions to concepts of percent, ratio, rate, and unit analysis. Chapter 2 adds the negative side of the number line and the concept of vectors to discuss rational numbers and their arithmetic in the same way. The book in these first two chapters also acknowledges a Fundamental Assumption of School Mathematics (FASM) which permits all real numbers to follow the same arithmetic rules as rational numbers, but cannot be proven at the pre-algebra level. Chapter 3 uses the Euclidean algorithm to find the reduced form of factions through prime factorization, prove certain divisibility shortcuts, and prove the fundamental theorem of arithmetic. Chapter 4 moves to principles of geometry, including basic isometries, congruence, dilation, and similarity, focusing on how precise definitions of commonsense phrases like "same shape" help students gain intuition. Chapter 5, finally, derives the length, area, and volume from the definition of geometric measurement. Chapters end with proof exercises. Annotation ©2016 Ringgold, Inc., Portland, OR (protoview.com)
