Essentials of Elementary School Mathematics

PrefaceNote to the InstructorNote to the StudentPart One Fundamentals 1 The Language of Mathematics 1 Conjunction (And); Negation (Not) 2 Disjunction (Or) 3 Conditional (If..., Then...) 4 Biconditional (If and Only If) 5 Quantifiers Quiz 2 Sets 1 Subset 2 Intersection and Union 3 Complement 4 Cartesian Product Quiz 3 Binary Operations 1 Definition of Binary Operation 2 Commutativity 3 Associativity 4 Distributivity 5 Identity Element 6 Inverses Quiz 4 Relations 1 Reflexive Relations 2 Symmetric Relations 3 Transitive Relations 4 Equivalence Relations 5 One-to-One Correspondence QuizPart Two The Theory of Arithmetic 5 The System of Whole Numbers 1 Definitions of Whole Numbers 2 Addition of Whole Numbers 3 Multiplication of Whole Numbers 4 Ordering of Whole Numbers Quiz 6 The System of Integers 1 Definition of Integers 2 Addition of Integers 3 Subtraction of Integers 4 Multiplication of Integers 5 Ordering of Integers Quiz 7 Place-Value Numeration Systems 1 The Nature of Our Decimal 2 Other Bases 3 Algorithms 4 Addition 5 Subtraction 6 Multiplication 7 Division Quiz 8 Systems of Rational and Real Numbers 1 Definition of Rational Numbers 2 Addition of Rational Numbers 3 Multiplication of Rational Numbers 4 Ordering of Rational Numbers 5 Division of Rational Numbers 6 Real Numbers QuizPart Three Expanding Mathematical Experiences 9 Number Theory 1 Divisors, Factors, and Primes 2 Division Algorithm 3 The Greatest Common Divisor Quiz 10 Clock Arithmetic 1 Introduction 2 An Equivalence Relation 3 Choosing Clocks Quiz 11 Counting Techniques and Probability 1 Permutations 2 Combinations 3 Probability QuizPart Four Geometry 12 Motion Geometry I 1 Congruence 2 Slides, Turns, and Flips 3 Successive Motions 4 Invariance 5 Angles 6 Symmetry Quiz 13 Motion Geometry II 1 Parallel Lines 2 Perpendicular Lines 3 Triangles 4 Quadrilaterals 5 Area 6 Similarity 7 Construction Quiz 14 Functions and Coordinate Geometry 1 Definition 2 Onto and One-To-One Functions 3 Graphing Functions 4 Graphing In R x R 5 Distance 6 Lines QuizAppendixBibliographyAnswers to Selected ExercisesSubject Index