Course Outline: Chapter Topics Ch. 1: Introduction to Problem Solving: strategy and approach -----3 classes (1) Inductive and deductive reasoning. (2) Pattern recognition. (3) Giving clear explanations. (4) Problem solving strategies. Ch. 2: Sets, Whole Numbers, and Numeration ----3 classes (1) Hindu-Arabic number system. (2) Set operations, Venn diagrams and their applications. (3) Number systems in other cultures. (4) Binary number systems and number systems in other bases. (5) Relations and functions in daily life. Ch. 3: Whole Numbers: Operations and Properties ----3 classes (1) Closure, Commutative, Associative, Distributive and Identity properties. (2) Division Algorithm. (3) Laws of Exponents. Ch. 4: Whole Number Computation: Mental, Electronic and Written -----3 classes (1) Review briefly the standard algorithms for addition, subtraction, multiplication and division. (2) Explore other algorithms and understand why they work. (3) Arithmetic in other bases. (4) Estimation and approximation. Ch. 5: Number Theory ---4 classes (1) Factors and multiples, divisibility, primes (2) Primality testing. (3) Factor trees and prime factorizations. (4) Counting factors, GCDs and LCMs. Ch. 6: Fractions ---4 classes (1) Develop models for fractions and their arithmetic. (2) Drill on addition, subtraction, multiplication and division of fractions. Ch. 7: Decimals,Ratio and Proportion, and Percent --- 4 classes (1) Representing numbers as decimals. (2) Converting decimals to fractions and vice versa. (3) Ordering decimals and fractions. (4) Decimal arithmetic. (5) Ratio and proportion. (6) Percentage and interest rates. Ch 12: Geometric Shapes ---3 classes (1) Vocabulary: square, rectangle, rhombus, kite, trapezoid, congruent, isosceles, etc. (2) Paper folding. (3) Symmetry (4) Angle measurement. (5) 3-dim shapes Ch 13: Measurements ---3 classes (1) Metric system and English system. (2) Converting between different units. (3) Areas, Volumes and Perimeters. (4) The meaning of pi. Ch. 8: Integers ---2 classes (1) Models for negative numbers. (2) Review properties of integers and operations on integers. (3) Negative exponents. Ch. 9: Rational Numbers and Real Numbers, with introduction to algebra -- 3 classes (1) Summarize number systems and basic properties (2) Roots and and irrational numbers. (3) Understand infinite decimals Math320 Competencies
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