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College Math for Elementary Education – Patterns through Exploration and Play, with Algebra Extensions
Introduction and Table of Contents – College Math for Elementary Education
Introduction to Chapter 1
Sec. 1.1 – Introduction to Base Ten Additive, Multiplicative and Place Value Numeration Systems
Sec. 1.2 – The Mayan Number System, Place value in Base 20
A 1.1 – Algebra Extension: Introduction to Exponents and Rules for Exponents
A 1.2 – Algebra Extension: the Meaning of Negative and Zero Exponents
Sec. 1.3 – Adding and Subtracting in Egyptian; Base Ten Blocks and Combining like Terms
A 1.3 – Algebra Extension: Adding and Subtracting Polynomials
Sec. 1.4 – Converting Between Base Ten and Other Bases
A 1.4 - Algebra Extension: Scientific Notation and Relative Size
Sec. 1.5 – The Babylonian Number System; Review of Converting between Bases
A 1.5 – Algebra Extension: the Order of Operations and Exponents
Sec. 1.6 – Adding and Subtracting in Bases
Sec. 1.7 – Adding the Numbers from 1 to 100; Alternate Methods of Subtraction
Introduction to Chapter 2
Sec. 2.1 - The Sieve of Eratosthenes, Prime Numbers, Goldbach’s Conjecture, Mersenne Primes
A 2.1 Algebra Extension: What is a Variable? Writing and Solving Equations
Sec. 2.2 – Multiplication as Area; Commutative and Distributive Properties; Slope
A 2.2 Algebra Extension: Operations on Polynomials - Adding, Subtracting, Multiplying and Factoring
Sec. 2.3 – Problem Solving Strategies for All Ages
A 2.3: Solving Equations, Literal Equations; Finding Solution Sets
Sec. 2.4 – Fibonacci Numbers, Figurate Numbers, Non-Linear Equations; Using Subscripts to Find Patterns
A 2.4 Algebra Extension: The meaning of Slope; Parallel Versus Intersecting Lines; Systems of Equations
Sec. 2.5 – Fractions, Patterns in Pascal's Triangle
A 2.5 Algebra Topics – Simple Algebraic Fractions; Simplifying, Adding and Subtracting
Sec. 2.6 – Babylonian Fractions; Writing Terminating and Repeating Decimals as Fractions; Multiplying Fractions Visually
A 2.6 Exponential Equations: Graphing and Applications
Sec. 2.7 – Irrational and Rational Numbers, Pi, Multiplying and Dividing Fractions Using Models
A 2.7 Solving Quadratic Equations by Graphing and by Factoring
A 2.8: Solving Exponential Equations using Logarithms and by Graphing
A 2.9: Optional Topic: Solving Systems of Equations by Elimination; Graphing and Writing Equations Given a Point and a Slope, or Given Two Points
Introduction to Chapter 3
Sec. 3.1 - Venn Diagrams, Complement, Intersection and Union
A 3.1: Common Factors and Multiples in Algebraic Expressions; Using Sets to Find Common Factors
Sec. 3.2 – Set Operations with Two- and Three-Circle Venn Diagrams
A 3.2: Multiplying and Dividing Algebraic Fractions; Graphing Rational Equations
Sec. 3.3 – More Set Operations with Three Circle Venn Diagrams, Using Regions, DeMorgan's Laws
Sec. 3.4 – Writing Sets Using Inequalities, Subsets
A 3.3: Solving Inequalities
A 3.4 Complex Fractions; Solving Equations with Fractions
Sec. 3.5 – Continuing with Subsets; Euler Diagrams: “All”, “Some” and “None”
Sec. 3.6 – Euler Diagrams and Logical Arguments
A 3.5: Complex Numbers
A 3.6: The Pythagorean Theorem
Sec. 3.7 – The Contrapositive, Combining Argument Types
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College Mathematics for Elementary Education with Algebra Extensions Copyright © by Kathleen Offenholley and Fatima Prioleau. All Rights Reserved.