Math Foundations

Introduction

1 Integer Arithmetic Foundations
      Launch Exploration: Grouping and Regrouping
1.1 Understanding Counting Numbers
      1.1.1 Numeration
      1.1.2 Rounding
      1.1.3 Number Comparison
      1.1.4 The Number Line
               Exercises
1.2 The First-Order Operations
      1.2.1 Addition
      1.2.2 Subtraction
      1.2.3 The Integers
      1.2.4 Operations with Integers
               Exercises
1.3 The Second-Order Operations
      1.3.1 Multiplication
      1.3.2 Division
      1.3.3 Operations with Integers
      1.3.4 Properties of Operations
      1.3.5 Order of Operations
      1.3.6 Numerical Expressions: Translations
               Exercises
1.4 Structure and Properties of Integers
      1.4.1 Divisors and Multiples
      1.4.2 Prime Numbers
      1.4.3 Divisibility Criteria
      1.4.4 Division with Remainder
      1.4.5 Mental Math
               Exercises

2 Rational Number Arithmetic
      Launch Exploration: Part of a Whole
2.1 Introduction to Fractions
      2.1.1 The Fractional Unit and Mixed Numbers
      2.1.2 The Area Model and Equivalent Fractions
      2.1.3 Number Line Representations
      2.1.4 Comparing Ordinary Fractions
               Exercises
2.2 Fraction Operations
      2.2.1 Adding and Subtracting Fractions
      2.2.2 Multiplying and Dividing Fractions
      2.2.3 Properties and Order of Operations 
              Exercises
2.3 Working with Decimal Fractions
      2.3.1 Comparing and Rounding Decimal Fractions
      2.3.2 Operations with Decimal Fractions
               Exercises
2.4 Proportional Reasoning and Percent
      2.4.1 Ratios and Proportions
      2.4.2 Derived Proportions 
      2.4.3 Direct and Inverse Proportionality
      2.4.4 Percent Representations
      2.4.5 Solving Percent Problems
               Exercises

3 Algebra Foundations
     Launch Exploration: Mystery Number Games
3.1 Higher-Order Operations
      3.1.1 Exponents
      3.1.2 Radicals 
      3.1.3 Real and Imaginary Numbers
      3.1.4 Logarithms
      3.1.5 Order of Operations
               Exercises
3.2 Building Blocks of Algebra
      3.2.1 A Primer on the Language of Sets
      3.2.2 Properties of Real Numbers
      3.2.3 Introduction to Algebraic Expressions
               Exercises 
3.3 Algabraic Equations
      3.3.1 Introduction to Algebraic Equations
      3.3.2 Linear and Power Equations
      3.3.3 The Mapping Diagram
      3.3.4 Problem Solving with Linear Equations
               Exercises

4 Geometry Foundations
      Launch Exploration: Construct a Square from Two Squares
4.1 Fundamentals of Angles and Triangles
      4.1.1 Primitive Notions
      4.1.2 Angles and Circles
      4.1.3 Parallel Lines
      4.1.4 Triangles
               Exercises
4.2 Area and Perimeter of 2D Shapes
      4.2.1 Rectangles and Parallelograms
      4.2.2 Perimeter versus Area
               Exercises
4.3 Exploring Volume in 3D Geometry
      4.3.1 Shapes Generated by Translation
      4.3.2 Volumes of Prisms and Cylinders
               Exercises

5 Teaching Notes
5.1 Units, Numeration, and the Foundations of Arithmetic
5.2 Understanding Fractions, Decimals, and Percentages
5.3 Integrating Geometry and Arithmetic: Key Concepts
5.4 Using Algebra to Simplify Arithmetic and Geometry
5.5 Assessment Based on Learning Objectives

Index