How To Add and Subtract- And How We Got This Far

1. Numeration Systems

1.1. Tally

1.2. Roman Numeration

1.3. Hindu-Arabic

1.3.1. History

1.3.2. Place Value

1.3.3. Face Value

1.3.4. Digits

1.4. Other Base Systems

1.4.1. Bianary

1.4.2. Quinary

2. Patterns

2.1. Inductive Reasoning

2.1.1. Conjecture

2.1.2. Counterexample

2.2. Arithmetic Sequence

2.3. Geometric Sequence

2.4. Figurate Numbers

2.4.1. Triangular Numbers

2.4.2. Square Numbers

3. Addition of Whole Numbers

3.1. Set Model

3.2. Number Line Model

4. Subtraction of Whole Numbers

4.1. Comparison Model

4.2. Take away Model

4.3. Missing-Addend Model

4.4. Number Line Model

5. Addition Properties

5.1. Identity

5.2. Associative

5.3. Commutative

5.4. Closure

6. Algorithms

6.1. Equal-Additions Algorthm

6.2. Addition Algorithms

6.2.1. Left to Right

6.2.2. Lattice

6.2.3. Scratch