Problem Solving

1. Introduction to Problem Solving

1.1. draw sketches and diagrams.

1.2. trial-and-error procedures.

1.3. list some or all of the possibilities

1.4. use a model to aid in visualizing the problem.

1.5. work backward.

2. Problem Solving with Algebra

2.1. Properties of Equality

2.1.1. Addition or Subtraction Property of Equality

2.1.2. Multiplication or Division Property of Equality

2.1.3. Simplification

2.2. Properties of Inequality

2.2.1. Addition or Subtraction Property of Inequality

2.2.2. Multiplication or Division Property of Inequality

2.2.3. Simplification

3. Patterns and Problem Solving

3.1. Compare and Contrast

3.2. Fibonacci numbers

3.3. Pascal's Triangle-triangular pattern of numbers.

3.4. Arithmetic Sequence

3.5. Geometric Sequence

3.6. Triangular Numbers

4. Sets, Functions, and Reasoning

4.1. Sets and Venn Diagrams

4.1.1. Sets And Their Elements

4.1.2. Attribute Pieces

4.1.3. Relationships Between Sets

4.1.4. Intersection of Sets

4.1.5. Union of Sets

4.1.6. Complement of a Set

4.2. Functions, Coordinates, and Graphs

4.2.1. Function

4.2.2. Rectangular Coordinates

4.2.3. Linear Functions and Slope

4.2.4. Deductive Reasoning