# Problem Solving

# Problem Solving

by Christina Bird
# 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. Patterns and Problem Solving

## 2.1. Compare and Contrast

## 2.2. Fibonacci numbers

## 2.3. Pascal's Triangle-triangular pattern of numbers.

## 2.4. Arithmetic Sequence

## 2.5. Geometric Sequence

## 2.6. Triangular Numbers

# 3. Problem Solving with Algebra

## 3.1. Properties of Equality

### 3.1.1. Addition or Subtraction Property of Equality

### 3.1.2. Multiplication or Division Property of Equality

### 3.1.3. Simplification

## 3.2. Properties of Inequality

### 3.2.1. Addition or Subtraction Property of Inequality

### 3.2.2. Multiplication or Division Property of Inequality

### 3.2.3. Simplification

# 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

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