# Ch 2: Introduction to Mathematical Problem Solving

### About This Chapter

## Introduction to Mathematical Problem Solving - Chapter Summary

This chapter explains strategies used for problem-solving in mathematics such as estimation; models; and the guess, check, and revise method. Brief video lessons enable you to quickly brush up on problem-solving with ratios, decimals, and percents. By the end of this chapter, you will be proficient with the following:

- Apply various methods for problem-solving
- Explain how to use operations with integers
- Define ratio and rates, proportions, and the average rate of change
- Perform calculations with fractions and mixed numbers

Our experienced educators can help to simplify and increase your knowledge of problem-solving. You will have access to help from our subject matter experts should you need clarification on any topic. The Dashboard is an excellent tool to help with tracking your progress through the chapter.

### 1. Mathematical Principles for Problem Solving

Solving problems is not just a simple, straightforward process. There are a few principles that can help you as you approach any problem solving scenarios. This lesson covers those principles with examples.

### 2. Solving Problems With the Guess, Check & Revise Method

In this lesson, we will look at how to solve problems using the guess, check, and revise method in mathematics. Through examples, we will look at each step involved and see exactly how this process works.

### 3. Solving Mathematical Problems Using Estimation

Estimating is a method of calculating a result that is close to, but not exactly, the correct answer to a math problem. Why would you ever need to do this? This lesson reviews estimating and answers the question as to why you would do it.

### 4. Using Mathematical Models to Solve Problems

Mathematical modeling simply refers to the creation of mathematical formulas to represent a real world problem in mathematical terms. This lesson reviews the creation and pitfalls of mathematical models.

### 5. Operations with Integers: Add, Subtract, Multiply & Divide

Read this lesson to learn about the four basic arithmetic operations you can perform with integers. You'll also learn how you can visualize these operations in your head.

### 6. Solving Problems using Fractions and Mixed Numbers

Fractions don't just live in math problems. They're all around us, helping us through our lives. In this lesson, we'll look at real scenarios where your ability to work with fractions can save the day.

### 7. Solving Problems Using Decimal Numbers

Problems involving decimal numbers might sound like a way to torture you, but learning how important these types of problems are in the real world is important. In this lesson, you will see a couple areas in life where you routinely encounter decimal number problems.

### 8. Solve Problems Using Percents

Percents are your friend. Think of all the cool things percents do for you. They save you money, and they tell you how well you are doing in school. Learn how you can solve problems with percents in this video lesson.

### 9. Ratios & Rates: Definitions & Examples

If we have two items, or two numbers, and we want to compare them, what language can we use? How do we write the comparison? Find out as we learn about ratios and rates in this lesson.

### 10. Proportion: Definition, Application & Examples

When we want to compare one ratio, or fraction, to another equivalent ratio, it's a proportion. Learn all about proportions and practice solving proportion problems in this lesson.

### 11. Calculations with Ratios and Proportions

Even if only 99 out of 100 people need to know how to work with ratios, the odds that they'll be useful to you are very high. In this lesson, we'll practice performing calculations with ratios and proportions.

### 12. Average Rate of Change: Definition, Formula & Examples

Average rate of change and slope of a line are very interconnected. They are actually one in the same. In this lesson, we will be discovering how they are interconnected.

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### Other Chapters

Other chapters within the NES Mathematics Middle Grades & Early Secondary (105): Practice & Study Guide course

- Overview of Mathematical Reasoning
- NES Math: Properties of Real Numbers
- Understanding Relations & Functions
- Overview of Linear Functions & Equations
- Quadratic Equations, Functions & Inequalities
- Overview of Polynomial Equations, Functions & Inequalities
- Working with Absolute Values
- Overview of Rational & Radical Functions
- NES Math: Piecewise Functions
- NES Math: Exponential & Logarithmic Functions
- Scientific Measurement Principles & Calculations
- NES Math: Foundations of Geometry
- NES Math: Geometric Figures
- Triangle Properties & Proofs
- NES Math: Parallel Lines & Polygons
- NES Math: Circles & Arc of a Circle
- NES Math: Conic Sections
- NES Math: Geometric Solids
- NES Math: Analytical Geometry
- Statistics: Principles & Techniques
- Probability: Principles & Techniques
- Overview of Discrete Mathematics
- Performing Operations on Matrices & Vectors
- Solving Problems with Sequences & Series
- NES Mathematics Middle Grades & Early Secondary Flashcards