# Ch 3: FTCE Middle Grades Math: Problem-Solving Strategies

### About This Chapter

## FTCE Middle Grades Math: Problem-Solving Strategies - Chapter Summary

In this fun chapter, you'll review the problem-solving strategies needed to answer questions on the FTCE Middle Grades Math test. Our lessons cover Polya's four-step problem-solving process, plus the mathematical principles you need to know to successfully solve problems. You'll go over several different types of math problems and the different problem-solving strategies needed to answer them. Once you complete this chapter, you should be able to:

- Use tables, graphs and mathematical models to solve problems
- Detail the three-way principle of mathematics
- Use estimations to solve math problems
- Solve one- and two-operation problems using guess and check
- Use mental math to add, subtract, multiply and solve equations
- Answer visualizing geometry problems
- Work backwards to solve word problems

The video and text lessons in this chapter are professionally designed, mobile friendly and accessible 24 hours a day for convenient study. You can review the entire chapter as a great test prep exercise or study only the lessons that correspond with the topics you need to know. Skip ahead or jump back to specific section in a video lesson using the video tabs feature. Our instructors are available to offer their assistance if you need it.

### 1. Polya's Four-Step Problem-Solving Process

Problem solving can be a problem. Any problem is solved easier with an action plan. Polya's 4-Step Problem-Solving Process is discussed in this lesson to help students develop an action plan for addressing problems.

### 2. 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.

### 3. The Three-Way Principle of Mathematics

What methods are there to solve and understand mathematical problems? This lesson will review three methods to understand mathematical problems (verbal, graphical, and by example). Each will be illustrated with examples.

### 4. Types of Problems & Problem Solving Strategies

We solve hundreds of small problems everyday. This lesson covers different types of problems, such as routine vs. non-routine, and many of the different problem-solving strategies we use, including algorithms, heuristics, graphic representations and the IDEAL Strategy.

### 5. 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.

### 6. Guess and Check: One & Two Operation Problems with Positive Decimals

In this video lesson, you will learn how to use your guessing skills in finding the correct answer to a decimal problem. Learn how you can refine your guess to make an even better guess and get closer to finding your answer.

### 7. 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.

### 8. Mental Math: Addition and Subtraction

After watching this video lesson, you will get better at adding and subtracting numbers in your head without a calculator. Learn how breaking apart your addition and subtraction problems makes them easier and quicker to solve in your head.

### 9. Using Mental Math for Multiplication

Do you want to impress your friends and family with your amazing brain? You can when you learn a really easy way to multiply single digits by multiples of 10 and 100 in this lesson.

### 10. How to Use Mental Math to Solve Equations

You may be used to solving arithmetic problems, like addition or subtraction, in your head. In this lesson, we are going to take that mental math a step further and look at how to use mental math to solve equations.

### 11. How to Solve Visualizing Geometry Problems

A picture is worth a thousand words, but sometimes drawing that picture can be like doing origami with your eyes closed. Practice translating complex problems into simple, meaningful images in this lesson.

### 12. Working Backwards to Solve Word Problems

There are many ways to go about solving word problems in mathematics. This lesson will illustrate a particular solving process called working backwards. We'll see how and when to use this process to solve word problems.

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### Other Chapters

Other chapters within the FTCE Middle Grades Mathematics 5-9 (025): Practice & Study Guide course

- About the FTCE Middle Grades Mathematics Test
- FTCE Middle Grades Math: Mathematical Reasoning
- FTCE Middle Grades Math: The Real Number System
- FTCE Middle Grades Math: Fractions, Decimals & Percents
- FTCE Middle Grades Math: Ratios & Proportions
- FTCE Middle Grades Math: Factoring
- FTCE Middle Grades Math: Solving Word Problems
- FTCE Middle Grades Math: Exponents & Exponential Expressions
- FTCE Middle Grades Math: Basic Algebraic Expressions
- FTCE Middle Grades Math: Distributing in Algebra
- FTCE Middle Grades Math: Rational Expressions
- FTCE Middle Grades Math: Square Roots
- FTCE Middle Grades Math: Radical Expressions
- FTCE Middle Grades Math: Linear Equations
- FTCE Middle Grades Math: Systems of Linear Equations
- FTCE Middle Grades Math: Solving & Graphing Inequalities
- FTCE Middle Grades Math: Introduction to Functions
- FTCE Middle Grades Math: Graphing Functions
- FTCE Middle Grades Math: Quadratic Functions
- FTCE Middle Grades Math: Polynomial Functions
- FTCE Middle Grades Math: Summarizing Data
- FTCE Middle Grades Math: Charting Data
- FTCE Middle Grades Math: Sampling
- FTCE Middle Grades Math: Probability Distributions
- FTCE Middle Grades Math: Lines & Angles
- FTCE Middle Grades Math: Properties of Triangles
- FTCE Middle Grades Math: Similar & Congruent Triangle Proofs
- FTCE Middle Grades Math: Right Triangle Proofs
- FTCE Middle Grades Math: Quadrilaterals & Polygons
- FTCE Middle Grades Math: Area & Perimeter
- FTCE Middle Grades Math: Circles & Arc of a Circle
- FTCE Middle Grades Math: Coordinate Geometry
- FTCE Middle Grades Math: Transformations in Geometry
- FTCE Middle Grades Math: Principles of Measurement
- FTCE Middle Grades Math: Surface Area & Volume
- FTCE Middle Grades Math: Connecting Math Concepts
- FTCE Middle Grades Math: Instructional Strategies & Tools
- FTCE Middle Grades Math: Assessing Student Learning
- FTCE Middle Grades Mathematics 5-9 Flashcards