# Ch 9: MTLE Mathematics: Mathematical Reasoning & Problem Solving

### About This Chapter

## MTLE Mathematics: Mathematical Reasoning & Problem Solving - Chapter Summary

Use these lessons to pick up effective strategies for solving the types of questions that you might find on the MTLE Mathematic exam and boosting your mathematical reasoning and problem-solving skills. You'll take a look at the use of mental math and the role critical thinking plays in mathematics, among other topics. When you complete this chapter, you should understand how to do the following:

- Outline logic and critical thinking in math
- Define estimation in math and explain how it's used
- Solve one-step problems using mental math
- Differentiate between inductive and deductive reasoning
- Explain connective reasoning
- Detail Polya's four-step problem-solving process
- Identify mathematical principles for problem solving

Getting familiar with different types of reasoning and problem solving tactics is easy thanks to this chapter. The lessons help you outline these concepts in an easy-to-follow manner. You also have access to brief quizzes that can help you quickly assess your mathematical reasoning knowledge and skills.

### 1. Critical Thinking and Logic in Mathematics

Logic has its own unique language and way of defining what is true and false. Watch this video lesson to learn how you can critically think in the language of logic while working with math.

### 2. How to Estimate in Math: Definition & Concept

Learn how to use estimate values in this lesson. It can help you answer math problems that use more complicated numbers and even make it easier to split a check at the restaurant next time you are out with friends!

### 3. Using Mental Math to Solve One-Step Problems

After reading this lesson, you'll know how you can solve one-step math problems without having to write anything down. Learn the technique you can use to help you solve the problem in your head.

### 4. Using Mental Math to Solve Two-Step Problems

For this lesson you will learn how to solve two step word problems using addition and subtraction. We will explore ways to solve simple problems by identifying key information in the word problem.

### 5. Reasoning in Mathematics: Inductive and Deductive Reasoning

Many people think that deductive and inductive reasoning are the same thing. It is assumed these words are synonymous. They are not. This lesson reveals the reality of these two types of reasoning.

### 6. Reasoning in Mathematics: Connective Reasoning

Connective reasoning is reasoning that has an operation, or a way to connect two phrases. The five main logic connectives will be reviewed in this lesson.

### 7. 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.

### 8. 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.

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### Other Chapters

Other chapters within the MTLE Mathematics: Practice & Study Guide course

- MTLE Mathematics: Basic Arithmetic Operations
- MTLE Mathematics: Properties of Real Numbers
- MTLE Mathematics: Operations with Real Numbers
- MTLE Mathematics: Fractions
- MTLE Mathematics: Decimals
- MTLE Mathematics: Percents
- MTLE Mathematics: Ratios, Rates & Proportions
- MTLE Mathematics: Exponents & Exponential Expressions
- MTLE Mathematics: Complex Numbers
- MTLE Mathematics: Sequences & Series
- MTLE Mathematics: Functions
- MTLE Mathematics: Algebraic Expressions & Equations
- MTLE Mathematics: Exponential & Logarithmic Functions
- MTLE Mathematics: Vector Operations
- MTLE Mathematics: Matrices in Linear Algebra
- MTLE Mathematics: Linear Functions
- MTLE Mathematics: Linear Inequalities
- MTLE Mathematics: Quadratic Functions
- MTLE Mathematics: Polynomial Functions
- MTLE Mathematics: Rational Expressions
- MTLE Mathematics: Radical Expressions
- MTLE Mathematics: Absolute Value Functions
- MTLE Mathematics: Continuity & Limits
- MTLE Mathematics: Rate of Change & Derivatives
- MTLE Mathematics: Area Under the Curve & Integrals
- MTLE Mathematics: Trigonometric Functions
- MTLE Mathematics: Solving Trigonometric Equations
- MTLE Mathematics: Trigonometric Identities
- MTLE Mathematics: Principles of Measurement
- MTLE Mathematics: Area & Perimeter
- MTLE Mathematics: Surface Area & Volume
- MTLE Mathematics: Foundations of Geometry
- MTLE Mathematics: Lines & Angles
- MTLE Mathematics: Properties of Triangles
- MTLE Mathematics: Similar & Congruent Triangle Proofs
- MTLE Mathematics: Right Triangle Proofs
- MTLE Mathematics: Quadrilaterals & Polygons
- MTLE Mathematics: Circles & Arc of a Circle
- MTLE Mathematics: Coordinate Geometry
- MTLE Mathematics: Geometric Transformations
- MTLE Mathematics: Parametric, Polar & Vector Functions
- MTLE Mathematics: Organizing Data
- MTLE Mathematics: Summarizing & Analyzing Data
- MTLE Mathematics: Random Sampling
- MTLE Mathematics: Probability
- MTLE Mathematics: Probability Distributions
- MTLE Mathematics: Discrete Mathematics
- MTLE Mathematics: Mathematical Connections & Communication
- MTLE Mathematics: From Words to Equations, Expressions & Graphs
- MTLE Mathematics: Content Area Reading Skills
- MTLE Mathematics: Instructional Design & Delivery
- MTLE Mathematics: Teaching & Assessing Diverse Learners
- MTLE Mathematics Flashcards