# Ch 7: NES Math: Reasoning

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### About This Chapter

## NES Math: Reasoning - Chapter Summary

This chapter's lessons offer an opportunity to review reasoning in mathematics and rediscover how it can be used to solve problems. Use our videos and quizzes to prepare for NES Math test questions on topics that include:

- Inductive, deductive and connective reasoning
- Math principles for problem solving
- The guess, check and revise method of problem solving
- Estimation
- How to solve problems using mathematical models

You can watch these video lessons as your schedule allows using a computer, smartphone or tablet. They are short, averaging about five minutes each, and filled with examples and animations that can make your review for the NES Math test enjoyable. You can take short quizzes and a chapter exam to evaluate your learning, and there's a sheet of quiz questions you can print and use for offline study. A text transcript of each lesson is available, with important concepts and terms highlighted.

### NES Math: Reasoning Objectives

Five states use the NES Math test as one of the conditions for licensing to teach mathematics at the secondary school level. The test contains five content domains, and questions on reasoning are in the Mathematical Processes and Number Sense content domain. This makes up 19% of the test's total score.

All questions on the NES Math test are multiple-choice, like the questions in our lesson quizzes and the chapter exam. Our tests let you get a feel for what you'll encounter on the NES test, and they also let you assess your learning. The answer keys contain links back to the lessons, so if you answer a question incorrectly, it's easy to jump back to the right spot and review that information.

### 1. 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.

### 2. 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.

### 3. 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.

### 4. 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.

### 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. Using Mathematical Models to Solve Problems

Mathematical modelling 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.

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### Other Chapters

Other chapters within the NES Mathematics (304): Practice & Study Guide course

- NES Math: Properties of Real Numbers
- NES Math: Fractions
- NES Math: Decimals & Percents
- NES Math: Ratios & Proportions
- NES Math: Units of Measure & Conversions
- NES Math: Logic
- NES Math: Vector Operations
- NES Math: Matrix Operations & Determinants
- NES Math: Exponents & Exponential Expressions
- NES Math: Algebraic Expressions
- NES Math: Linear Equations
- NES Math: Inequalities
- NES Math: Absolute Value
- NES Math: Quadratic Equations
- NES Math: Polynomials
- NES Math: Rational Expressions
- NES Math: Radical Expressions
- NES Math: Systems of Equations
- NES Math: Complex Numbers
- NES Math: Functions
- NES Math: Piecewise Functions
- NES Math: Exponential & Logarithmic Functions
- NES Math: Continuity of Functions
- NES Math: Limits
- NES Math: Rate of Change
- NES Math: Derivative Rules
- NES Math: Graphing Derivatives
- NES Math: Applications of Derivatives
- NES Math: Area Under the Curve & Integrals
- NES Math: Integration Techniques
- NES Math: Applications of Integration
- NES Math: Foundations of Geometry
- NES Math: Geometric Figures
- NES Math: Properties of Triangles
- NES Math: Triangle Theorems & Proofs
- NES Math: Parallel Lines & Polygons
- NES Math: Quadrilaterals
- NES Math: Circles & Arc of a Circle
- NES Math: Conic Sections
- NES Math: Geometric Solids
- NES Math: Analytical Geometry
- NES Math: Trigonometric Functions
- NES Math: Trigonometric Graphs
- NES Math: Solving Trigonometric Equations
- NES Math: Trigonometric Identities
- NES Math: Sequences & Series
- NES Math: Graph Theory
- NES Math: Set Theory
- NES Math: Statistics Overview
- NES Math: Summarizing Data
- NES Math: Tables, Plots & Graphs
- NES Math: Probability
- NES Math: Discrete Probability Distributions
- NES Math: Continuous Probability Distributions
- NES Math: Sampling
- NES Math: Regression & Correlation