Ch 44: Problem Solving & Mathematical Reasoning

About This Chapter

Acquire important information about problem solving and mathematical reasoning through the lessons in this chapter. We have put together this study guide to help you better understand topics including conditional statements, logic and principles of problem solving through resources such as self-assessment quizzes and videos.

Problem Solving & Mathematical Reasoning - Chapter Summary

You can discover new strategies or review ones you already know about how to solve mathematical problems by taking a look at the lessons in this chapter. When you are done, you will be more familiar with the following topics:

  • Using the language of logic
  • Analyzing truth tables
  • How statements and math differ from the real world
  • Difference between converse, inverse, contrapositive and counterexamples
  • Deductive reasoning vs. inductive reasoning
  • Five major logic connectives
  • Method for solving problems
  • Examples of how to use principles for problem solving
  • How to use verbal, graphical and example methods to understand math problems
  • How to use estimation techniques
  • Using formulas for math problems

You have the convenience and flexibility to study how you want. All of the resources in this chapter, such as the video lessons, timeline feature, lesson quizzes and chapter test, are mobile-friendly. Whether you like studying on your home computer or on-the-go on your tablet or phone, you have choices.

11 Lessons in Chapter 44: Problem Solving & Mathematical Reasoning
Test your knowledge with a 30-question chapter practice test
Critical Thinking and Logic in Mathematics

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.

Propositions, Truth Values and Truth Tables

2. Propositions, Truth Values and Truth Tables

Watch this video lesson and learn what truth values are and what a truth table looks like. Learn how to go from a proposition to its negation and how that affects the truth values and the truth tables.

Conditional Statements in Math

3. Conditional Statements in Math

Sometimes, what is true in the mathematical world of logic is false in the real world. Check out this lesson to learn how to identify conditional statements and how you can differentiate between what is logically true and what is true in reality.

Logic Laws: Converse, Inverse, Contrapositive & Counterexample

4. Logic Laws: Converse, Inverse, Contrapositive & Counterexample

Logical statements can be useful, but only if we are able to determine their validity. In this lesson, we'll look at the various forms of a logical statement and see how they relate to each other.

Reasoning in Mathematics: Inductive and Deductive Reasoning

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.

Reasoning in Mathematics: Connective 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.

Polya's Four-Step Problem-Solving Process

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.

Mathematical Principles for Problem Solving

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.

The Three-Way Principle of Mathematics

9. 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.

Solving Mathematical Problems Using Estimation

10. 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.

Using Mathematical Models to Solve Problems

11. 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.

Chapter Practice Exam
Test your knowledge of this chapter with a 30 question practice chapter exam.
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Practice Final Exam
Test your knowledge of the entire course with a 50 question practice final exam.
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