Ch 1: Mathematical Reasoning & Problem-Solving

About This Chapter

Watch mathematical reasoning and problem-solving video lessons to learn about logical fallacies, inductive and deductive reasoning, conditional statements and more. Each lesson is accompanied by a short multiple-choice quiz you can use to check your understanding of these math topics.

Mathematical Reasoning and Problem-Solving - Chapter Summary and Learning Objectives

A lot of people have a hard time seeing the practical applications of math to everyday situations, but this chapter aims to help you understand just that. You'll learn how to use mathematical concepts to make arguments and solve problems. This chapter can help you understand the following:

  • Logical fallacies
  • Conditional propositions
  • Logical equivalence
  • Inductive and deductive reasoning
  • Using estimation to solve problems
  • Using mathematical models to solve problems

Video Objective
Critical Thinking and Logic in Mathematics Learn to make logical arguments, premises and conclusions
Logical Fallacies: Hasty Generalization, Circular Reasoning, False Cause and Limited Choice Look at the logical fallacies of limited choice, hasty generalization, false cause and circular reasoning
Logical Fallacies: Appeals to Ignorance, Emotion or Popularity Look at the logical fallacies of appeal to emotion, appeal to ignorance and appeal to popularity
Propositions, Truth Values and Truth Tables Use truth tables to determine truth values and negations
Logical Math Connectors: Conjunctions and Disjunctions Recognize conjunctions and disjunctions
Conditional Statements in Math Use conditional statements to make hypotheses and propositions
Logical Equivalence: Converse, Inverse, Contrapositive and Counterexample Recognize when statements are logically equivalent
Reasoning in Mathematics: Inductive and Deductive Reasoning Describe how inductive and deductive reasoning apply to mathematical reasoning and problem solving
Reasoning in Mathematics: Connective Reasoning Look at the concepts of connective reasoning, compound statements and simple statements
Polya's Four-Step Problem-Solving Process Learn to solve problems using Polya's problem-solving method
Mathematical Principles for Problem Solving Learn to give examples of the five principles of mathematical problem solving
The Three-Way Principle of Mathematics Make analogies, draw graphs or diagrams and make examples to illustrate situations
Solving Mathematical Problems Using Estimation Use estimation to solve mathematical problems
Using Mathematical Models to Solve Problems Formulate mathematical models and solve complex problems using problem-solving techniques

14 Lessons in Chapter 1: Mathematical Reasoning & Problem-Solving
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.

Logical Fallacies: Hasty Generalization, Circular Reasoning, False Cause & Limited Choice

2. Logical Fallacies: Hasty Generalization, Circular Reasoning, False Cause & Limited Choice

Watch this video lesson to see how you can identify cases where logic is not sound. Learn the characteristic traits of hasty generalization, circular reasoning, false cause, and limited choice.

Logical Fallacies: Appeals to Ignorance, Emotion or Popularity

3. Logical Fallacies: Appeals to Ignorance, Emotion or Popularity

Watch this video lesson to see examples of the logical fallacies of appeals to ignorance, emotion, and popularity. You will also see how to identify them.

Propositions, Truth Values and Truth Tables

4. 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.

Logical Math Connectors: Conjunctions and Disjunctions

5. Logical Math Connectors: Conjunctions and Disjunctions

Watch this video lesson to learn how to identify conjunctions and disjunctions. Also learn the connectors that are used with each. Learn how you can use them to make statements.

Conditional Statements in Math

6. 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

7. 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

8. 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

9. 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

10. 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

11. 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

12. 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

13. 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

14. 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.

Chapter Practice Exam
Test your knowledge of this chapter with a 30 question practice chapter exam.
Not Taken
Practice Final Exam
Test your knowledge of the entire course with a 50 question practice final exam.
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