# Ch 1: Mathematical Reasoning & Problem-Solving

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
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.
Not Taken

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