Ch 2: FTCE Middle Grades Math: Mathematical Reasoning

About This Chapter

If you're struggling to prepare for the FTCE Middle Grades Math exam, our informative chapter on mathematical reasoning can help. Our easy-to-follow video and text lessons highlight all the topics you'll find on the exam to help you get ready for exam day.

FTCE Middle Grades Math: Mathematical Reasoning - Chapter Summary

This engaging chapter contains brief lessons that can help you prepare for the mathematical reasoning questions you'll find on the FTCE Middle Grades Math exam. Lesson topics include logic and critical thinking as they're used in mathematics, plus truth values, truth tables and propositions. You'll also learn about disjunctions and conjunctions, plus conditional statements in math. After you complete this chapter, you should be ready to:

  • Explain logic laws for the inverse, counterexample, contrapositive and converse of a logical statement
  • Differentiate between inductive and deductive reasoning
  • Define connective reasoning
  • Describe some of the applications for direct proofs
  • Give an example of an indirect geometric proof

It's easy to study any time you'd like on any computer, tablet or mobile device with our convenient and flexible learning tools. For video lessons, you can watch an entire video, or directly skip to the topic you'd like to study by using the timeline tabs feature. Our multiple-choice lesson quizzes and chapter test make great prep tools before taking an exam. If you need help as you work through the lessons, you can reach out to an instructor for assistance.

9 Lessons in Chapter 2: FTCE Middle Grades Math: 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.

Logical Math Connectors: Conjunctions and Disjunctions

3. 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

4. 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

5. 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

6. 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

7. 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.

Direct Proofs: Definition and Applications

8. Direct Proofs: Definition and Applications

In math, we can't explain that something is true just because. That's not enough. In this lesson, we'll learn to prove things using one of our most straightforward tools, the direct proof.

Indirect Proof in Geometry: Definition & Examples

9. Indirect Proof in Geometry: Definition & Examples

There are many different methods that can be used to prove a given theory. One of those methods is indirect proof. In this lesson, we will explore indirect proof and learn the steps taken to use this method to prove a given theory.

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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Other Chapters

Other chapters within the FTCE Middle Grades Mathematics 5-9 (025): Practice & Study Guide course

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