Ch 5: Algebraic Reasoning: NBPTS Math - Adolescence & Young Adult

About This Chapter

Let us help you prepare for your upcoming National Board for Professional Teaching Standards (NBPTS) Math certification exam. These lessons, quizzes and other study aids are on algebraic reasoning.

Algebraic Reasoning: NBPTS Math - Adolescence & Young Adult - Chapter Summary

Our expert instructors developed the lessons in this chapter as a refresher for you before you take the NBPTS Math test. These lessons will aid you in answering test questions about algebraic reasoning with lesson material like:

  • Getting to know the nomenclature of algebra
  • Examining what a variable is in algebra
  • Getting to understand the concept of the algebraic rule
  • Getting familiar factoring
  • Seeing how to express relationships as algebraic expressions
  • Making algebraic expressions out of word problems
  • Using commutative and associative properties with algebraic expressions
  • Learning the distributive and inverse properties in algebra
  • Simplifying expressions in algebra

These lessons are brief, and each includes a multiple-choice quiz to check your understanding of the material. You can review the lessons as often as needed or use the timeline tool in the video lessons to go right to the section you want to replay. You can also ask a question of the instructor in both types of lessons.

11 Lessons in Chapter 5: Algebraic Reasoning: NBPTS Math - Adolescence & Young Adult
Test your knowledge with a 30-question chapter practice test
Algebra Vocabulary Terms

1. Algebra Vocabulary Terms

Watch this video lesson to learn about some basic vocabulary words that you will come across again and again in the course of your studies in algebra. After you finish this video, you should know and be able to identify each term.

What is a Variable in Algebra?

2. What is a Variable in Algebra?

Did you ever encounter something like a + b = c and wonder how all these letters snuck into a math problem? In this lesson, we'll learn about variables, as well as other parts of equations, constants and coefficients.

Algebraic Rule: Definition & Concept

3. Algebraic Rule: Definition & Concept

An algebraic rule is a method for describing the relationship between two variables. This lesson will give a definition of an algebraic rule, show some examples and give you the steps to create rules when given a set of data.

What is Factoring in Algebra? - Definition & Example

4. What is Factoring in Algebra? - Definition & Example

Factoring with ordinary numbers involves knowing that 6 is the product of 2 and 3. But what about factoring in algebra? In this lesson, we'll learn the essential elements of algebra factoring.

Expressing Relationships as Algebraic Expressions

5. Expressing Relationships as Algebraic Expressions

What do you do when you don't know what a number is but you do know how it relates to something else? You use an algebraic expression. In this lesson, we'll learn how to express relationships as algebraic expressions.

Translating Words to Algebraic Expressions

6. Translating Words to Algebraic Expressions

When it comes to word problems, the easiest way to solve them is to look for keywords and change them into math symbols. Watch this video lesson to find out what keywords you should look for and what math symbols they represent.

Restating Word Problems Using Words or Images

7. Restating Word Problems Using Words or Images

Watch this video lesson to learn how you can use sketches and notes to help you visualize a problem. Watch how easy it becomes to solve your problem once you have visualized it.

The Commutative and Associative Properties and Algebraic Expressions

8. The Commutative and Associative Properties and Algebraic Expressions

The order of operations is important and useful, but a few mathematical properties highlight cases where order doesn't matter. In this lesson, we'll learn about the commutative and associative properties, which may save you time and effort.

The Distributive Property and Algebraic Expressions

9. The Distributive Property and Algebraic Expressions

The order of operations is great. But sometimes we need to bend the rules to simplify an equation. Fortunately, the distributive property gives us a scenario in which this is okay. Learn all about it in this lesson.

Inverse Property: Definition & Examples

10. Inverse Property: Definition & Examples

In this lesson, you will learn the definition of inverse property as it applies to different types of numbers. You will also look at examples that show you how to find the additive inverse and multiplicative inverse of a number.

Practice Simplifying Algebraic Expressions

11. Practice Simplifying Algebraic Expressions

In this lesson, we'll practice simplifying a variety of algebraic expressions. We'll use two key concepts, combining like terms and the distributive property, to help us simplify.

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 National Board Certification Exam - Mathematics/Adolescence & Young Adulthood: Practice & Study Guide course

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