About This Chapter
Patterns & Relationships in Algebra - Chapter Summary
In this chapter on patterns and relationships in algebra, engaging lessons cover subjects like commutative properties of algebraic expressions and how to evaluate variable expressions. There is also an opportunity for you to practice simplifying algebraic expressions. After completing the chapter, you should be poised to do the following:
- Evaluate algebraic expressions
- Discuss variables in algebra
- Explain associative properties of algebraic expressions
- Describe the distributive property and algebraic expressions
- Combine like terms to simplify algebraic expressions
- Write variable expressions for arithmetic sequences
- Recognize patterns in math
Each video is accompanied by a full written transcript, which can be used for a text-based learning option. If you get stuck on a topic, you can use the Help feature to submit questions to instructors. You can confirm your understanding of the concepts covered by taking a short quiz, which is available for each lesson.
1. Evaluating Simple Algebraic Expressions
In this lesson, we'll learn how to evaluate algebraic expressions, which involves substituting numbers for variables and following the order of operations. By the end of the lesson, you'll be an algebraic expression expert.
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.
3. 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.
4. 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.
5. Combining Like Terms in Algebraic Expressions
When you have an algebraic expression that's much too long, it would be great if you could simplify it. That's when knowing how to combine like terms comes in. In this lesson, we'll learn the process of combining like terms and practice simplifying expressions.
6. 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.
7. How to Evaluate & Write Variable Expressions for Arithmetic Sequences
Being able to figure out sequences as well as describe them are some of the most important skills in math. In this lesson, we learn how to evaluate and write arithmetic sequences and geometric sequences.
8. Recognizing & Generalizing Patterns in Math
Being able to recognize patterns is one of the most important aspects of studying math, and one that has definite advantages in other fields of study. In this lesson, we'll look at how to recognize the most common patterns in math: sequences.
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