A Parent's Guide To Algebra's Basic Concepts - Algebra As a Language and Definition of Equation

In our discussion of algebraic properties so far, we have looked at the "Manipulation Properties" (my name for them)--the properties that allow us to change the Order of Operations when manipulating numbers or terms. Can you still name them? (Commutative, Associative, & Distributive Properties) In this article, we will be discussing Algebra as a language and defining "equation.

" First, we need to establish some terminology so that we are all thinking about and mentally picturing the same things at the same times as we move forward.
Remember that Algebra is a language, so it contains many of the same structures as the English language.

For example, in Algebra as in English, we have expressions or incomplete thoughts.

An example of an expression in English class might be "In my after school club we.

.." This is very much an incomplete thought--we did what? An Algebra expression might look like 3x - 4.
Again, an incomplete thought--3x - 4 is what? In English, we also have sentences or statements. Statements (sentences) express complete thoughts. They have verbs. (You have probably heard Dr.
Phil, on his TV program, say "after this break..
.
and I'm going to put verbs in my sentences.) Sentences must have verbs. In Algebra, we also have statements/sentences and they, too, have verbs.
Probably the most common math verb is = or is equal to.

Examples of other math verbs include: is not equal to, is greater than, is less than, is greater than or equal to, etc.

An algebraic sentence might look like 3x - 4 = 11 or 7y + 5 < 12.

In words, these would say "three times some number minus four is equal to eleven" and "seven times some number plus five is less than twelve." With this is mind, a definition: An equation is a statement that says two expressions are equal. Before we go any further, I want you to say that definition as many times as it takes to say it without looking.

Then say it 5 more times. Be sure you know the meaning of every word! Thus, 3x - 4 = 11 is an equation because it fits the definition; but 7y + 5 inequality since the symbol in the middle means "is less than." Now that we have defined "equation", we are almost ready to start solving equations. Solving equations is the MAIN CONCEPT of Algebra. Algebra students spend the entire course learning techniques for solving various types of equations; but for now, we just need to know what an equation IS. Can you still say the definition? If not, then go back and memorize it.

There is no point moving ahead until you understand this!