Teaching Middle-School Math: Combining "Like Terms"

Students often need to combine "like terms" when solving math equations. A middle-school student generally faces her first encounter with combining like terms in sixth or seventh grade math class. Having a basic understanding of like terms will aid students when they transition to higher-level algebra problems. As a seventh-grade math teacher, I found the following ideas and websites beneficial when helping students understand the concept of combining like terms.

Prerequisite
Students should know how to perform arithmetic operations with positive and negative numbers (click on these links for tips on adding, subtracting, and multiplying/dividing integers.) If you decide to teach younger students-who haven't yet worked with integers-to combine like terms, keep all the signs positive.

Terminology
Students should understand the following:
constant: has a fixed value that doesn't change. In 5 + x, 5 is a constant. (In other words, it's the number part of the term.)

variable: a symbol-usually a letter-that represents a number or value. It can "vary" or change. In 8x, x is a variable. (In other words, it's the letter part of the term.)

coefficient: the numerical factor that is next to the variable. In 8x, 8 is a coefficient. (In other words, coefficients are the numbers hooked onto the letters.)

What are Like Terms?
Like terms have the same variables raised to the same power.

Examples of Like Terms
8 and 9 are like terms. Neither has a variable.
2x and 6x are like terms. They both have the same variable, x.
8y² and 19y² are like terms. They both have the same variable, y².
29m and -m are like terms. They both have the same variable, m.

Examples of Terms that Are Not Like Terms
8m and 7y are not like terms. Their variables are different, m and y.
4x²and 5x are not like terms. Their variables are different, x² and x.

Danica McKellar's Tip in Her Book, Kiss My Math
Danica advises students to use their love of doodling when combining like terms. For example, put squiggly lines under all the x's, put 2 straight lines under all the y's, and so on. If students use this method to first identify like terms before trying to combine them, they'll be less apt to leave out terms.

Alerts
Students often confuse the following, so it's good to emphasize these points.

The coefficients, 1 and -1 are generally omitted. Tell students to write them in until they get used to combining terms. For example, y is really 1y.

Bring attention to the fact that terms such as x²y and xy² are not like terms.
x² and x are not raised to the same power; y and y² are not raised to the same power.

xy² and y²x are like terms. The variables are still the same in both terms, x and y², no matter what their order (associative property.)

You Tube Video
In this video, "Combining Like Terms," you'll meet Professor Perez and his rather uninterested student, Charlie. It's a good transition tool to use after students have been introduced to basics, and before they try to combine like terms on their own. The video lasts about 7 and ½ minutes. It starts out simply and increases in difficulty. Preview it, of course, to decide how much of the video would be appropriate for your age group.

Online Flashcard Practice
Next, use Study Stack's online flashcard practice, as the entire class tries to combine terms. Students can discuss with their partners, as you present the expressions from this online program to the whole group. Work on one expression at a time. "Flip" the cards to see the solutions; choose students to explain them.

Online Practice
If you have access to computers, your students can work through The Math Page's online lesson, "Adding Like Terms." This easy format has students practicing such skills as identifying coefficients, removing parentheses, and combining like terms. Immediate feedback is provided. This might also be good for those needing extra practice.

Printable Practice Worksheets
Of course, at some point, we need to put pencil to paper. Kuta Software provides a free, printable worksheet on combining like terms. This can be used for practice or as a quiz. The problems are appropriate for the middle-school level. Students are asked to simplify 30 expressions. An answer key is provided.

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