In this lesson, students will learn how to combine like terms. Students will review the integer rules, and then apply them to help simplify algebraic expressions with one or two variables by combining like terms. You can expect this lesson with additional practice to take one `45`-minute class period. This lesson builds on the understanding they have developed in `6`th grade.
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To begin the lesson, students should review operations with integers.
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Have students answer these problems independently and then check their work with a shoulder partner. If students disagree, they should work together to determine where the error was. As students work, circulate around the class to look for common errors that students might make, such as not recognizing that subtracting a negative becomes adding a positive.
When reviewing the answers with students, it will be essential that students can explain their reasoning. It may help to let students know that these skills will be needed later when combining like terms.
Because students should be familiar with like terms, ask them which terms can be combined based on the expression given.
Give students a moment to consider and discuss with a shoulder partner. Ideally, students will recognize that the terms with a variable can be combined, and the constants can be combined. As students provide the like terms, you should use different colors or shapes around terms that are like. For example, you may circle the variable terms in pink and box the constant terms in blue. Point out to students that they should keep the addition or subtraction sign with the term behind it.
Now students can try to simplify the expression. Students can do one of the following to organize the like terms:
I prefer the latter since it breaks up the expression in more manageable chunks. Notice that I did not color code the operations. We will talk about that choice in the next section.
As you discuss how students simplified the expression, talk about how you have to add the coefficients when there are variable like terms. Make sure to remind them of the definition of the word coefficient.
Now present a problem to the students that has subtraction in it. Ask them to combine them to identify the like terms and combine them.
There are two ways to teach students how to take care of subtraction while combining like terms.
Rewrite all the subtraction with Add the opposite. Some teachers call it Add the negative - largely that works; however if there is already a negative number after the subtraction `(4x - (-3) + 2x)`, then you cannot just say add the negative.
Here is how you would rewrite the expression above.
`-6x` `-7` `-2x` `+5`
Rewriting it like this makes students consciously aware of the subtraction operation. It allows them to move around the terms since there is only addition as operation.
Rewriting subtraction as adding the opposite lends itself well to doing integer operations. You can break up the expression into two expressions - you are allowed to do that since there is only addition.
In expressions like these, it is so tempting for students to add the `7` and `2` and then attach a subtraction sign.
When you rewrite the expression with addition, students are unlikely to make that mistake.
You can also ask students to box the terms in such a way that you include the sign along with the term that comes after it. It serves the same purpose as rewriting subtraction as add the opposite.
After doing this, students can rearrange the terms or write them as two separate expressions - in either case they should carry the sign with the term after it.
With the next example, students will need to recognize that the coefficient of `x` is just `1` if it is not written.
Allow students a few minutes to try and combine like terms to simplify the expression on their own. If students finish early, they can check their work with a shoulder partner. As you discuss the solution to this expression, students are likely to explain to each other how to deal with a term without any visible coefficient.
This is an extension of the earlier work. It combines subtraction, variable terms without a visible coefficient, and multiple variables.
Here is where it really helps to write subtraction as add the opposite. You get rid of the subtraction and negaitve number combination.
After you’ve completed the examples with the whole class, it’s time for some independent practice! ByteLearn gives you access to tons of mild, medium, and spicy practice problems for combining like terms. Check out the online practice and assign to your students for classwork and/or homework!
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