How To Teach Combining Like Terms

Key Concepts of Combining Like Terms

Students are introduced to combining like terms in 6th grade. A big piece of the understanding in that grade is that expressions with different variables cannot be combined and that constant don’t go with anything that has a variable. Combining like terms gets a lot more complicated in 7th grade with integer coefficients and constants and powers more than 1. 

Introduce students to combining like terms with a real-world task. Coach students to circle, box, and underline like terms with the sign in front to help them add and subtract with ease. 

For more math resources you can click here

How do you teach combining like terms? 

Explain to students what like terms are. Like terms are terms whose variables and their exponents (like 2 in x^2) are the same. For example, 5x and -2x are like terms because they are both terms with x. Explain that like terms can be combined and unlike terms cannot be combined. Defining examples and non-examples will help formalize your students’ understanding of math vocabulary. 

Step 1: Identify the like terms 

Start out circling one set of like terms. Remind students that they should include the + or – sign in front of the number. Then box or underline the remaining sets of like terms.

Step 2: Rearrange the expression so the like terms are next to each other. 

Write an equivalent expression with each pair of like terms next to each other. 

Step 3: Simplify the expression. 

Combine each set of like terms. Provide your students with integer tiles so they practice adding and subtracting positive and negative integers. Encourage students to practice writing expressions with subtraction instead of adding a negative. In this example, have students write -28j – 11 instead of -28 + -11

Examples

Example 1 (Two Constants and One Coefficient): 

Step 1: 

Step 2:  

Step 3: 

The digital co-teacher made with ❤️ by teachers

ByteLearn saves you time and ensures every student gets the support they need

Try for Free

Example 2 (Two Constants and Two Like Coefficients):

Step 1: 

Step 2: 

Step 3: 

Example 3 (Two Unlike Coefficients):

Step 1: 

Step 2: 

Step 3: 

Why teach combining like terms this way?

Using shapes and colors can help students visually see the like terms that will be combined. Then students can rearrange the expression as needed to combine the like terms. It also reminds students to take the + or – sign into consideration when marking like terms. 

Using Byte’s practice problems and virtual manipulatives will give your students the chance to make mistakes, get feedback, and try again until they master this essential concept!  

Vocabulary for teaching combining like terms 

Term: Part of an expression separated by + or – operations.

Like Term: Terms that have the same variables, raised to the same power. Constants are like terms.

Unlike Term: Terms that have different variables, or the same variables but raised to different powers.

Coefficient: A number that multiplies a variable. If there is no coefficient in front of a variable, the coefficient is 1.

Constant: A term that does not contain a variable.

Variable: A symbol (usually a letter) that is used to represent a number in an expression or equation.

Misconceptions and errors students are likely to have on Combining Like Terms:

• Students might combine terms from left to right and disregard the variables. For example, students could simplify the expression 2 + 3x + 4 as 9xy.
  • Address this conceptual misunderstanding by assigning each variable with a specific noun. For example, if B represents Beyonce, and D represents Drake, does it make sense that 2B (or 2 Beyonces) + 3D (or 3 Drakes) is the same as 5BD (or 5 Beyonce Drakes?). 
• Students might combine every term with the same variable. For example, students might think that x + xy is the same as 2xy.
  • Try assigning a noun for each variable and ask your students if it makes sense to combine two nouns together. If this doesn’t click, try providing your students with integer tiles. It will “click” more easily for students if each set of tiles are color-coded. If this is not possible, provide colored pencils to your students and coach them to write each term in expanded form. For example, 2x + 3y is the same as x + x + y + y + y. Guide students to identify why the terms are unlike versus like. 

• Students may commit integer mistakes. For example, students may mistake -8x + 3y + 10x as 18x + 3y.
  • Provide your students with integer chips so they can model canceling out opposites. 
  • If the previous suggestion doesn’t work, coach your students to write each term with a coefficient in expanded form with colored pencils. 

• Students may not recognize the minus signs as negative terms. For example, in 6x – 5 – 2x + 3, students might combine 6x and 2x and 5 and 3 and ignore the minus signs.
  • Remind students to circle the + or – in front of a term indicating if the term is positive or negative. 

Also read: Solving Equations With Variables On One Side

Resources: 

• Downloadable worksheet for practicing combining like terms
• Practice Problems for assessing combining like terms 

Frequently Asked Questions for Combining Like Terms