Combining Like Terms

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SWBAT combine like terms to generate equivalent expressions

Big Idea

We can combine terms that have the same variable raised to the same exponent. This allows us to simplify expressions.

Think About It

7 minutes

Students work independently on the Think About It problem.  After 2-3 minutes of work time, I have students share out the expressions they've written.  They should have some form of a + a + a + a + a + a + p + p + p and 6a + 3p.

I ask students how the first and second expressions could both represent the problem.  I then ask why they didn't write 9a or 9p, given that there are 8 pieces of fruit in all.

I frame the lesson by letting students know that we will be taking terms, which are parts of expressions like we discussed in the previous lesson and combining them to make equivalent, simplified expressions.  

Intro to New Material

15 minutes

To start the Intro to New Material section, I guide students through filling in the key ideas for the lesson:

  • A term is part of an expression
  • Like terms are terms that have the same variable raised to the same exponent
  • Expressions can be simplified by combining like terms.  Both the original expression and the simplified expression are equivalent.

I then call on students to read each of the steps provided.

For the first example, I take the time to ask students about each of the terms in the expression. Students box the first term, 4x.  When we look at the second term, I have students articulate that it is not a like term to 4x, because it does not have the same base raised to the same exponent.  We talk about how the base, x, is the same, but the exponent is not.  We go through each term in a similar fashion.  When we get to -2x, it is important that I stress to students that the box the -2x, and not just 2x.  It's a common error for students to disregard the negative/subtraction sign, and I want be proactive in addressing it.  Once we get to the end of the expression, we start all over again - this time, circling any term that is squared (because that's the second term that we come to in the expression).  We go through the expression a third time, underlining the rational numbers.

I spend a fair amount of time on Example 1, which is a pretty simple problem.  By investing the time in this first problem, I can set students up with a clear system for combining like terms.  It might be tempting to rush through this first example, but time spent here is a good investment. 

In Example 3, students have to apply the concept of perimeter before combining like terms.  If students struggle to make sense of this problem, draw a triangle with integer side lengths and ask how they'd find the perimeter.  They can then help to create an expression for the perimeter of the triangle in this problem, and simplify.


Partner Practice

15 minutes

Students work in pairs on the Partner Practice problem set.  As students work, I circulate around the room and check in with each group.  I'm looking for:

  • Are scholars correctly identifying like terms?
  • Are scholars correctly combining like terms?
  • Are students considering the sign of each term when combining?
  • Are scholars correctly showing work by boxing, circling, and underlining?

I'm asking: 

  • How did you know which terms were like terms?
  • How did you know how to combine like terms?
  • How did you know what the final expression was?

Some students may benefit from using colored pencils to annotate the expression, and I make sure I have some on hand for this lesson.  

Independent Practice

15 minutes

Students work on the Independent Practice problem set.  

Problems 6 and 7 are more rigorous for students, because they involve decimals and fractions, rather than just integers.  Although the process is the same, some students will find these problems to be a bit more difficult.  

Problems 8-12 are all application problems.  When I circulate, I use these problems to engage in conversation with students.  I want them to articulate their thinking here. I generally start with a broad 'tell me what you did' sort of statement, to get the conversation started.

Closing and Exit Ticket

8 minutes

After Independent Work time, I have the class look at two pieces of 'student' work that I've created. I use Problem 6.  Both pieces of work are incorrect:  in the first sample, I'll combine the m-squared terms and the n-squared term together.  In the second example, I'll incorrectly add 1.2 to 3.5, rather than subtract.  I ask students to critique my work and identify the errors.  I'll then call on a student to share the correct equivalent expression.

Students then work independently on the Exit Ticket to close the lesson.