Combining Like Terms (Part 2)

5 min

Teacher Prep
Setup
Groups of 2. 3 minutes of quiet work time and time to share their thoughts with a partner, followed by whole-class discussion. Access to index cards.

Narrative

This Warm-up prompts students to compare four expressions. It gives students a reason to use language precisely (MP6). It gives the teacher an opportunity to hear how students use terminology and talk about characteristics of the items in comparison to one another.

Launch

Arrange students in groups of 2–4. Display the expressions for all to see. Give students 1 minute of quiet think time and ask them to indicate when they have noticed three expressions that go together and can explain why. Next, tell students to share their response with their group and then together find as many sets of three as they can.

Student Task

Which three go together? Why do they go together?

A

-6x+9\text-6x+9

B

-7x+9y+x\text-7x + 9y + x

C

10x+7−4x+210x + 7 - 4x + 2

D

-2(3x−4)+1\text-2(3x - 4) + 1

Sample Response

Sample responses:

  • A, B, and C go together because they are all expanded expressions (there are no parentheses).
  • A, B, and D go together because they have the term -6x\text-6x.
  • A, C, and D go together because they have xx's and numbers but no yy's. They only have one variable, xx.
  • B, C, and D go together because they can be rewritten with fewer terms.
Activity Synthesis (Teacher Notes)

Invite each group to share one reason why a particular set of three go together. Record and display the responses for all to see. After each response, ask the class if they agree or disagree. Since there is no single correct answer to the question of which three go together, attend to students’ explanations and ensure the reasons given are correct.

During the discussion, prompt students to explain the meaning of any terminology they use, such as “terms,” “coefficient,” “combine,” or “distribute” and to clarify their reasoning as needed. Consider asking:

  • “How do you know . . . ?”
  • “What do you mean by . . . ?”
  • “Can you say that in another way?”
Standards
Building On
  • 6.EE.4·Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into them). <em>For example, the expressions y + y + y and 3y are equivalent because they name the same number regardless of which number y stands for.</em>
  • 6.EE.A.4·Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into them). <span>For example, the expressions <span class="math">\(y + y + y\)</span> and <span class="math">\(3y\)</span> are equivalent because they name the same number regardless of which number <span class="math">\(y\)</span> stands for.</span>
Building Toward
  • 7.EE.1·Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.
  • 7.EE.A.1·Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.

15 min

15 min