Combining Like Terms (Part 1)

10 min

Narrative

In this Warm-up, students encounter some algebraic moves they have studied in the past several lessons and explain why these moves are allowed. The moves discussed here are important to understand as students work toward fluency in writing expressions with fewer terms.

Launch

Display one statement at a time. Give students 30 seconds of quiet think time for each statement and ask them to give a signal when they have an explanation. Ask them to share their explanation with a partner and then follow with whole-class discussion.

Student Task

Explain why each statement is true.

  1. 5+2+3=5+(2+3)5+2+3=5+(2+3)
  2. 7.6+4.8−2.5=7.6−2.5+4.87.6 + 4.8 - 2.5 = 7.6 - 2.5 + 4.8
  3. 9a9a is equivalent to 11a−2a11a-2a.

Sample Response

Sample responses:

  1. Associative property: The convention is to add left to right so 5+25+2 is added first, but the associative property says grouping differently with addition gives the same result.
  2. Subtraction can be written as adding the opposite, and then the order can be switched with the commutative property of addition: 7.6+4.8+-2.5=7.6+-2.5+4.87.6+4.8+\text-2.5=7.6+\text-2.5+4.8.
  3. Distributive property: 11a−2a=(11−2)a=9a11a-2a=(11-2)a=9a

Synthesis

The purpose of this discussion is to refresh students’ memories of algebra moves that will be useful in this lesson. Ask students to share their reasons why each statement is true. Record and display their responses for all to see. Highlight correct use of precise, mathematical language and give students opportunities to revise their responses to be more precise.

Some questions to spark discussion include:

  • “How does the placement of the parentheses change how the first expression is evaluated?”
  • “Why is it okay to change the order of the terms, even though there’s subtraction in the expression?”
  • “Can you draw a diagram to show why 9a9a is equivalent to 11a−2a11a-2a?”
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.

20 min

15 min