Reasoning about Solving Equations (Part 2)

5 min

Narrative

In this activity, students identify expressions that are equivalent to a given expression, which involves applying the distributive property. In order to understand the two ways of solving an equation of the form p(x+q)=rp(x+q)=r in upcoming lessons, it is helpful to have some fluency with the distributive property.

Launch

Arrange students in groups of 2. Give 3 minutes of quiet work time and then invite students to share their responses with their partner, followed by a whole-class discussion.

Student Task

Select all the expressions equivalent to 2(x+3)2(x+3).

  1. 2⋅(x+3)2 \boldcdot (x+3)
  2. (x+3)2(x + 3)2
  3. 2⋅x+2⋅32 \boldcdot x + 2 \boldcdot 3
  4. 2⋅x+32 \boldcdot x + 3
  5. (2⋅x)+3(2 \boldcdot x) + 3
  6. (2+x)3(2 + x)3

Sample Response

1, 2, 3

Synthesis

The purpose of this discussion is to recall that 2⋅(x+3)2 \boldcdot (x+3) is equivalent to 2⋅x+2⋅32 \boldcdot x + 2 \boldcdot 3 because of the distributive property.

Possible discussion questions:

  • “What does it mean for expressions to be equivalent?” (They have the same value, no matter what the value of the variable is.)
  • “Why is 2⋅(x+3)2 \boldcdot (x+3) equivalent to 2⋅x+2⋅32 \boldcdot x + 2 \boldcdot 3?” (because of the distributive property)
  • “Can you think of another expression that is equivalent to 2(x+3)2(x+3)? (One example is 2x+62x+6.)
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>

15 min

15 min