Distinguishing between Two Types of Situations

5 min

Teacher Prep
Setup
Students in groups of 2–4. Display the equations for all to see. 1 minute of quiet think time, followed by small-group discussions.

Narrative

This Warm-up prompts students to compare four equations. 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 equations in comparison to one another.

Launch

Arrange students in groups of 2–4. Display the equations for all to see. Give students 1 minute of quiet think time, and ask them to indicate when they have noticed three equations 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

4(x+3)=94(x+3)=9

B

4⋅x+12=94 \boldcdot x + 12 = 9

C

4+3x=94 + 3x = 9

D

9=12+4x9 = 12 + 4x

Sample Response

Sample responses:

  • A, B, and C go together because they all have the total, 9, on the right side of the equal sign.
  • A, B, and D go together because they are all equivalent (and they all have negative solutions).
  • A, C, and D go together because they all use “next to” notation for multiplication.
  • B, C, and D go together because they have two terms that are added (there are no parentheses).
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 “times,” “plus,” “minus,” “distribute,” “dot,” or “same answer,” 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 Toward
  • 7.EE.4.a·Solve word problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach. <em>For example, the perimeter of a rectangle is 54 cm. Its length is 6 cm. What is its width?</em>
  • 7.EE.B.4.a·Solve word problems leading to equations of the form <span class="math">\(px + q = r\)</span> and <span class="math">\(p(x + q) = r\)</span>, where <span class="math">\(p\)</span>, <span class="math">\(q\)</span>, and <span class="math">\(r\)</span> are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach. <span>For example, the perimeter of a rectangle is <span class="math">\(54\)</span> cm. Its length is <span class="math">\(6\)</span> cm. What is its width?</span>

15 min

15 min