Explaining Steps for Rewriting Equations

5 min

Narrative

This Math Talk focuses on solutions to equations. It encourages students to think about solutions to equations and to rely on properties of operations to mentally solve problems. It also prompts students to recall that dividing a number by 0 leads to an undefined result, preparing them for the work later in the lesson. (In that activity, students will consider why dividing by a variable is not considered an acceptable move when writing equivalent equations or solving equations.)

To determine if 0 is a solution to the equations, students could substitute 0 into the expressions and evaluate them. For some equations, however, the answer can be efficiently found by making use of structure (MP7). In explaining their strategies, students need to be precise in their word choice and use of language (MP6).

Launch

Tell students to close their books or devices (or to keep them closed). Reveal one problem at a time. For each problem:

  • Give students quiet think time, and ask them to give a signal when they have an answer and a strategy.
  • Invite students to share their strategies, and record and display their responses for all to see.
  • Use the questions in the Activity Synthesis to involve more students in the conversation before moving to the next problem. 

Keep all previous problems and work displayed throughout the talk.

Action and Expression: Internalize Executive Functions. To support working memory, provide students with sticky notes or mini whiteboards.
Supports accessibility for: Memory, Organization

Student Task

Is 0 a solution to each equation?

  • 4(x+2)=104(x + 2) = 10
  • 12−8x=3(x+4)12 - 8x = 3(x + 4)
  • 5x=12x5x = \frac12 x
  • 6x+1=8\frac {6}{x} + 1 = 8

Sample Response

  • No. Sample reasoning: If x=0x=0, then the expression on the left has the value 8, which makes the equation false.
  • Yes. Sample reasoning: Substituting 0 for xx gives 12=1212=12, which is true.
  • Yes. Sample reasoning: 5 multiplied by 0 is 0, and 12\frac12 multiplied by 0 is also 0, so the two sides of the equation are equal.
  • No. Sample reasoning: Dividing by 0 gives an undefined result, so it cannot be added to 1 to equal 8.
Activity Synthesis (Teacher Notes)

Ask students to share their strategies for each problem. Record and display their responses for all to see. To involve more students in the conversation, consider asking:

  • “Who can restate ‾\underline{\hspace{.5in}}’s reasoning in a different way?”
  • “Did anyone have the same strategy but would explain it differently?”
  • “Did anyone solve the problem in a different way?”
  • “Does anyone want to add on to ‾\underline{\hspace{.5in}}’s strategy?”
  • “Do you agree or disagree? Why?”
MLR8 Discussion Supports. Display sentence frames to support students when they explain their strategy. For example, “First, I _____ because . . . .” or “I noticed _____ so I . . . .” Some students may benefit from the opportunity to rehearse what they will say with a partner before they share with the whole class.
Advances: Speaking, Representing
Standards
Addressing
  • A-REI.A·Understand solving equations as a process of reasoning and explain the reasoning
  • HSA-REI.A·Understand solving equations as a process of reasoning and explain the reasoning.

15 min

15 min