Subtraction in Equivalent Expressions

5 min

Teacher Prep
Setup
Display one problem at a time. Allow 30 seconds of quiet think time, followed by a whole-class discussion.

Narrative

This Math Talk focuses on adding and subtracting signed numbers. It encourages students to think about rewriting subtracting as adding and to rely on the properties of operations to mentally solve problems. The fluency elicited here will be helpful later in the lesson when students need to rewrite subtraction as adding the opposite.

To rewrite expressions using a different operation, students need to look for and make use of structure (MP7).

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 access to sticky notes or mini whiteboards.
Supports accessibility for: Memory, Organization

Student Task

Find the value of each expression mentally.

  • 64−964 - 9
  • 64+-964 + \text-9
  • -9+64\text- 9 + 64
  • -9−64\text-9 - 64

Sample Response

  • 55. Sample reasoning: 64−10=5464 - 10 = 54 and 54+1=5554 + 1 = 55.
  • 55. Sample reasoning: Adding -9 is the same as subtracting 9.
  • 55. Sample reasoning: Addition is commutative.
  • -73. Sample reasoning: Subtracting 64 is the same as adding -64. This can be represented on the number line with an arrow pointing left from 0 to -9 and another arrow pointing left from -9 and going down 64 more.
Activity Synthesis (Teacher Notes)

To involve more students in the conversation, consider asking:

  • “Who can restate ‾\underline{\hspace{.5in}}’s reasoning in a different way?”
  • “Did anyone use 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?”
  • “What connections to previous problems do you see?”

Emphasize that “Subtract 10” can be rewritten as “Add negative 10” and that addition is commutative, but subtraction is not. Mention these points even if students do not bring them up.

MLR8 Discussion Supports. Display sentence frames to support students when they explain their strategy. For example, “First, I ‾\underline{\hspace{.5in}} because . . . .” or “I noticed ‾\underline{\hspace{.5in}} 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
  • 7.NS.1·Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram.
  • 7.NS.A.1·Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram.

15 min

15 min