Finding Differences

5 min

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

Narrative

This Math Talk focuses on finding a missing addend. It encourages students to think about using subtraction to solve an addition equation and to rely on strategies they know for finding unknown values to mentally solve problems. The strategies elicited here will be helpful later in the lesson when students find the difference between two values.

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

Solve each equation mentally. 

  • 247+c=458247 + c = 458
  • c+389=721c+389=721
  • c+43.87=58.92c + 43.87 = 58.92
  • 158+c=518\frac{15}{8} + c = \frac{51}{8}

Sample Response

  • c=211c=211. Sample reasoning: I can subtract 458−247458-247 to find the value of cc.
  • c=332c=332. Sample reasoning: 389 is 11 less than 400 and 400 is 321 less than 721, which means 389 is 11+321=33211+321=332 less than 721.
  • c=15.05c=15.05. Sample reasoning: 43.87+5=48.8743.87+5=48.87; 48.87+10=58.8748.87+10=58.87; 58.87+0.05=58.9258.87+0.05=58.92; and 5+10+0.05=15.055+10+0.05=15.05.
  • c=368c=\frac{36}{8} (or equivalent). Sample reasoning: Since both terms have the same denominator, we can subtract 51−15=3651-15=36 to find the number of eighths.
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?”
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
Building On
  • 6.EE.B·Reason about and solve one-variable equations and inequalities.
  • 6.EE.B·Reason about and solve one-variable equations and inequalities.
Building Toward
  • 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.

10 min

10 min