Applications of Expressions

5 min

Narrative

This Math Talk focuses on rewriting expressions in different, equivalent ways. It encourages students to think about relevant terminology and to rely on the distributive property to mentally solve problems. The strategy elicited here will be helpful later in the lesson when students show that two different ways of calculating are equivalent.

In explaining how they know whether expressions are equivalent, 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 access to sticky notes or mini whiteboards.
Supports accessibility for: Memory, Organization

Student Task

Decide mentally whether each expression is equivalent to 0.75t−210.75t-21.

  • 34t−21\frac34t - 21
  • 34(t−21)\frac34(t - 21)
  • 0.75(t−28)0.75(t - 28)
  • t−0.25t−21t - 0.25t - 21

Sample Response

  • Yes. Sample reasoning: 34t−21\frac34t - 21 is equivalent to 0.75t−210.75t-21 because 0.75=340.75=\frac34.
  • No. Sample reasoning: 34(t−21)\frac34(t - 21) is not equivalent to 0.75t−210.75t-21 because by the distributive property, it is equivalent to 34t−15.75\frac34t - 15.75.
  • Yes. Sample reasoning: 0.75(t−28)0.75(t - 28) is equivalent to 0.75t−210.75t-21 because of the distributive property.
  • Yes. Sample reasoning: t−0.25t−21t - 0.25t - 21 is equivalent to 0.75t−210.75t-21 because if you combine t−0.25tt-0.25t, you get 0.75t0.75t.
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
  • 7.EE.1·Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.
  • 7.EE.A.1·Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.

15 min

15 min