Expressions with Rational Numbers

5 min

Teacher Prep
Setup
Display one problem at a time. 1 minute of quiet think time per problem; students signal when they have an answer. Follow with a whole-class discussion.

Narrative

This Math Talk focuses on reasoning about the values of numeric expressions. It encourages students to think about positive and negative values without necessarily computing anything and to rely on what they know about operations with negative and positive numbers to mentally solve problems. The strategies elicited here will be helpful later in the lesson when students find expressions that have the same value.

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

Decide mentally whether each statement is true.

  • (-38.76)(-15.6)(\text-38.76)(\text-15.6) is negative.
  • 10,000−99,999< 010,000 - 99,999 < 0
  • (34)(-43)=0\left( \frac34 \right)\left( \text- \frac43 \right) = 0
  • (30)(-80)−50=50− (30)(-80)(30)(\text- 80) - 50 = 50 - (30)(\text- 80)

Sample Response

  1. False. Sample reasoning: The product of 2 negative numbers is positive.
  2. True. Sample reasoning: Subtracting a greater number from a lesser number will result in a negative number, which means the difference will be less than 0.
  3. False. Sample reasoning: Since neither factor is 0, the product cannot be 0.
  4. False. Sample reasoning: The left side of the equation is -290 while the right side of the equation is 290, so the two expressions are not equal.
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
Addressing
  • 7.NS.1.d·Apply properties of operations as strategies to add and subtract rational numbers.
  • 7.NS.2.c·Apply properties of operations as strategies to multiply and divide rational numbers.
  • 7.NS.A.1.d·Apply properties of operations as strategies to add and subtract rational numbers.
  • 7.NS.A.2.c·Apply properties of operations as strategies to multiply and divide rational numbers.

15 min

15 min