Dealing with Negative Numbers

5 min

Teacher Prep
Setup
Students in groups of 2–4. Display the image for all to see. 2 minutes of quiet think time, followed by small-group discussions.

Narrative

This Warm-up prompts students to compare four equations. It gives students a reason to use language precisely (MP6). It gives the teacher an opportunity to hear how students use terminology and talk about characteristics of the items in comparison to one another.

During the discussion, listen for strategies for evaluating expressions with rational numbers that will be helpful in the work of this lesson.

Launch

Arrange students in groups of 2–4. Display the equations for all to see. Give students 1 minute of quiet think time, and ask them to indicate when they have noticed three equations that go together and can explain why. Next, tell students to share their response with their group and then together find as many sets of three as they can.

Student Task

Which three go together? Why do they go together?

A

15=-5-315 = \text- 5 \boldcdot \text- 3

B

2+-5=-32 + \text- 5 = \text- 3

C

42-1=94 \boldcdot 2 - \text{-}1=9

D

-3-4=-12\text- 3 \boldcdot \text- 4 = \text- 12

Sample Response

  • A, B, and C go together because they are all true equations.
  • A, B, and D go together because they all have the number -3 and they all involve only one operation.
  • A, C, and D go together because they all involve multiplication.
  • B, C, and D go together because they all have the total on the right side of the equal sign.
Activity Synthesis (Teacher Notes)

Invite each group to share one reason why a particular set of three go together. Record and display the responses for all to see. After each response, ask the class if they agree or disagree. Since there is no single correct answer to the question of which three go together, attend to students’ explanations, and ensure the reasons given are correct.

During the discussion, prompt students to explain the meaning of any terminology they use, especially related to strategies for adding, subtracting, or multiplying signed numbers.

Standards
Building On
  • 7.NS.A·Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers.
  • 7.NS.A·Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers.

15 min

15 min