Changing Temperatures

5 min

Narrative

This Warm-up prompts students to compare four number line diagrams with arrows. 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.

Launch

Arrange students in groups of 2–4. Display the images for all to see. Give students 1 minute of quiet think time, and ask them to indicate when they have noticed three images 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?

  1.  
    A number line.
    Number line. 21 evenly spaced tick marks. Scale negative 10 to 10, by 1's. Two arrows. One arrow points to the right from 0 to 3. One arrow points to the right from 3 to 7. 
  2.  
    Number line.
    Number line. 21 evenly spaced tick marks. Scale negative 10 to 10, by 1's. Two arrows. One arrow points to the right from 0 to 3. One arrow points to the left from 3 to negative 6.  
  3.  
    Number line.
    Number line. 21 evenly spaced tick marks. Scale negative 10 to 10, by 1's. Two arrows. One arrow points to the right from 0 to 3. One arrow points to the left from 3 to 0. 
  4.  
    Number line.
    Number line. 21 evenly spaced tick marks. Scale negative 10 to 10, by 1's. Two arrows pointing to the left, one from 0 to negative 4 and another from negative 4 to negative 9. 

Sample Response

Sample responses:
A, B, and C go together because:
  • At least one arrow in each pair is pointing to the right.
  • Each pair has an arrow pointing from 0 to 3.
A, B, and D go together because:
  • Each pair has arrows of different lengths.
A, C, and D go together because:
  • Each arrow is no longer than 5 units.
  • Each pair of arrows stay on the same side of 0.
B, C, and D go together because:
  • At least one arrow in each pair is pointing to the left.

Synthesis

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, such as “positive,” “negative,” “addition,” and “subtraction,” and to clarify their reasoning as needed. Consider asking:

  • “How do you know . . . ?”
  • “What do you mean by . . . ?”
  • “Can you say that in another way?”
Standards
Building Toward
  • 7.NS.1.b·Understand p + q as the number located a distance |q| from p, in the positive or negative direction depending on whether q is positive or negative. Show that a number and its opposite have a sum of 0 (are additive inverses). Interpret sums of rational numbers by describing real-world contexts.
  • 7.NS.A.1.b·Understand <span class="math">\(p + q\)</span> as the number located a distance <span class="math">\(|q|\)</span> from <span class="math">\(p\)</span>, in the positive or negative direction depending on whether <span class="math">\(q\)</span> is positive or negative. Show that a number and its opposite have a sum of 0 (are additive inverses). Interpret sums of rational numbers by describing real-world contexts.

15 min

10 min