The purpose of this task is to build understanding of the negative side of the number line, both by reading values and assigning values to equally spaced divisions. Non-integer negative numbers are also used. Students reason abstractly and quantitatively as they interpret positive and negative numbers in context (MP2).

The purpose of the discussion is for students to share their strategies for making sense of negative values on the number line. Begin by inviting students to share their reasoning as to whether they agreed with Jada or Elena in the last question. If not mentioned by students, connect this question to the Warm-up by pointing out that the temperature is halfway between -1 and -2 on the number line, so it must be -1.5 degrees.

Then display this number line for all to see.

Discuss the following questions:

• “What could be the value of point ? Explain your reasoning.” (A value between 3 and 3.5 is reasonable. The point is between 3 and 4 but looks closer to 3.)

• “What could be the value of point ? Explain your reasoning.” (A value between -3 and -3.5 is reasonable. The point is between -3 and -4 but looks closer to -3.)

• “Do you think the value of point is closer to -0.75 or -1.25? Why?” (Point is closer to -0.75 because it is located between 0 and -1.)

• “What do you notice about the location of negative values on a vertical number line?” (Negative numbers are at the bottom. The negative numbers are like a mirror of the positive numbers.)

The purpose of this activity is to build an understanding of the structure of the number line by observing symmetry across zero on the number line (MP7). This is also the first time students work with negative numbers on a horizontal number line. If students have difficulty, consider displaying a vertical number from a previous activity to connect with. 

While this activity also introduces the notion of distance on a number line, students do not need to know the term "absolute value," as it will be introduced in a following lesson. 

Monitor for students who use these different strategies when finding the values of points , , and on the number line:

• Use tracing paper to recreate the number line and fold it at 0
• Use a ruler, tracing paper, or other tool to measure distances
   

The goal of this discussion is to compare different ways students determined the locations of points , , and on the number line and to reinforce the meaning of the term "opposites."

Display 2–3 approaches from previously selected students for all to see. If time allows, invite students to briefly describe their approach, then use Compare and Connect to help students compare, contrast, and connect the different approaches. Here are some questions for discussion:

• “What do the approaches have in common? How are they different?” (They are all about measuring distance, just in different ways.)

• “Did anyone solve the problem the same way, but would explain it differently?” 

• “Are there any benefits or drawbacks to one approach compared to another?”

The main idea for students to understand is that opposites are the same distance from 0 and on different sides of the number line. Display the horizontal number line and these sentence frames for all to see:

• “The opposite of is .”
• “The opposite of the opposite of is .”

Ask students to use the first sentence frame to describe the opposites of the labeled points and add them to the number line. (The opposite of -4 is 4. The opposite of 1.5 is -1.5.) 

Repeat this with the second sentence frame. (The opposite of the opposite of -4 is -4. The opposite of the opposite of 1.5 is 1.5.) Point out that the opposite of the opposite of a number is always the number itself.