In this activity, students connect a visual number line representation of positive and negative numbers with inequality symbols in a real-world situation. Students compare signed numbers and see that larger numbers are to the right on a horizontal number line and at the top of a vertical number line, and that smaller numbers are to the left or bottom. The familiar context of temperature helps students connect “less than” or “greater than” language to signed numbers. Students also evaluate and critique another's reasoning (MP3).

Monitor for students who use these different representations when creating a number line in the first question:

• A vertical number line
• A horizontal number line

Students have seen both horizontal and vertical number lines in previous activities, and either one can be used to represent the temperatures given in the table. Visualizing both vertical and horizontal number lines here prepares students for later work in the coordinate plane.

The goal of this discussion is for students to compare horizontal and vertical number lines, and then to use them to help write inequality statements. Display two representations from previously selected students for all to see. Use Compare and Connect to help students compare, contrast, and connect the different representations of a number line. Here are some questions for discussion: 

• “What do the representations have in common? How are they different?” (They both show the same information, but one is horizontal, and one is vertical.)
• “How do colder temperatures show up in each representation?” (Colder temperatures are to the left in a horizontal number line and towards the bottom in a vertical number line.)
• “How do warmer temperatures show up in each representation?” (Warmer temperatures are to the right in a horizontal number line and towards the top in a vertical number line.)
• “Are there any benefits or drawbacks to one representation compared to another?” (Answers vary.)

Then explain to students that numbers don’t only describe temperature, though. We use the word “greater” to describe a number that is farther to the right or farther up, and “less” to describe numbers that are farther to the left or farther down. Display this image and the inequality statement for all to see:

Say, “6 is greater than -50 because it is farther to the right on the number line.” We could also write and say, “-50 is less than 6 because -50 is farther to the left on the number line.”

In this activity, students plot positive and negative numbers on a horizontal number line and use their location to evaluate whether given inequality statements are true or false. Students also consider a number’s distance from 0 in preparation for the concept of “absolute value,” which will be introduced in a following lesson.

The goal of this discussion is for students to practice using a number line to compare numbers in statements using inequality symbols. Begin by inviting students to share their reasoning and responses to whether each given inequality statement was true or false. Record and display their reasoning for all to see. The key idea to emphasize is that the greater number is the number farther to the right on a horizontal number line. Then display this number line for all to see:

Display one inequality at a time, and ask students to indicate whether they think the statement is true or false and to explain their reasoning:

• (true)
• is farther from 0 than . (false)
• (true)
• is farther from 0 than . (true)