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Arrange students in groups of 2–4. Display the inequality statements for all to see. Give students 1 minute of quiet think time, and ask them to indicate when they have noticed three statements 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.
Which three go together? Why do they go together?
A
B
C
D
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 “less than” or “greater than,” and to clarify their reasoning as needed. Consider asking:
Explain to students that they have used the > and < symbols previously. Remind students that:
Tell students that a statement that uses these symbols to compare two values or expressions is called an inequality.
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:
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.
Give students 4–5 minutes quiet work time, and follow with whole-class discussion.
Select work from students with different strategies, such as those described in the Activity Narrative, to share later.
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:
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
Say, “6 is greater than -50 because it is farther to the right on the number line.” We could also write
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.
Give students 6–7 minutes of quiet work time, and follow with a whole-class discussion.
Plot the numbers -2, 4, -7, and 10 on the number line. Label each point with its numeric value.
Decide whether each inequality statement is true or false. Be prepared to explain your reasoning.
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:
Introduce the word sign to mean whether a number is positive or negative, and give a few examples. For example, “The sign of -3 is negative. The sign of 5 is positive.” Explain that 0 has no sign because it is neither positive nor negative. Then display the number line for all to see.
The phrases “greater than” and “less than” can be used to compare numbers on the number line. For example, the numbers -2.7, 0.8, and -1.3, are shown on the number line.
Because -2.7 is to the left of -1.3, we say that -2.7 is less than -1.3. We write:
In general, any number that is to the left of a number
We can see that -1.3 is greater than -2.7 because -1.3 is to the right of -2.7. We write:
In general, any number that is to the right of a number
We can also see that
Help us improve by sharing suggestions or reporting issues.
Here are the low temperatures, in degrees Celsius, for a week in Anchorage, Alaska.
| day | Mon | Tue | Wed | Thurs | Fri | Sat | Sun |
|---|---|---|---|---|---|---|---|
| temperature | 5 | -1 | -5.5 | -2 | 3 | 4 | 0 |
Plot the temperatures on a number line.
Which day of the week had the lowest low temperature?
On a winter day, the low temperature in Anchorage, Alaska, was -21 degrees Celsius, and the low temperature in Minneapolis, Minnesota, was -14 degrees Celsius.
Jada said, “I know that 14 is less than 21, so -14 is also less than -21. This means that it was colder in Minneapolis than in Anchorage.”
Do you agree? Explain your reasoning.