In this lesson, students plot rational numbers on a number line and compare them. They write inequality statements that include negative numbers. 

Students begin by considering four inequality statements. They are formally introduced to an inequality as a statement that uses symbols, such as > or <, to compare two values or expressions.

Next they plot a set of temperatures on a vertical or horizontal number line. By seeing the data represented in both ways, students are primed to recognize the - and -axes as number lines when introduced to the coordinate plane in following lessons. Students abstract from “hotter” and “colder” to “greater” and “less,” and observe that if a number is to the right of a number , we can write the inequality statements and .

Students use the structure of the number line to reason about relationships between numbers (MP7). They compare the size of two numbers as well as the distance from zero, finding that the greatest number is not always the one farthest from zero. Students are introduced to the word sign as a way to talk about whether numbers are positive or negative. 

Students are also introduced to the term rational number as a number that can be expressed as a positive or negative fraction or zero. Students will have more practice placing rational numbers on the number line in future lessons.