Lesson 3

Returning to the temperature context, students compare rational numbers representing temperatures and learn to write inequality statements that include negative numbers. Students then consider rational numbers in all forms (fractions, decimals) and learn to compare them by plotting on a number line and considering their relative positions. Students abstract from “hotter” and “colder” to “greater” and “less,” so if a number \(a\) is to the right of a number \(b\), we can write the inequality statements \(a>b\) and \(b<a\). Students also find that the greatest number is not always the one farthest from zero, which was the case before students encountered negative numbers. For example, -100 is much farther away from zero than \(\text-\frac{1}{100}\), but since \(\text-\frac{1}{100}\) is to the right of -100, it is larger and we can write \(\text-\frac{1}{100}>\text-100\). Students are briefly introduced to the word sign (i.e., algebraic sign) since it is often used to talk about whether numbers are positive or negative. Students use the structure of the number line to reason about relationships between numbers (MP7).