Using temperature, students compare rational numbers and learn to write inequality statements that include negative numbers. Students then consider rational numbers in all forms (fractions, decimals) and 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, inequality statements a > b and b < a can be written. Students also find that the greatest number is not always the one farthest from zero. For example, -100 is much farther away from zero than -1/100, but since -1/100 is to the right of -100, it is larger and can be written -1/100 > -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).

Grade 6, Episode 20: Unit 7, Lesson 3 | Illustrative Math