Lesson 3
Comparing Positive and Negative Numbers
Lesson Narrative
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 \(\text\frac{1}{100}>\text100\). 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).
Learning Goals
Teacher Facing
 Compare rational numbers in the context of temperature or elevation, and express the comparisons (in writing) using the symbols > and <.>
 Comprehend the word “sign” (in spoken language) to refer to whether a number is positive or negative.
 Critique (orally and in writing) statements comparing rational numbers, including claims about relative position and claims about distance from zero.
Student Facing
Let’s compare numbers on the number line.
Learning Targets
Student Facing
 I can explain how to use the positions of numbers on a number line to compare them.
 I can explain what a rational number is.
 I can use inequalities to compare positive and negative numbers.
CCSS Standards
Building On
Addressing
Building Towards
Glossary Entries

negative number
A negative number is a number that is less than zero. On a horizontal number line, negative numbers are usually shown to the left of 0.

opposite
Two numbers are opposites if they are the same distance from 0 and on different sides of the number line.
For example, 4 is the opposite of 4, and 4 is the opposite of 4. They are both the same distance from 0. One is negative, and the other is positive.

positive number
A positive number is a number that is greater than zero. On a horizontal number line, positive numbers are usually shown to the right of 0.

rational number
A rational number is a fraction or the opposite of a fraction.
For example, 8 and 8 are rational numbers because they can be written as \(\frac81\) and \(\text\frac81\).
Also, 0.75 and 0.75 are rational numbers because they can be written as \(\frac{75}{100}\) and \(\text\frac{75}{100}\).

sign
The sign of any number other than 0 is either positive or negative.
For example, the sign of 6 is positive. The sign of 6 is negative. Zero does not have a sign, because it is not positive or negative.