Lesson 3: Comparing Positive and Negative Numbers
About this lesson
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 \(\frac{1}{100}\), but since \(\frac{1}{100}\) is to the right of 100, it is larger and we can write \(\frac{1}{100}>100\). 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).
Lesson overview
 3.1 Warmup: Which One Doesn’t Belong: Inequalities (5 minutes)

3.2 Activity: Comparing Temperatures (10 minutes)
 Includes "Are you Ready for More?" extension problem

3.3 Activity: Rational Numbers on a Number Line (15 minutes)
 There is a digital applet in this activity.
 Lesson Synthesis
 3.4 Cooldown: Making More Comparisons (10 minutes)
Learning goals:
 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.
Learning goals (student facing):
 Let’s compare numbers on the number line.
Learning targets (student facing):
 I can use inequalities to compare positive and negative numbers.
 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.
Glossary:
 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.
 Access the complete Grade 6 glossary.
Standards:
 This lesson builds on the standards: CCSS.4.NBT.A.2CCSS.5.NBT.A.3.bMS.4.NBT.2
 This lesson builds towards the standards: CCSS.6.NS.C.7.aCCSS.6.NS.C.7.dMS.6.NS.7a
IM 6–8 Math was originally developed by Open Up Resources and authored by Illustrative Mathematics, and is copyright 20172019 by Open Up Resources. It is licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0). OUR's 6–8 Math Curriculum is available at https://openupresources.org/mathcurriculum/.
Adaptations and updates to IM 6–8 Math are copyright 2019 by Illustrative Mathematics, and are licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0).
Adaptations to add additional English language learner supports are copyright 2019 by Open Up Resources, and are licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0).
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