In this second lesson on signed numbers, students learn about opposites. First they revisit the context of temperature, represented on a vertical number line, extending previous work with interpreting equally spaced divisions to the negative part of the number line. The purpose of this activity is to reestablish the interpretation of distance on the number line in the context of negative numbers. They then create folded number lines to reason about opposites, which are numbers that are on opposite sides of 0 but the same distance from zero. Students will have more practice placing rational numbers of all kinds on the number line in future lessons. In this lesson, it is more important to focus on the concept of opposites than plotting different kinds of rational numbers.
Lesson overview
 2.1 Warmup: A Point on the Number Line (5 minutes)
 2.2 Activity: What’s the Temperature? (10 minutes)

2.3 Activity: Folded Number Lines (20 minutes)
 Includes "Are you Ready for More?" extension problem
 Lesson Synthesis
 2.4 Cooldown: Positive, Negative, and Opposite (5 minutes)
Learning goals:
 Comprehend that two numbers are called “opposites” when they are the same distance from zero, but on different sides of the number line.
 Interpret a point on the number line that represents a positive or negative rational number.
 Plot a point on a number line to represent a positive or negative rational number.
Learning goals (student facing):
 Let’s plot positive and negative numbers on the number line.
Learning targets (student facing):
 I can represent negative numbers on a number line.
 I can determine or approximate the value of any point on a number line.
 I understand what it means for numbers to be opposites.
Required materials:
 tracing paper
 rulers marked with centimeters
Required preparation:
 Each student needs access to a ruler marked with centimeters and at least 1 sheet of tracing paper.
 If the tracing paper is less than 20 cm wide, then students will need to construct their number lines in the “Folded Number Lines” activity to go from 7 to 7, or otherwise construct their number line on the diagonal of the tracing paper.
Glossary:
 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.
 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 \(\text\frac{75}{100}\).
 Access the complete Grade 6 glossary.
Standards:
 This lesson builds on the standards: CCSS.3.NF.ACCSS.4.NF.CMS.3.NFMS.4.NF
 This lesson builds towards the standard: CCSS.6.NS.C.6.cMS.6.NS.6c
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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