In this lesson, students represent a subtraction of signed numbers on a number line by relating it to an addition equation with a missing addend. The convention for representing subtraction on the number line fits with the convention for representing addition. When we represent \(a+b=c\), we represent \(a\) with an arrow starting at zero, \(b\) with an arrow starting where the first arrow ends, and \(c\) with a point at the end of the second arrow. So when we want to represent \(c−a=b\), we represent \(c\) with a point, \(a\) with an arrow starting at zero, and the difference \(b\) is the other arrow that is needed to reach from the end of the first arrow to the point.
At the beginning of the lesson, students see that a subtraction equation like \(8−3=?\) can be thought of as the related addition equation \(3+?=8\). After repeatedly calculating differences this way (MP8), students recognize that the answer to each subtraction problem is the same number they would get by adding the opposite of the number. For example, by the end of the lesson, students see that \(8−3=?\) can also be thought of as \(8+3=?\)
Lesson overview
 5.1 Warmup: Equivalent Equations (5 minutes)
 5.2 Activity: Subtraction with Number Lines (10 minutes)

5.3 Activity: We Can Add Instead (15 minutes)
 Includes "Are you Ready for More?" extension problem
 Lesson Synthesis
 5.4 Cooldown: Same Value (5 minutes)
Learning goals:
 Generalize (orally and in writing) that subtracting a number results in the same value as adding the additive inverse.
 Interpret a number line diagram that represents subtracting signed numbers as adding with an unknown addend.
 Use a number line diagram to find the difference of signed numbers, and explain (orally) the reasoning.
Learning goals (student facing):
 Let's subtract signed numbers.
Learning targets (student facing):
 I can use a number line to subtract positive and negative numbers.
 I can explain the relationship between addition and subtraction of rational numbers.
Glossary:
 Access the complete Grade 7 glossary.
Standards:
 This lesson builds on the standard:CCSS.1.OA.B.4MS.1.OA.4MO.1.RA.B.6
 This lesson builds towards the standard:CCSS.7.NS.A.1MS.7.NS.1MO.7.NS.A
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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