Lesson 9

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 \(\text-8 - 3 = {?}\) can be thought of as the related addition equation \(3 + {?} = \text-8\). 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 \(\text-8 - 3 = {?}\) can also be thought of as \(\text-8 + \text-3 = {?}\)