Multiplying Rational Numbers

The purpose of this lesson is to develop the rules for multiplying two negative numbers. Students use the familiar fact that distance = velocity x time to make sense of this rule. They interpret negative time as time before a chosen starting time and then determine the position of an object moving with a negative velocity at a negative time. An object moving with a negative velocity is moving from right to left along the number line. At a negative time it has not yet reached its starting point of zero, so it is to the right of zero, and therefore its position is positive. So a negative velocity times a negative time gives a positive position. When students connect reasoning about quantities with abstract properties of numbers, they engage in MP2.

Grade 7, Episode 13: Unit 5, Lesson 9 | Illustrative Math