In this lesson, students explore multiplying a negative number by a positive number. To make sense of why such a product is negative, they use the context of constant velocity.

Scientists use the term velocity to describe the speed of an object in a specified direction. If one object is moving with a positive velocity, then any object moving in the opposite direction will have a negative velocity. Building on their previous work with constant speed, students calculate the final position for several different combinations of velocities and times. They see that the product of a negative velocity and a positive travel time results in a negative position relative to the starting point. As students reason through multiple examples to develop these generalizations about multiplication, they are making use of repeated reasoning (MP8).

Next, students apply their understanding of multiplying a negative number times a positive number to calculate the total amount of carbon dioxide that is absorbed or released by different objects in a year. A positive value represents carbon dioxide being released by the object, while a negative value represents carbon dioxide being absorbed.