In this lesson, students are introduced to multiplying a negative number with a positive number, using the context of velocity, time, and position. In the next lesson, they multiply two negative numbers.
The context of elevation is an example of using signed numbers to represent the position of an object along a line relative to a reference position (sea level in the case of elevation). In the general case, zero represents the reference position, positive numbers represent positions on one side of the reference position, and negative numbers represent positions on the other side. In this lesson, students see that signed numbers can also be used to represent speed with direction. 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.
In previous units, students solved problems about moving objects, using the fact that the product of the (positive) speed and the (positive) travel time gives the (positive) distance traveled. In this lesson, students use several examples in the context of moving along a line to see that the product of a negative velocity and a positive travel time results in a negative position relative to the starting point.
Lesson overview
 8.1 Warmup: Distance, Rate, Time (5 minutes)
 8.2 Activity: Going Left, Going Right (10 minutes)

8.3 Activity: Velocity (15 minutes)
 Includes "Are you Ready for More?" extension problem
 Lesson Synthesis
 8.4 Cooldown: Multiplication Expressions (5 minutes)
Learning goals:
 Explain (orally and in writing) how signed numbers can be used to represent positions and speeds in opposite directions.
 Generalize (orally) that the product of a negative number and a positive number is negative.
 Write a multiplication equation to represent a situation involving constant speed with direction.
Learning goals (student facing):
 Let's use signed numbers to represent movement.
Learning targets (student facing):
 I can multiply a positive number with a negative number.
 I can use rational numbers to represent speed and direction.
Glossary:
 Access the complete Grade 7 glossary.
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).
The Illustrative Mathematics name and logo are not subject to the Creative Commons license and may not be used without the prior and express written consent of Illustrative Mathematics.
This site includes public domain images or openly licensed images that are copyrighted by their respective owners. Openly licensed images remain under the terms of their respective licenses.