Position, Speed, and Direction
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.
- 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.
Let's use signed numbers to represent movement.
- I can multiply a positive number with a negative number.
- I can use rational numbers to represent speed and direction.
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