Unit 7, Lesson 17
Negative Rates
Accelerated 6
Preparation
Lesson Narrative
In this lesson, students solve problems that involve proportional reasoning with negative rates of change. Earlier in the course students saw that proportional relationships can be represented with equations of the form , where was a positive value. Now they apply their understanding of multiplying and dividing signed numbers to work with situations that involve negative values of .
The first activity involves a fish tank that is being drained and filled. The second problem deals with historic voyages in a bathyscaphe (deep-sea submarine) and a high-altitude hot-air balloon. The activities in this lesson involve more reading than most lessons. Some math language routines are recommended to help all students have access to the activities.
As students interpret the rates to understand the situation, they are making sense of the problem and persevering in solving it (MP1).
This lesson is optional in this course. It provides opportunities for students to apply multiplying and dividing rational numbers to solve problems.
- Apply operations with signed numbers to solve problems involving constant rates, and explain (orally) the solution method.
- Explain (orally and in writing) how signed numbers can be used to represent situations involving constant rates.
- Write an equation of the form $y=\text-kx$ to represent a situation that involves descending at a constant rate.
Let's apply what we know about signed numbers.
Required Preparation
None