The purpose of this lesson is to introduce students to negative rates of change, which will become important when they start learning about linear functions in later lessons. Students apply their understanding of operating with signed numbers to solve problems in context. The first problem involves a fish tank that is being filled and drained. The second problem deals with historic voyages in a bathyscaphe (deep-sea submarine) and a high-altitude hot air balloon. When students reason quantitatively about what it means for a rate to be negative, they engage in MP2.
The activities in this lesson involve more reading than most lessons. Be prepared to support students with unfamiliar words.
- 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.
- I can solve problems that involve multiplying and dividing rational numbers.
- I can solve problems that involve negative rates.
solution to an equation
A solution to an equation is a number that can be used in place of the variable to make the equation true.
For example, 7 is the solution to the equation \(m+1=8\), because it is true that \(7+1=8\). The solution to \(m+1=8\) is not 9, because \(9+1 \ne 8\).