Lesson objective: Solve problems involving nonlinear functions by using tables or graphs to find a rule or pattern.

This lesson provides an opportunity for students to apply their knowledge and understanding of rates of change and unit rate to a real-life situation. Students are asked to make a recommendation for which charter bus service to use for an 8th grade field trip. The pricing for one company is linear and the other is nonlinear.

Key Concept students will use:

- Some nonlinear functions behave in predictable ways, and we can describe this behavior qualitatively.

Skills students will use:

- Calculate rates of change to look for patterns.
- Create graphs to look for patterns.

Students engage in Mathematical Practice MP.4 (model with mathematics) as they solve a real-world problem with mathematics. Students will use tables or graphs to determine the per-student pricing for two different companies. Some students may use guess-and-check, while others may look for patterns.

**Key vocabulary: **

- nonlinear
- rates of change
- unit rate

**Special materials needed:**