## Profit Maximization Problems.docx - Section 2: Investigation

# More Profit Maximization Investigations

Lesson 2 of 17

## Objective: SWBAT write function rules to describe relationships in the profit maximization problem and to find the best possible solution to the problem.

## Big Idea: Continuing work done yesterday, students employ mathematical practices to drill deeper into the Prom Ticket Story or work on different versions of the problem.

*65 minutes*

#### Closing

*5 min*

Towards the end of the workshop, I ask students to find a partner who does not sit at their table to discuss their work with. If you think that this will be too chaotic, you can write partner assignments on the board or overhead, or just have pre-assigned partners. The idea is to get them to talk to each other so that they gain knowledge about the problems, or get in the habit of comparing solutions and methods. The more often that they have the experience of learning from each other, the less dependent they will be on the teacher for answers and ideas.

After giving them a chance to discuss their work with each other, I ask them to write a brief check-out summarizing their progress on these problems and identifying what is still confusing for them. Often they write things like, “I did problems 1 and 2 but I got stuck on problem 3.” I discourage these types of answers, and instead model answers like, “I can solve the problems easily when I see the vertex in the table, but I don’t really know how to write an equation in vertex form that will fit the data.” I talk with students about how writing sentences like the latter help them make more meaningful progress, because they can ask better questions based on their self-assessments. I believe it is even worth the time to make students re-write their answers so that they develop this habit.

*expand content*

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- UNIT 1: Linear and Nonlinear Functions
- UNIT 2: Piecewise Functions
- UNIT 3: Absolute Value Functions and More Piecewise Functions
- UNIT 4: Introduction to Quadratic Functions through Applications
- UNIT 5: More Abstract Work with Quadratic Functions
- UNIT 6: Rational Functions
- UNIT 7: Polynomial Functions
- UNIT 8: Exponential Functions
- UNIT 9: Ferris Wheels
- UNIT 10: Circles
- UNIT 11: Radical Functions
- UNIT 12: Cubic Functions

- LESSON 1: Investigating Profit with Products
- LESSON 2: More Profit Maximization Investigations
- LESSON 3: Profit Maximization Problems Workshop: Multiple Methods
- LESSON 4: Multiple Methods to Solve Problems with Quadratic Functions
- LESSON 5: More Multiple Methods to Solve Problems involving Quadratic Functions
- LESSON 6: 4-Column Quadratic Data Tables
- LESSON 7: More 4-Column Data Tables
- LESSON 8: Applying Data Tables to Word Problems
- LESSON 9: Profit Maximization and 4-Column Data Tables Review
- LESSON 10: Profit Maximization and 4-Column Data Tables Summative Assessment
- LESSON 11: Different Forms of Quadratic Functions
- LESSON 12: Quadratic Data Tables
- LESSON 13: Finding Vertices of Parabolas
- LESSON 14: Heights of Falling Objects
- LESSON 15: Profit Maximization
- LESSON 16: Quadratic Functions Review and Portfolio
- LESSON 17: Quadratic Functions Summative Assessment