## profit maximization warm-up 5.docx - Section 1: Warm-Up

# More Multiple Methods to Solve Problems involving Quadratic Functions

Lesson 5 of 17

## Objective: SWBAT use more than one method to solve problems involving quadratic functions.

## Big Idea: Now that students have solved different problems using a preferred method, they can apply their understanding to try and learn from different solution methods.

*60 minutes*

#### Warm-Up

*30 min*

The focus today is for students to learn a method to solve these problems that is different from their preferred method. I tell students this goal from the beginning of the day. Then, I ask them to use the warm-up time to try to figure out a different method.

In my classrooms, it always seems to work out that different students prefer different methods. I am always surprised how uniform the distribution of strategy preference is, although I do believe that slightly more students prefer the method of finding a linear relationship between two factors and then writing the quadratic function as the product of these factors.

I tell them that I am happy to explain any of the methods to small groups of students, but I also create a list of student experts for each method on the board. I add to this throughout the class period. I tell students that I want them to understand all of the methods, but that they only need to master two of them today.

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Once students have figured some things out on the warm-up, I ask them to work on the same assessment they started yesterday, but to solve the same problems using a different method:

One interesting confusion that arises for many students during this lesson is the difference between solving a problem using two different methods and writing two difference equivalent functions to fit a situation. At first, I was confused by this, then I realized that they were used to writing equivalent expressions to fit a set of data. This means that many students solved the problem one way and then algebraically manipulated the equation into a different form. Once I figured this out, I asked students to find a whole different method. Some students complained about this requirement, but it was worth the time and effort.

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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