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# Quadratic Modeling (DAY 4)

Lesson 14 of 16

## Objective: SWBAT apply the concept of a quadratic function to 4 classic application problems: projectile motion, revenue maximization, area, and number puzzles.

#### Warm-up

*15 min*

Students will complete Warm-up Quadratic Forms which is a set of exercises about switching from one representation of a quadratic function to another. The unit test is fast approaching and this warm us is designed to provide a bit of review on something we learned some time ago.

#### Resources

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#### Application Stations

*60 min*

To summarize our polynomial modeling activities and practice the four classic quadratic problem types, students will cycle through Review Stations Quadratic Word Problems. I discuss these stations and why I spend 4 days on quadratic modeling in the video Quadratic Modeling.

The stations are tables for four that have multiple copies of exercises printed on half sheets of colored paper (one color for each station). I use stations for practice when there are a few distinct skills that are best learned by practicing each individually before seeing them mixed together in a problem set.

I know the students well by this time of the year and can easily assign them to groups in which they will be most likely to stay on task and help each other persevere [MP1]. I choose groups of three and make sure that each group has at least one member who is confident with word problems so that they can help manage the frustration level. Each group will cycle through 4 unique stations (there are two of each). The application stations are organized as follows [MP4].

- Station 1: projectile motion problems
- Station 2: revenue problems
- Station 3: geometry applications
- Station 4: number puzzles

(A fifth station with more projectile motion problems is included in case the number of students works out better with five stations rather than four.)

I give students a quick overview of the problem types found at each station, reminding them that they should pick up a paper for their folder at each station they visit. Each group will start at one of the 4 stations, spend 12 minutes at each station, and then rotate to the next station. I use the overhead timer to make everyone aware of how much time is left. After the timer rings, each group advances to the next station.

As students work, I use the 3-Cup System to encourage perseverance provide help where it is needed [MP1]. The goal of this activity is for students to practice solving quadratic equations and make connections between the concept of a quadratic functions and a quadratic equations [MP2].

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#### Closure and Assignment

*15 min*

For homework, students will continue where they left off with the set of Quadratic Application Problems that we began two lessons back. This problem set consists of 18 modeling questions arranged by application type according to application type.

The solutions to these problems will be available on Edmodo so that students will have the ability to check their answers before they come to class tomorrow.

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- LESSON 1: Introduction to Polynomials
- LESSON 2: Seeing Structure in Expressions - Factoring GCF's and Quadratics
- LESSON 3: Connecting Polynomials to Sequences
- LESSON 4: Connecting Polynomials to Geometric Series
- LESSON 5: Quadratic Functions: Standard and Intercept Forms
- LESSON 6: Quadratic Functions: Vertex Form
- LESSON 7: Flexibility with Quadratic Functions
- LESSON 8: Connecting Quadratic Functions and Quadratic Equations
- LESSON 9: Solving Quadratic Equations
- LESSON 10: Quadratic Performance Task
- LESSON 11: Quadratic Modeling (DAY 1)
- LESSON 12: Quadratic Modeling (DAY 2)
- LESSON 13: Quadratic Modeling (DAY 3)
- LESSON 14: Quadratic Modeling (DAY 4)
- LESSON 15: Review Workshop: Polynomial Functions and Expressions
- LESSON 16: Unit Assessment: Polynomial Functions and Expressions