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# Putting the Pieces of Polynomials Together (Day 1 of 2)

Lesson 11 of 15

## Objective: SWBAT find a polynomial function given its roots and end behaviors, sketch the graph of a polynomial and identify key features of these graphs, and factor a polynomial equation to find the zeros and its graph.

## Big Idea: Today’s project has students use roots and end behaviors to write the equation of a polynomial function and then work with a team to graph.

*40 minutes*

#### Homework Quiz

*10 min*

Students will take their homework quiz over last week’s homework:

**Old note on homework quizzes: **In my class, we do a Homework Quiz every Monday. So for my calendar this lesson is landing on a Monday, so we will take about 10 minutes out of class to do that. I am not posting my homework quizzes at this time because I like to be selective of the problems I put on the quiz based on whatis happening in the classroom. If students are really struggling on a particular topic as a whole then I won’t put that question on the quiz. Or if we have gone over a problem in class, I won’t put that on the quiz but would probably choose a similar problem. So for minimal prep work, I would recommend having students do a written homework quiz. Just make a list of problems that you want to check in more detail and give students an allotment of time to copy down their work and answer for this problem. I also sometimes have students do their homework quizzes in their clickers. I will share an example of that, once one is made.

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I plan to assign the polynomials test review for homework for this entire week. For my classes, we aren’t going to have much time for in-class review leading up to this test. So students will be expected to complete their test review before coming to class on the review day and be prepared with any questions that they have.

#### Resources

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I'm on a block schedule, so I have 90 minute periods. This lesson took them FOREVER. But it was so worth it. They needed it really badly to consolidate all their learning in this unit. It also made really evident that I definitely over-scaffolded on the Multiplicity of Zeros activity I adapted for my class from yours. I also ended up skipping the closure (on accident) and it was a BIG mistake. Definitely needs a closure for that. Multiple actually. I still had students saying that every even polynomial produced a parabola. They completely missed that it can have several turns, as long as the end behavior holds. Of course, they have not been through any Common Core math classes before mine, so they think they can just go through it like practice problems on a worksheet, skipping problems they don't get, and just moving on. I kept having to ask, "Uh, how did you answer this question when you skipped this one? It requires the answer before it..." For them to say, "oh yeah, I just plugged in this so I could keep going. I didn't get it." Sooooo frustrating. They definitely need to work on MP1.

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- UNIT 1: Basic Functions and Equations
- UNIT 2: Polynomial Functions and Equations
- UNIT 3: Rational Functions and Equations
- UNIT 4: Exponential Functions and Equations
- UNIT 5: Logarithmic Functions and Equations
- UNIT 6: Conic Sections
- UNIT 7: Rotations and Cyclical Functions
- UNIT 8: Cyclical Patterns and Periodic Functions
- UNIT 9: Trigonometric Equations
- UNIT 10: Matrices
- UNIT 11: Review
- UNIT 12: Fundamentals of Trigonometry

- LESSON 1: Puzzling Polynomials and Quizzical Quadratics
- LESSON 2: Building Connections: Building Polynomials (Day 1 of 2)
- LESSON 3: Building Connections: Building Polynomials (Day 2 of 2)
- LESSON 4: Detailed Descriptions of our Puzzling Polynomials
- LESSON 5: Got zeros? Polynomials do! Multiplicity of Zeros (Day 1 of 3)
- LESSON 6: Got zeros? Polynomials do! Multiplicity of Zeros (Day 2 of 3)
- LESSON 7: Got zeros? Polynomials do! Multiplicity of Zeros (Day 3 of 3)
- LESSON 8: Long, Synthetic, and Square! Oh my! Polynomial Division
- LESSON 9: Rational Roots and Remainders: Important Theorems of Polynomials
- LESSON 10: Polynomials with Complexes… Complex Zeros that is!
- LESSON 11: Putting the Pieces of Polynomials Together (Day 1 of 2)
- LESSON 12: Putting the Pieces of Polynomials Together (Day 2 of 2)
- LESSON 13: Roller Coaster Polynomials
- LESSON 14: Test Review
- LESSON 15: Polynomials Unit Test