## MP5.MP4 - Section 3: Calculator Investigation: Multiplicity of Zeros

# Got zeros? Polynomials do! Multiplicity of Zeros (Day 2 of 3)

Lesson 6 of 15

## Objective: SWBAT• Determine the degree of the polynomial functions and the effect the degree has upon the end behavior of the functions. • Write possible equations for a polynomial function, given information about its zeros. • Write the equations in factored form, given the graphs of three functions.

## Big Idea: Using Nspire Calculators, students investigate the relationships of polynomial functions, their degree, end behaviors, zeros and x-intercepts.

*51 minutes*

#### Homework Quiz

*10 min*

Students will take their homework quiz over last week’s homework (worksheets #1-3).

**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. 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 have shared an example of the homework quiz in the resources and check out the reflection for more details on how homework quizzes drive my instructional decisions.

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At the start of class today, I am going to present students with their focus area today: End Behvaiors. I am going to draw this non-completed End Behaviors Table (without the green and red writing) on the board and assign students the task of figuring out how we generalize this by the end of the hour. Students should continue their work on the Student Handout - Multiplicity_of_Zeros_of_Functions to help answer this.

We should also just take a moment to remind students about their mathematical practices they should be focusing on today (**Mathematical Practice 5: Use appropriate tools strategically** and

**Mathematical Practice 7: Look for and make use of structure**). See yesterday’s lesson, day 1, for more details on milestones and predicted struggles that students will have in this activity.

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#### Closure

*10 min*

To wrap up today's learning I am going to have students stop and take about 3 minutes to try to fill in the End Behaviors table they were presented with at the beginning of class on their own. Then I will lead the class discussion that I mention in the video Got zeros day 2, video reflection, end behaviors about end behaviors.

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#### Homework

*1 min*

Assign Homework 4 - Polynomials from this unit for homework. The assignment has some great questions to assess students understanding of end behaviors.

#### Resources

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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