##
* *Reflection:
Got zeros? Polynomials do! Multiplicity of Zeros (Day 2 of 3) - Section 1: Homework Quiz

My students take their homework quizzes on their personal response systems. I ask 10 questions ‘randomly’ from the homework. I try to do a nice blend of difficult and easy problems and problems that are both new to students and review. Homework has two major purposes for this course:

- to revisit and practice concepts learned in the class [pretty typical of most homework assignment in most classes I would assume :)]
- to review basic skills that are required for upcoming lesson

Here is an example of the Homework Quiz Questions from this week over worksheets #1-3 in this unit.

The purpose of the homework quiz is mainly to hold my students accountable for completing their work. I really feel that even the homework quiz is somewhat of a learning experience too. The rigor level of the homework is dropped significantly when I give students multiple choice answers. However, it is a great way to communicate to students that their free response answers are probably correct if they are finding it in their possible answer choices. I also program the clickers to give students a quick ‘correct’ or ‘incorrect’ so they are getting feedback on their homework with very little work on my part. I also allow time at the end of the quiz for students to ask question on the problems they got wrong and can’t figure out why.

Even without personal response systems a multiple choice homework quiz can certainly save teachers time as the grading is very easy. By no means is their ‘quiz’ a summative assessment in my class. It is far more of a formative assessment to give me an overview of how the class is doing. When I pull the data from the clickers I can view it by individual students or by question.

Here is how the Individual Student Scores display. This gives me a great idea of who either really needs help or is not doing their homework. I can then talk with these students about what I can do to help them be more successful and assign tutoring as needed.

I can also view results by questions. This gives me such a great opportunity to identify where my students are struggling as a whole. For example, if a question returns results like this (Students displaying mastery) I can conclude that students understand this concept. Note how the kids that did get the question wrong took over a minute to answer it. They didn’t do their homework. However, if a question produces results like this (Students not displaying mastery) I know that this needs to be re-addressed again in class. As a matter of fact, this was a question I reviewed with student immediately following the homework quiz. I will also be sure to spiral in this concept as the test approaches in the test review days.

# 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