##
* *Reflection:
Got zeros? Polynomials do! Multiplicity of Zeros (Day 3 of 3) - Section 3: Calculator Investigation: Multiplicity of Zeros

The three learning targets in this lesson are big concepts in this unit and are key to student success in understanding polynomial graphs. By analyzing just a few questions from students’ work I can really see whether or not they met these learnings targets.

**Question/Learning Objective Correlation**

- Question 5 - SWBAT determine the degree of the polynomial functions and the effect the degree has upon the end behavior of the functions.

- Question 6 - SWBAT write possible equations for a polynomial function, given information about its zeros.

- Question 7 – proves an even deeper understanding of learning objective above

- Questions 8-10a - SWBAT write the equations in factored form, given the graphs of three functions.

**Analysis of Student Work Samples**

Student 1: Student 1 - Work Sample doesn’t answer questions 3-4 with much detail and really doesn’t demonstrate a thorough understanding of degree of a function and how the exponents affect the graph. However, this student does show an understanding the relationship between zeros and factors and factors with exponents in question 6. To me this shows that this student was probably influenced by their team in question 6 and that some learning is occurring. By questions 8-10, the student has demonstrated mastery of the last learning target. I wonder now if the student had time (maybe for homework?) to go back and look at their past answers if they would change their incorrect responses in questions 3-4 and find their missing exponent in 6.

Student 2: Student 2 - Work Sample demonstrates mastery of all learning targets.

Student 3: Student 3 - Work Sample Student 3 had an interesting answer for question 4. “How many times it curves minus one” is definitely how the degree affects the graph. And essentially the exponents in each term in the factored form affect the degree. So it wasn’t an answer I was looking for. But I liked it!

Student 3 also demonstrates mastery of all learning targets.

All students: Student 4 - Work Sample After reading over my students’ work, I don’t think this lesson helped them build an in-depth understanding of how even and odd exponents affect the graphs of polynomials. My students struggled greatly over question 7. No student in class correctly answered question 7. You can see from student work samples the question was skipped.

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

Lesson 7 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.

*41 minutes*

#### Warm-up

*5 min*

To warm-up students’ brains today and get them back focused on today’s task, review their new learning about zeros of a function with the clicker question on page 2 of the flipchart - Multiplicity of Zeros Day 3(p. 1-2).

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Students should continue their work on the Student Handout - Multiplicity_of_Zeros_of_Functions.

It is important that students are able to accurately answer question 6 before they will be able to identify the relationship between the x-intercepts/zeros and the factored form of a polynomial and write the factored form of the polynomial equation from a graph (and thus meet the learning target!) So as students are working today I will be checking their answers to that question. If students ask for help on this question or have the incorrect answer, I will take them all the way back to question 3 and 4 to insure there is a correct answer there as these two questions build to develop the understandings of the connection between factors and zeros and the connection between factors with exponents and the graph, which is needed for question 6.

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#### Closure

*5 min*

To wrap up and help students solidify the understandings they were supposed to pull from this lesson have students answer the Clicker Questions on pages 3-5 of the flipchart. I am going to have students work independently on these questions so I can assess the current progress of individual students so far.

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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