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.

  Student Work Samples
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Got zeros? Polynomials do! Multiplicity of Zeros (Day 3 of 3)

Unit 2: Polynomial Functions and Equations
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.

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Subject(s):
Math, degree of a polynomial, end behavior (polynomials), Precalculus and Calculus, polynomials, x-intercepts, Algebra 2, PreCalculus, zeros of functions, Algebra, Multiplicity of Zeros, Nspire Calculators, Texas Instruments
  41 minutes
calculator screen shot
 
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