##
* *Reflection: Checks for Understanding
Polynomial Function Workshop - Section 1: Review Workshop

While students were working I would stop in to each table group or they would come to ask me questions. I received some interesting questions that were a way to formatively assess students' understanding of polynomial functions.

1. For question #2, students were to find the equation for the graph below. I gave the students the answers to this worksheet so they could check their work as they went, and many students asked about how to find the leading coefficient of this function. One thing that students continually asked is, "how do we know if a function has an *a* value or not?"

When we got back together and discussed as a class, I was sure to point out that every polynomial function has an *a* value, although if it is 1 you can't "see" it. This was not really a misconception, but something that definitely had to be clarified.

2. Another theme I saw was students trying to use the vertex formula (*x* = -*b*/(2*a*)) for all types of polynomial functions instead of just quadratics. Students were thinking that it could be used to find relative extrema for third and fourth degree polynomials.

Again, this is something I definitely wanted to address when we had our class discussion. My guess is that part of the misconception stems from the fact that students are probably not given a verification for this formula when they learn it in Algebra 1 - it is just presented as a fact. Proving this formula uses sophisticated math that an Algebra 1 student may not be ready for, so students may never really understand why it works.

*Do Students Understand Polynomial Functions?*

*Checks for Understanding: Do Students Understand Polynomial Functions?*

# Polynomial Function Workshop

Lesson 5 of 12

## Objective: SWBAT solve problems that involve polynomial functions.

*50 minutes*

#### Review Workshop

*35 min*

We have spent the last four days studying polynomial functions, so it is a good idea to take a breather and review some of the important concepts we have learned. For today's review, put students in groups of three and have them work on the assignment. Have them work collaboratively and without their textbooks and notes to see what they can recall without help. Once they go through as much as they can, instruct them to circle the problems that they could not get to without help. This will be a good indication that they will need to study these concepts and problems in greater depth. After identifying problem areas, students can use resources to try to solve the remaining problems.

In the video below I identify some common misconceptions and areas that may be problematic for your students. In my experience, these have been problems that will stump my students.

*expand content*

#### Class Discussion

*15 min*

For the last 15-20 minutes of class, post the answers and walk around to help students who are still stuck. Notice the problems that a majority of students are struggling with and pull the class together to have a discussion about these problems. You can ask students who did get the correct answer to show their work on the document camera and explain their solution strategy.

*expand content*

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- UNIT 1: Functioning with Functions
- UNIT 2: Polynomial and Rational Functions
- UNIT 3: Exponential and Logarithmic Functions
- UNIT 4: Trigonometric Functions
- UNIT 5: Trigonometric Relationships
- UNIT 6: Additional Trigonometry Topics
- UNIT 7: Midterm Review and Exam
- UNIT 8: Matrices and Systems
- UNIT 9: Sequences and Series
- UNIT 10: Conic Sections
- UNIT 11: Parametric Equations and Polar Coordinates
- UNIT 12: Math in 3D
- UNIT 13: Limits and Derivatives

- LESSON 1: Quadratic Function Jigsaw
- LESSON 2: Sketching Graphs of Polynomial Functions
- LESSON 3: Roots of Polynomial Functions - Day 1 of 2
- LESSON 4: Roots of Polynomial Functions - Day 2 of 2
- LESSON 5: Polynomial Function Workshop
- LESSON 6: Ultramarathon Pacing and Rational Functions
- LESSON 7: Homecoming and the Five Pound Gummy Bear
- LESSON 8: Graphing Rational Functions
- LESSON 9: Inequalities: The Next Generation
- LESSON 10: Rational Functions and Inequalities Formative Assessment
- LESSON 11: Unit Review Game: Pictionary
- LESSON 12: Polynomial and Rational Functions: Unit Assessment