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# Review of Polynomial Roots and Complex Numbers

Lesson 7 of 15

## Objective: SWBAT put together what they have learned about polynomials roots and complex numbers.

## Big Idea: Arithmetic with polynomials and complex numbers are performed in similar ways, but powers of i have a meaning distinct from powers of variables.

*90 minutes*

#### Warm-Up

*15 min*

For homework, students completed Complex Numbers Intro, which was a substantial assignment. As I check this assignment, I display the solutions on the overhead and ask students to mark on their packets any questions they missed. After I check everyone's work we review the assignment to prepare for the day's review and the next day's summative assessment.

The warm up is an additional set of complex number questions - mostly about simplifying powers of i. I send my students the formative assessment Warm-up- Simplifying Powers of i with the TI NSpire Navigator so that we can all see how the class is progressing in their ability to simplify complex expressions.

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In this lesson, I give students a chance to put their new understanding of imaginary numbers together with what they learned earlier about polynomials. They will be assessed on this material in a quiz the following day.

The activity Waterfall Trivia- Polynomials and Imaginary Roots is a self-advancing powerpoint with three rounds of 5 questions each. In each round, the question is displayed for five minutes. Students copy the problem onto a sheet of paper and work on it independently for five minutes [MP1]. They continue doing this until all 5 problems in the set have been displayed. At the end of each round, students submit their papers to me so I can tally up the points. The top three scorer in all three rounds win a prize, which is candy or some type of school supply.

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- LESSON 1: Seeing Structure in Expressions - Factoring Higher Order Polynomials
- LESSON 2: Proving Polynomial Identities
- LESSON 3: Polynomial Long Division and Solving Polynomial Equations
- LESSON 4: The Remainder Theorem
- LESSON 5: The Fundamental Theorem of Algebra and Imaginary Solutions
- LESSON 6: Arithmetic with Complex Numbers
- LESSON 7: Review of Polynomial Roots and Complex Numbers
- LESSON 8: Quiz and Intro to Graphs of Polynomials
- LESSON 9: Graphing Polynomials - End Behavior
- LESSON 10: Graphing Polynomials - Roots and the Fundamental Theorem of Algebra
- LESSON 11: Analyzing Polynomial Functions
- LESSON 12: Quiz on Graphing Polynomials and Intro to Modeling with Polynomials
- LESSON 13: Performance Task - Representing Polynomials
- LESSON 14: Review of Polynomial Theorems and Graphs
- LESSON 15: Unit Assessment: Polynomial Theorems and Graphs