## Hamgo Problems (for teacher to display).pdf - Section 3: Polynomial Roots HAMGO

*Hamgo Problems (for teacher to display).pdf*

# The Fundamental Theorem of Algebra - Day #2

Lesson 6 of 8

## Objective: SWBAT use the Fundamental Theorem of Algebra and show that it is true for quadratic polynomials.

*45 minutes*

#### Intro Poll Question

*5 min*

As the students enter the classroom, I ask for them to respond to the **Poll Question**. To simplify this process, I use **Poll Everywhere,** a website where the students can submit their response via cell phone or iPad. (I prefer my students NOT use their cell phone. Although professional use of cell phones is permitted in our building, standard messaging rates still apply and I do not want to upset any parents, especially when the students can use their iPads instead.)

I highly recommend looking into creating a Poll Everywhere account (for free!). You will be able to save poll results as a PowerPoint slide, and re-use previously created polls. This site can literally be creatively implemented at virtually any point in a lesson.

#### Resources

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#### Scavenger Hunt: Carl Gauss

*15 min*

As a student, I only vaguely recall talking about important historical mathematical figures in class - this includes high school and college. It is certainly not the fault of any of my teachers that I do not remember - I am sure that they gave a shout out to these bright minds in class. What little I do remember is largely because the handful of formal reports that I had done mathematicians.

I believe I remember the instances where I had ownership over the direction of my work. I researched the mathematician, documented sources, and watched him or her come to life in my writing. Although I will not have time for students to write a formal report in this lesson, I approach this brief history lesson with the philosophy of giving the students ownership over what they find, rather than just reciting facts to them. This is much easier today than when I was a student, because the students have a whole world of sources right at their fingertips (MP5).

For this part of the lesson I project the **Scavenger Hunt ** and ask students to get busy. I gather responses in real time using a **Poll Everywhere** that I set up to collect free responses. As the students respond, I remind them also list their information source (MP5). Without going through the process of formally writing a paper and citing sources, this allows us to investigate potentially credible vs non-credible sources. It is a great discussion that serves the students well beyond this class and for many years ahead. Even if they forget that Gauss proved the Fundamental Theorem of Algebra, they will at least become responsible consumers of mathematical resources. I commonly tell my kids to "put your filter on" when searching the internet looking for information.

#### Resources

*expand content*

#### Homework

*10 min*

To conclude the lesson, I have the students attack **6 problems**. These problems ask the students to go the reverse their thinking, from HAMGO game, that is, I ask them now to start with the zeros of the polynomial and go to create the original function. I brought this up in the **previous lesson.** Thinking "forwards and backwards" and will help ensure that the students understand all angles of the Fundamental Theorem of Algebra.

#### Resources

*expand content*

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- UNIT 1: Culture Building Unit - Welcome to the New Year!
- UNIT 2: Exponential and Logarithmic Functions
- UNIT 3: Sequences and Series
- UNIT 4: Statistics: Something for Everyone
- UNIT 5: Review Lessons
- UNIT 6: Writing Prompts in Mathematics
- UNIT 7: Trig Tidbits
- UNIT 8: Functions, Problem Solving, and 21st Century Skills
- UNIT 9: Polynomials and Problem Solving
- UNIT 10: Probability
- UNIT 11: Imagine This! Imaginary and Complex Numbers
- UNIT 12: Let's Explore Radicals!

- LESSON 1: Imagine THIS!
- LESSON 2: Complex and Imaginary Battleship!
- LESSON 3: Introductory Concepts Quiz
- LESSON 4: Complex Solutions of Quadratics
- LESSON 5: The Fundamental Theorem of Algebra - Day #1
- LESSON 6: The Fundamental Theorem of Algebra - Day #2
- LESSON 7: Unit Review
- LESSON 8: Unit Test