# Solving and Building Polynomials

## Overview

This lesson plan is a unit on solving and building polynomials, modeling polynomials, and using transformations to graph functions.

# Summary

This lesson plan spans a whole 5 day unit (7 days for reveiw and test) on solving and building polynomials and one day on graphing rationals for my next unit. This lesson can be done virtually (need to record lesson videos), synchronously, asynchronouosly, or face-to-face.

# Background for Teachers

To teach this lesson, you'll need an understanding of the Remainder Theorem, Zero Product Property, Rational Root Theorem, using synthetic division, and writing factors and roots from solutions.

Use the links below to help:

https://www.youtube.com/watch?v=ZaXaBcZxhq4

https://www.youtube.com/watch?v=vu0JmblDgog

# Step 1 - Goals and Outcomes

Learning Intentions:

Students will be able to solve a polynomial written in factored form.

Students will be able to solve a polynomial of any degree when written in standard form.

Students will be able to build a polynomial equation given the zeros of the polynomial.

Success Criteria:

Students will use the Zero Product Property to solve a polynomial written in factored form.

Students will be able to solve a polynomial of any degree when written in standard form by using the Rational Root Therorem, Synthetic Division, Factoring, and the Quadratic Formula.

Students will be able to build a polynomial equation given the zeros of the polynomial by writing the correct factors and distributing appropriately.

# Step 2 - Planning Instruction

**Student Background Knowledge**

- Prior to this lesson, students will need to have an understanding of how Synthetic Division works, how to factor, and how to solve a Quadratic equation by factoring and/or using the Quadratic Formula.

**Strategies for Diverse Learners**

If you have students that struggle, maybe give them polynomials that have a highest degree of 3. That way they can be successful when solving polynomials. Another suggestion is to provide symplified guided notes, or paper copies of guided notes. You may also think about simplifying their assignments (some have a lot of problems).

# Step 3 - Instruction

Use this link to access all resources: Learning Hub

My learning hub is build through google sites. The main page is the home page and at the bottom of the home page are buttons to each day in the unit. Each day has a lesson video and the link to their assignment through canvas. There are also buttons that have an activity and a digital notetaking lesson for another day. This google site/learning hub is a great resource for my students, and you are more than welcome to use it. Please make a copy and then change whatever you need.

Day 1: Theorems on Polynomials

Day 2: Solving Polynomials with Rational Roots

Day 3: Solving and Building Polynomials

Day 4: Modeling Polynomials

Day 5: Transformations

Day 6: Review

Day 7: Test

Each day, give students the opportunity to try several problems from the notes and discuss their ways to solve it or their mistakes when solving them. For example, each lesson has multiple sections within the lesson, and in each section there are multiple problems. I do the first two problems and have them try the next one on their own so that we can discuss the problems and the mistakes they are making throughout each one. It also gives us a chance to expand on their knowledge of the current content being taught.

# Step 4 - Assessments

Formative Assessments: Homework assignments, the problems from the lessons they are trying on their own, and then I also do a daily quiz on the previous days' material. All formative assessments (specific problems) are up to the teacher.

Summative Assessment: I give a test at the end of the unit.

Rubric: https://www.uen.org/rubric/previewRubric?id=37109