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* *Reflection: Intervention and Extension
Polynomial Long Division - Section 4: Homework Assignment

I had one of those amazing experiences with a students due to this homework assignment. The final problem has the students compare a numerical division problem with a polynomial division problem. I carefully planned this problem so the coefficients and the digits match up. When we talked about this problem in class, I had a young man ask me how often this will occur. I told him, and the class, that I didn’t know but I would give extra credit to anyone who does some experimenting to find out. As a side note, I have found that offering extra credit as an extension activity, when a good opportunity arises, is a great way to get kids to push themselves mathematically. So often, students will work harder for Extra Credit than they will for regular assignments.

The young man who originally asked the question got really excited about the idea and started experimenting. I would say he came to visit me 3 or 4 times after school to talk about it. This student, by the way, is at best a C student. He’s the one whose seat is always in the front so I can help him stay on task. He got as far as finding certain cases that worked while realizing that most cases don’t fit this pattern. I was so proud of his interest and effort.

*Intervention and Extension: Why I Teach...*

# Polynomial Long Division

Lesson 1 of 15

## Objective: Students will be able to divide polynomials using long division.

#### Warm Up

*5 min*

I include **Warm ups** with a **Rubric** as part of my daily routine. My goal is to allow students to work on **Math Practice 3** each day. Grouping students into homogeneous pairs provides an opportunity for appropriately differentiated math conversations. The Video Narrative specifically explains this lesson’s Warm Up- Polynomial Long Division, which asks students to determine the missing side of a rectangle with an area represented by a polynomial.

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I begin this lesson by asking the students to dividing 7 into 18 by hand. Through this problem, my students review the concepts of division including the concept of remainder. Many students will automatically attempt to find the decimal. This is an excellent opportunity to discuss the pros and cons of using the decimal or fractional version of a remainder, particularly in regards to accuracy (**Math Practice 6**). I then provide them with increasing complex problems to ensure that they are comfortable with this skill in preparation for the introduction of polynomials.

Next, I introduce them to polynomial long division. The first problem is done together. Often, as a scaffolding method, I do a regular long division problem at the same time to highlight to similarities. While this is a brand new skill for most students, I never like to do a problem with out providing opportunities for students involvement. I demonstrate a portion of the problem, and then give them an opportunity to try the next step.

Students often struggle with the subtraction portion of this process. A teacher friend of mine shared this little rhyme “Draw the line, switch the sign”. This seems to help many of the students.

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The remainder of the lesson is a Guided Practice that helps students build the skill of polynomial long division. Students may struggle when missing terms are introduced. I like to give the students a problem with something new like this without warning them about the change. Sometimes I tease them that I am trying to “trick” them with the problem to let them know that there is something different. I give them a chance to work and then do a think-pair-share on the differences in this problem as well as possible ways to deal with the differences (**Math Practice 3**).

Detailed presentation notes can be found in the PowerPoint.

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#### Homework Assignment

*1 min*

The main portion of this Assignment asks students to practice the skill of polynomial long division. These problems build in complexity so this assignment can be differentiated by assigning different numbers. The final problem connects a problem that divides numbers with a problem that divides polynomials and then asks students to compare them (**Math Practice 7**).

This worksheet was created with Kuta Software which is an excellent resource for a mathematics teacher.

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#### Exit Ticket

*2 min*

I use an exit ticket each day as a quick formative assessment to judge the success of the lesson.

Today's Exit Ticket ensures that students understand how to divide polynomials given some missing terms.

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- UNIT 1: Modeling with Expressions and Equations
- UNIT 2: Modeling with Functions
- UNIT 3: Polynomials
- UNIT 4: Complex Numbers and Quadratic Equations
- UNIT 5: Radical Functions and Equations
- UNIT 6: Polynomial Functions
- UNIT 7: Rational Functions
- UNIT 8: Exponential and Logarithmic Functions
- UNIT 9: Trigonometric Functions
- UNIT 10: Modeling Data with Statistics and Probability
- UNIT 11: Semester 1 Review
- UNIT 12: Semester 2 Review

- LESSON 1: Polynomial Long Division
- LESSON 2: Synthetic Division
- LESSON 3: Uses of Polynomial Division- The Factor and Remainder Theorems
- LESSON 4: Introduction to Polynomial Equations
- LESSON 5: Solving Polynomial Equations Graphically
- LESSON 6: Graphs of Polynomial Functions
- LESSON 7: Intercepts of Polynomial Functions
- LESSON 8: Solving Polynomial Equations Day 1
- LESSON 9: Solving Polynomial Equations Day 2
- LESSON 10: Transformation of Polynomial Functions
- LESSON 11: Modeling Volume with Polynomials Day 1
- LESSON 12: Modeling Volume with Polynomials Day 2
- LESSON 13: Polynomial Functions Review Day 1
- LESSON 14: Polynomial Functions Review Day 2
- LESSON 15: Polynomial Functions Test