Polynomial Long Division

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Students will be able to divide polynomials using long division.

Big Idea

Connect students to the math they did in fifth grade with this lesson on polynomial long division.

Warm Up

5 minutes

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.

Connecting the Division of Numbers with the Division of Polynomials

15 minutes

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.

Polynomial Long Division Guided Practice

25 minutes

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.

Homework Assignment

1 minutes

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.

Exit Ticket

2 minutes

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.