Rhonda Leichliter ROGERS HIGH SCHOOL, ROGERS, AR
Algebra I : Unit #7 - Polynomial Operations and Applications : Lesson #8

Polynomials and Factor by Grouping

Objective: SWBAT factor four terms of a Polynomial using the Factor by Grouping method and apply it to finding the dimensions of a garden.
Standards: HSA-SSE.A.1a MP1 MP7 MP8
Subject(s): Math
60 minutes
1 Warm Up - 15 minutes

The purpose of this lesson is to present to all of the students that Factor by Grouping is the only method to apply to factor four terms in a Polynomial.  However, after teaching several methods previously in this unit including Factor by Grouping to factor Quadratic Trinomials, some students are still struggling with factoring.  

So I use the Warm Up of this lesson to demonstrate that Factor by Grouping can be used to factor any of the methods including Difference of Squares.  My reasoning is to provide lower level students with one method to factor all of the Polynomials.  I demonstrate the Warm Up in the video below.

Link

2 Partner Activity - 15 minutes

For the Partner Activity, I use this Card Game from the website listed below.

http://mathconceptualized.com/DEMO/Concepts/15_SolveQuadEqnsByFactor/Activities/FactorPolyCardGame.pdf

 

In this game as the instructions state, the Polynomial cards are placed face down in a stack in the middle of the table.  The factors are handed out to four students evenly.  The students turn a Polynomial Card over from the stack in the middle of the table, and each student tries to factor the Polynomial on their worksheet.  Once the students factor the Polynomial, the student(s) with the correct factors discards those factors from their hand.  The student who discards all of their factors first, wins the game.  

 

I  did not use the Factor and Polynomial labels for the back of the cards.  I made copies of the Polynomials and the Factors on regular Copy Paper so the students could write on the cards if they desired.  However, Card Stock would probably provide a more permanent set of cards to use later.

Interacting with the Objective
High Quality Task

After introducing students to the lesson with the Warm Up, I like to provide some activity where the student interacts with the objective. Usually this is in a collaborative setting, which may be with a Partner, or a small group.  

The students enjoyed the Card Activity in this Lesson I think because there was an actual winner.  It was more than just trying to match the cards.  It also made each student participate to contribute the cards, and every student had to try to factor each Polynomial.

Factoring Polynomials is a difficult skill for students to master.  Most of the time, it takes more time beyond the Algebra I curriculum for this to happen.  However, I do believe that students will get better with practice and interacting with other students who may factor better than they do.

3 Exit Slip - 20 minutes

I provide students with about 20 minutes to complete the Exit Slip for this lesson.  I use the Exit Slip for a formative assessment on the students ability to Factor Polynomials. Students may use any method to factor the binomials and the trinomials.  Students must apply Factor by Grouping to the Polynomial with four terms.

In this Exit Slip, I provide students with an application problem.  The application problem provides the area of given crops of a farm as Polynomials.  Students have to factor the Polynomials to find the dimensions of each crop.  I have students submit their responses for this Exit Slip online, but it can be handed in as well.  There are two student responses to compare below. 

 

Continually Assessing
Intervention and Extension

You can see from the first student example of the Exit Slip that the student does provide the correct factors for problems a through e.  However, it does look like that the student continued solving for x in problem c.  Students continually get confused between the instructions to Factor or Solve.  Repeating and modeling the difference between these two verbs is important for student success in this Unit and the next Unit which is Quadratic Functions.  

Another Important reflection about this lesson, is that students need to understand that factoring and multiplying are inverses of each other.  The student that turned in the second example of the Exit Slip made several mistakes which may have been prevented if the student would have checked that the product of the factors was the original problem.  Encouraging students to continually check factors by multiplying them back together is another way to ensure students success with this such important skill of Factoring.