Polynomials and Factor by Grouping

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Objective

SWBAT factor four terms of a Polynomial using the Factor by Grouping method and apply it to finding the dimensions of a garden.

Big Idea

To observe that Factoring by Grouping can be used for Difference of Squares, and Factoring Trinomials, but must be the method used to factor four terms.

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.

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.

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.