Multiplying Polynomials

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Objective

SWBAT apply Distributive Property, multiply Polynomials, and recognize Special Products.

Big Idea

To see finding the product of Polynomials as equivalent to applying the distributive property once or multiple times.

Introduction

15 minutes

For this introduction to multiplying Polynomials, I have selected five problems to work with my students. To begin, I will give students about 10 minutes to work on the problems on their own. As students complete the problems, I will help them to find a partner with whom to compare their answers. I encourage students to try to explain why the answers are different when their are discrepancies. I will also encourage students to share and discuss their methods. I'll say, "When your answers are the same, did you use the same method? The same steps?" During this time I am observing and listening to gain a sense of whether or not my students are explicitly using or mentioning the Distributive Property.  I am also curious as to how students will use the Product of Powers of Exponents Property. 

For these introductory problems I have deliberately included the following types of binomial expressions:

  1. The Product of a Sum and a Difference
  2. Squaring a binomial

After students have compared and discussed each other's work, I will review these problems with the class focusing on Properties, skills and ideas that were raised (or not) as students worked the problems. I will ask my students to take notes on the page and make revisions as I present. I encourage my students to turn this sheet into a useful reference for further learning.   I demonstrate reviewing the Introduction problems in the video below. We will dig deeper into the patterns for special products of binomials during the Partner Activity that follows this demonstration.

 

 

 

 

Partner Activity

15 minutes

After reviewing the Introduction, I will hand each of my students a copy of Partner Activity. In this activity, my students work to identify patterns that result when multiplying special binomials. My goals for this activity are for my students to recognize products of certain binomials. I also want them to begin to recognize that multiplying polynomials is a process of combining factors, a process that can be reversed to identify the factors. We will not finalize the students' learning today. We revisit today's work in lessons on factoring a Difference of Squares and factoring Perfect Square Trinomials later in this unit.  

On the second page of the Partner Activity, there is a grouping task that asks students to look for patterns in their results. Students are asked to identify the binomials that are the product of a sum and a difference, or, that result from squaring a binomial. Some of the expressions cannot be grouped into either category.

In the final task, students are asked to find the product that results from multiplying each expression. For this task, I will have Table Partners check each others work. For this review I post answers to the problems on the board.  After the partner review, I will answer questions about any remaining points of disagreement.

Exit Slip

10 minutes

To conclude today's lesson I will give them an Exit Slip. The task asks students to create binomials that form products that fit certain criteria.

  1.  The first question ask students to create two binomials that form another binomial as its product.  Students have to synthesize what they have learned about multiplying binomials to develop their answer.  Students have to recognize that a Sum and Difference of identical terms in a binomial produce a Difference of Squares, which is a binomial product.
  2. The second question ask students to create two binomials that form a product that is not a binomial. Students can either create identical binomials that form a Perfect Square Trinomial product, or different binomials that create a trinomial that is not a Perfect Square.

These are higher level questions in which students have to develop their own problems to find certain products. In order to be successful at creating these problems, students have to understand the objective.  In this Exit Slip, students are demonstrating their understanding of multiplying binomials, and the products that are formed.