Multiplying Polynomials - Part I

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Objective

SWBAT multiply two binomial expression together using the FOIL method.

Big Idea

Students will develop an understanding of what it means to multiply polynomial expressions through the use of Algebra Tiles.

Do-Now

10 minutes

Students will use the properties of exponents to complete the Do Now in 4 minutes. I will prompt students to refer to their notes as they work, since this concept was covered in a previous class.

Volunteers will then come up to the board to show the class their answers. Then, a student will read the objective, "SWBAT multiply polynomials using the FOIL method".

I will ask the class to briefly recap what polynomial operations we have done thus far.

Introduction: Algebra Tiles

20 minutes

This activity lays the groundwork for future lessons involving Algebra Tiles, so it is important to spend a enough time during today's class to ensure student's comfortability with these manipulatives. Students worked with Algebra Tiles during our last class, but today's lesson will requires students to extend their thinking in a different way. I will use Algebra Tiles and the Multiplication Board to demonstrate polynomial multiplication to my students. 

First, I will ask students some simple multiplication problems, but ask them to find the product by tracing the corresponding multiplicand and multiplier using the multiplication table (The goal of this activity is to get students comfortable with motions needed to multiply polynomials with the algebra tiles).

Next, I will draw a visual representation of the simple products we found on the board using an array. After a few examples, I will ask students to make a generalization about the shape of a multiplication array. I will ask students how they can use the shape of an array to verify a product.

We will then explore the product of polynomials using the Algebra Tiles and Board. I will ask students to join in with me after I have modeled the first 2-3 problems.

  1. x*x
  2. 2x*x
  3. 2x*2x
  4. 3x*2x
  5. x*1
  6. 2x*1
  7. 3x*1

I will emphasize that our final answer results in a rectangular shape, just as it did with the numerical problems we modeled with an array. I will ask students if they see any patterns, or any connections to the properties of exponents.

Next, I will ask students to to use the Algebra Tiles to model on their own: x(x +1) and 2x(x + 1). After explaining our answers, I will ask students to model (x + 1)(x + 2) and (x + 3)(x + 1).

After multiplying a few more binomial pairs, I will ask students to again identify any patterns in the resulting products. I will ask students to use these patterns to multiply polynomials without paper.

Guided Notes + Practice

20 minutes

After the Introduction, students will follow along using these Guided Notes. I will ask students to draw in the Algebra Tiles needed to model the the three example multiplication problems on their paper, in order to transfer the pattern that we discover during the investigation to their classwork.

I will also use the patterns students found with the Algebra Tiles to introduce the FOIL method to students. I will explain to students that the acronym, FOIL, is an acronym that helps a student ensure that all parts of both binomials are multiplied with each other. 

We will then complete the example problems on the front of their notes together. Students will work on the back side of their notes with a partner. We will then review answers as a whole group. 

I will still allow students to use Algebra Tiles to check their answers as we work, if they want to continue using them. If a student gets a problem wrong, I will ask them to correct their answer using Algebra Tiles.

Independent Practice - Versatiles

20 minutes

Students will practice multiplying binomials using the ETA Hand to Mind product VersaTiles and this handout. Students will match correct responses to the numbered tiles in the black VersaTile case. If you do not have a VersaTiles classroom set, the assignment can still be completed by having students match questions and responses with pencil and paper.

Closing

10 minutes

Before we close, I will ask students to think about the problem (x + 1)(x + 5). I will then tell the class that a mystery student multiplied these two binomials together and got x^2 + 5. I will ask a few volunteers to identify the mistake, and to explain the student's incorrect reasoning. I will then ask the class to correct the error, and to describe how they could use Algebra Tiles to prove their response and disprove the mystery student's initial response. 

I will ask a student to summarize what we did in class today, and to describe how they would teach this lesson to an absent classmate. I will ask students to think about the FOIL method, and to decide if it can be applied to all polynomial multiplication.

Students will complete the Exit Card.