Multiplying Polynomials: Distribute Like a Champ!

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SWBAT multiply polynomials using the distributive property. and demonstrate understanding of the properties for multiplying polynomial expressions.

Big Idea

Students learn that distributing is the key to success in multiplying polynomials and in life!

Instructional Note to Teachers: Setup and Pre-Teaching

●       Environment for this lesson: This lesson is taught as a 90 minute block. I like having students seated in groups of 2 or 4, mainly to provide more opportunities for students to have academic conversations with each other. The work on academic conversations and language comes from the fantastic theory and practice of Jeff Zwiers. This unit is focusing on the academic conversation (and writing) skill of paraphrasing/summarizing. For more information on Academic Language and Conversations see the strategy folder.

●       Tools and Instructional Technology or Software:

SmartBoard, Virtual Nerd, Khan Academy, Calculator, Word Processor (optional, for written responses) 

 ●       Extensions and Scaffolds: I like to add in peer editing and feedback for the writing portion of this lesson ideally for all students, but often there is not enough time. Adding the peer reflection piece as an extension for students who have completed the written response can be a quick and easy way to keep all students engaged in learning and on relevant material that is still tied to the objective of the lesson.

Entry Ticket: Distribute Like a Champ!

15 minutes

The purpose of the Entry Ticket: Multiplying Polynomials is to activate students’ prior knowledge about working with polynomials. I start by having students work on the Entry Ticket as soon as they enter the class – as the year has progressed it has become more and more automatic that students take out their binders and get to work on the Entry Ticket rather than milling around or socializing. This also frees up a couple of quick minutes for me to take care of housekeeping (attendance, etc.) and not waste valuable instructional time. Please see my strategy folder for more information of how I use the in the classroom and as an assessment tool.

I typically give students a 2 minute warning so they know we will be talking as a group soon. About 5 minutes into class, I ask students to talk and turn to a partner about the Entry Ticket, specifically to converse about how they solved the problem and to identify the rules used to solve each problem. We then review the Entry Ticket as a class and ask groups to share out any discrepancies/errors and how to correct them.

I then turn my attention to the agenda board which has the lesson and language objectives, agenda and homework written on it. We review the objective(s) as a class, and I talk about how this lesson’s objective fits into the bigger objectives of the unit (to support students who have difficulty seeing the big picture and/or shifting back and forth between the gestalt and the details of lessons and units). I typically have students write down the homework assignment during this time and hand out copies of the homework, but have students file the homework in their binders (I have also had classes where having the homework was too much of a distraction – in these cases I handed the homework out at the end of class).  

The lesson objective is referred to with verbal and non-verbal cues throughout the lesson to contextualize the lesson for students. I ask students what they think they will need to do in order to be successful and meet the day’s objective. The reason for this is to scaffold and model metacognitive strategies in the hopes of students learning these skills and using them with increasing independence. After the day’s agenda has been reviewed, the class shifts to the middle of the lesson.


Videos on Distributing - Tom Brady Highlights and Alma Harris on Distributive Leadership (10 minutes) and Think-Pair-Share (10 minutes)

20 minutes

To begin this section of class, I cue students to make sure they all have their binders and something to write with. I also explicitly tell students they need to take notes on the video we are about to watch (I recently have realized that I have a deeply engrained assumption that most students know when I want them to take notes, but in reality the majority of my 9th graders need explicit instruction of not only when to take notes, but how to take notes.

I recommend to students that they take notes in two-column format, with the term or example on the left column and notes, definitions work on the right column. In addition the top of the notes should always have a clear topic, which I try to provide each class and the date. At the conclusion of the note-taking, I have students write a “Elevator Ride” statement at the end of their notes to support them in paraphrasing/identifying the main idea(s) of the session. Guided notes is a good example of how I try to Differentiate instruction in the classroom.

Once students are all set up with their notes I write the topic for the day “Distribute like a Champion: Multiplying Polynomials” on the board and ask them to be sure to have that as their topic for their notes. I then let students know we will be watching a video on the topic and that they should be taking notes and that I will be asking questions throughout the video.

To start this section, I write the word “distribute” on the whiteboard (separate from the SmartBoard projector so the word is accessible throughout the lesson). I ask students to tell me some synonyms or “ballpark” words for distribute and make a word web with their responses. I then explain that we are going to use this idea to help understand how to multiply polynomials.

I then show the introductory video on Tom Brady Highlights as an example of distribution (passing to a number of different players):

And then I show a video from Alma Harris on distributed leadership 

I then have students complete a think-pair-share on the following prompt: Describe a time in your life when you distribute. What are the benefits on distributing in this example? Students write down their thoughts quietly for 2-3 minutes, share with a partner for 2-3 minutes, and then we have each pair of students share their discussion points with the class. The intent of spending this much time on the concept of distribution is to give students multiple means of representation for the idea of distribution which hopefully will make for a smoother application of the concept to multiplying polynomials.


Explicit Instruction and Active Note-taking

20 minutes

After the think-pair-share on the videos, I teach a focus lesson (see Class Notes Distribute Like a Champ! Multiplying Polynomials, using explicit instruction as a tool to name what we are learning about as well as showing students how to apply the strategy of distribution to factor polynomials.

During this time, students are engaging in the four domains of language. Students are using expressive language by asking questions (speaking) and writing notes in two-column format (writing). Receptively, students are listening to the focus lesson and are reading the material.

Providing students with opportunities to engage in the four domains of language is a natural way to differentiate the lesson and provide support to a variety of learners.

Guided Practice

20 minutes

I show the following Khan Academy video:

During the video I pause after each problem is written out to allow students to write the problem down. For the first problem I let the video play until the end of the solution and then pause for a couple of minutes to give students time to write out their notes. I also ask students to talk with a partner for 1 minute to identify any questions/unclear areas they have on that first example and then discuss the questions that the class has.

For the remaining problems I:

-pause the video after the example is written out

-give students time to write down the problem and attempt to answer it in pairs

-play the explanation of the problem with the video

-give students a couple of minutes to revise and edit their notes

-repeat with the next example

Exit Ticket and Homework

15 minutes

For the Exit Ticket: Multiplying Polynomials Compare and Contrast students are asked to engage in the all important task of paraphrasing and summarizing information. To accomplish this task, students are asked to distribute an integer expression and a polynomial expression. 

I then have the class compare and contrast the processes of solving the two expressions. My goal is for students to see the connections between manipulating integers and polynomials, which is directly related to Common Core standard APRP.A.1

I typically set up the brainstorming section in a think-pair share format, giving students a few minutes to jot their ideas down independently, talk it through with a partner and then generate a Venn diagram or other graphic organizer as a class. This particular exercise utilizes (and give students all important practice) the critical thinking skill of comparing and contrasting as a tool to access the Common Core standards. 

Students then work independently on mapping their Venn diagram onto an Idea Organizer as a way to translate their organized ideas into more conventional text structure. The next step is for students to write out a polished complex paragraph as a written response. If time is tight, I tend to assign the writing up portion of the assignment for homework or have students complete the writing assignment as an entry ticket for the next class. 

The Homework: Multiplying Polynomials for the class is to create at least three multiplication of polynomial problems. In addition, the students have to write out a clear explanation of how to solve 1 of the multiplication problems using the term distribution at least once. The rational for this task is I want students to be able to engage in the critical thinking skill of creating as a means to demonstrate their understanding of the day's learning objectives.