Adding and Subtracting Polynomials: The Terms Have to Like Each Other

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SWBAT identify characteristics of polynomials, including terms, coefficients and degree. SWBAT add and subtract polynomials and demonstrate understanding of the rules for adding and subtracting polynomials.

Big Idea

Adding and subtracting polynomials is framed as another application of arithmetic with integers rather than another group of isolated and novel concepts!

Entry Ticket: Adding Polynomials

15 minutes

The purpose of the Entry Ticket: Adding 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.

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.



BrainPop Video: Introduction to Polynomials and Reviewing Questions and Examples

20 minutes

In the middle of this 90 minute lesson, we complete three main activities: 1. An introductory video on polynomials to preview and/or refresh characteristics of polynomials for students, 2. a lecture and note-taking section and 2. Group/guided practice. 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.

Once students are all set up with their notes I write the topic for the day “Adding and Subtracting Polynomials: They have to like each other” 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.

I show the introductory video on polynomials from Brain Pop

While we are reviewing the answers and examples to the questions from Brain Popa, I am giving students explicit cues to write down the examples and notes including how to solve each example as well as any questions they have. Once we are done reviewing the video and examples, we complete more guided practice with the guidance and structure of two Khan Academy videos.  

Khan Academy Videos (10 minutes) and Reviewing Notes (15 minutes)

25 minutes

I show the following three Khan Academy videos. After EACH video I follow the Reviewing Notes protocol (description is below the video links in this lesson plan)

1. “Terms, coeffficients and exponents in polynomials” (2-3 minutes)

2. “Adding Polynomials” (2-3 minutes) 

3. “Subtracting Polynomials” (2 minutes)

Reviewing Notes: I complete the following protocol after EACH of the three short videos. The reason for I pause and have students talk, discuss and update notes after each video is to support students with difficulties with working memory. I don’t want to show them three videos in a row without having them enage in the work through conversation and note-taking in fear of some students forgetting what the first video was even aboutAfter showing the video, I ask students to complete the following protocol: 1 minutes to add more details to their notes, 1 minute sharing their notes with a partner (during this time the partner adds to/revises their notes), and 1 minutes flipping roles (the partner who initially revised now reviews their notes while the other partner now revises their notes). The intent of this protocol is to engage students in academic conversations with each other, but perhaps more importantly is to provide students with an immediate and different perspective on the important aspects of the video and the mathematics behind it. Another strategy I use to assess students understanding is to pause the video before a step and ask students to explain to a partner what they think the next step will be and why (I stress the “why component of the conversation and am constantly telling students that I am not only interested in them getting the right answer, but want them to get the right answer AND explain their thinking behind the answer).

I ask students if they have any additional questions, including if they would like to review one of the examples from the video or review an additional practice problem similar to the ones on the video on the SmartBoard as a class.

Guided Practice

15 minutes

The students work in pairs to solve a set of problems that get at the skill of adding and subtracting polynomials. While students are working I circulate the room, asking questions and checking in on any students who are having difficulty (and try to ask deeper/next step questions to students who understand the problems well).

One example problem set I like to use comes from the Oswego District Regents Prep Center on Adding and Subtracting Polynomials.

As time allows, I have a different pair of students re-teach the problem on the SmartBoard to the class, along with an explanation of how they solved the problem. This time allows for differentiation, as I can ask questions that get at the steps of the problem for students who may be struggling with the core idea behind the lesson. I also can ask questions, like “what would happen if the second term was xy instead of x – how would that change your thinking” to push gifted students who benefit from more of a challenge.


Lesson End + Homework

15 minutes

In this activity students are asked to engage in the all important task of paraphrasing and summarizing information. To accomplish this task, students are asked to complete the Exit Ticket: The Terms Have to Like Each Other (Adding and Subtracting Polynomials) in partners in response to the prompt: “Compare and contrast adding and subtracting polynomials with adding and subtracting integers." This task is the exit ticket or ticket to leave for this lesson.

The Homework: Adding and Subtracting Polynomials for the class is to generate at least three addition and three subtraction of polynomial problems. In addition, the students have to write out a clear explanation of how to solve 1 of the addition problems and 1 of the subtraction problems that they make. By creating and simplifying different polynomial expressions, it is my hope that students continue to see stucture in repeated reasoning (MP.8) but also see the connections between the systems of polynomials and real numbers.