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# Factoring Quadratic Expressions

Lesson 4 of 7

## Objective: SWBAT factor simple polynomials using their previous understanding of polynomials. SWABT paraphrase key ideas and points from the lesson.

*90 minutes*

The purpose of the **Entry Ticket Solving a System to Help Factor** 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.

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The class then turns to a Focus Lesson on Factoring Quadratic Expressions: **Class Notes: Factoring Quadratic Expressions**

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 videos 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 9^{th} 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 “Factoring Quadratics” 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 write the word “factor” on the whiteboard and have students generate a definition and examples of factors (two numbers, like 9 and 3 that have a common factor of 3).

We then go through the powerpoint slides, and students take **2-column **notes during the process to engage with the material through the 4 domains of language (reading, listening, speaking and writing). There are a number of **Turn and Talk **prompts in the slides as well to help facilitate student academic conversations.

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In this section, I have students practice factoring by completing the **Guided Practice Problems Factoring Quadratics **in groups of 2-3 students. During this time I check in with the different groups to help them get started and/or complete an additional problem as a model for students who are struggling with the concept.

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#### Exit Ticket + Homework

*15 min*

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: Factoring Quadratics** in partners in response to the prompt: “Consider the following three polynomials: 1. X^{2}+10x+24, 2. X^{2}-3x-40, and 3. X^{2}+18X+81. Solve the problem AND explain how the way you solved the problems is related to the first three entry ticket problems.” This task is the exit ticket or ticket to leave for this lesson. The reason for connecting this exercise to the entry ticket is again to reinforce how and why students can factor quadratics.

The **Homework: Factoring Quadratics** for the class is to generate at least three addition and three quadratic expressions to factor. In addition, the students have to write out a clear explanation of how to factor 1 of the three problems they create.

As an alternative, many times I will use the Homework worksheet as additional practice/extra credit and assign a **Deltamath** website problem set for homework.

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Hi Michelle,

Thanks so much for the comment. I typically teach the ac method for factoring when a>1. I also will help students set up/expand their equations for magic square.

For example, in the expression 2x2 + 14x + 20 I would have students set up the following system of equations:

Rule/Equation 1: 2(a) + b = 14 and

Rule/Equation 2: a*b = 20

so a = 5 and b = 4

So, students are still looking for factors of 20, but now they have to double one of the numbers to get to 14x's.

The one drawback to this method is students have a tough time understanding why the a (number that gets doubled, 5 in the example above) goes with the parenthesis opposite of the 2x - the most common mistake I get is (2x + 5)(x + 4). To challenge this misconception, I have students distribute their answer and compare it to the original quadratic expression.

Thanks again for the positive comments and I hope the lessons are going well in the classroom!

-Jason

| 3 years ago | Reply

What method do you use to teach when a>1 Do you divide it out or teach the AC method? It's hard to tell from your notes. I really love your lessons!

Thank you,

Michelle Birkhead

Lewisville High School,

Lewisville TX

birkheadm@lisd.net

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- UNIT 1: Thinking Like a Mathematician: Modeling with Functions
- UNIT 2: Its Not Always a Straight Answer: Linear Equations and Inequalities in 1 Variable
- UNIT 3: Everything is Relative: Linear Functions
- UNIT 4: Making Informed Decisions with Systems of Equations
- UNIT 5: Exponential Functions
- UNIT 6: Operations on Polynomials
- UNIT 7: Interpret and Build Quadratic Functions and Equations
- UNIT 8: Our City Statistics: Who We Are and Where We are Going

- LESSON 1: Multiplying and Dividing Exponents: To Add or Not to Add
- LESSON 2: Adding and Subtracting Polynomials: The Terms Have to Like Each Other
- LESSON 3: Multiplying Polynomials: Distribute Like a Champ!
- LESSON 4: Factoring Quadratic Expressions
- LESSON 5: Working with Polynomials: Practice and Study Session
- LESSON 6: Generating Polynomials: A Math Assessment Project Formative Assessment
- LESSON 7: Unit Assessment: Polynomials