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.
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 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 “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.
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.
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. X2+10x+24, 2. X2-3x-40, and 3. X2+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.