Working with Polynomials: Practice and Study Session

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SWBAT add, subtract, multiply and divide polynomials. SWBAT factor polynomials, understanding the properties that support polynomial operations.

Big Idea

Students dig deep into solving a smaller number of problems and teach their classmates as a study method!

Entry Ticket: Practice Manipulating Polynomials

15 minutes

The purpose of the Entry Ticket Manipulating Quadratic Functions as a review of what we have been working on over the past few lessons 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.

For this lesson I use the following entry ticket:

For the two problems below,

  • Circle like terms for the following polynomials – explain, in writing, why the terms are like.
  • Simplify the polynomials

1.    2x4 + 3x3 – 2x5 +7x4 + 11 - 7

2.  x+ 14x5 – x2 + 12x2

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.

Guided and Group Practice: Manipulating Polynomials

60 minutes

Think Pair Share: Manipulating Polynomials

15 minutes

To conclude the lesson, I have students complete the Classwork/Homework: Study Guide for Polynomials through a think-pair-share as a way to recap and review major concepts and ideas that they will be assessed on for manipulating polynomials. I remind students that the intent of this lesson was to practice the main ideas that will be on an upcoming test (the test is given to all students taking Algebra I and is a common assessment developed by Algebra I teachers in the school).

Students then count by 4’s and pair up with 1 other student that has the same number. The number the student has corresponds to the section of the study guide (all number 1’s are assigned adding and subtracting polynomials, all number 2’s are assigned multiplying polynomials, etc.). This way students focus on paraphrasing/summarizing the key ideas to one of the four main sections in the study guide.

Think – I ask students to take 2 minutes to write down 2-3 major ideas/important concepts they will need to know for the section they are assigned. Students working on adding and subtracting polynomials, for example, may identify one key concept is the ability to identify like terms in order to know which terms can be combined.  As students are writing, I rotate around the room, providing starters and cues to students that I know have relative difficulties with initiation and/or identifying the main idea of lessons as a means to differentiate instruction.

Pair – I then give students 5 minutes to talk to a partner (it is important to remind students they need to pair up with a student with the same number – that way each pair of students will be discussing the same topic – factoring, dividing polynomials, etc.). By the end of the 5 minutes I ask each pair of students to agree to the most important 2-3 things they need to know about the topic they are discussing. This section allows students to take the perspective of other classmates and navigate academic conversations through the use of academic language.  

Share – To wrap up class, I have each pair of students share their ideas by number (each pair of number 1’s go first, etc.) As students are sharing I am either sitting at my computer and typing (during this time students can see what I am typing on the Smart Board) or writing down notes on the SmartBoard). Each pair shares and we discuss as a class whether each idea is a new idea or could fit in with one already on the board.

Once all groups have gone, I save the notes and email or print out copies of the notes for students – this way the class has generated a study guide of the main ideas and concepts to remember for the test in an environment that has a high level of support and structure. Many 9th graders I work with have not internalized productive study habits, so using some class-time in an organized manner both gives them practice and a model by which to prepare for tests and other assessments.

For homework, I assign students to work on the remaining study guide questions they have – I remind students to complete the problems on their own, then check their answers with the answer key and also use the class-generated study notes as a reference to help with any problems they have difficulty with.