# Polynomial Rewrite

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## Objective

SWBAT use the structure of a polynomial expression to rewrite the expression.

#### Big Idea

Why should we learn this? Your students learn to rewrite polynomial expressions AND learn concrete reasons to value this skill!

## Set the Stage

5 minutes

You will need the  polynomials handout if your students did not already complete the lesson "Puzzle it Out".  This lesson continues what we began yesterday by taking the same polynomials and rewriting them.  I begin by asking my students to take out their Polynomials handout from yesterday and a clean piece of lined paper.  I ask them to copy the first expression onto their lined paper then walk them through how to simplify the expression.  You can see how we do this on the educreations video.  As I'm writing on the board, I ask my students for each step and I ask them to explain why they chose to take that action or to explain how they knew what to do next (this part is particularly tough for some of my brighter students who are accustomed to just "knowing" the answer). (MP3)  When we finish this first expression as a class we're ready to move on to the next part of the lesson.

## Put it into Action

40 minutes

Independent work 15 min: I've found that some students are ready to make the transition to simplifying these more complicated expressions and equations, while others need more support to be successful.  As we begin the main portion of this lesson, I make a point of reassuring my students that there are several ways to simplify each problem and there will be no prizes for the fastest work but there will be recognition of the most accurate and complete work.  I have my students work independently to re-write each of the polynomials on the polynomials handout in the simplest form they can.  Sometimes my students ask for clarification about what constitutes "simplest form", but instead of reviewing the definitions and rules they learned in Algebra I, I allow them to become the experts.  I encourage a class discussion including students looking their questions up in either their own textbook or one of the other Algebra I or Algebra II books I keep in my room and sharing what they find.  When these questions are addressed, I have my students work on the handout while I walk around giving encouragement, redirection, and one-to-one assistance as needed. (MP1)

Team work 10 min: When all my students have completed the handout, I tell them they get to work with their front partner to compare and critique their work and that they will be sharing at least one problem with the class.  I explain that the sharing will include all the steps they took to simplify the problem as well as how/why they chose each step.  While the teams are working, I walk around and select problems for each team to present, based on what I hear them saying to each other.  When all the teams have received their problem assignments, I tell them that they have 3 minutes to finish preparing to share with the class.  (I intentionally select a strong team for the first presentation to provide an example for the weaker teams) (MP3)

Class Presentations 15min: To close this section of the lesson, I have each team present one or more of the problems and explain how/why they chose the steps to simplify the way they did.  I also encourage the students who are not currently presenting to ask appropriate questions and/or offer suggestions for other ways to simplify the same problems.  (MP3) I also emphasize the use of appropriate vocabulary by both the presenters and those students asking questions, an important part of attending to precision in mathematical communication. (MP6)  My Polynomial video discusses why I chose to have my students present their work.

## Wrap it Up

10 minutes

I like to give my students a chance to find their own reasons for valuing what we do.  I borrow the chromebooks for this part of the lesson and challenge each student or team to find at least one example of a polynomial expression or equation online.  The catch is that they can't just go to a math site, they have to find their expression/equation actually being used by someone in the career or occupation. (MP4) Some students are stumped at first, but generally they get excited when I ask them what they're interested in and we search for mathematics connections to that topic/field.  This activity gives nice closure to a couple of days spent working with polynomials.