Adding and Subtracting Polynomials

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Objective

SWBAT identify like terms, find the sum or difference of Polynomials, and apply these skills to solve a real world problem.

Big Idea

To be able to explain why adding polynomials is viable and why subtracting a Polynomial is the same as multiplying through the Polynomial by a -1, then adding.

Warm Up

10 minutes

I expect for the Warm Up to take the students about 10 minutes to complete and for us to review Questions 2 and 3 as a class.  

After about six minutes, I will call on a student to share what they found as the total sum of all of the terms on the page (Question 2). I will share the expression on the board. Then, I will ask him/her to explain his/her strategy for completing the work. Then, I will ask students who disagree with this initial sum to state their own sum. Again, I will ask for an explanation of a strategy and I will write the sum on the board. We can now compare the two expressions to see if they are equivalent, or if an error has been made. If other answers are available, we can share them as well, using the same method. As this conversation progresses, we will discuss the necessary changes to the expressions to combine all like terms.

Next, I will call on students who have not yet participated to answer Question 3. I will first ask them to explain how they identify like terms. Then, I will ask them to explain how to combine like terms. Although this question may review ideas covered in our discussion of Question 2, this followup enables more students to participate, perhaps creating opportunities for students who initially struggled to test out new ideas (for them).

Guided Notes

15 minutes

After reviewing the Warm Up, I will provide each student with a copy of today's Guided Notes. Today, I will discuss adding and subtracting polynomials. My students have seen this content in Grade 8, so the presentation is review, focused on precise vocabulary and application. 

I expect that some of my students will get confused when using parentheses. I suspect that we simply do not use them often enough. I instruct my students to pay attention to the symbol between the parentheses as they initially read an expression. Then, to think carefully about the application of the Distributive Property. In the examples presented today, a value of +1 or -1 is to be distributed through the polynomial. Then, I will ask students to help me work through the problem. 

The removal of the parentheses so that like terms can be combined is an important step in the problem. In the subtraction problems it is helpful for students to reflect on the fact that all of the terms inside the parentheses are being subtracted, taken away, or removed from the whole expression. Students should also understand this as distributing a negative one, which changes the sign of each term. In the case of addition, students should remember that each term is being added, as well as thinking about the application of the Distributive Property. 

 

Independent Practice

15 minutes

Today's Independent Practice should take students about 15 minutes to complete.  I want my students to practice what was covered in the Guided Notes and begin to think beyond. Of course, I also want to check for individual student understanding.

The Independent Practice is only seven questions, chosen to provide students with a variety problems to find the sum and difference of Polynomials. I will be looking to see how many students rewrite the problem without the parentheses before combining like terms (I show the strategy of rewriting without the parentheses in the video below). I have promoted this idea earlier in the lesson. The feedback that I will give to students as they work will focus on working and communicating one's work precisely (MP6). Since some of my students tend to make sign errors when adding and subtracting polynomials, I am looking to see if there are students for whom this is a problem.  

 

Exit Slip

10 minutes

This Exit Slip asks students to solve three application problems. Students need to set up the problems based on key words of the problem, and then simplify the polynomial expressions. Students need to understand the meaning of Cost, Revenue, and Profit to be able to set up the first problem (see my Modeling Profit and Working with Fractions Reflection). Problems 2 and 3 ask students to model the perimeter of a trapezoidal yard and find a missing measurement.

I will use the Exit Slip to check for each student's ability to add and subtract polynomials.