Classifying Polynomials

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Objective

SWBAT classify and name polynomials by degree and by their number of terms.

Big Idea

Students use their prior knowledge of prefixes to build their mathematical vocabulary as they classify polynomials.

Warm Up

10 minutes

My plan is to spend about ten minutes of class time on today's Warm Up. The Warm Up contains 6 questions. I expect that my students can answer the first five questions easily. Perhaps too easily, but that helps to set them up for Question 6. I want my students to focus on the prefix of each word, to think about the pattern in the sentences, and open up their minds to consider how it related to polynomials.  

As we review the Warm up, I will encourage my students to write down everything that they can remember about Polynomials. It is often the case that my students do not volunteer very much. If there contributions are really limited, I will ask them to look up the definition of a Polynomial. Then, beginning with the definition, I want my students to write a definition in their own words. I'll say, "Try to explain what a Polynomial is and what it is not." After giving them time to write I will have students share out their ideas.

Here are some of the things that I hope will appear on our list about Polynomials at the end of the Warmup:  

  • Contains several terms separated by addition and subtraction only
  • An expression that contains constants, variables, and exponents
  • The exponents can only be Whole Numbers (0,1,2,3.......)
  • No division by a variable
  • Coefficients of terms are real numbers
  • Does not have an infinite number of terms

 

 

Partner Activity

30 minutes

With our freshly created Properties of Polynomials list on the board, we will progress to the main activity for today's lesson. To begin, I hand out the Polynomial Cards.  I also hand each student an Activity Sheet with three activities on it. 

Students will categorize the expressions on the Polynomial Cards as "a Polynomial" or "Not a Polynomial."  I have students work with their table partner on this task to promote discussion. Students have markers that they can use to write directly on their tables. As we begin I ask them to write the heading of the two categories, Polynomial or Not a Polynomial. Then I have the students cut the cards apart. I ask the students to take turns placing each card under the correct category. As a student places the card, he or she should state the reason for their choice. The other partner may agree or disagree with their choice, and the pair should try to come to a consensus where the card should be placed.  Students should write their final answers on the activity sheet.

As students are working on the sorting task, I walk around the room to monitor student progress.  If students are stuck or confused, I try to pose a question instead of providing answers.  For example, if several students are confused about card number six I will ask the question, "What are the conditions for the coefficients of Polynomials?" 

Once the groups have finished sorting the cards, I will randomly call on students to share their placement for different cards that I post under the document camera. (All of the cards are Polynomials except cards three, seven, eleven, and twelve.)

After we discuss the sorting task I will have my students finish the last two activities. I tell students that they are only to use the cards with Polynomials on them for these two activities. I'll ask if anyone can explain the terms Degree of a Polynomial and Number of Terms of a Polynomial before we get down to work. If the definitions are incomplete or unclear, I will ask all of my students to look up the definitions. We also discuss what is meant by the leading coefficient.

 

 

Exit Slip

10 minutes

With about 10 minutes remaining in the period, I will hand each student an Exit Slip.  The Exit Slip is a check for student understanding of how to classify polynomials by degree, and, by the number of terms. After I collect the Exit Slips, I will provide the answers under the document camera. For this task I want to give my students immediate feedback. I want them to be thinking about the correct answers as they leave for the day. And, I want to leave them with a correct presentation using precise mathematical vocabulary. One of the challenges to mastering the content of this unit is the acquisition of the vocabulary in today's lesson.