Megan&Johnson& 10 &Grade& Algebra&II& Polynomials&€¦ · Megan&Johnson& 10th&Grade& Algebra&II&...
Transcript of Megan&Johnson& 10 &Grade& Algebra&II& Polynomials&€¦ · Megan&Johnson& 10th&Grade& Algebra&II&...
Megan Johnson 10th Grade Algebra II Polynomials
5.5 Division of Polynomials I. Setting the Stage: How can we use our knowledge of exponents and fractions to help us divide polynomials? A. Mathematics Curriculum Frameworks
A-‐APR -‐ 1. Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials.
B. A thorough understanding will be needed to complete this section that is the last in the chapter. The understanding of polynomials relates to other content areas in mathematics as well as science. The use of exponents is a practical way to write very small and very large numbers. It is also the ground work for being able to factor polynomials that is the next chapter.
C. Objectives – -‐ students will divide monomials
-‐ students will divide a polynomial by a monomial D. This material will be assessed through the homework at the beginning of the next class. I want the student to use various colors through a problem to demonstrate their understanding of like terms. The students will be given an exit survey on concepts of the lesson to make sure that the objectives are met.
II. Content of the Lesson
A. Content of Skills – This lesson will jump right in with using our knowledge of fractions and the quotient rule of exponents (from last chapter) to help us divide monomials. The lesson will continue with dividing a polynomial by a monomial. There will be a reminder that we can rewrite the fraction as the sum of two fractions with the same denominator. B. The understanding of working with polynomials relates to other content areas in mathematics as well as science. The concept of being able to multiply and divide polynomials grows on the knowledge that students already have. The students are applying the laws and rules that they have already had in the past to further their learning in mathematics. This section is also the ground work for being able to factor polynomials in the next chapter.
III. Knowledge of Students This classroom would contain between 18-‐25 students in 10th grade. The students would have already taken the Algebra I course. The students would have a thorough comprehension of
solving linear equations with single and two variables, working with word problems and solving inequalities with graphing. This would be the year that the students take the MCAS, so there would be emphases on understanding what the question is asking. There exist two students with IEPs in this class. For confidentiality reasons, the accommodations were not explicitly explained. A plan has been made with the cooperating teacher(s) regarding the additional needs of the student. Accommodations have been addressed and strategized with cooperating teacher(s) and parents of that student. Additional steps would be taken to ensure that student was able to learn the material that is necessary for them to succeed. IV. Preparation for the Procedure
A. The power point will be used to display techniques and examples. The smart board would display the examples that were going to be done in class. This would allow for multiple colors to be used to really demonstrate the process.
V. Sequence of Teaching A. The lesson will begin with dividing monomials. We can divide monomials by our
knowledge of fractions and exponents. Consider, 8𝑥! ÷ 4𝑥!
We can place this in fraction form,
8𝑥! ÷ 4𝑥! =8𝑥!
4𝑥!
= !!∗ !
!
!!
The students will then be instructed to divide the coefficients and use the quotient rule of exponents.
= 2𝑥!!! = 2𝑥!
The students will then be given practice problems. 1. −12𝑛! ÷ 3𝑛
2. !!"!!!!!
!"!"!
3. (20𝑝!𝑟!) ÷ (−5𝑝!𝑞!) B. Middle of the Lesson, I will have the students continue with these concepts by dividing a polynomial by a monomial. We will consider
(10𝑥! + 15𝑥) ÷ (5𝑥) We can place this in fraction form,
(10𝑥! + 15𝑥)5𝑥
We can then rewrite the fraction as the sum of two fractions with the same denominator. 10𝑥!
5𝑥+15𝑥5𝑥
= 2𝑥 + 3
The students will then be given practice problems.
1. !"!!!!"!!!!!!
!!!!
2. !!!!!!!!!"!!
!!!!
3. !!!!!!!!!!!
!!"!
C. If time allows, in small groups the students can work on the chapter 5 packet. This will allow the students to ask questions on an individual basis. I will walk around to make sure that the students are all at the same level of understanding and evaluate who may need a little more time or explanation. This is the last section of the chapter. I want the student to be able to ask questions regarding this concept since they will have less time to practice it. D. At the end of the class, I would assign problems from the textbook for homework for additional practice.
VI. Reflection after Teaching
A. This lesson was not taught to students, thus it is not applicable. B. This lesson was not taught, thus it is not applicable.
C. The preparation for the lesson was rather simple. Since I now have practice writing four other lessons, I was able to get through this one rather quickly. I do not believe that the students would have an issue with this section as long as they remember the quotient rule of exponents and how to work with fractions.