Lesson+Plan

Scott DePutron Julie Christman Dr. Hasan Dividing Polynomials Lesson Plan Algebra 2 35 Students 2/7/12 80 minutes

__Common Core: __ 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.
 * __Established Goals (Standards) __**__: __

A-APR.6.  Rewrite simple rational expressions in different forms; write //a//(//x//)///b//(//x//) in the form //q//(//x//) +//r//(//x//)///b//(//x//), where //a//(//x//), //b//(//x//), //q//(//x//), and //r//(//x//) are polynomials with the degree of //r//(//x//) less than the degree of //b//(//x//), using inspection, long division, or, for the more complicated examples, a computer algebra system.

A-APR.7. <span style="color: #3b3b3a; font-family: 'Times New Roman',serif; font-size: 12pt;"> (+) Understand that rational expressions form a system analogous to the rational numbers, closed under addition, subtraction, multiplication, and division by a nonzero rational expression; add, subtract, multiply, and divide rational expressions.

__<span style="font-family: 'Times New Roman',serif; font-size: 12pt;">California Math Content __
 * <span style="font-family: 'Times New Roman',serif; font-size: 12pt;">3.0 **<span style="font-family: 'Times New Roman',serif; font-size: 12pt;"> Students are adept at operations on polynomials, including long division.

<span style="font-family: 'Times New Roman',serif; font-size: 12pt;">Students will be able to:
 * __<span style="font-family: 'Times New Roman',serif; font-size: 12pt;">Learning Objective __****<span style="font-family: 'Times New Roman',serif; font-size: 12pt;">: **
 * <span style="font-family: 'Times New Roman',serif; font-size: 12pt;">Divide polynomials using the methods of long division and synthetic division.


 * __<span style="font-family: 'Times New Roman',serif; font-size: 12pt;">Key Ideas __****<span style="font-family: 'Times New Roman',serif; font-size: 12pt;">: **
 * <span style="font-family: 'Times New Roman',serif; font-size: 12pt;">Long division
 * <span style="font-family: 'Times New Roman',serif; font-size: 12pt;">Synthetic division


 * __<span style="font-family: 'Times New Roman',serif; font-size: 12pt;">Essential Questions __****<span style="font-family: 'Times New Roman',serif; font-size: 12pt;">: **
 * <span style="font-family: 'Times New Roman',serif; font-size: 12pt;">What are the steps used to divide polynomials using long division?
 * <span style="font-family: 'Times New Roman',serif; font-size: 12pt;">What are the steps used to divide polynomials using synthetic division?


 * __<span style="font-family: 'Times New Roman',serif; font-size: 12pt;">Academic Language: __**
 * <span style="font-family: 'Times New Roman',serif; font-size: 12pt;">Monomial, binomial, trinomial, polynomial, numerator, denominator, dividend, divisor, quotient, remainder, terms, degree, FOIL, coefficients, “like terms,” factor, GCF, difference, sum, product, variable


 * __<span style="font-family: 'Times New Roman',serif; font-size: 12pt;">Key Academic Genres __****<span style="font-family: 'Times New Roman',serif; font-size: 12pt;">: **
 * <span style="font-family: 'Times New Roman',serif; font-size: 12pt;">Polynomials
 * <span style="font-family: 'Times New Roman',serif; font-size: 12pt;">Rational Expressions


 * __<span style="font-family: 'Times New Roman',serif; font-size: 12pt;">Needed Materials: __**
 * <span style="font-family: 'Times New Roman',serif; font-size: 12pt;">SmartBoard notes
 * <span style="font-family: 'Times New Roman',serif; font-size: 12pt;">Whiteboards
 * <span style="font-family: 'Times New Roman',serif; font-size: 12pt;">YouTube video
 * <span style="font-family: 'Times New Roman',serif; font-size: 12pt;">Group chart


 * __<span style="font-family: 'Times New Roman',serif; font-size: 12pt;">Lesson Activities: __**
 * <span style="font-family: 'Times New Roman',serif; font-size: 12pt;">Warm-up Video (Mr. Duey)
 * <span style="font-family: 'Times New Roman',serif; font-size: 12pt;">Vocabulary Review
 * <span style="font-family: 'Times New Roman',serif; font-size: 12pt;">Warm-up problems
 * o <span style="font-family: 'Times New Roman',serif; font-size: 12pt;">Long division
 * o <span style="font-family: 'Times New Roman',serif; font-size: 12pt;">Dividing Polynomials by a Monomial
 * <span style="font-family: 'Times New Roman',serif; font-size: 12pt;">Dividing Polynomials by Binomials
 * <span style="font-family: 'Times New Roman',serif; font-size: 12pt;">Pair Activity
 * <span style="font-family: 'Times New Roman',serif; font-size: 12pt;">Group Activity
 * <span style="font-family: 'Times New Roman',serif; font-size: 12pt;">Group Inquiry-Exploration
 * <span style="font-family: 'Times New Roman',serif; font-size: 12pt;">Reflection (What did we learn?)


 * __<span style="font-family: 'Times New Roman',serif; font-size: 12pt;">Assessments: __**
 * __<span style="font-family: 'Times New Roman',serif; font-size: 12pt;">Informal __<span style="font-family: 'Times New Roman',serif; font-size: 12pt;">:
 * o <span style="font-family: 'Times New Roman',serif; font-size: 12pt;">Whiteboard answers
 * o <span style="font-family: 'Times New Roman',serif; font-size: 12pt;">Answers to classroom questions
 * o <span style="font-family: 'Times New Roman',serif; font-size: 12pt;">Group interactions
 * o <span style="font-family: 'Times New Roman',serif; font-size: 12pt;">Group answers
 * __<span style="font-family: 'Times New Roman',serif; font-size: 12pt;">Formal __<span style="font-family: 'Times New Roman',serif; font-size: 12pt;">:
 * o <span style="font-family: 'Times New Roman',serif; font-size: 12pt;">Class Presentations of Problems
 * o <span style="font-family: 'Times New Roman',serif; font-size: 12pt;">Homework Review Quiz
 * o <span style="font-family: 'Times New Roman',serif; font-size: 12pt;">Homework Presentations

<span style="font-family: Arial,sans-serif; font-size: 12pt;">3. (27x4 - 18x2 + 9x) <span style="font-family: 'Lucida Sans Unicode',sans-serif; font-size: 12pt;">÷ <span style="font-family: Arial,sans-serif; font-size: 12pt;">9x <span style="font-family: Arial,sans-serif; font-size: 12pt;">4. (x2 + 12x - 160) <span style="font-family: 'Lucida Sans Unicode',sans-serif; font-size: 12pt;">÷ ( <span style="font-family: Arial,sans-serif; font-size: 12pt;">x - 8) <span style="font-family: Arial,sans-serif; font-size: 12pt;">7. (21x2 - 29x - 10) <span style="font-family: 'Lucida Sans Unicode',sans-serif; font-size: 12pt;">÷ <span style="font-family: Arial,sans-serif; font-size: 12pt;">(3x - 5) <span style="font-family: Arial,sans-serif; font-size: 12pt;">10. (4x3 - 7x + 8) <span style="font-family: 'Lucida Sans Unicode',sans-serif; font-size: 12pt;">÷ <span style="font-family: Arial,sans-serif; font-size: 12pt;">(2x - 1)
 * __<span style="font-family: 'Times New Roman',serif; font-size: 12pt;">Problems that the students will be doing __****<span style="font-family: 'Times New Roman',serif; font-size: 12pt;">: **


 * __<span style="font-family: 'Times New Roman',serif; font-size: 12pt;">Other ways students might solve these problems __****<span style="font-family: 'Times New Roman',serif; font-size: 12pt;">: **
 * <span style="font-family: 'Times New Roman',serif; font-size: 12pt;">Students may set up the division vertically and attempt to cancel terms or use the method of long division.


 * __<span style="font-family: 'Times New Roman',serif; font-size: 12pt;">Misconceptions and challenges might students have __****<span style="font-family: 'Times New Roman',serif; font-size: 12pt;">: **
 * <span style="font-family: 'Times New Roman',serif; font-size: 12pt;">Students may not divide each term in the numerator by the denominator.
 * <span style="font-family: 'Times New Roman',serif; font-size: 12pt;">Students may cancel out exponents from solely one term in the numerator with one term in the denominator rather than distributing the whole denominator to each term in the numerator.
 * <span style="font-family: 'Times New Roman',serif; font-size: 12pt;">Students may not distribute the negative sign to the whole binomial when subtracting in long division.
 * <span style="font-family: 'Times New Roman',serif; font-size: 12pt;">Students may forget to use placeholders for missing terms when using long division.
 * <span style="font-family: 'Times New Roman',serif; font-size: 12pt;">Students may not remember the steps involved when the remainder is not zero.
 * <span style="font-family: 'Times New Roman',serif; font-size: 12pt;">Students may not bring down the first term before following to multiply and add when using synthetic division.


 * __<span style="font-family: 'Times New Roman',serif; font-size: 12pt;">Extension Activities __****<span style="font-family: 'Times New Roman',serif; font-size: 12pt;">: **
 * <span style="font-family: 'Times New Roman',serif; font-size: 12pt;">Dividing Polynomials HW 1
 * <span style="font-family: 'Times New Roman',serif; font-size: 12pt;">Introduction to synthetic division in following lesson.