AL1-5Unit9Polynomials_Factoring

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```					                                                Campus: High School

Author(s): Miller and McIntyre                  Date Created / Revised: August 7, 2009

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Six Weeks Period: Fifth Six Weeks - P1          Grade Level & Course: 9 Grade Algebra

Timeline: 9 days                                Lesson Unit Title: Unit 9. Polynomials and Factoring

a. Which subject-specific TEKS are going to be addressed in the lesson unit?

Continuation of A.9 and A.10: Quadratics and other nonlinear functions.
Stated Objectives:     A.11 Quadratic and other nonlinear functions: The student understands there are
TEKS Addressed in      situations modeled by functions that are neither linear nor quadratic and models the
the Lesson Unit        situations.
A.11B Analyze data and represent situations involving inverse variation using concrete models,
(Include TEK           tables, graphs, or algebraic methods.
number and (SE)        A.11C Analyze data and represent situations involving exponential growth and decay using
student expectation    concrete models, tables, graphs, or algebraic methods.
description
b. Which specific (TA) Technology Application TEKS are going to be addressed in the
lesson unit? : N/A

What specific concepts will be included that clarify the content and satisfy the goal of the TEKS

Chapter 7 Exponents and Polynomials Continued:
Clarifiers:                     C7.5 Polynomials
     C7.6 Adding and Subtracting Polynomials
(Specific concepts
     C7.7 Multiplying Polynomials
to be included to
     C7.8 Special Products of Binomials
     C8.1 Factors and Greatest Common Factors
     C8.2 Factoring by GCF

2
C8.3 Factoring x +bx+c

2
C8.4 Factoring ax +bx+c
     C8.5 Factoring: Special Products
     C8.6 Choosing a Factoring Method

What unfamiliar terms will be introduced to the students that will enhance their understanding of
the concept?
Vocabulary
Monomial, Degree of a monomial, Polynomial, Degree of a polynomial
Binomial, Trinomial, Perfect square trinomial, Difference of two squares
Prime factorization, Greatest common factor

What activity will focus attention on the subject matter of the upcoming lesson unit, establishing a
Anticipatory Set or    mental set to pique the students' interest?
Introduction to
Lesson Unit            Focus Materials:
 Countdown to TAKS (Holt- beginning page “TX4” - 24weeks)

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   Higher Order Thinking Skills (see P: drive – highschool/millermath/Focuses)
   Missed questions from previous test

Technology Integration: N/A

What specific teaching strategies are going to be used to teach this lesson unit? What approach
will be used to provide information (explain) the lesson unit to the students?
Textbook – Holt: Algebra 1

Auxiliary Text - “Step-Up-to-TAKS “- Assessment for Ninth Grade Math” by GF Educators, Inc.

Re-teach Text: TAKS Study Guide for 9th Grade by TEA

Focuses – “Countdown to TAKS” (Holt- beginning page “TX4” - 24weeks)

Teaching             Class work – “Guided Practice plus Independent Practice”(Holt)
Strategies
Homework – From Chapter 0 and “Skills Bank” (Holt) and Independent Practice.

Quizzes – “Ready To Go On?” (Holt – 2 per chapter)

Tests – “Chapter Tests” (Holt) or teacher generated.

Vocabulary – From “Study Guide Preview” for each Chapter (Holt)

TAKS – “Step-Up-to-TAKS “- Assessment for Ninth Grade Math” by GF Educators, Inc. (Two
tests for each objective)

Six Weeks Tests – Use reviews and tests from Webccat. (Region 10)

What modeling will take place to demonstrate what the students will do?
Modeling
The teacher will model examples of each type of problem showing the style and steps that
the students will be expected to master.

Activities           What initial practice of lesson skill will be used under direct supervision of the teacher? What
practice of the skill concept of the lesson, without direct (step-by-step) adult supervision will take
(Guided Practice     place? (List for each day of the unit: Example: Day 1, Day 2, Day 3).
and Independent
Practice)            Day 1. C7.5 Polynomials: Page 476
The teacher will explain monomials, binomials, trinomials, and polynomials. The terms will be
(Include: Day 1,     identified as constants, coefficients, and the degree of the polynomial.
Day 2, etc…)
Example 1: Finding the Degree of a Monomial
2a2b4 The degree is 6. Add the exponents of the variables 2+4=6.

Example 2: Finding the Degree of a Polynomial
Find the degree of each term. Assign the highest degree to the polynomial.

Example 3: Writing Polynomials in Standard Form
Find the degree of each term. Then arrange in descending order.

Guided Practice: P479. Students will practice the new material.
Independent Practice: P479. # 27-49

Day 2. C7.6 Adding and Subtracting Polynomials: Page 484

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The teacher will explain adding and subtracting of monomials, binomials, trinomials, and
polynomials.

Example 1: Adding and Subtracting Monomials
Example 3: Subtracting Polynomials

Guided Practice: P487. Students will practice the new material.
Independent Practice: P487. # 16-24

Day 3. C7.7 Multiplying Polynomials: Page 492
The teacher will review the distributive method (FOIL) and then show how the box method can
be used in the general case for a poly times a poly. Algebra tiles may be used the reinforce
instruction.

Example 1: Multiplying Monomials
2    3
(5X )(4X ) Group factors with like bases and then multiply.

Example 2: Multiplying a Polynomial by a Monomial
2              2
5(2X +X+4) = 10X +5Xx+20 Distribute the 5 and multiply.

Example 3: Multiplying Binomials
(X+2)(X+5) Use the FOIL method. First, Outside, Inside , Last
XX+X5+2X+2(5)
2
X +7X+10

Also teach the Box Method which will be the preferred method:
X   +2

X2        2X             Multiply rows times the columns.
X                                Combine terms
5       5X        10

2
Answer = X + 7X +10

Guided Practice: P497. Students will practice the new material.

Independent Practice: P497. # 26-52

Day 4. C7.8 –Special Products of Binomials: Page 501
2
Example 1: finding Products in the Form (a + b)
2
Example 2: finding Products in the Form (a - b)

Day 5. Quiz Lessons 7.5 through 7.8 ”Ready to go on?” page 509

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Chapter 8: Factoring Polynomials

Day 6. C8.3 Factoring Quadratic Trinomials. x  bx  c Page 540
2

Example 1: Factoring Trinomials by Guess and Check
Example 2: Factoring x  bx  c When c is Positive
2

Example 3: Factoring x  bx  c When c is Negative
2

Example 4: Evaluating Polynomials

Guided Practice: P544. Students will practice the new material.
Independent Practice: P544. # 17-31

Factoring is just the reverse of multiplying. This may be demonstrated using algebra tiles. The
teacher will hand out tiles for the students to use to solve problems listed on the board.

Day 7. C8.4 Factoring ax  bx  c
2

Example 1: Factoring ax  bx  c by Guess and Check
2

Example 2: Factoring ax  bx  c When c is Positive
2

Example 3: Factoring ax  bx  c When c is Negative
2

Guided Practice: P552. Students will practice the new material.
Independent Practice: P552. # 34-51

Day 8. Review Quadratics and Polynomials.

Day 9 Test on Quadratics and Polynomials.

What check(s) will be used to determine if learners have understood the material and activities of
the lesson?
 Monitor students working at desks
 Ask questions of the class for understanding
Checking for               Ask questions individuals for understanding
Understanding

If necessary, what alternative teaching methods will be used to teach the same information or
skill? Consider teaching methods that address different learning styles, e.g., auditory, visual,
tactile, and kinesthetic.
    Re-teaching Worksheets from Algebra 1 P: drive.
Opportunities to           TAKS Study Guide for 9th Grade by TEA
Relearn                       T3 Lab
(Reteach)                     Peer tutoring

Technology Integration:
 MySatori software for individual practice
   A+ software in T3 Lab for individual practice

Accommodations       What alternative instructional modifications and adaptations that address all learners' needs are

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for Special          necessary, if any?
Populations          Accommodations for instruction will be provided as stated on each student’s (IEP)
Individual Education Plan for special education, 504, at risk, and ESL/Bilingual.

What additional teaching strategies will be used to accommodate the needs of English Language
Strategies for
Learners during this lesson unit?
English Language
Learners (ELLs)
Pair students with difficulty understanding English with a student who is proficient in
both languages

What formal assessment that provides learning criteria and indicators through traditional or
alternative assessment means will be used? State what the learner will do to demonstrate
Assessment or        understanding and mastery of objectives (this should be directly tied to the lesson unit
Evaluation           objectives).
 Tests covering material learned
(Formative and
 Quizzes covering material learned
Summative to
 Assessments will be graded and missed questions will be clarified
Assess Mastery)
 If needed tutoring and retesting is available.

What challenging instructional activities can be provided for students who demonstrate academic
proficiency of curriculum objectives? Focus on Application and Transference to the "Real World".
Make a connection between past and present.
Enrichment /
Extension            Enrichment activities from the supplements to Holt Algebra 1.
Extra Credit puzzles or games.

Technology Integration: N/A

What very brief activity will take place that has students state or demonstrate the main
Closure or Ending    objective(s) of the lesson.
the Lesson Unit
Review test results and clarify missed questions.

What preparation must occur before the lesson is ready?

The following materials are available for Units 4 and 6 as needed by the teacher:

1.    Power Points (P: share/5high school/millermath/power points)
2.   Brain Pops (brainpop.com)
 Monomials
 Polynomials
Materials:               3.    Re-teaching Worksheets (P: drive- “highschool/millermath”)
Preparation and                Parentheses. 4A06/4A07
Resources                      The FOIL Box 4A09/4A10
 Review FOIL 4T3R
 Test FOIL 4T3
 Factor FOIL 4A11

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What resources should be available to the instructor and learner to appropriately and
successfully complete the lesson unit’s stated objective(s), purpose(s) or goal(s)?

Textbook – Holt: Algebra 1

Auxiliary Text- “Step-Up-to-TAKS “- Assessment for Ninth Grade Math” by GF Educators, Inc.

TAKS Study Guide for 9th Grade by TEA

Projector

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