FACTOR IT!

Topic: Factoring PolynomialsCourse: Advanced Algebra IGrade Level: EighthClass time: 45 minutesStudent Population: Coeducational Independent School Honors, 20 students, 11 boys, 9 girlsUnit Designer: Stirling SullivanNumber of Days: 10FACTOR IT! will follow the unit on multiplying polynomials and will lead into SOLVE THAT QUADRATIC! in which equations will be solved using factoring as well as the quadratic formula and graphing. TABLE OF CONTENTS

I. Goals and Rationale……………………………………………………… 1II. Desired Results…..………………………………………………………… 2III. Scope and Sequencing..…………………………………………………… 3IV. Acceptable Evidence..…….………………………………………………….3V. Instructional Resources.……………………………………………………. 4

a) Day1….……….………..……………………………………………………..5b) Day 2 …….……..…………………………………………………………….8c) Day 3 ……..…….………………………………………………….............10d) Day 4…………….…..………………………………………………………12e) Day 5 ……...……………………………………………………………..…13f) Day 6 ….……..…………………………………………………..…………15g) Day 7 ….……..……………………………………………………………..16h) Day 8 ……...………………………………………………………………..18i) Day 9 ….…..………………………………………………………………..19j) Day 10………..……………………………………………………………..19k) Appendix…………………………………………………………………….20

GOALSNorth Carolina Standard Course of Study COMPETENCY GOAL 1: The learner will perform operations with numbers and expressions to solve problems.Objective 1.01 Write equivalent forms of algebraic expressions to solve problems. c) Factor polynomials.

RATIONALEThe concept of prime factorization learned in earlier grades will be connected and applied to higher order equations. Students need to understand that factoring polynomials is similar to finding the prime factorization of integers, as factoring completely is rewriting a polynomial as the product of its prime factors, ultimately for the purpose of solving equations. Students need to recognize various cases both explicitly and within more advanced contexts. Not only will this enhance their mathematical ability but also their ability to analyze and apply concepts to less explicit cases and use logic to solve more challenging problems. Factoring more complex problems improves student problem-solving ability as students discover that concepts they know may be extended to concepts they have not yet seen.

1

LEARNING OUTCOMES

Upon completion of factoring unit, students will be able to:

Factor polynomials using the GCF and the distributive property. Factor trinomials with and without lead coefficients. Identify and factor differences of squares. Identify and factor perfect square trinomials. Factor by Grouping Factor by combining methods Select the appropriate method and factor polynomials completely Recognize quadratic and higher order expressions and apply appropriate

factoring methods Solve an equation using the Zero Product Property

Prior KnowledgePrime factorization · Prime numbers · Greatest common factor (GCF) Find the greatest common factor (GCF) for a set of monomialsSquares and square rootsMultiplying polynomials – Foil and Special Cases

UNIT GOALS

Enduring UnderstandingsStudents will

Recognize linear vs. nonlinear expressions Analyze expression by number and types of terms Apply appropriate factoring method(s) for a given expression Explain the relationship between factoring and multiplying polynomials Apply factoring skills to solve higher order equations

Essential QuestionWhat skills and tools do we need to solve equations which may have more than one possible solution?

Topical Questions What is factoring? How will we recognize problems which can be factored? How will we know which factoring methods to apply?

Topical Understandings Why is it necessary to factor out the GCF? How does the number of terms affect the factoring method we choose? How will we decide which factoring method to use? How can we factor expressions of higher order? How can we use factoring in geometry problems? How many factors exist in a given expression? What methods can be used to solve higher order equations and word problems?

Student Knowledge and Skills

2

Students will know that polynomials have factors. how factoring and multiplying are related. that factoring can be used to solve higher order equations

Students will be able to identify expressions which can be factored select the appropriate factoring method base on the degree and number of terms apply the appropriate factoring methods in order to factor a polynomial

completely solve equations by factoring and applying the Zero Product Property

SCOPE AND SEQUENCING

I. Factoring GCF - Monomial and BinomialII. Factoring Trinomials of the form x + bx + cIII. Factoring Differences of Squares and Factoring Perfect Square TrinomialsIV. Mixed Review I, II, IIIV. Factoring with Lead Coefficient (tie in to FOIL) VI. Factoring by Grouping and Geometry ApplicationsVII. Mixed Review allVIII. Solving by Factoring and the Zero Product PropertyIX. Unit Review and Wrap upX. Test

GRAPHIC ORGANIZER

EVIDENCE

Board work (informal) Working problems at desk which are similar to previous problems but which have

a “catch” during lesson Group white board practice Verbal “work through” of problem on board Review worksheets in pairs or small groups 10-15 problem quizzes on two related concepts (2 or 3 during unit) 25-30 problem test which mixes together 20-25 factoring problems under one set

of directions (e.g. simplify)

RESOURCES

3

Dolciani, M., Swanson, R. & Graham, J. (1992). Algebra 1. Boston: Houghton Mifflin.Holliday, Marks, etal. (2004). Algebra I. New York: McGraw Hill Glencoe.

http://www.coolmath.com/algebra/Algebra1/index.html#Algebra_1:_Factoring_&_Dividing_Polynomialshttp://www.quia.com/rr/36611.html

Worksheet Special CasesWorksheet Mixed Practice 1Worksheet Mixed Practice 2Putty WorksheetClasswork Word ProblemsUnit Review/practice TestStudent Factoring Graphic Organizer OutlineFactoring QuizTest.

ACTIVITIESDay 1 Factoring GCF - Monomial and BinomialHomework: Text page 347 #2- 44 evenDay 2 Factoring Trinomials of the form x + bx + cHomework: Text page 357 #2-42 even, #48,50Day 3 Factoring with Lead Coefficient (tie in to FOIL) Homework: Text page 360 #2-42 evenDay 4 Mixed Review I, II, III with online practiceHomework: Complete Worksheet Mixed Practice 1 and Study for QuizDay 5 Quiz

Factoring Differences of Squares and Factoring Perfect Square Trinomials Homework: Worksheet Special CasesDay 6 Mixed Review all including white boardsHomework: Worksheet Mixed Practice 2Day 7 Factoring by Grouping and the Zero Product PropertyHomework: Putty Worksheet and text p. 352 #38-44 evenDay 8 Solving by Factoring and Word ProblemsHomework: Text p. 366 #2-42 even, and p. 368 #2-10 evenDay 9 Unit Review and Wrap upHomework: Study for TestDay 10 TestNo homework

Lesson 1

4

Factoring GCF - Monomial and Binomial

UNIT GOAL: Factoring Expressions CompletelyOBJECTIVE: Factoring Monomial and Binomial GCFsCOMPETENCY GOAL 1: The learner will perform operations with numbers and expressions to solve problems.

Objective 1.01 Write equivalent forms of algebraic expressions to solve problems. c) Factor polynomials.

Prerequisites

Factor Trees

Prime, Composite Definitions: constants, terms, monomials, binomials, polynomials GCF of constants and monomials LCM of constants and monomials

Resources White Board and Markers Dolciani Text Graphing calculator not encouraged.

Return and review previous chapter test (10 min)

Review of Prime factorization of constants (5 min) Factor trees prime numbers how to write factorization Listing factors Finding other factors using combinations of prime factors GCF – Factors in common LCM – Highest (STRONGEST) power of each factor – MUSCLE Stress PRODUCT OF PRIME FACTORS

Lesson (25 min)

ST= optimal student responseG = Guided PracticeI =Independent Practice

Teacher Input: Students will recognize Patterns to discover GCF in expressions. They will use knowledge of Distributive property to understand factoring out the GCF. Class examples are designed to help with homework concepts.

Dolciani 7-6

UNIT GOAL: Factoring Expressions Completely

Hook: (On Board) 7x + 14yLook at terms in expression. Is there a way to make this expression look simpler?St: take out 7 from each

5

What is 7 in relation to the two terms?St: gcfWhat property are we using?DISTRIBUTIVE

Reveal Objective: 7-6 Factoring expressions by factoring out the GCF GCF as factor GCF makes simpler

G: Factor 5m2 – 6m Emphasize PRODUCT

G: Factor 6x4-15x3+3x2

Dividing each term by GCF Is entire GCF out? Should be NO GCF LEFT IN PARENS. What do you do if it is not? Emphasize PRODUCT. Examine final answer. Does it look less complicated in Parentheses? GCF is one of the factors of the expression. First step in factoring is ALWAYS to

look for GCF and factor it out if there is one to make expression easier to examine for more factors.

I: 36r3s2 – 60r2s3

I: #19G: #25 z(z-1)+2(z-1)

Underline terms Cross out common factor and write remaining PRODUCT

I: #27G: #31 9(1-q) – q(q-1) = 9(1-q) - q(1-q)

Subtraction ‘Turnaround’ subtraction

I: x(x-3) – 7(3-x)G: y2(y-2) - (y-2)

Insert 1: y2(y-2) - 1(y-2) Point out difference of squares (future lesson)

I: #39G: 3(a-1)2 + 2 (a-1)

Binomial factor from squared Binomial

Homework (on assignment board) Text page 347 #2- 44 even

Summary/Review (5 min) What is first step in factoring expressions? Look for GCF What property allows us to take it out? Distributive Our goal is to write expressions as ___________ (product of its prime factors)

Teacher ReflectionTeacher will reflect on student understanding during guided and independent practice as well as homework review. Teacher will also reflect on learning during review day as well as on quiz and unit test.

6

Evaluation: Homework tonight will be selected so that most students will develop self-awareness. Hopefully they will make some mistakes on hw (it is only graded on completion, not on accuracy) so that they can see where pitfalls can occur. Quiz - day after review WorksheetUnit test will include problems which have only a GCF and those in which GCF is one of the factors.

7

Lesson 2Factoring Trinomials of the form x + bx + c (Lead Coefficient of 1)

UNIT GOAL: Factoring Expressions CompletelyOBJECTIVE: 7-8 How to recognize and factor Trinomials of the form x + bx + cCOMPETENCY GOAL 1: The learner will perform operations with numbers and expressions to solve problems.

Objective 1.01 Write equivalent forms of algebraic expressions to solve problems. c) Factor polynomials.

Prerequisites Factors Factoring out the GCF

Resources Text Overhead Projector

ReviewDaily Homework Check (10 min)What is first step in factoring completely? FACTOR OUT THE GCFWhat types of GCFs have we seen? constants, monomials, binomialsI: Factor x(x-1) + 3(1-x) (x-1)(x-3)I: Factor x3+7x2+10x

x(x2 + 7x + 10)* leave space underneath

LessonG = Guided PracticeI =Independent Practice

Teacher Input: We have learned that the first step in factoring is to factor out the GCF if there is one. That may not be the only thing we can do! After factoring out the GCF we want to look back at the expression to see if we can factor it more. Remember our goal is to factor completely, which is WRITING AN EXPRESSION AS THE PRODUCT OF ITS PRIME FACTORS. (This skill will become very important when we factor nonlinear equations.) Today we will learn how to recognize and factor trinomials, using skills learned in FOIL.

Dolciani section 7-8TIE IN TO FOIL: Multiply (x+4)(x+5)How did we get each term in answer?

Product of first FSum of outers and inners O+IProduct of last L

G: x2 + 7x + 10How many terms? TRINOMIAL. Are they in descending order?We need to figure out what (if anything) was multiplied together to get this. Does expression look like something we’ve done before? Result of FOIL.( )( )x2 = x times x (x )(x )What two numbers have a product of +10 and add up to +7?(x+5)(x+2)

Foil to check.

8

Return to previous problem to complete solution.G: x2+16x+15 What 2 factors of 15 add up to 16?I: y2+10y+21

Middle term is sum of outers and inners (FOIL) Notice power of middle term is ½ power of first term

G: x2-5x+4 Middle term negative Look at signs: Pattern? Last term + means same sign.

G: y2-12y+32I: y2-18y+32G: y2-5y-14 Minus sign: Different signs

What two factors of 14 differ by 5? Place factors, then determine signs.

G: y2+5y-14 Compare to aboveI: x2-10x-24

Notice factors. In order to DIFFER, one of them must be higher than middle.I: x2+5x-24I: x2+7x+15 Students will struggle to find solution –

IRREDUCIBLE. PRIME = has only itself and 1 as factors.

G: - x2-15x-36 Want first term positive. Factor out -1 as GCF.

HW #1-18 all if we stop here.G: 2a3+10a2-28a GCF!G: 8+7x-x2

Descending order and neg.#21 Remove GCF#33 GCF and rearrange#39 2 variables – First and last term squared. MIDDLE TERM HAS A PIECE OF EACH.#49 Higher powers. Middle term is half lead power.

Homework (on assignment board) Text page 357 #2-42 even, #48,50

Summary/Review (5 min) First step in Factoring? GCF Process we are undoing? FOIL Last term Plus? same sign Last term minus? different signs Middle term power? Half the first or half of each (if 2).

Teacher Reflection Teacher will reflect on student understanding during guided and independent practice as well as homework review. Teacher will also reflect on learning during review day as well as on quiz and unit test.

Evaluation: Homework tonight will be selected so that most students will develop self-awareness. Hopefully they will make some mistakes on hw (it is only graded on completion, not on accuracy) so that they can see where pitfalls can occur. Quiz - day after review WorksheetUnit test will include problems which have are only x + bx + c and those in which GCF is one of the factors.

9

Lesson 3Factoring with Lead Coefficient Other than 1(tie in to FOIL)

UNIT GOAL: Factoring Expressions CompletelyOBJECTIVE: 7-9 How to recognize and factor Trinomials of the form ax + bx + cCOMPETENCY GOAL 1: The learner will perform operations with numbers and expressions to solve problems.

Objective 1.01 Write equivalent forms of algebraic expressions to solve problems. c) Factor polynomials.

Prerequisites Factoring trinomials with lead coefficient 1

Resources *if smartboard is available, show organizer and fill it in using smartboard. Text

Student Factoring Graphic Organizer Outline http://www.kutasoftware.com/FreeWorksheets/Alg1Worksheets/Factoring%202.pdf

(extra resource if needed) Overhead projector and Homework solution overhead

ReviewDaily Homework Check (10 min)Begin Filling In Student Factoring Graphic Organizer Outline

LessonG = Guided PracticeI =Independent Practice

Teacher Input: Remember our goal is to factor completely, which is WRITING AN EXPRESSION AS THE PRODUCT OF ITS PRIME FACTORS. (This skill will become very important when we factor nonlinear equations.) Yesterday we factored trinomials that had lead coefficient 1, or if there was one, we could factor it out and then have a lead coefficient of 1. Today we will learn how to recognize and factor trinomials with a lead coefficient, using skills learned in FOIL.

G: 2x2 – 16x + 24 GCF? yes. Factor it out and lead coefficient becomes 1. Then factor again. 2(x-2)(x-6)

G: 2x2+9x+9 GCF? no ( ) ( ) and both signs same – put in signs 2x2 = 2x times x - put in parens Factors of 9? Think about where to put them. Middle term as sum of outers and inners, so use 3 and 3.

G: 3a2 + 7a + 2G: 2a2 – 11a + 12

GCF? no ( ) ( ) and 2a times a. look at last term. It’s even, just like the 2. GCF in original problem? No. So there can’t be a GCF in parens. Are 6 and 2 options as factors of 12? No. Common factor with 2. Need one even and one odd or two odds.

10

Can even factor go in parens with 2? Options reduced. Try 3 and 4.

I: 3a2+14a+8I: 6m3 – 39m2 + 45m

Looks strange? Remember first step! 3m(2m-3)(m-5)

G: 8r2 + 3r – 5 One pos, one neg. Looking for difference of outers and inners Decide on factors, THEN signs

G: -20u2-17u+10 Looks strange? Factor out negative. Try 10u and 2u. Won’t work because 10 has an even factor. Need Odd factor: 5u and 4u. Place in parens. Where can 5 and 2 go? Check outers and inners. Put in signs.

G: #31 6x5-22x3-8x GCF then 4th power. 2x(3x2+1)( x2-4) Will soon learn how to factor 2nd parens.

I: #11 8m2+2m-15 (4m-5)(2m+3)

I: #13 10j2 – 37j – 12 (10j+3)(j-4)

G:#37 6u3+23u2v-18uv2

Homework (on assignment board) Text page 360 #2-42 even

Summary How many terms? 3 What is first step after GCF? Factors of first GCF allowed in parentheses? No Middle term is _______ Sum of outers and inners.

Teacher Reflection Teacher will reflect on student understanding during guided and independent practice as well as homework review. Teacher will look at homework. Teacher will also reflect on learning during review day as well as on quiz and unit test.

Evaluation: Homework tonight will be selected so that most students will develop self-awareness. Hopefully they will make some mistakes on hw (it is only graded on completion, not on accuracy) so that they can see where pitfalls can occur. Quiz - day after review WorksheetUnit test will include problems which have only ax + bx + c and those in which GCF is one of the factors.

11

Lesson 4

Mixed Review I, II, III

UNIT GOAL: Factoring Expressions CompletelyOBJECTIVE: Review of Factoring GCFs and TrinomialsCOMPETENCY GOAL 1: The learner will perform operations with numbers and expressions to solve problems.

Objective 1.01 Write equivalent forms of algebraic expressions to solve problems. c) Factor polynomials.

Prerequisites Factors Factoring out the GCF

ResourcesWorksheet Mixed Practice 1OverheadHomework solution overhead

Mixed Review Practice in PairsDaily Homework Check (10 min)Online practice: http://www.quia.com/rr/36611.htmlPlay Rags to Riches.Each student will write problem and correct solution – to be turned in.(Teacher will circulate to assist and ensure all students are working the problems.)Desk work mixed review worksheet.

Homework: Complete worksheet and study for quiz. Solutions posted online.

Teacher Reflection Teacher will reflect on student understanding during online practice as well as review sheet. Teacher will also reflect on learning with quiz and unit test.

Individual DifferencesIf student has trouble transferring visual information to paper, one student may turn in problems for both.

Diverse learnerCalculator only if needed due to learning challenges. Students are expected to work without calculator.

Evaluation Online practice provides immediate feedback. Students can also self-assess by checking solutions online.

12

Lesson 5Factoring Differences of Squares and Perfect Square Trinomials

UNIT GOAL: Factoring Expressions CompletelyOBJECTIVE: 7-7 How to recognize and factor Special Cases: Difference of Squares and Trinomial Perfect SquaresCOMPETENCY GOAL 1: The learner will perform operations with numbers and expressions to solve problems.

Objective 1.01 Write equivalent forms of algebraic expressions to solve problems. c) Factor polynomials.

Prerequisites Perfect Squares Factoring trinomials

Resources

Factoring Quiz Worksheet Special Cases Difference of Squares Activity Sheet Overhead Projector

QUIZ (10 minutes)

Review With students, list perfect squares to 202 on overhead. Overhead: Even powers of variables as perfect squares. Summarize Factoring thus far

LessonTeacher Input: Today we are looking at special cases. We will look at special trinomials as well as 2 term expressions which involve perfect squares. Students will recognize that the special cases may exist when they see perfect squares in the problem. Emphasize looking for perfect squares.

Difference of Squares Activity Sheet Students will discover patterns in differences of squares of integers. (4)Line 5: x,yLine 6: x, 5Line 7: y,12Line 8: 2x, 9 Foil and middle term disappears. “Difference of Squares” - # of terms, operation

Practice: x2 – 100x2 – 14x2 – 49x2 + 81 (prime – no Sum of Squares)x4 – 16 (continues) x4– 1

13

More squares and trinomialsx2 +25Note perfect squaresRefer back to squaring binomialPut +10x in middle to make perfect squareMiddle term: Double the square roots.( )2

Practice – Check Criteria for Trinomial Perfect Square # Terms Last sign Bookend perfect squares Middle termx2 – 12x + 36

x2 + 20x + 100

x2 – 24x – 144 (No)

2x2-28x+98 (GCF)

x2 - ____ + 64 Fill in

Homework Worksheet Special Cases

Evaluation Worksheet and Test

Lesson 6

14

Mixed Review all including white boardsUNIT GOAL: Factoring Expressions CompletelyObjective: Review

COMPETENCY GOAL 1: The learner will perform operations with numbers and expressions to solve problems.

Objective 1.01 Write equivalent forms of algebraic expressions to solve problems. c) Factor polynomials.

Resources Overhead Transparency with Homework Solutions White Boards with Markers and erasers Student Factoring Graphic Organizer Outline

Review Homework Check Difference of Squares Trinomial Perfect Squares Fill in Student Factoring Graphic Organizer Outline

Lesson Give out whiteboards to each student Call out practice problems for students to do on white boards. Students raise white

boards with answers

Teacher InputFun, energetic, positive reinforcement of factoring concepts

Homework Worksheet Mixed Practice 2

EvaluationWhiteboard practice and homework worksheet and test

Lesson 7Factoring by Grouping and the Zero Product Property

15

UNIT GOAL: Factoring Expressions CompletelyObjective: Factoring by Grouping and the Zero Product Property

COMPETENCY GOAL 1: The learner will perform operations with numbers and expressions to solve problems.

Objective 1.01 Write equivalent forms of algebraic expressions to solve problems. c) Factor polynomials.

Resources Overhead Transparency with Homework Solutions Student Factoring Graphic Organizer Outline Putty Worksheet

Review Homework Check Quick review when looking at and filling in Graphic Organizer

LessonFill in Student Factoring Graphic Organizer OutlineG: Factor m2-6m + 9 – n2.

How is this different? 4 terms Do you see anything familiar in it? Trinomial perfect square. Try factoring TPS. Now what? Difference of Squares

I: Factor p2 + 4p + 4- 4n2

G: Factor 3a2 – 3ab + 2a – 2b Trinomial Square? No 2 by 2 grouping

I: Factor x2 – 2x + xy – 2yG: Factor 5r + r2 – 5s – rs

Minus in the middle! What happens if just insert parentheses? (rewrite to insert parens) Is it still the same as

the initial problem? Change operation in 2nd parens

I: w2 + 7w – xw – 7x

Summary of 4 term grouping:4 Terms – GroupingFirst look for _______? trinomial squareIf none, _________? ParensIf minus in middle? ______ Change operation

(Shifting topics slightly) Question: If I know that the product of 2 ‘things’ is 0, what does at least one of the ‘things’ have to be? Zero.

If AB =0then A=0 or B=0. Zero product property.

If 5a = 0, then a = 0.

If (x+5) (x+6) = 0, what value(s) of x would make this true?

16

x+5 = 0 or x+6 = 0.

What is (x+5) (x+6)?What type of equation is that?Have we ever found solutions to those before?

G: Solve x2 + 11x + 30 = 0(x+5) (x+6) = 0x+5 = 0 or x+6 = 0. Two different factors = 2 solutions

Solve x2 – 11x + 28 = 0x = 4,7

G: x ( x+2) (x – 8) = 0 How many factors? Three different factors = 3 solutionsx = 0, -2, 8

Rule?To find solutions to factored quadratic equations, set each factor = 0 and solve for the variable.

Teacher Input: Test will only include solving equations which are already factored. This will lead us into tomorrow’s lesson in which we will be solving basic quadratic equations. Once students are comfortable recognizing the factors and setting them = 0, they should be able to easily make the transition to factoring to solve quadratic equations.

Homework: Putty Worksheet and text p. 352 #38-44 even

Evaluation: Worksheet and test

Lesson 8Solving by Factoring and Word Problems

UNIT GOAL: Factoring Expressions CompletelyOBJECTIVE: Solving by Factoring and Word Problems

17

COMPETENCY GOAL 1: The learner will perform operations with numbers and expressions to solve problems.

Objective 1.01 Write equivalent forms of algebraic expressions to solve problems. c) Factor polynomials.

Resources Classwork Word Problems Handouts and Overhead Overhead Projector

Review Homework Check Yesterday: Solve (3n + 4) (5n + 4) = 0

LessonG: Solve x2 – 5x + 4 = 0

Since it’s equal to zero, what can we do? Factors and Zero Product property. (x-4) (x-1) = 0 x = 4,1

G: Solve x2– 9 = 0 Suggestions? Factor! Factor. Now what? Set each factor = 0.

I: 3c2 + 5c – 12 = 0 c = 4/3, -3

G: 6u2 + 7u = 3 Could factor, but how would you know what factors =? Suggestions? Get zero on one side. Then factor.

I: 29v = 10 + 10v2 v = 5/2, 2/5

I: 3g2 = 12g g = 0,4

G: (2m-1)(m-3) =18 Could we solve if it were 0 instead of 18? Yes Bring over 18, remultiply then include 18, refactor.

Now we will apply our solving to some word problem applications.

Hand out Classwork Word Problems and put on overhead.Work through problems on board as students work on handout. Guide through 1st and let students try 2 and 3 independently.

Homework Text p. 366 #2-42 even, and p. 368 #2-10 even

Lesson 9UNIT REVIEW

UNIT GOAL: Factoring Expressions Completely

COMPETENCY GOAL 1: The learner will perform operations with numbers and expressions to solve problems.

Objective 1.01 Write equivalent forms of algebraic expressions to solve problems.

18

c) Factor polynomials.

Resources Practice test Solutions to Practice test (give out near end of class or post online)

Review Homework Check

ActivitiesStudents work Practice test. May assist each other as needed.

Homework: STUDY FOR TEST!

Lesson 10TEST – 100 pointsResources: Test

19

APPENDIX

Daily homework check (10-15 minutes)At beginning of each lesson if homework has been assigned:Students check homework answers and solutions on overhead while I circulate and check homework for completion and answer brief questions. I will work out and discuss hw problems of concern on board or if there are several, solicit volunteers to work at board.

Individual Differences Visual: Written Initial Explanation as well as added written notes from oral responses/explanation and Problem Solving. Use different colored markers. Underline individual parts of problems (different factors) and draw bubbles around major written concepts. Independent written practice.Copies of notes if needed.

Auditory: Oral Questions and feedback. Oral Instruction in conjunction with written instruction.

Diverse learner (if applicable)Student is allowed extra time as needed (she may work in Learning resources office across the hall) on quizzes and tests due to diagnosed processing disorder.

20