Table of Contents for the Entire Year - Teacher Created Materials

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Table of Contents for the Entire Year - Teacher Created Materials

Table of Contents for the Entire Year

Unit 1: Algebraic Expressions

and Integers

Lesson 1: Introduction to Algebra I

Lesson 2: Writing Algebraic Expressions

Lesson 3: Properties and Order of

Operations

Lesson 4: Order of Operations

Lesson 5: Adding Integers with Chips

Lesson 6: Multiplying and Dividing Integers

Lesson 7: Mixed Integers

Lesson 8: Integers Review 1

Lesson 9: Integers Review 2

Lesson 10: Collecting Like Terms

Lesson 11: Distributing and Collecting 1

Lesson 12: Distributing and Collecting 2

Lesson 13: Distributing and Collecting

Review

Lesson 14: Writing One-Variable Equations

Lesson 15: Writing Expressions and

Equations 1

Lesson 16 Writing Expressions and

Equations 2

Lesson 17: Integers Unit Test

Unit 2: Linear Equations

Lesson 18: Solving Linear Equations with

Cups and Chips 1

Lesson 19: Solving Linear Equations with

Cups and Chips 2

Lesson 20: Solving Equations 1

Lesson 21: Solving Equations 2

Lesson 22: Solving Equations with Fractions 1

Lesson 23: Solving Equations with Fractions 2

Lesson 24: Algebra Applications with

Angles 1

Lesson 25: Solving Equations with Fractions 3

Lesson 26: Algebra Applications with

Angles 2

Lesson 27: Solving Literal Equations 1

Lesson 28: Solving Literal Equations 2

Lesson 29: Solving Literal Equations 3

Lesson 30: Solving Literal Equations 4

Lesson 31: Linear Equations Test

Unit 3: Probability, Percent,

and Proportion

Lesson 32: Percent of Region 1

Lesson 33: Percent of Region 2

Lesson 34: Probability

Lesson 35: Fraction-to-Decimal Conversions

Lesson 36: Review

Lesson 37: Percent and Probability 1

Lesson 38: Percent and Probability 2

Lesson 39: Proportions

Lesson 40: Unit Review 1

Lesson 41: Unit Review 2

Lesson 42: Probability, Percent, and

Proportion Test

Unit 4: Graphing

Lesson 43: Coordinate Plane

Lesson 44: Relations and Functions

Lesson 45: Equations as Relations 1

Lesson 46: Equations as Relations 2

Lesson 47: Lines and Curves

Lesson 48: Functions

Lesson 49: Writing Equations from Patterns

Lesson 50: Mid-Unit Review 1

Lesson 51: Mid-Unit Review 2

Lesson 52: Slope 1

Lesson 53: Slope 2

Lesson 54: Slope 3

Lesson 55: Point-Slope Form 1

Lesson 56: Point-Slope Form 2

Lesson 57: Slope-Intercept Form

Lesson 58: Slope Formulas 1

Lesson 59: Slope Formulas 2

Lesson 60: Graphing Linear Equations

Lesson 61: Parameter Changes 1

Lesson 62: Parameter Changes 2

Lesson 63: Graphing Unit Review and Test

Unit 5: Inequalities

Lesson 64: Graphing Inequalities

Lesson 65: Solving Multistep Inequalities

Lesson 66: Union and Intersection

Lesson 67: Compound Inequalities 1

Lesson 68: Compound Inequalities 2

Lesson 69: Compound Inequalities 3

Lesson 70: Absolute Value Inequalities 1

Lesson 71: Absolute Value Inequalities 2

Lesson 72: Graphing Two-Variable

Inequalities

Unit 6: Systems of Equations &

Semester Review

Lesson 73: Comparing Systems

Lesson 74: Substitution Method 1

Lesson 75: Substitution Method 2

Lesson 76: Addition Method 1

Lesson 77: Addition Method 2

Lesson 78: Solving Systems of Equations

Lesson 79: Review Systems of Equations 1

Lesson 80: Review Systems of Equations 2

Lesson 81: Review Systems of Equations 3

Lesson 82: Review Systems of Equations 4

Lesson 83: Review Systems of Equations 5

Lesson 84: Standardized Test Practice

Lesson 85: Graphing, One-Variable

Equations, and Mixed Objectives

Lesson 86: Graphing and Two-Variable

Equations

Lesson 87: Final Semester Review

Lesson 88: Semester 1 Exam

Unit 7: Polynomials

Lesson 89: Multiplying Monomials

Lesson 90: Dividing Monomials

Lesson 91: Mixed Operations with

Monomials

Lesson 92: Adding Polynomials with Algebra

Tiles

Lesson 93: Multiplying Binomials

Lesson 94: Distributing Monomials

Lesson 95: Representing Geometric Figures

with Algebraic Expressions

Lesson 96: Self-Paced Geometry 1

Lesson 97: Self-Paced Geometry 2

Lesson 98: Self-Paced Geometry 3

Lesson 99: Self-Paced Geometry 4

Lesson 100: Self-Paced Geometry 5

Lesson 101: Polynomials Unit Review

Lesson 102: Polynomials Unit Test

Unit 8: Factoring

Lesson 103: Factoring the Greatest Common

Factor

Lesson 104: Factoring Trinomials

(Third Term Negative)

Lesson 105: Factoring Trinomials

(Third Term Positive)

Lesson 106: Factoring Trinomials with

Algebra Tiles

Lesson 107: Factoring All Types of Problems 1

Lesson 108: Factoring Special Types of

Problems

Lesson 109: Factoring All Types of Problems 2

Lesson 110: Solving Quadratic Equations 1

Lesson 111: Solving Quadratic Equations 2

Lesson 112: Factoring Unit Review 1

Lesson 113: Factoring Unit Review 2

Lesson 114: Factoring Unit Test

Lesson 115: Solving Rational Equations 1

Lesson 116: Solving Rational Equations 2

Lesson 117: Solving Rational Equations 3

Unit 9: Radicals and Quadratics

Lesson 118: Using the Pythagorean Theorem

Lesson 119: Pythagorean Triples

Lesson 120: Simplifying Radical Expressions 1

Lesson 121: Simplifying Radical Expressions 2

Lesson 122: Adding Radical Expressions

Lesson 123: Multiplying Radical Expressions

Lesson 124: Radical Operations

Lesson 125: Solving Radical Equations 1

Lesson 126: Solving Radical Equations 2

Lesson 127: Radicals Unit Review and Test

Lesson 128: The Properties of Parabolas

Lesson 129: Identifying the Axis of Symmetry

and the Vertex

Lesson 130: Graphing Quadratic Equations 1

Lesson 131: Graphing Quadratic Equations 2

Lesson 132: The Quadratic Formula 1

Lesson 133: The Quadratic Formula 2

Lesson 134: Graphing and Solving Quadratic

Equations

Lesson 135: Quadratics Unit Assessment

Unit 10: Rational Expressions &

Semester Review

Lesson 136: Simplifying Rational Expressions 1

Lesson 137: Simplifying Rational Expressions 2

Lesson 138: Multiplying and Dividing

Rational Expressions

Lesson 139: Rational Expressions Mid-Unit

Review

Lesson 140: Rational Expressions Mid-Unit

Test

Lesson 141: Adding Rational Expressions 1

Lesson 142: Adding Rational Expressions 2

Lesson 143: Adding Rational Expressions Quiz

Lesson 144: Solving Rational Equations 1

Lesson 145: Solving Rational Equations 2

Lesson 146: Solving Rational Equations Quiz

Lesson 147: Rational Expressions Unit

Review 1

Lesson 148: Rational Expressions Unit

Review 2

Lesson 149: Rational Expressions Unit Test

Lesson 150: Game Day!

Lesson 151: Standardized Practice Posttest

Lesson 152: Creating Algebra Aces Games

Lesson 153: Playing Algebra Aces Games

Lesson 154: Algebra I Second Semester

Review

Lesson 155: Algebra I Second Semester Exam

4 #10357 (i1534)—Active Algebra—Algebra I, Unit 1


Introduction

This curriculum is intended to give schools a foundation for developing a successful

Algebra I program. There are many factors involved in developing a program. The

teacher is encouraged to use this curriculum, while addressing the factors below, to help

make Algebra I accessible to all students.

These factors include the following:

Teachers’ philosophies

• Having high expectations of students

• Horizontal teaming as well as K–12 vertical teaming

• Supportive administration

• An adequate amount of instructional time (90 minutes a day is recommended)

• Classroom management skills

• Regular team-planning time

• Training teachers in the use of manipulatives, cooperative learning,

and the use of the graphing calculator

PowerPoint Slide Shows

To support the teaching of this unit, there are PowerPoint presentations of some of the

lessons. These slides shows are intended to give guidance on how to introduce new

topics to students. The presentations provide a prepared copy of the notes from the

lesson plans so that the notes do not have to be recopied. The slide shows also serve as

excellent visual aids for English-language learners (ELL). There is a list of all the

presentations provided on pages 57–59 of the Teacher Resource Guide.

Transparencies Folder on the CD

This unit has a number of word problems to help students apply their learning from the

unit. To complete these problems, create transparencies from the PDFs on the Teacher

Resource CD, or simply copy the pages and give them to the students. The pages are

located in the Transparencies folder on the CD. Specific filenames are provided within

each lesson’s Materials list.

Standardized Test Preparation

To maximize students’ scores on standardized tests, it is imperative that the students

review test items throughout the year. It is recommended that the teacher make

transparencies of the Standardized Test Preparation activity sheets. These

two-page files are located in the Standardized Test Prep folder on the CD. Teachers

should try to review one sheet per unit with the class. After reviewing all of the

problems on an overhead, the teacher should assign that sheet as a homework

assignment, making sure students have a few days to work on it before it is due.

If it is difficult to complete one sheet within each unit, the teacher should make sure to

cover Standardized Test Preparation activity sheets 1–6 by the end of the first

semester. Sheets 7–10 should be completed before any state standardized tests are given

during the second semester.

#10357 (i1534)—Active Algebra—Algebra I, Unit 1

5


Introduction (cont.)

Algebridge Tutorials

Even though a student may have done poorly in eighth-grade mathematics, he or she is

expected to pass Algebra I in the ninth grade. To help bridge the gap of knowledge

students may have in mathematics, teachers may want to hold Algebridge Tutorials.

Algebridge Tutorials should be held from the third through the ninth week of school.

The teacher is responsible for using the assessments and activity sheets in Units 1 and 2

to determine which students will benefit from participating in the program. The teacher

should then hold tutorials to reteach the objectives that students did not master in class.

The tutorials can be held before school, after school, or on Saturdays.

After covering the objectives again, give students the opportunity to retake any quizzes

or tests. Students can earn a new replacement grade of up to 100%. The Algebridge

folder on the Teacher Resource CD includes a new version of each quiz or test. By

reteaching the objectives from these units, the teacher prepares students to participate

in the lessons for the rest of the year. This tutorial program requires a commitment on

the teacher’s part, but the results can be outstanding.

Some of the questions that Algebra I teachers should address before beginning the

program include the following:

• Will the school provide transportation?

• Do the teachers want the highest retake grade to be 100%, or do they want it to

be lower? (The higher the retake grade, the more participation there will be in

the program.)

• The teachers should also consider the issue of averaging the first semester and

second semester grades if the school holds Algebridge Tutorials. The first

semester grade will be higher than it would have been if the school did not offer

the program.

Professional Development DVD

Included in this kit is the Professional Development DVD. This DVD includes segments

showing how to use manipulatives with the students. The teacher should watch the

video before teaching any of the lessons with manipulatives or games.

Teacher Resource CD

The Teacher Resource CD features many important components that support this unit. It

contains a second copy of each assessment. The teacher can use the second copies as

pretests or during the posttest to prevent copying. All of the guided practice sheets are

provided on the CD. If the teacher does not want to use the student consumable, the

Guided Practice Book, he or she will need to print these files for students. Also included

on the CD are files necessary to play the games within this unit, if applicable. Many

application problems are provided within the Transparencies folder. Completing these

problems with students will help students learn how to apply the abstract concepts to

real-world situations. For specific information about the contents of the CD, see the

Teacher Resource Guide (pages 84–86). Information about the necessary materials is also

provided with each lesson.

6 #10357 (i1534)—Active Algebra—Algebra I, Unit 1


Introduction (cont.)

Grading Procedures

It is up to the teacher and the administrator to determine how to assess student work.

The following information is intended to be helpful in this decision-making process. The

chart only lists the tests and quizzes from this unit. A comprehensive plan for the

grading procedures is included in the Teacher Resource Guide (pages 39–55).

Homework, Classwork, and Guided Practice Sheets

Give a completion grade (see below) for each assignment. Subtract each completion

grade from a starting grade of 100%. At the end of this unit, record each student’s

completion grade as a quiz grade. Allow students one free late assignment to minimize

time spent evaluating students’ excuses. To make grading easier, have students

exchange papers and check for completion. Then, use the chart in the Teacher Resource

Guide (page 47) to record student scores.

Completion Grade

–0 if all problems were attempted

–3 if half of the problems were attempted

–6 if no problems were attempted

Notes

Check students’ notes halfway through this unit.

Make students revise their notes if they are not

correct, neat, and in order. Give a quiz grade.

Grade again at the end of the unit, but do not give a quiz grade. Instead, if a student’s

notes are in good condition, drop his or her lowest quiz score.

Assessments—Unit 1

For Example

100 (everyone starts here)

–3 p.7 (only half was attempted)

–6 p.8 (no work was attempted)

–0 p.9 (all work was attempted)

–3 p.10 (only half was attempted)

88

Essay quiz grade of 100

if students followed

instructions

Algebraic Expressions

and Operations Test 4 pts. each problem

Adding Integers Quiz 3 pts. each problem

Speed Quiz Practice not for a grade

Multiplying and Dividing

Integers Quiz

1 pt. each problem

Speed Quiz 1

1 pt. each problem

Integers Packet

quiz grade;

25 pts. per page

Mixed Integers Quiz 1 pt. each problem

Speed Quiz 2

1 pt. each problem

Speed Quiz 3

1 pt. each problem

Speed Quiz 4

1 pt. each problem

Collecting Like Terms

Quiz

5 pts. each problem

#10357 (i1534)—Active Algebra—Algebra I, Unit 1

Speed Quiz 5

Mixed Integers Test

Speed Quiz 6

Distributing and

Collecting Quiz

Speed Quiz 7

Writing Equations

Packet

Distributing and

Collecting Test

Integers Unit Test

1 pt. each problem

1 pt. each problem;

+1 each for bonus

1 pt. each problem

10 pts. each problem

1 pt. each problem

quiz grade;

credit for completion

1 pt. each problem

1 to 25—1 pt. each;

26 to 35—6 pts. each;

36 to 38—1 pt. each

for first two lines,

3 pts. for equation

7


Introduction (cont.)

How to Use This Program

Teacher Resource Guide

NCTM standards correlation • Outline of lessons for entire course •

Classroom management and differentiation suggestions • Assessment

suggestions and data-driven instruction charts • Graphing calculator

information • Steps for preparing games and manipulatives • Contents of

the Teacher Resource CD • Segments on the Professional Development DVD

Lesson Plans

Content standard • Specific materials list • Step-by-step procedure •

Notes and practice problems • Review • Reteaching suggestions •

Teacher tips • Assessment appendix • Games appendix • Answer keys

Transparencies

• The kit includes 40 overhead transparencies. These are utilized in various

lessons throughout the program. So, the teacher may or may not have to use

any in a given unit.

• The transparencies are located in a folder within the Active Algebra box.

For teacher reference, each transparency features the unit and lesson numbers

in the header.

Guided Practice Book

• All necessary activity sheets for the students are provided in the student

Guided Practice Book. There are page references to this book within the

lessons. The activity sheets are also provided on the Teacher Resource CD.

• Call 888-333-4551 or visit http://www.tcmpub.com to order more copies

of this consumable product.

Teacher Resource CD

PowerPoint slide shows • Application transparencies • Standardized test

preparation sheets • Algebridge assessments • Form B of all assessments •

Preparation materials for games

Professional Development DVD

Demonstrations and explanations for how to complete the lessons that involve

manipulatives or games.

Lesson Plan Icons

The following

icons are used

throughout the

lessons to guide

teachers in their

planning.

Teacher Tips

Notes

Schedule

Assessment

Practice

Assignment

Mathematics

Game

CD File

Cooperative

Groups

Overhead

Transparency

Transparency

in a CD File

8 #10357 (i1534)—Active Algebra—Algebra I, Unit 1


Lesson

5

Adding Integers with Chips

Algebraic Expressions and Integers Unit

Steps 1–4

30 min.

Steps 5–6

20 min.

Lesson Description

• Adds, subtracts, multiplies, and divides integers and rational

numbers. (McREL Mathematics Standard)

• Students will use manipulatives to add integers.

Materials

• PowerPoint folder on the CD—Adding Integers with Chips

(lessn05.ppt) (optional)

• Overhead chips

• Bag of 15 bicolor chips for each student

Steps 7–9

25 min.

Steps 10–12

15 min.

• Guided Practice Book—Adding Integers 1 (page 7; intgrs01.pdf)

• Guided Practice Book—Adding Integers 2 (page 8; intgrs02.pdf)

Step 1

Procedure

Collect students’ graph paper and highlighters to keep in the

classroom so they are always available when needed.

• Check to see how many students have their notes books.

Let them know that their notebooks or folders (with up-todate

notes and extra paper) will be checked later this week.

• Remind them of the due date for their essays.

Step 2

Review for the Algebraic Expressions and Operations Test,

which is tomorrow.

• Review the properties. Have students study their notes.

Then, make up some examples, using both the algebraic

and numeric properties.

Step 3

Practice

Review the order of operations by solving these problems

together in preparation for the test.

a. 4 2 ÷ 2[6 – (2 – 1) 2 ] 3 – 3 + 4 = 1,001

b. a = 2, b = 3, c = 4

ac + bc 2 = 56

24 #10357 (i1534)—Active Algebra—Algebra I, Unit 1


Adding Integers with Chips

Algebraic Expressions and Integers Unit

Lesson

5

Procedure (cont.)

Step 4

Go over the Notes on Adding Integers with Chips

(pages 25–27).

• Practice saying these notes until you feel comfortable.

• There will be some students who protest. Usually these

students cannot add integers with pencil and paper either.

Just tell them to humor you. This activity will help them better

understand the process of adding integers.

• Give a completion grade at the end of the day for their notes.

• These notes are provided as part of the lesson’s PowerPoint

slide show on the CD (lessn05.ppt).

Notes on Adding Integers with Chips

• Have students draw the following in their notes.

yellow (+) red (–) zero pair

• Have a “pop quiz” by holding up a yellow chip and asking,

“What does this stand for?” Then, do the same for the red chip

and the zero pair.

• As the students watch, demonstrate the process for the first five

problems. Talk them through each step as you work. Do not

distribute chips yet.

• Call on at least three students as you work on each problem.

Example 1

2 + 4 = 6 (first-grade problem)

What do I put for 2? (two yellows)

What do I put for 4? (four yellows)

What is the answer? (six yellows, or 6)

#10357 (i1534)—Active Algebra—Algebra I, Unit 1

25


Lesson

5

Adding Integers with Chips

Algebraic Expressions and Integers Unit

Notes on Adding Integers with Chips (cont.)

Example 2

–2 + 1 = –1

–2 + 1

After setting up the

problem, pull one zero

pair off to the side.

There is one red chip left.

So, the answer is –1.

Example 3

–2 + 3 = 1

–2 + 3

After setting up

the problem, pull

two zero pairs off to

the side.

There is one yellow chip left.

So, the answer is 1.

26 #10357 (i1534)—Active Algebra—Algebra I, Unit 1


Adding Integers with Chips

Algebraic Expressions and Integers Unit

Lesson

5

Notes on Adding Integers with Chips (cont.)

Example 4

3 – 1 = 2

Official Definition of

Subtract—Add the

opposite. This means begin

with a yellow to set up the

problem. Then, change it

to red.

3 – 1

After setting up the

problem, pull one zero

pair off to the side.

There are two yellow chips left.

So, the answer is 2.

Example 5

2 – 5 = –3

Official Definition of

Subtract—Add the

opposite. This means

begin with five yellows

to set up the problem.

Then, change them to

red.

2 – 5

After setting up the

problem, pull two zero

pairs off to the side.

There are three red chips left.

So, the answer is –3.

#10357 (i1534)—Active Algebra—Algebra I, Unit 1

27


Lesson

5

Adding Integers with Chips

Algebraic Expressions and Integers Unit

Step 5

Practice

Procedure (cont.)

Solve these eight problems using the overhead chips. Students can

stop taking notes at this time if they are starting to understand the

process.

• Call on students to help solve the problems. They should tell

you how many chips of each color to use. Also have them call

out the answers after the problem is set up.

• Continue to put yellow chips and change them to red to

indicate subtraction. Stress that subtraction is adding the

opposite.

c. 1 – 6 = –5

d. –5 – 2 = –7

e. –1 – 1 = –2

f. –3 + 4 = 1

g. –2 – 2 = –4

h. 4 – 6 = –2

i. –3 + 4 = 1

j. –6 – 2 = –8

Step 6

Practice

If time allows, let students come up and use the manipulatives on

the overhead with you to solve the following problems.

k. 3 – 5 = –2

l. –1 + 3 = 2

m. –3 – 3 = –6

n. –1 – 3 = –4

o. 1 – 4 = –3

28 #10357 (i1534)—Active Algebra—Algebra I, Unit 1


Adding Integers with Chips

Algebraic Expressions and Integers Unit

Lesson

5

Procedure (cont.)

Step 7

Assignment

When it is clear that all students know what to do, distribute the

Adding Integers 1 activity sheet. Then, give each student

his or her own bag of 15 chips.

Teacher Tip

Tell students not to show “adding the opposite” on their papers.

They should think only about the colors of the chips and write

the answer. This will help them as algebra gets more difficult.

For example, with 3 – 5, encourage them not to write 3 + –5.

Step 8 Before beginning . . .

• Tell students to humor you; do not let students do the activity

sheet without chips.

• Tell students that if they finish quickly, it means that they did

not use chips. You will take the activity sheet away and give

them another one.

Step 9 After they are finished . . .

• Have each student compare answers with one other person

and sign the bottom of the activity sheet.

• After all students are finished, call out the answers to the

activity sheet, and pick up the papers.

Step 10

The next step is to connect from the manipulatives (concrete) to

the abstract. Explain to students that they will not have their bags

of chips in Algebra II or real-life situations. So, discuss how to add

integers without chips.

Do not use chips to solve this problem.

p. –3 + 2

Ask, “Is there more red or yellow?” There is more red.

So, the answer is –1.

#10357 (i1534)—Active Algebra—Algebra I, Unit 1

29


Lesson

5

Adding Integers with Chips

Algebraic Expressions and Integers Unit

Procedure (cont.)

Step 11

Practice

Do not use chips to solve the problems below.

q. –3 – 1 =

Discuss the process of putting out a yellow chip for the –1

and then changing it to red. Say, “They are all red.

How many red chips are there?” There are four red chips,

so the answer is –4.

r. –3 + 5 = 2

s. –1 – 1 = –2

t. 4 – 8 = –4

u. –2 + 8 = 6

v. –6 + 10 = 4

w. –3 – 5 = –8

Teacher Tip

In examples p through u, continue to ask, “Are there more red

or yellow chips? If the chips are all red, how many red chips

are there?”

Step 12

Assignment

Distribute the Adding Integers 2 activity sheet for students to

complete without using chips.

• As students finish, have them compare their answers with

partners and sign their names on the bottoms of their activity

sheets.

• If you have run out of time, assign this sheet as homework,

and have students compare sheets at the beginning of the

next lesson.

30 #10357 (i1534)—Active Algebra—Algebra I, Unit 1


Mixed Operations with Monomials

Polynomials Unit

Steps 1–2

20 min.

Lesson

91

Steps 3–5

15 min.

Lesson Description

• Understands the general properties and characteristics of many

types of functions, including polynomials. (McREL Mathematics

Standard)

• Students will review adding and multiplying monomials.

Materials

Step 6

25 min.

• Appendix A: Assessments—Multiplying Monomials Quiz

(page 52; asess54a.pdf)

• Guided Practice Book—Adding and Multiplying Monomials 1

(page 158; poly01.pdf)

Step 7

30 min.

Step 1

Procedure

Review how to multiply monomials by asking student volunteers

to do the following problems on the overhead:

Practice

a. m(m 2 )(m 5 ) = m 8

2

3

4

9

b. ( m) 2 = m 2

c. (–3p)(2p 2 ) 2 = –12p 5

Step 2

Assessment

Give the Multiplying Monomials Quiz.

• There are two versions of this assessment. Form A is in

Appendix A: Assessments (page 52). Form B is on the CD

(asess54b.pdf). You can use both versions at the same time to

discourage copying, or use one version as the initial assessment

and the other version as the makeup assessment.

• Answers for both versions of the quiz are on page 68.

Step 3

Practice

Review scientific notation and standard notation.

• There will be an assignment on scientific notation and

standard notation in a few days.

d. 8,640,000 = 8.64 x 10 6

e. .00007 = 7.0 x 10 –5

f. 4.63 x 10 3 = 4,630

#10357 (i1543)—Active Algebra—Algebra I, Unit 7

g. 3.37 x 10 –2 = .0337

17


Lesson

91

Mixed Operations with Monomials

Polynomials Unit

Step 4

Procedure (cont.)

Review the definitions for the following vocabulary words, which

were introduced in the Notes on Polynomials in Lesson 90.

• monomial—1 term

• binomial—2 terms

• trinomial—3 terms

• polynomial—a monomial or a sum of monomials

Step 5

Practice

Go over adding monomials, and review multiplying monomials

on the overhead or board.

• Stress to students that terms must look alike to add them.

They do not have to look alike to multiply them.

Adding Monomials

h. 2x + 3x = 5x

i. 6x 2 – 8x 2 = –2x 2

j. 3xy 2 – 6xy 2 + 4x 2 y = –3xy 2 + 4x 2 y

k. 2x + 5y = 2x + 5y

l. –2x – 2x = –4x

Multiplying Monomials

m. 2x(3x) = 6x 2

n. –6x(–3x 2 ) = 18x 3

o. 4mn 2 (–3m 2 n) = –12m 3 n 3

p. –2p(4p – 6q) = –8p 2 + 12pq

q. –3x 3 (4y) = –12x 3 y

18 #10357 (i1543)—Active Algebra—Algebra I, Unit 7


Mixed Operations with Monomials

Polynomials Unit

Lesson

91

Step 6

Practice

Cooperative

Groups

Procedure (cont.)

Review mixed operations (adding and multiplying).

• Place students into groups of four and give each group two

problems. Have groups present the problems to the class using

the overhead projector or board.

r. 4x – 6x = –2x

s. 4x(6x) = 24x 2

t. xy(–3x 2 y) = –3x 3 y 2

u. –4mn – 6mn = –10mn

v. –3m(2m – 4n) = –6m 2 + 12mn

w. –3x 2 y – 6xy 2 + 4x 2 y = x 2 y – 6xy 2

x. –6mn – 8mn = –14mn

y. –6mn(–8mn) = 48m 2 n 2

Step 7

Assignment

Create groups of three to four students to complete the

Adding and Multiplying Monomials 1 activity sheet.

Teacher Tips

Before you put the students into groups, remind them:

• Use a “ruler voice.” (Their voices should only be heard

12 inches away.)

• They should immediately choose leaders for their groups.

• After all students have finished at least 10–15 problems, the

leader calls out his or her answers. Everyone needs to agree

on the answers.

When group members agree on all the answers:

• They should all come to you with their papers.

• Shuffle the papers and pick one to grade.

• Assign a grade based on the number of correct answers.

• You may want to give a reward to the group that misses the

fewest problems.

#10357 (i1543)—Active Algebra—Algebra I, Unit 7

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