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:

• **Teacher**s’ 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, **the**re 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 **the**ir learning from **the**

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

Resource CD, or simply copy **the** pages and give **the**m 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. **Teacher**s

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 be**for**e 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 be**for**e 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 ma**the**matics, he or she is

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

students may have in ma**the**matics, 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 **the**n hold tutorials to reteach **the** objectives that students did not master in class.

The tutorials can be held be**for**e 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 **the**se 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 be**for**e beginning **the**

program include **the** following:

• Will **the** school provide transportation?

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

be lower? (The higher **the** retake grade, **the** more participation **the**re 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 **of**fer

**the** program.

Pr**of**essional Development DVD

Included in this kit is **the** Pr**of**essional Development DVD. This DVD includes segments

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

video be**for**e 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 **the**se 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 **the**se

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

real-world situations. For specific in**for**mation about **the** contents **of** **the** CD, see **the**

**Teacher** Resource Guide (pages 84–86). In**for**mation 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 in**for**mation 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 **the**ir notes if **the**y 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

in**for**mation • Steps **for** preparing games and manipulatives • **Contents** **of**

**the** **Teacher** Resource CD • Segments on **the** Pr**of**essional 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

Pr**of**essional 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 **the**ir

planning.

**Teacher** Tips

Notes

Schedule

Assessment

Practice

Assignment

Ma**the**matics

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 Ma**the**matics 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 **the**y are always available when needed.

• Check to see how many students have **the**ir notes books.

Let **the**m know that **the**ir notebooks or folders (with up-todate

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

• Remind **the**m **of** **the** due date **for** **the**ir essays.

Step 2

Review **for** **the** Algebraic Expressions and Operations Test,

which is tomorrow.

• Review **the** properties. Have students study **the**ir notes.

Then, make up some examples, using both **the** algebraic

and numeric properties.

Step 3

Practice

Review **the** order **of** operations by solving **the**se problems

toge**the**r 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 **the**se notes until you feel com**for**table.

• There will be some students who protest. Usually **the**se

students cannot add integers with pencil and paper ei**the**r.

Just tell **the**m to humor you. This activity will help **the**m better

understand **the** process **of** adding integers.

• Give a completion grade at **the** end **of** **the** day **for** **the**ir 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 **the**ir 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 **the**m 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 **of**f 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 **of**f 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 **of**f 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 **the**m to

red.

2 – 5

After setting up **the**

problem, pull two zero

pairs **of**f 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 **the**se eight problems using **the** overhead chips. Students can

stop taking notes at this time if **the**y 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 **the**m call

out **the** answers after **the** problem is set up.

• Continue to put yellow chips and change **the**m 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 **the**ir papers.

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

**the** answer. This will help **the**m as algebra gets more difficult.

For example, with 3 – 5, encourage **the**m not to write 3 + –5.

Step 8 Be**for**e beginning . . .

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

sheet without chips.

• Tell students that if **the**y finish quickly, it means that **the**y did

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

**the**m ano**the**r one.

Step 9 After **the**y are finished . . .

• Have each student compare answers with one o**the**r 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 **the**y will not have **the**ir 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 **the**re 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 **the**n changing it to red. Say, “They are all red.

How many red chips are **the**re?” 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 **the**re more red

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

are **the**re?”

Step 12

Assignment

Distribute **the** Adding Integers 2 activity sheet **for** students to

complete without using chips.

• As students finish, have **the**m compare **the**ir answers with

partners and sign **the**ir names on **the** bottoms **of** **the**ir 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 Ma**the**matics

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** o**the**r 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

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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 **the**m.

They do not have to look alike to multiply **the**m.

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

Be**for**e you put **the** students into groups, remind **the**m:

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

12 inches away.)

• They should immediately choose leaders **for** **the**ir 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 **the**ir 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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