Algebra 1 - Glencoe

Glencoe

Algebra 1Multimedia Applications

Teacher’sGuide with StudentWorksheets

Windows/Macintosh

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Glencoe/McGraw-Hill

© Glencoe/McGraw-Hill iii Algebra 1 Multimedia Applications

OverviewAlgebra 1 Multimedia Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

About this Teacher’s Guide . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

Getting Started Algebra 1 Multimedia Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

Windows Operating System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4Macintosh Operating System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

Using the CD-ROM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6Main Menu . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6Navigation Buttons. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6Help Button . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6Interactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7Special Features . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

Content Chart . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

Teaching Suggestions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13lntroducing Students to the Program . . . . . . . . . . . . . . . . . . . . . . . . . . 13Students in a Lab Setting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13Whole Class . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14lndividual Students . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14Assessment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

Teacher’s Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16Chapter 1 Batter Up! . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16Chapter 2 Pizza Place . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18Chapter 3 Ratios and Proportions in Racing. . . . . . . . . . . . . . . . . 20

The Fireworks Factory: Making a Profit . . . . . . . . . . . . 22Chapter 5 Exploring the Ocean’s Depths . . . . . . . . . . . . . . . . . . . 24

Linear Relationships in Car Racing. . . . . . . . . . . . . . . . 26Chapter 6 Fireworks, Mathematics, and Safety! . . . . . . . . . . . . . . . 28Chapter 7 Systems of Equations: An Aid to Decision Making . . . . 30Chapter 8 Pools and Polynomials . . . . . . . . . . . . . . . . . . . . . . . . . 32Chapter 9 The Factoring Farmer . . . . . . . . . . . . . . . . . . . . . . . . . 34Chapter 10 Quadratics and Fireworks: A Perfect Match! . . . . . . . . 36Chapter 11 Mathematics in the Movies . . . . . . . . . . . . . . . . . . . . . 38Chapter 12 lnvestigating Underwater Sound . . . . . . . . . . . . . . . . . 40

Contents

© Glencoe/McGraw-Hill iv Algebra 1 Multimedia Applications

Student Worksheets. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42Worksheet 1 Batter Up! . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42Worksheet 2 Pizza Place . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45Worksheet 3 Ratios and Proportions in Racing. . . . . . . . . . . . . . . . . 48

Fireworks Factory: Making a Profit. . . . . . . . . . . . . . . . 51Worksheet 5 Exploring the Ocean’s Depths . . . . . . . . . . . . . . . . . . . 54

Linear Relationships in Car Racing. . . . . . . . . . . . . . . . 57Worksheet 6 Fireworks, Mathematics, and Safety! . . . . . . . . . . . . . . . 60Worksheet 7 Systems of Equations: An Aid to Decision Making . . . . 63Worksheet 8 Pools and Polynomials . . . . . . . . . . . . . . . . . . . . . . . . . 66Worksheet 9 The Factoring Farmer . . . . . . . . . . . . . . . . . . . . . . . . . 69Worksheet 10 Quadratics and Fireworks: A Perfect Match! . . . . . . . . 72Worksheet 11 Mathematics in the Movies . . . . . . . . . . . . . . . . . . . . . 75Worksheet 12 Investigating Underwater Sound . . . . . . . . . . . . . . . . . 78

Answer Keys . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81

Troubleshooting Guide . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97Windows . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97Macintosh . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98

Customer Service Guide . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101

Contents

© Glencoe/McGraw-Hill 1 Algebra 1 Multimedia Applications

OverviewAlgebra 1 Multimedia ApplicationsEngaging computer simulations, plus videos of real people using mathematics, bring the world into your classroom. These highly interactive multimedia materials are carefully correlated to theAlgebra 1 textbook chapters.

Choose some or all of theapplications to extend andreinforce concepts.

Involve your students inapplying mathematics and solving problems inrealistic situations.

Data collection and analysisform the basis of manyexplorations. Students areactively engaged in theinteractions. They makedecisions, operate simulateddevices, collect data, recorddata, and interpret results.

Complete onscreeninstructions guide studentsthrough the interactions. Hot links explain new terminology. Explore buttons lead to animated in-depth explorations of selected topics.

Each chapter engages students in a compelling scenario.

• Timing the swing of a baseball bat

• Determining bicycle gear ratios

• Testing fireworks for safety

• Tracking a firework’slaunch path

• Keeping accounts for a pizza restaurant

• Relating waterpressure and depth

• Comparing costs of phone plans

• Exploring underwatersound

• Calculating profit for a fireworks factory

• Distance, speed, andtime in auto racing

• Calculating volume of pool coatings

• Planning for moviestunts

Real-World Activities Correlated to Curriculum


Video of people who use mathematics in their careers provide genuine, credible evidence thatmathematics is vital to students’ future employment.

Overview

Easy to UseEach chapter is packed with activities and is easy to use. Just click to move to a page and then followthe onscreen instructions.

English and Spanish Spoken TextYou can hear the text spoken in either English or Spanish.

Classroom SettingsIdeal for student partners in a lab setting, thesematerials are also appropriatefor individual or whole classuse.

WorksheetsAccompanying worksheetsensure that students recordtheir results and reflect ontheir work at the computer.

HomeworkStudent worksheets for eachchapter include an After theComputer page, which can be assigned as homework.

QuizEach chapter ends with aninformal quiz for students tocheck their understanding.

• Softball player, Alexa Guitierrez

• Accountant, Wendy Guisturte

• Business owner, Rudy Schaffner

• Road-bike racer, Amy Strommer

• Marine biologist, Lai Ngai Chin

• Fireworks manufacturer,Rudy Schaffner

• Businesswoman, Mireya M. Gavert

• Financial planner, Ann Geddes

• Petroleum engineer, Larry Owusu

• Civil engineer, Ngyra Stebbins


About this Teacher’s GuideRead the Getting Started section before you begin. After you start the program, refer to the Using theCD-ROM section as needed.

For information on using the applications with your curriculum, see the Content Chart and theTeaching Suggestions sections.

As you make plans to use these activities with your students, refer to the Teacher Notes on each chapter.Student worksheets and answer keys are included.

Getting Started • Installing Algebra 1 Multimedia Applications on a Macintosh or Windows system (p. 4)

Using the CD-ROM • Main Menu (p. 6)

• Navigation Buttons (p. 6)

• Help Button (p. 7)

• Interactions (p. 7)

• Special Features: Video, Spoken Text, English/Spanish, Quizzes, and Student Worksheets (p. 8)

Content Chart • Each chapter’s content (p. 10)

• Learning objectives

Teaching Suggestions • Introducing Students to the Program (p. 13)

• Students in a Lab Setting (p. 13)

• Whole Class (p. 14)

• Individual Students (p. 14)

• Assessment (p. 15)

Teacher’s Notes • Notes on each chapter (p. 16)

• Description of content

• Goals and objectives

Student Worksheets • Reproducible worksheets for each chapter (p. 42)

• Answer Key (p. 81)

Overview


Getting Started Algebra 1 Multimedia Applications

Windows® Operating System

Minimum System Requirements• 486SX/33MHz processor or higher; 486DX/66MHz recommended

• 8 MB RAM, 16 MB recommended

• Windows-compatible 16-bit sound card

• 2X CD-ROM drive or higher; 4X CD-ROM recommended

• 256 color VGA monitor

• Microsoft-compatible mouse

• Keyboard

• Microsoft Windows 3.1 operating system or higher; Windows 95 recommended

• No hard disk space needed, except for installation of QuickTimeTM

lnstallation lnstructions1. Insert the Algebra 1 Multimedia Applications CD-ROM disk into the CD-ROM drive.

2. From Windows 3.1, open Program Manager and choose Run from the File menu. From Windows 95, click the Start button and choose Run.

3. In the Command Line text box, type the drive letter for your CD-ROM drive, a colon,and then the word setup. (Example: d:setup) Press Enter or click OK.

4. If your computer does not already have QuickTime for Windows, you must install it. The Windows 95 version of Algebra requires the 32-bit version of QuickTime for Windows.Repeat steps 2 and 3, substituting QTSetup for setup. Follow the setup instructions.

5. To use Algebra 1 Multimedia Applications from Windows 3.1, open the Glencoe program group and double-click the Glencoe Algebra 1 icon. From Windows 95, click the Start button,select Glencoe, and select Glencoe Algebra 1.

Note: The CD-ROM disk must remain in the drive while the program is in use.


Macintosh Operating System

Minimum® System Requirements• 68030 processor or higher required; 68040 or PowerPC processor recommended

• 8 MB RAM, 16 MB recommended

• 3.6 MB available space on startup hard disk

• 2X CD-ROM drive or higher, 4X CD-ROM recommended

• 256 color monitor

• Mouse

• Keyboard

• Macintosh System 7.0 or higher

lnstallation lnstructions1. Insert the Algebra 1 Multimedia Applications CD-ROM disk into the CD-ROM drive.

The CD-ROM will open a window on the desktop.

2. In the Glencoe Algebra 1 window, double-click the Read Me file for more information oninstalling software for video.

3. If your system does not have current versions of QuickTime and Indeo® Video Codec, you will need to install them. They are both included on the Glencoe CD-ROM disk.

Double-click the Install QuickTime icon. The installer will automatically restart your computer when it is finished.

Double-click the Install Indeo Video icon. Your computer will automatically restart again when the installation is finished.

4. To use Algebra 1 Multimedia Applications, double-click the Start Algebra 1 icon.

Note: The CD-ROM disk must remain in the drive while the program is in use.

Getting Started


Using the CD-ROM

Main MenuThe main menu appears automatically after the title screen. The titles are shown. Choose one byclicking the red button.

If you want to switch from English to Spanish spoken text, click the button at the bottom of the menu screen.

Navigation ButtonsRed buttons at the bottom left of each screen enable you to move from page to page, return to the mainmenu, or quit the program.

Click the forward arrow button to move to page 1.

Go to main menu.

Quit theprogram.

current page

View the help screens.

Go back one page.

Go ahead one page.


Click the Jump button on the title screen or the page number button to show the Jump Bar.

Click on a page number to move directly to that page in the chapter.

Help ButtonClick the Help button to see more information on pointers (cursors), navigation buttons, activityinstructions, activities, video, speech, “hot links,” and Explore features.

lnteractionsEach chapter consists of five or six pages. The pages and their content are varied to fit each specificchapter, but the following general format is used.

Title

Page 1 Introduction and goals

Page 2 An exploratory interaction

Page 3 Explanation or further explorations

Page 4 A major investigation

Page 5 Real-world applications

Page 6 Quiz

Students follow the step-by-step instructions on the left side of the interaction pages. Each set of instructions begins with an overview of the activity. Click each numbered step in sequence. Go back to reread previous screens if necessary.

Students complete worksheets as they work through the chapter. (See the section on StudentWorksheets in this guide.)

Using the CD-ROM


Special Features

VideoVideo controls are located under the video window. They simulate the standard control buttons andslider used on video equipment. Click the forward button to begin play. The sound control button onthe far left adjusts the sound level.

The slider lets you replay part of the video. The pause button lets you stop the action.

Spoken TextThe printed information and instructions on all pages can be heard by clicking the speaker button at the beginning of each text block.

Set the spoken text to English or Spanish on the main menu screen.

Using the CD-ROM


English or SpanishThe spoken text can be heard in English or Spanish. Click the corresponding button at the bottom ofthe main menu. The printed text is always in English; the recorded voice provides the Spanishtranslation.

QuizEach chapter concludes with a quiz of four to six questions. This enables students to check that theyhave mastered the mathematics used in the activities. A score is reported at the end of the quiz, but it is not recorded. Students can click the Reset button to try the quiz again or let their partner take the quiz.

Student WorksheetsA three-page worksheet accompanies each chapter on the CD-ROM. Reproducible worksheets areincluded in this guide. An answer key for each is also provided. Each worksheet consists of two parts:

At the ComputerStudents should complete this section at the computer to record theirresults and to further focus their thinking.

After the ComputerYou may choose to use this page as homework. It does not require thatthe student have access to the CD-ROM, but reinforces and extends thecomputer activity. It includes a Mathematics Journal writing exercise.

Using the CD-ROM


Content ChartThis chart provides an overview of the applications. For more detailed information, refer to the TeacherNotes for each chapter, which are included in this guide.

Chapter

1. ExploringExpressions,Equations, andFunctions

2. Exploring RationalNumbers

3. UsingProportionalReasoning

3. Solving LinearEquations

5. GraphingRelations andFunctions

Title

Batter Up!

Pizza Place

Ratios andProportions in Racing

The FireworksFactory: Making a Profit

Exploring theOcean’s Depths

Goals

1. Apply variables inreal-worldsituations.

2. Collect andorganize data.

3. Solve equations.

1. Add and subtractrational numbers.

2. Use positive andnegative numbersfor businesstransactions.

3. Use data andgraphs to makedecisions.

1. Use ratios todescribe bicyclegears.

2. Collect, graph, andanalyze data ongear ratios andheart rate.

3. Applymathematics to sportsperformance.

1. Write a profitequation.

2. Graph points from profitequation.

3. Find break-evenpoints.

1. Collect, graph, andanalyze data.

2. Find a functionthat describesdata.

3. Create a linegraph based oncollected data.

Activities

• Relate pitch speedto fair and foulballs.

• Calculate when toswing the bat.

• Relate moneytransactions toaccount balance.

• Write checks,make deposits,and balance anaccount.

• Relate sprocketsand gear ratios.

• Choose asprocket to keepheart rateacceptable onvarying terrain.

• Relate graphs ofexpenses, revenue,profit, and numbersold.

• Design a firework,set a selling price,and find the profit.

• Experiment withwater pressure.

• Collect depth and pressure data andfind function to fit data.

Videos

Player describes herrole in Girls’ VarsitySoftball.

An accountantdescribes how sheuses positive andnegative numbers inher work.

A road-bike racerexplains the relationbetween steepness,pedaling effort, heartrate, and bike gears.

A fireworksmanufacturerexplains why heneeds to calculatecosts and profits inhis business.

A marine biologistexplains how datacollection andmodeling are used inhis field.


Chapter

5. Analyzing LinearEquations

6. Solving LinearInequalities

7. Solving Systems ofLinear Equationsand Inequalities

8. ExploringPolynomials

Title

Linear Relationshipsin Car Racing

Fireworks,Mathematics,and Safety!

Systems ofEquations:An Aid to Decision Making

Pools andPolynomials

Goals

1. Collect andanalyze data.

2. Interpret graphs.3. Find equations to

fit data.4. Use slope to

represent speed.

1. Collect and graphdata related tofireworks.

2. Model situationswhere quantitieshave a range ofvalues.

3. Use variables,expressions, andinequalities tomake decisions.

1. Write equationsthat modelsituations.

2. Graph and solvesystems ofequations.

3. Analyze situationsusing graphs andequations.

4. Make decisionsbased on youranalysis.

1. Use theDistributiveProperty.

2. Add, subtract, andmultiplypolynomials.

3. Create polynomialexpressions andapply them todimension andvolume.

Activities

• Change racing car speed andobserve change in time.

• Relate distance,time, and speedfor Grand Prixtrials.

• Test fireworks todetermine a rangeof safe fuselengths.

• Collect and graphdata on fireworks’height and radius.Find a safe range.

• Explore costs ofphone plans.

• Compare cost perminute andnumber ofminutes for twophone plans’costs.

• Decide which planis best.

• Use algebra tilesto add, subtract,and multiplypolynomials.

• Create and applya polynomialequation forswimming poolvolume.

Videos

A video of autoracing describes howmathematics isessential to thedesign of racing cars.

A fireworksmanufacturerexplains howfireworks safetydepends ondetonation heightand radius of thefireball.

A business womandescribes how sheuses mathematics tosave her companytime and money.

A financial plannerdescribes howpolynomials calculatecompound interestof a savings account.

Content Chart


Chapter

9. Using Factoring

10. ExploringQuadratic andExponentialFunctions

11. Exploring RadicalExpressions andEquations

12. Exploring RationalExpressions andEquations

Title

The FactoringFarmer

Quadratics andFireworks:A Perfect Match!

Mathematics in theMovies

InvestigatingUnderwater Sound

Goals

1. Model polynomialswith algebra tiles.

2. Use polynomialsto represent area.

3. Factor quadraticexpressions andsolve equations.

1. Collect and graphdata.

2. Determine aquadratic functionthat matches aparabola.

3. Use a quadraticfunction topredict.

1. Evaluate radicalexpressions.

2. Collect and graphdata.

3. Find radical andquadraticfunctions to fitdata.

1. Collect and graphdata onunderwatersound.

2. Explore therelationshipbetween distanceand intensity.

3. Use rationalfunctions tomodel soundintensity.

Activities

• Use algebra tilesto modelmultiplication.

• Use polynomialsto model farmfields.

• Explore initialvelocity and heightof fireworks.

• Find a quadraticequation that fitsthe firework’spath.

• Find the length ofwire for a moviestunt explosion.

• Find the functionsto fit the data, andplan the stunt.

• Change thedistance of asound source andrecord surfacearea and intensity.

• Collect data anddetermine anequation to modelsound intensity.

Videos

A petroleumengineer explainshow he usesfactoring to speed upcomputercalculations.

A civil engineerdescribes how sheuses quadraticequations in herwork with thehighway department.

A civil engineerdescribes how sheuses radical functionsfor distance whenplanning roads.

A video showingwhales tells whyoceanographersstudy marinemammals and thesounds they make.

Content Chart


Teaching Suggestions

lntroducing Students to the ProgramThese materials are extremely easy to use. Students do not require training to operate this program. A brief demonstration will help them use their time most efficiently. You may want to show how tomove from page to page, access the help feature, and follow the steps for an activity. A demonstrationcomputer system with either a large monitor or projection device works well for whole-classdemonstrations.

Emphasize that students will explore real-world situations. Many activities involve collecting andanalyzing data. The video segments describe how people use mathematics in their careers.

Be sure to explain how the worksheets are used to record students’ results and help clarify theirthinking. Students should read, view, or explore a page on the screen and then do the worksheetexercises that correspond to that page. Then they are ready to move to the next page on the computer.

Explain how you want your students to use the quiz at the end of the chapter, individually or with apartner, and whether you will assign the After the Computer worksheet as homework.

Students in a Lab SettingA lab setting with two students at a computer is ideal for using these materials. Pairing students withpartners is highly recommended, even if there are enough computers for every student.

Working with PartnersBenefits of working with a partner include increased communication, sharing of ideas, and morethoughtful work. Also, partners can check results and keep track of worksheet exercises. Be sure to havepartners share responsibilities equally.

In the LabAfter a brief demonstration of the program, students can easily work independently in a lab setting.Briefly describe how the computer activities relate to recent class activities. Distribute worksheets, anddirect students to the chapter they will use. Clarify how much time is available and how they shoulduse the worksheets and the computer quiz.

After the lab, have students compare their results using the worksheet exercises as a guide.


Whole ClassIf only one computer is available, use it with one or more large monitors or a projection device for thewhole class. Test your system to be sure that the screens are clearly visible to your students and that theaudio levels enable all students to hear the video segments.

Using WorksheetsDistribute the worksheets for the chapter. Briefly describe how the computer activities relate to recentclass activities.

Either operate the program yourself or have a student operate it. Pause at each page to allow time forstudents to complete ths corresponding worksheet exercises. As time permits, have students discusstheir responses to the computer activities as you go.

In activities that involve data gathering, have one or more students operate the program to decide whatdata to gather. Then the rest of the class will record and use these same data.

lndividual StudentsStudents can also use the program individually (or with partners) at a computer located in a classroomor media center. If possible, provide a brief demonstration to all students before they begin using theprogram independently. You may want to designate a few experienced students as “computerconsultants” to assist other students if the need arises.

Using WorksheetsMake copies of the worksheets available. Although the CD-ROM is effective on its own, the worksheetsprovide a record of student work and focus student thinking on the mathematics in the activity. Thiscan be especially valuable when students work with the program individually.

Follow up with discussions of the activity, either in small groups or as a whole class.



AssessmentA major assessment tool for these applications is teacher observations of students at work at thecomputer. Are students able to follow the instructions to complete the activities? Do students makechoices in the program that demonstrate their understanding of the mathematics involved?

Listen to the discussions between student pairs to assess how well the concepts are understood. Dostudents discuss, explain, and defend their ideas and conclusions with their partners? Do studentsrecord appropriate responses to worksheet exercises?

After the computer activity, discuss the activity and have student groups share their results.

The quiz at the end of each chapter enables students to assess their understanding of concepts and skillsin the chapter. You may want students to take the quiz individually and record their score on theirworksheet. You may encourage students to retake the quiz to try to make a “perfect score.” You maychoose to have students who are working with partners take the quiz jointly.

The worksheet exercises provide a written record of student work. You may choose to assign the Afterthe Computer worksheet page as homework.


Exploring Expressions, Equations, and FunctionsCHAPTER 1


lnteractive Activities • Relate pitch speed to fair

and foul balls.• Calculate when to swing

the bat.

Video• Player describes her role

in Girls’ Varsity Softball.

Prerequisites • Read tables.• Calculate with decimals.• Evaluate equations.• Translate verbal

expressions intomathematicalexpressions.

Batter Up!

In this baseball batting simulation, students explore the relationshipsamong speed, time, and distance. They collect data on pitched balls ofvarying speeds and write an expression for distance using time and rate.

Using the time equation, time � distance/rate, students decide when toswing the bat. Using the equation wait time � time to plate � swing time,they calculate the wait time before the batter begins the swing.

Sample Screen

Goals1. Apply variables in real-world situations. 2. Collect and organize data. 3. Solve equations.

ContentPage 1 Introduction and Goals Page 2 Exploration: Distance, Rate, and Time Page 3 Application: Wait Time for BatterPage 4 Video: Softball StrategyPage 5 Quiz

ObjectivesPage 2 Exploration Explore the relationships among speed, time, and distance.

Page 3 ApplicationUse equations to decide when to swing a bat.

Tips & Suggestions• Relate this simulation to students’ own baseball or softball experiences. Ask students to describe

how they decide when to swing the bat. Perhaps their coaches have talked to them about swingingtoo early or too late. Some students may know the approximate speed of a pitch in professionalbaseball.

• The Calculator button displays an onscreen calculator. Students can also use their own calculators ifthey wish.

• In the activity on page 2, pitch speeds between 86 and 99 feet per second result in fair balls. A pitch speed of 92 ft/sec is “right down the middle” over second base.

• In the activity on page 3, students must enter the correct value for Time to Plate and a value forWait Time before the Pitch and Swing button can be used.

• In the quiz, the numerical values in the questions are different each time. However, the correctresponse is always in the same position for a given question.

• Students need to understand the following terms: fair, foul, wait time, swing time, and time to plate.

Extensions• Exercise 13 on the worksheet deals with changing units of measure, which provides a review of

arithmetic operations.

• Exercise 15 on the worksheet explores the type of angle the bat makes with the path of the ball.


Exploring Expressions, Equations, and FunctionsCHAPTER 1

Exploring Rational NumbersCHAPTER 2

Pizza Place

Students handle the financial account of a pizza restaurant, using positivenumbers to represent deposits and negative numbers for expenses.

They write deposit slips for deposits and checks for expenses. Theyinterpret bar graphs of the account balance.

Sample Screen


lnteractive Activities • Relate money

transactions to accountbalance.

• Write checks, makedeposits, and balance anaccount.

Video• An accountant describes

how she uses positiveand negative numbers inher work.

Prerequisites • Calculate with rational

numbers.• Interpret bar graphs.

Goals1. Add and subtract rational numbers. 2. Use positive and negative numbers for business transactions.3. Use data and graphs to make decisions.

ContentPage 1 Introduction, Goals, and Video: RestaurantPage 2 Exploration: TransactionsPage 3 Application: A Business AccountPage 4 Video: AccountantPage 5 Quiz

ObjectivesPage 2 Exploration Use rational numbers in an account.

Page 3 Application Keep an accurate business account.

Tips & Suggestions• Students need to understand the difference between deposits and withdrawals (writing checks)

in a bank account.

• You may want to relate the business account simulated here to students’ own savings accounts.

• In the interactions on pages 2 and 3, the transactions and numerical values remain constant.

• Students need to understand the following terms: transaction, account balance, check, deposit, credit, and debit.

Extensions• You or your students may know someone who runs a small business and can provide an actual

account record for a period of a month or two. Students might examine the record and report onthe way positive and negative numbers are used and shown.


Exploring Rational NumbersCHAPTER 2

Using Proportional ReasoningCHAPTER 3

Ratios and Proportionsin RacingStudents investigate bicycle gears and the ratios of front and backsprocket teeth. They explore the use of various gears on flat or hillyground.

They relate gear ratios to maintaining the cyclist’s heartbeat and pedaling rates.

By interpreting gear ratios, they determine a missing back sprocket and specify the number of teeth it should have.

Sample Screen


lnteractive Activities • Relate sprockets and

gear ratios.• Choose a sprocket

to keep heart rateacceptable on varyingterrain.

Video • A road-bike racer

explains the relationbetween steepness,pedaling effort, heart rate, and bike gears.

Prerequisites • Compare decimal

numbers.• Interpret graphs.

Goals1. Use ratios to describe bicycle gears.2. Collect, graph, and analyze data on gear ratios and heart rate.3. Apply mathematics to sports performance.

ContentPage 1 Introduction and Goals Page 2 Video: Racing Cyclist Page 3 Exploration: Bicycle Gears Page 4 Application: Changing Gears in Racing Page 5 Information: The Golden RatioPage 6 Quiz

ObjectivesPage 3 Exploration Explore ratios.

Page 4 Application Apply gear ratios to bicycle racing.

Tips & Suggestions• If some students are not familiar with multiple-speed bicycles, you may want to arrange to have

one brought to class for observation.

• Be sure students notice that the gear ratio uses the front sprocket teeth as the numerator.

• On page 4, the pedal rotations per minute (rpm) is a constant 90 rpm. The grade or slope of theterrain is assigned integer values from �4 through �4. Heart rate is calculated by the formula:

rpm*ratio

heart rate � 56 5*grade

51 51

• Students need to understand the following terms: gear, sprocket, teeth, ten-speed bicycle,and revolution.

Extensions• Students might research the racing bicycles available at a local bicycle shop and report on the

sprocket ratios and number of gears.

� �


Using Proportional ReasoningCHAPTER 3

Solving Linear EquationsCHAPTER 3

The Fireworks Factory:Making a ProfitStudents explore expenses, revenue, and profit from the point of view ofthe owner of a fireworks manufacturing company. They decide thenumber of fireworks to make and interpret graphs of variable and fixedexpenses. They observe how revenue depends on selling price andinterpret a graph showing the break-even point.

Students create the profit equation:

Profit = (selling price) � (number sold) �(expense per item) � (number sold) �(fixed expenses).

They design a firework, set a selling price, collect profit data, and use theprofit equation to predict profits.

Sample Screen


lnteractive Activities • Relate graphs of

expenses, revenue, profit,and number sold. Designa firework, set a sellingprice, and find the profit.

Video• The owner of a graphic

design company discussesthe profit equation.

• A fireworks manufacturerexplains why he needs tocalculate costs and profitsin his business.

Prerequisites • Evaluate equations.• Write equations from

relationship statements.

Goals1. Write a profit equation.2. Graphs points from a profit equation. 3. Find break-even points.

ContentPage 1 Introduction, Goals, and Video: Graphic Design Company Owner Page 2 Exploration: Graphing Profit Page 3 Activity: Create a Profit Equation Page 4 Application: Predicting Profit Page 5 Video: Fireworks Manufacturer Page 6 Quiz

ObjectivesPage 2 Exploration Explore profit equations.

Page 3 Application Use an equation to predict profits.

Tips & Suggestions• On page 2, the Expense, Revenue, and Profit/Loss buttons display bar graphs.

Fixed Expenses � $500; Variable Expenses � $10 per firework; Selling Price � $40.

• On the second screen of page 2, the profit graph corresponds to the Number of Fireworks thestudent chose. Change this by returning to the first screen and dragging the slider.

0 � Number of Fireworks � 30

• The profit equation is central to this interaction. Be sure students complete and understand theequation activity on page 3 before they begin page 4.

• Be sure that students understand that number sold is the independent variable. This is the casebecause the factory makes fireworks “to order,” so all of the product is sold.

• On page 4, the cost of a firework is between $21 and $38. The minimum Selling Price is the cost;the maximum is $50. The number sold is 1 � 50. The Fixed Expenses are random integers between200 and 300.

• Students need to understand the following terms: expenses, fixed expenses, variable expenses, revenue,profit, break-even point, cost per unt, and selling price.

Extensions• Students might apply the profit equation to a school fundraising event.


Solving Linear EquationsCHAPTER 3

Graphing Relations and FunctionsCHAPTER 5

Exploring the Ocean’s Depths

Students explore the relation between water depth and pressure. Theychange the dimensions of an aquarium full of water and observe thechange in water pressure.

They learn why water pressure is important to divers.

Students collect data on depth and pressure by lowering a pressure gaugeto various depths. They graph the data and find a linear equation to fitthe data points. They use this model to predict pressure at variousdepths.

Sample Screen


lnteractive Activities• Experiment with water

pressure.• Collect depth and

pressure data and find a function to fit it.

Video • A marine biologist

explains how datacollection and modelingare used in his field.

Prerequisites • Plot ordered pairs.• Interpret the graph

of a linear equation.

Goals1. Collect, graph, and analyze data.2. Find a function that describes data.3. Create a line graph based on collected data.

ContentPage 1 Introduction and Goals Page 2 Exploration: Water Pressure Page 3 Video: Diver Page 4 Application: Linear Model for Pressure Page 5 Video: Marine Biologist Page 6 Quiz

ObjectivesPage 2 Exploration Explore ratios.

Page 4 Application Find a function to model water pressure.

Tips & Suggestions• The concept of mathematical model is central to this interaction. The model is a fitted line, a linear

equation. You may want to present additional activities that involve fitting lines to data before andafter this interaction. You may want to relate this interaction to your students’ science activities onpressure.

• The value for water pressure used in this activity is 0.434 psi per foot of depth. For example, at a depth of ten feet, the pressure is 4.34 psi.

• On page 2, the pressure gauge digits represent tenths. On page 4, the pressure gauge digits are ones.

• On page 2, be sure that students understand that the height of the water column is the same as thedepth of the water.

• On page 4, points are marked on the grid if the cursor is within 12 units of the actual coordinatesin either direction.

• On page 4, the correct value for k is 0.434, but values such as 0.45 are acceptable.

• Students need to understand the following terms: water pressure, depth, area, volume, weight, pressuregauge, and model.

Extensions• Students might calculate and explore the inverse of the depth and pressure function used in

this activity.


Graphing Relations and FunctionsCHAPTER 5

Analyzing Linear EquationsCHAPTER 5

Linear Relationships in Car RacingStudents take the role of a member of a pit crew for a race car driver.They set a speed and collect data on the time for each lap (2000 meters).They compare the graphs of the equations, distance � speed � time, for eachlap. They observe that the steeper lines represent laps with greater speed.

Students then collect time data for each lap of a Grand Prix course. Theycalculate the speed and write an equation that models each lap. Theyinterpret the graphs for the laps. Each graph has a different y-interceptand slope.

Sample Screen


lnteractive Activities • Change racing car speed

and observe change intime.

• Relate distance, time, andspeed for Grand Prixtrials.

Video • A video of auto

racing describes howmathematics is essentialto the design of racing cars.

Prerequisites • Graph linear equations.• Read and interpret linear

graphs.

Goals1. Collect and analyze data.2. Interpret graphs.3. Find equations to fit data. 4. Use slope to represent speed.

ContentPage 1 Introduction and Goals Page 2 Exploration: Speed as Slope Page 3 Video: Auto Racing Car Design Page 4 Application: Distance Equations Page 5 Information: Linear Models Page 6 Quiz

ObjectivesPage 2 Exploration Interpret graphs of equations that represent time and distance.

Page 4 Application Use equations to model time and distance.

Tips & Suggestions• On page 2, distance is measured in meters and time in seconds, rather than the more familiar

miles-per-hour. These units work better because of the high speeds and small distance traveled.

• On page 2, the lap time depends on the selected speed.

• On page 4, the distance is given as total meters, not the length of the lap. Be sure that studentsunderstand that difference. This situation creates five equations with varying y-intercepts as well as varying slopes.

• On page 4, the onscreen calculator is useful for calculating the speed. Click the yellow calculatorbutton.

• On page 4, the lap-time data are integers, increase for each lap, and are different each time thischapter is used.

• Students need to understand the following terms: lap, odometer, y-intercept, and slope.

Extensions• Research times for auto races. What are typical average speeds in meters-per-second and

miles-per-hour? Does a car’s speed vary greatly from one lap to another?


Analyzing Linear EquationsCHAPTER 5

Solving Linear lnequalitiesCHAPTER 6

Fireworks, Mathematics,and Safety!Students set the length of the fuse that will detonate a simulatedfirework. The length determines the height at which the fireworkexplodes.

In order to keep viewers safe, fireworks’ particles must be extinguishedabove a given height. Students simulate a firework’s launch and observewhether it is safe. They use the data they collect to determine a range ofsafe fuse lengths. They express this range as an inequality in one variable.

In the second activity, students investigate two variables: the detonationheight and the radius of the explosion. They develop a rule for decidingwhether a firework is safe for a specific safe height, given its height andradius. This is an inequality in two variables. Detonation Height Safe Height � Radius

Sample Screen


lnteractive Activities • Test fireworks to

determine a range of safe fuse lengths.

• Collect and graph data on fireworks’ height andradius. Find a safe range.

Video• A fireworks manufacturer

explains how fireworkssafety depends ondetonation height andradius of the fireball.

Prerequisites • Read inequalities.• Write inequalities to

express relationships.

Goals1. Collect and graph data about fireworks safety. 2. Model situations using inequalities. 3. Use models to make decisions.

ContentPage 1 Introduction, Goals, and Video: Fireworks SafetyPage 2 Exploration: Detonation Fuse LengthPage 3 Video: Detonation Height and RadiusPage 4 Application: Safe FireworksPage 5 Quiz

ObjectivesPage 2 ExplorationUse an inequality as a model.

Page 3 Application Write an inequality in two variables.

Tips & Suggestions• Emphasize that fireworks are safely handled only by professionals. Buying, possessing, or

detonating fireworks by the public is illegal in some states in the U.S.

• The mathematical models in this interaction are inequalities. Functions are the most commonlyused models. Point out that inequalities, probability models, and geometric models are also useful.

• Be sure that students realize that the inequality on page 2 has one variable, fuse length, while theinequality on page 4 has two variables, detonation height and fireball radius. The detonationheight depends on the fuse length. On page 2, the radius remains constant.

• The fuse burns at 1 cm per second. Detonation occurs when the entire fuse is burnt. The firework’spath is determined only by initial velocity and gravity. Other factors are ignored.

• On page 4, the test fireworks and the fireworks in the Company Data table on screen 3 aredifferent and vary.

• Students need to understand the following terms: fuse, velocity, and detonation.

Extensions• Find out about your state’s laws regarding the use, possession, and sale of fireworks.

• Locate and analyze data on fireworks accidents.

• Research the sound ranges used in rock concerts.


Solving Linear lnequalitiesCHAPTER 6

Solving Systems of Linear Equations and lnequalitiesCHAPTER 7

Systems of Equations:An Aid to Decision MakingStudents explore an animated graph of the linear equation that modelsthe costs of a phone plan.

Total monthly cost � Cost per minute � Number of minutes � Fixed monthly cost

Students are given the costs for two phone plans. They observe andinterpret a graph of points representing two plans.

Students write equations to model the two phone plans. They interpretthe graph of this system of two linear equations. The lines intersect at thenumber of minute at which the total costs are equal.

Sample Screen


lnteractive Activities• Explore costs of phone

plans.• Compare cost per

minute and number ofminutes for two phoneplans’ costs.

• Decide which plan is best.

Video• A business woman

describes how she usesmathematics to save hercompany time andmoney.

Prerequisites • Read and interpret linear

graphs.• Write linear equations

from information.

Goals1. Write equations that model situations. 2. Graph and solve systems of equations. 3. Analyze situations using graphs and equations. 4. Make decisions based on your analysis.

ContentPage 1 Introduction, Goals, and Video: Phone CostsPage 2 Activity: Graph ModelsPage 3 Exploration: Graphing Phone CostsPage 4 Application: Graphing Linear SystemsPage 5 Information: Systems of EquationsPage 6 Quiz

ObjectivesPage 3 ExplorationAnalyze graphs of phone cost data.

Page 4 Application Use systems of equations to make decisions.

Tips & Suggestions• On page 2, clicking the Reset button changes the cost per minute and the fixed monthly cost

values. This results in a different linear equation being graphed.

• On page 2, the cost per minute (m) varies between 10 and 30 cents. The monthly cost is a randomdollar amount between 10 and 30.

• The cellular phone plans on pages 3 and 4 are the same and do not vary. Plan A has fixed monthlycosts of $14.71 and a cost per minute of $0.06. Plan B has fixed monthly costs of $7.35 and a costper minute of $0.15.

• Students need to understand the following terms: fixed monthly cost, cost per minute, and total monthly cost.

Extensions• Students might research cellular phone plans currently available in your community.

• Make a list of other services that are sold on a similar basis. For example, some Internet servicescharge a fixed cost for a given amount of time, plus an additional cost per minute above that limit.


Solving Systems of Linear Equations and lnequalitiesCHAPTER 7

Exploring PolynomialsCHAPTER 8

Pools and Polynomials

Students manipulate both positive and negative algebra tiles to add andsubtract polynomials.

In a separate activity, students manipulate algebra tiles to modelmultiplication of binomials, such as (x � 2)(x � 1).

Students apply the volume formula, V� lwh, to find the volume ofsealant needed to coat a rectangular swimming pool. Each dimension is represented by a binomial.

V � (30 � 2x)(10 � 2x)(2 � x), where x is the thickness of the sealant.

Sample Screen


lnteractive Activities • Use algebra tiles to add

and subtract, and multiplypolynomials.

• Create and apply apolynomial equation forswimming pool volume.

Video• A financial planner

describes howpolynomials calculatecompound interest.

Prerequisites • Use the distributive

property.• Operate with variables.

Goals1. Use the distributive property.2. Add, subtract, and multiply polynomials. 3. Create polynomial expressions and apply them to dimension and volume.

ContentPage 1 Introduction and Goals Page 2 Exploration: Algebra Tiles Page 3 Activity: Multiplying Binomials Page 4 Application: Swimming Pool Sealant Page 5 Video: Financial Planner Page 6 Quiz

ObjectivesPage 2 Exploration Add and subtract polynomials using algebra tiles.

Page 4 Application Multiply polynomials to find volume.

Tips & Suggestions• On page 2, tiles can be dragged to mats with green borders; they will not stick on

gray-bordered mats.

• On page 2, clicking the New Problem button displays either an addition or a subtraction problem,selected at random.

• On page 3, clicking the New Problem button displays two new binomial factors, (x � n) or (x � n), where n � 0, 1, 2, or 3.

• On page 4, the dimensions of the pool are one of three sets of dimensions: 12 � 6 � 2, 20 � 8 � 2, and 30 � 10 � 2.

• On page 4, be sure that students realize that the polynomial represents the volume of the pool after the sealant is applied.

• Students need to understand the following terms: volume, sealant, FOIL, interest rate, and compounded annually.

Extensions• Research the current interest rates at local banks. Find out if it is compounded annually or more

frequently. Use the formula for compound interest to predict future account balances.


Exploring PolynomialsCHAPTER 8

Using FactoringCHAPTER 9

The Factoring Farmer

Students manipulate algebra tiles that represent polynomials that can befactored, such as x2 � 4x � 3. They record the products and the factors insymbolic form on their worksheets.

Polynomials are used to represent square farm fields. The current area and the side of the square are given. A new, desired area is shown. For example, (80 � x)(80 � z) � 3600 or (70 � x)(70 � x) � 6400

Students solve polynomial equations by factoring to find x, the change inthe side length.

Sample Screen


Interactive Activities • Use algebra tiles to

model multiplication.• Use polynomials to

model farm field areaproblems.

Video• A petroleum engineer

explains how he usesfactoring to speed upcomputer calculations.

Prerequisites • Multiply binomials.

Goals1. Model polynomials with algebra tiles. 2. Use polynomials to represent area.3. Factor quadratic expressions and solve equations.

ContentPage 1 Introduction and Goals Page 2 Exploration: Factoring with Algebra Tiles Page 3 Explanation: Land Measurement Page 4 Application: Polynomial Model for AreaPage 5 Activity: Volume; Video: Petroleum Engineer Page 6 Quiz

ObjectivesPage 2 Exploration Factor polynomials using algebra tiles.

Page 4 Application Factor polynomial equations.

Tips & Suggestions• On page 2, there are nine different polynomials, made up of the factors

x, (x�l), (x�2), and (x�3). The x2 tile must be placed first, followed by the x tiles.

• Page 3 includes information on measuring land in the U.S. The linear unit chains is used hererather than the more common square unit, acres.

• On page 4, the square fields are 50, 60, 70, 80, or 90 units on each side. Clicking the New Farmerbutton alternates between the factors (n�x) and (n�x).

• It is possible to solve the problems on page 4 without using polynomials. For example, if thecurrent area is 6400 square units and the desired area is 3600, the current farm side is 80 unitsand the desired farm side is 60 units (the square root of 3600). The method used in the softwaredemonstrates the use of polynomials to represent area.

Extensions• If your school district includes rural area, students might report on land measurement units

used today.

• If your district is located in an area that does not use square sectors for land measurement, researchwhat method is used and why.


Using FactoringCHAPTER 9

Exploring Quadratic and Exponential FunctionsCHAPTER 10

Quadratics and Fireworks:A Perfect Match!Students explore initial velocity and maximum height. They select alaunch velocity and observe the resulting height of a launched firework.They create a graph of their data (time, height). They observe that eachgraph is a parabola opening downward and that the maximum heightvaries depending on the initial velocity.

The equation for height

H � 2 at2 � Vt � k

is presented and explained.

Students fit the quadratic equation, the height equation, to a set of datapoints to determine the initial velocity, V, of the firework.

Sample Screen


lnteractive Activities • Explore initial velocity

and height of fireworks.• Find a quadratic equation

that fits the fireworkspath.

Video• A civil engineer describes

how she uses quadraticequations in her workwith the highwaydepartment.

Prerequisites • Interpret scatter plots.• Identify a parabola.• Graph quadratic

equations.

1

Goals1. Collect and graph data.2. Determine a quadratic function that matches a parabola. 3. Use a quadratic function to predict.

ContentPage 1 Introduction and Goals Activity: Height and Launch Speed Page 2 Exploration: Graph of Height and Time Page 3 Activity: Height Equation and Gravity Page 4 Application: Quadratic Model for Height Page 5 Video: Civil EngineerPage 6 Quiz

ObjectivesPage 2 ExplorationExplore the relation between initial velocity and height.

Page 4 Application Find a quadratic function to model the height of a firework.

Tips & Suggestions• The concept of mathematical model is central to this interaction. The model is quadratic, not linear.

Be sure that students realize how the concepts of fitting lines to data also apply to fitting curves.

• You may want to relate this interaction to your students’ science class activities involving tirne,distance, and velocity.

• On page 2, the range of initial velocity is 180 � V� 360 ft/sec.

• On page 4, the graphed data points change when Reset is clicked. The velocity and the platformheight vary.

• Students need to understand the following terms: velocity, initial velocity, maximum height, gravity,and platform height.

Extensions• Find photographs of bridges with curved supports. Determine which functions best model

the curves.


Exploring Quadratic and Exponential FunctionsCHAPTER 10

Exploring Radical Expressions and EquationsCHAPTER 11

Mathematics in the Movies

Students take the role of a movie stunt coordinator. In the stunt, a carexplodes in front of the camera when the trip wire is pulled taut.Students must determine the length of the wire, which is the hypotenuseof a right triangle. They measure lengths and collect data.

An Explore feature demonstrates the application of the Pythagoreantheorem.

Students compare the car’s motion to a graph of distance and wire length.

Using the data (distance, length), students find both a quadratic and asquare-root function to fit the data. They evaluate both functions todecide which is the better model. The model enables students to locate the correct position for the stunt coordinator.

Sample Screen


lnteractive Activities• Find the length of wire

for a movie stuntexplosion.

• Find functions to fit thedata, and plan the stunt.

Video• A civil engineer explains

how she uses radicalfunctions for distancewhen planning roads.

Prerequisites• Evaluate square-root

expressions.• Fit a function to graphed

points.

Goals1. Evaluate square-root expressions. 2. Collect and graph data.3. Find square-root and quadratic functions to fit data.

ContentPage 1 Introduction and Goals Page 2 Exploration: Using Square Roots Page 3 Activity: Graphing Distance and Length Page 4 Application: Fitting Curves to Data Page 5 Video: Civil EngineerPage 6 Quiz

ObjectivesPage 2 Exploration Use a square root expression to find distance.

Page 4 Application Fit square root and quadratic functions to distance data.

Tips & Suggestions• The concept of mathematical model is critical to this application. Students create and compare two

possible functions to model the data: quadratic and square root. You may want to emphasize that amodel is not right or wrong. The model for a situation is the function that best fits the data. Thisraises questions that are addressed in higher level mathematics. How good does the fit need to be? How can you know one fit is better than another?

• On page 2, distance A is always 9.3 meters. The criterion for a “take” is a rope length within 0.25 m of the correct length.

• On page 4, distance A and the graphed data points vary. Students can enter an integer value for A to approximate the function, and then use the arrow buttons to move the graph for a closer fit.The values change by 0.1 with each click.

• Students need to understand the following terms: Pythagorean theorem, quadratic function, and square root function.

Extensions• Research highway and bridge construction.

• Research the role of distances in movie stunts.


Exploring Radical Expressions and EquationsCHAPTER 11

Exploring Rational Expressions and EquationsCHAPTER 12

lnvestigating Underwater Sound

Underwater sounds made by marine mammals spre out along the surfaceof a sphere. Students collect data on both sound intensity and the surfacearea of the sphere as they change the distance from the sound source.

They compare graphs of distance and intensity with graphs of distanceand surface area.

The equation

Sound lntensity � PowerArea

is presented and explained.

Students collect data on the intensity at various distances. They plot the data and find a value for power, P, that makes the intensity equationfit their data.

This equation can be used to determine the location or distance of themarine mammal by measuring the sound intensity.

Sample Screen


lnteractive Activities • Change the distance of a

sound source and recordsurface area and intensity.

• Collect data anddetermine an equation tomodel sound intensity.

Video • A video of whales tells

why oceanographersstudy marine mammalsand the sounds theymake.

Prerequisites• Interpret scatter plots.• Evaluate equations.• Fit functions to data.

Goals1. Collect and graph data on underwater sound.2. Explore the relation between distance and intensity.3. Use rational functions to model sound intensity.

ContentPage 1 Introduction and Goals Video: Marine Mammal Sounds Page 2 Exploration: Graphing Sound Intensity Page 3 Sound Intensity Equation Page 4 Application: Modeling Sound Intensity Page 5 Rational Functions as Models Page 6 Quiz

ObjectivesPage 2 Exploration Relate sound intensity and distance.

Page 4 Application Use a rational function to model sound intensity.

Tips & Suggestions• The surface area of a sphere is introduced on page 2, because surface area is a variable in the sound

intensity equation used in the application on pages 3 and 4.

• Be sure that students notice that on page 2, two sets of data are plotted on one grid. The bluesquares represent intensity and the red circles stand for surface area.

• On page 2, the sound intensity is 260,000 .r2

On page 4, the sound intensity is 6,500 .4r2

• On page 4, students can move the ship by dragging it, as well as by using the arrow buttons. Datatoo large to be plotted on the graph is shown in gray in the data table. It is possible to zoom outon the y-axis by Ctrl-clicking (Windows) or Command-clicking (Macintosh) on the Intensity label.

• You may want to relate this application to the study of sound in your students’ science classes.

• Students need to understand the following terms: sound intensity and surface area of a sphere.

Extensions• Research whale and dolphin sounds. How do scientists categorize the various sounds made by one

species? How do they compare sounds made by various species?


Exploring Rational Expressions and EquationsCHAPTER 12

Batter Up!At the Computer

Variables1. List two variables involved in hitting a baseball.

Distance, Speed, and Time2. Record the pitch speed and the time the ball takes to reach the plate, time to plate.

3. Multiply the Pitch Speed by the Time to Plate. Record the products in the Distance column in thetable. Describe the numbers in the Distance column.

4. Write an expression for distance, using rate (or speed) and time.

distance �

Write this same expression using the variables r for rate and t for time.

d �

5. The batter in this simulation always waits 0.4 seconds before beginning to swing. Explain why this is or is not a good strategy.

Pitch Speed Time to Plate Distance(feet per second) (seconds) (feet)

NAME DATE

Exploring Expressions, Equations, and FunctionsWorksheet 1111


CD-ROM Page 1

CD-ROM Page 2

Timing the Swing6. Record your data in the table.

Pitch Pitch Time to Swing Wait ResultNumber Speed Plate Time Time

(ft per sec) (sec) (sec) (sec)1 50 0.252 60 0.253 70 0.254 80 0.255 90 0.25

7. Write an expression for time to plate, using the distance 60 feet and rate.

time to plate �

8. Label the diagram. Write wait time, swing time, and time to plate on the dotted lines.

9. Write an expression for wait time, based on the diagram above.

wait time �

Strategy and Timing the Swing10. In the video, Alexa tells why she sometimes swings early or late. Explain what it means to swing

early in terms of the wait time.


Exploring Expressions, Equations, and Functions(continued)

Worksheet 1111NAME DATE

CD-ROM Page 4

CD-ROM Page 3

NAME DATE

Exploring Expressions, Equations, and Functions(continued)

Worksheet 1111

After the Computer Session11. The pitch speed is 70 feet per second and it travels for 2.0 seconds. What distance does it travel?

Use the distance formula, d � rt, where r is rate or speed and t is time.

On a standard baseball diamond, where would this ball be after 2.0 seconds?

12. A certain pitcher’s fast ball travels at 85 feet per second. How long should the batter wait beforebeginning to swing? Assume the swing time is 0.2 seconds.

Use the time formula, t � r , and the expression for wait time.

13. Pitch speed is usually measured in miles per hour. A pitcher’s fast ball is clocked at 90 miles perhour. How fast is that in feet per second? Use the conversion formula 1 mile per hour � 1.47 feet per second.

14. A pitcher’s fast ball is travels at the rate of 90 feet per second. How fast is that in miles per hour?Use the conversion formula 1 foot per second � 0.68 miles per hour.

15. Integration–Geometry

a) The bat makes an angle with thepath of the ball. Record eachangle type. Use right angle, acuteangle, and obtuse angle.

b) Decide where each hit ball willgo. Write center, right (first base),or left (third base).

c) This batter wanted to hit the ballinto center field. Did the batterswing early, late, or just right?Record the swing timing.


a)

b)

c)

d

Pizza PlaceAt the Computer

Transactions, Accounts, and Rational Numbers1. In your own words, describe what a transaction is.

2. Record the beginning account balance.

3. Describe how an account balance changes. Use increases or decreases.

After a positive transaction, the balance _______________ .

After a negative transaction, the balance _______________ .

4. Click each of the transactions. Record the ending balance. _______________

Calculate the difference between the beginning and ending balances.

Record it here.

Is it positive or negative?

What does this number mean to the pizza company?

Deposits and Checks5. Describe how an account balance changes.

After writing a check, the balance _______________ .

After making a deposit, the balance _______________ .

Tell whether positive or negative numbers are used.

For checks

For deposits

6. Record the ending account balance for each day.

9/7

9/14

9/21

9/25

9/28


Exploring Rational NumbersWorksheet 2222NAME DATE

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CD-ROM Page 2

NAME DATE

Exploring Rational Numbers (continued)Worksheet 2222

7. Based on the graph, what is a typical daily balance for this company?

About how much does the account balance change from day to day?

8. Suppose these five days are typical. As the accountant, would you approve spending $400 on radioadvertising? Would you approve $2000 for a new neon sign? Explain why or why not.

Credits and Debits9. Watch the video and listen to the accountant explain credit and debit.

Write the correct term (credit or debit) in each blank below.

A positive number represents ________________ ;

a negative number represents _________________ .

___________________ increases an account balance;

___________________ decreases a balance.

Sales is a ___________________ ; expense is a ___________________ .


CD-ROM Page 4


Exploring Rational Numbers (continued)Worksheet 22NAME DATE

After the Computer Session10. Amber wants to create an account for her own finances.

Here is a list of her transactions. Create an account by listing each transaction and using either a positive or negative number. Calculate the new balance after each transaction.

Transaction Amount Account Balance

Has $4.00 right now.

Receives $5.00 allowance.

Buys a cassette tape for $6.99.

Earns $10.00 from baby-sitting.

Receives a birthday gift of $20.00.

Spends $4.00 on a matinee movie.

Math Journal11. Describe how positive and negative numbers are used in business accounts.

12. List examples of transactions that use positive numbers.

List examples of transactions that use negative numbers.

Ratios and Proportions in RacingAt the Computer

Variables in Racing1. According to the video, what variable do bicycle racers try to keep constant?

Sprockets and Gears 2. Record the definition of gear ratio.

gear ratio �

3. Compare the gear ratios of 1.17 and 2.24. Which ratio corresponds to the longer distance traveled?

4. After you sort the data, fill in this table.

Back Front Gear Ratio Gear Ratio Distance GearTeeth Teeth Fraction Decimal Traveled Name

smallest gear ratio

largest gear ratio

5. Describe the relation between the gear ratio and the distance traveled on one pedal revolution.

6. Suppose the gear ratio is 1.00. Describe the front and back sprockets.

For each revolution of the pedal, how many times does the back wheel revolve?

7. Suppose the gear ratio is 2.00. Describe the front and back sprockets.

For each revolution of the pedal, how many times does the back wheel revolve?

NAME DATE

Using Proportional ReasoningWorksheet 3333


8. Describe how bicycle gears are named.

9. Which gear results in the smallest distance in one pedal revolution?

Which gear results in the largest distance?

Steepness, Heart Rate, and Gear Ratios 10. Record the data in the table below.

Steepness Back Teeth Front Teeth Gear Ratio

11. Record the gear ratio or x-coordinate of the red point.

What gear ratio is needed to be in the green range at this steepness?

Is the needed gear ratio larger or smaller?

12. Use the gear ratio formula from Exercise 2. Use the numeric values for the needed gear ratio andthe front sprocket to calculate the needed back sprocket.

Does the needed back sprocket have more or fewer teeth than the current one?

Try this sprocket size and retest the steepness levels until the whole table turns green.


Using Proportional Reasoning (continued)Worksheet 3333NAME DATE

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Using Proportional Reasoning (continued)Worksheet 3333

After the Computer Session13. Look at the data table in Exercise 4. What is the circumference of the rear wheel?

(Hint: the circumference is also the distance traveled in one revolution).

14. Explain why on a flat road, a racer uses a higher gear, but on an uphill climb a racer uses a low gear.

15. The Golden ratio is about 1.62. Draw a golden rectangle. Use the golden ratio to calculate thelengths of the sides. Label the rectangle’s sides and show that their ratio is the golden ratio.

Math Journal16. Explain in your own words why it is easier to ride uphill using the gears on a 10-speed bike than

to ride uphill on a bike without gears.


Fireworks Factory: Making a ProfitAt the Computer

Profit 1. After you watch the video, write two terms that businesses use to calculate profit.

Sell Fireworks2. Record each equation.

Total Expenses =

Revenue =

Profit =

3. Which of these variables, expense, revenue, and profit, depend on the number of fireworks sold?

4. Record the values.

Number Sold Profit

The Profit Equation6. Record the Profit Equation.

Design a Firework7. After you design your firework, record the Cost per Unit.

$


Solving Linear EquationsWorksheet 3333NAME DATE

5. Define the term break-even point in your own words.

Record the break-even point.

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Calculate Profit8. Record the Fixed Expense amount. $

Record your chosen Selling Price. $

9. Write the Profit Equation again. Use P for Profit and N for Number Sold. Use the numerical values for Selling Price (a), Fixed Expenses (b), and Cost per Unit (c).

P � Na � (b � Nc)

P� ________ � ________ � ( ________ � ________ � ________ )

10. After you enter several values for N, Number Sold, sketch the graph shown on the computer.

11. Find the break-even point, (Number Sold, Profit) _____________________________________

Mark this point on your graph above.

12. Use the graph and the table.

Find how much profit you will make if you sell 90 fireworks. ____________

Find the number of fireworks you need to sell to make $500.00 profit. ____________

Change the Selling Price13. Enter a new value for the Selling Price. Record it here. ____________

14. Write the new Profit Equation (as in Exercise 9).

P� ________ � ________ � ( ________ � ________ � ________ )

15. Sketch the new line on the graph in Exercise 10.

Find the break-even point and mark it on the graph. ____________

16. Describe how the graphs of these two Profit Equations are alike and how they are different.

Note: Record one of your Profit Equations on the next page, After the Computer Session.

2400

2000

1600

1200

800

400

0

�4000 20 40 60 80 100

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Solving Linear Equations (continued)Worksheet 3333


After the Computer SessionChoose one of your two Profit Equations (Exercise 9 or 14).

Record it here for reference.

17. How much profit would you make if you sold 500 of these fireworks at this selling price? Use your equation and show each step of your work.

18. Using the same equation, how many of these fireworks would you have to sell in order to make aprofit of $10,000? Show all the steps of your work.

Math Journal19. Describe how businesses use the Profit Equation.

20. Explain how the amount of profit changes when the number of items sold changes.


Solving Linear Equations (continued)Worksheet 3333NAME DATE

Exploring the Ocean’s DepthsAt the Computer

Water Pressure 1. Define pressure.

2. In your own words, what is water pressure?

Write two different abbreviations for pounds per square inch.

3. Experiment with the water column. Change one quantity: width, length, or depth. Observe what else changed. Write “yes” in the empty box if that variable changed. Write “no” if it did not change. (See the example below.)

DepthVariables Width Length (Height) Area Volume Weight Pressure

A. Width no no yes

B. Length

C. Depth (Height)

Which of the three quantities (width, length, depth) affects the water pressure? Explain in your own words.

4. Why does the pressure stay the same when you change the width or length of the column of water?

NAME DATE

Graphing Relations and FunctionsWorksheet 5555


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Understanding Depth and Pressure5. Why do divers and oceanographers need to understand water pressure and depth?

6. What does a depth gauge tell a diver? What does it actually measure?

Measuring Depth and Pressure7. After you collect and graph your data and fit a line to the points, draw a sketch of the graph here.

Be sure to label the axes.

8. Record the function you found thatrelates depth and pressure.

9. Explain why the function you found is called a mathematical model for depth and water pressure.

Mathematical Models10. What do mathematical models enable Mr. Chen to do?

11. List the steps Mr. Chen follows to create and use models.

1. Observe and then form a hypothesis.

2.

3.

4.

5.


Graphing Relations and Functions (continued)Worksheet 5555NAME DATE

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Graphing Relations and Functions (continued)Worksheet 5555

After the Computer SessionUse your depth/pressure function to predict depth and pressure values in the following situations.

19. The Mariana Trench is the deepest spot in the ocean. It is over 36,000 feet deep. Predict the pressure an oceanographer would experience when exploring this trench.

20. The angler fish has been known to exist at depths of 9800 feet. Predict how much pressure the fishis experiencing at this depth.

21. Sea creatures that live in the deepest parts of the ocean have traits that enable them to survive.Examples include flat, crush-proof forms, glow-in-the-dark skin, translucent bodies, and built-infishing lures.

At what depth might an oceanographer expect to find each of the following creatures? The pressure at which they can survive is listed.

Name Pressure Depth

Snipe Eel 3029 psi _______________

Fantooth 2410 psi _______________

Cranchiid Squid 3255 psi _______________

Deep-Sea Shrimp 4792 psi _______________

Math Journal22. Write a summary of the mathematics you learned and used in this activity.

(Tip: Use words like function, data, and mathematical model.)


Linear Relationships in Car RacingAt the Computer

Distance,Time, and Speed1. Describe the relation between lap time (the time it takes to complete one lap) and speed.

When the speed increases, how does lap time change?

Graphs of Distance and Time2. Sketch the five line segments.

a. Mark the line segment that represents the fastest lap (the shortest lap time).

b. Mark the line segment that represents the slowest lap.

3. Describe how these line segments are alike and how they are different.

Slope4. On the graph, mark the line segment with the steepest slope. Identify two points on this line

segment, find the change in distance and time, and calculate the slope.

5. Write an equation to represent a car going 50 meters per second. Use the equation to find the timeneeded to complete one lap on this track.


Analyzing Linear Equations Worksheet 5555NAME DATE

Distance (meters)

Time (seconds)

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Analyzing Linear Equations (continued)Worksheet 5555

Mathematics and Car Racing 6. Summarize the main points in the video about car racing.

Linear Equations and Their Graphs 7. Sketch the five lines.

Describe how these lines are differentfrom the lines graphed on page 2.Explain why they are different.

8. Explain how you determined the values for the coefficient of t and the constant term in the linearequations.

Other Linear Situations 9. Describe another situation, besides racing cars, that can be modeled using linear equations.


Distance (meters)

Time (seconds)

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After the Computer Session

Using a Linear Equation for Distance,Time, and Speed 10. Suppose the lap is 2000 meters long and the car completes a lap in 15 seconds. How fast is the

car going?

11. Suppose the lap is 6000 meters long and the car’s speed is 90 meters per second. How long does ittake to complete a lap?

12. A race car travels 4000 meters in 50 seconds. Write a linear equation that relates distance and timefor this car.

Linear Equations and Simple lnterest13. Linear equations can model some financial situations. Suppose you invest $500 in a bank and earn

simple interest at a rate of 7% per year. Find the amount of money you will have in the bank after t years.

The equation that models this situation is: A � (0.07)(500t) � 500. Explain the meaning of eachterm in the equation. Use the equation to calculate the amount you will have after 1 year, 2 years,and 3.5 years.

14. Suppose you graphed this equation for simple interest. What would be the slope of the line?

Math Journal15. Explain slope in your own words. Consider both the graph of a linear equation and its equation.


Analyzing Linear Equations (continued)Worksheet 5555NAME DATE

NAME DATE

Solving Linear lnequalitiesWorksheet 6666

Fireworks, Mathematics, and Safety!At the Computer

Fireworks Fuses1. List the two types of fireworks fuses. Circle the type this activity uses.

lnequality Model2. Record the inequality that models safe fuse lengths.

Fuse Length and Detonation Height3. Describe how the fuse length affects the height at which the fireworks detonate.

Detonation Height and Radius4. Sketch a firework safely exploding. Show and label the detonation height,

explosion radius, and lowest spark height.

safe height

ground


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5. Record the radius and detonation height data and your calculated lowest spark height.

Record your predictions for Safe or Unsafe. Then record the actual results.

Firework Radius Height Lowest Spark Height Predicted Actually safe? safe?

A 180 1450

B

C

D

E

F

G

6. Explain how you calculated the lowest spark height.

7. Record your decision rule.

8. a. Write the equation of the line that is graphed when you click Apply Rule.

b. Describe the fireworks whose points lie above that line.

c. Which part of the graph represents the inequality in your decision rule?

9. List the fireworks in the Company Data table that are safe. Show that the radius and height of eachof these fireworks makes your inequality a true statement.

Firework Radius Height Makes the Inequality True

Applications of Inequalities10. Explain how a sound technician might use inequalities to describe a range of values.


Solving Linear lnequalities (continued)Worksheet 6666NAME DATE

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Solving Linear lnequalities (continued)Worksheet 6666

After the Computer Session11. Suppose the safe height is 1200 feet. By experimentation, you have created the inequality

2.5 cm � fuse length � 8.4 cm

to model the safe fuse lengths for a certain firework. Explain how the fireworks manufacturer coulduse this inequality to make this firework detonate safely.

12. You have seen that a linear inequality

detonation height radius � safe height or h r + safe height

is a model for safe fireworks.

h is the height at which the firework detonates and r is the radius of the fireball.

Suppose the safe height is 1200 feet and the radius of a firework is 50 feet. What is the range of safe detonation heights?

Math Journal13. Describe and give an example of an inequality in one variable.

14. Describe and give an example of an inequality in two variables (x and y).

15. Describe how an inequality in two variables is like an equation in two variables and how it is different.


Systems of Equations:An Aid to Decision MakingAt the Computer

Phone Plan Variables1. After you watch the video, write the variables that are used to calculate phone cost.

Total Monthly Cost Equation2. Record the equation for total monthly cost.

3. Compare this equation to the slope-intercept of a linear equation, y � mx � b. Tell what each term represents.

Comparing Two Phone Plans4. From the information in the table on the screen, which phone plan looks cheaper?

Why?

5. Fill in the table below by reading the graph of total monthly cost.

Number of Total Monthly Cost Total Monthly CostMinutes of Plan A of Plan B

0 $14.7130 $12.0060

$20.00 $21.00120 $25.00


Solving Systems of Linear Equations and lnequalities


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NAME DATE

Solving Systems of Linear Equations and lnequalities (continued)

Worksheet 7777

6. What can you say about the cost of the two phone plans at the point where there is both a red dotand a blue square?

7. In which part of the graph does Plan A cost more than Plan B?

8. Suppose you use 30 minutes. Which plan costs less? __________

Suppose you use 120 minutes. Which plan costs less? __________

System of Equations9. Record the equations for the two

phone plans.

Plan A y � __________

Plan B y � __________

11. Write an inequality to show the range of minutes where Plan A costs more than Plan B.

Write an inequality to show the range of minutes where Plan A costs less than Plan B.

Mark both inequalities on the x-axis on the graph above.

12. Solve the system of equations. Use substitution.

13. What point on the graph corresponds to this numerical solution? Write its coordinates. Describe itin terms of the graphed lines.


30

20

10

0 30 60 90 120Minutes

10. Sketch the two lines on the graph.

TotalMonthlyCost

CD-ROM Page 4

After the Computer Session14. Suppose you use 200 minutes of phone time. Which plan is cheaper? Write your answer.

Explain why you used either the graph or the equations to find the answer.

15. Suppose you use 200 minutes of phone time. How much does Plan A cost? Write your answer.Explain why you used either the graph or the equations to find the answer.

Math Journal16. Explain how to use a system of linear equations to compare two situations. Include at least some of

the following terms: linear equations, graphs, graphed lines, point of intersection, inequalities.


Solving Systems of Linear Equations and lnequalities (continued)


NAME DATE

Exploring PolynomialsWorksheet 8888

Pools and PolynomialsAt the Computer

Adding and Subtracting Polynomials1. Record the first three problems you solved using addition or subtraction.

First Polynomial � or � Second Polynomial Sum or Difference

2. Explain the method you used to subtract polynomials using tiles.

Multiplying Polynomials3. Record two of the multiplication problems you did. Sketch the product mat tiles.

( )( ) � ____________ ( )( ) � ____________


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CD-ROM Page 2

Calculating Pool Sealant4. Record the pool dimensions before and after the sealant is applied.

The thickness of the sealant is x.

Dimensions

pool before sealant

pool after sealant

5. Record the pool volume. Explain how each of these expressions for volume is calculated.

Pool volume before sealant (a number) ____________________

Volume after sealant (a polynomial) ____________________

6. Record the formula for calculating the volume of the sealant itself.

7. Record the thickness of sealant you chose. Record the volume of sealant needed to coat this pool at this thickness.

Thickness of sealant, x ____________________

Volume of sealant ____________________

8. Choose a different thickness and recalculate the volume of sealant.

Thickness of sealant, x ____________________

Volume of sealant ____________________

9. Explain how the polynomial for pool volume after sealant helps to calculate the volume of sealantfor various thicknesses of sealant?


Exploring Polynomials (continued)Worksheet 8888NAME DATE

CD-ROM Page 4

length width height

NAME DATE

Exploring Polynomials (continued)Worksheet 8888

After the Computer Session10. Use the distributive property to multiply these binomials.

(2 � 2x)(4 � 3x) � ( )( ) � ( )( )

11. Use the FOIL method to multiply these binomials.

(3 � 5x)(8 � 2x) �

12. Use the compound interest formula (shown below) to calculate the answer to the problem posed inthe video on page 5. You have the choice of receiving $5000 on your 15th birthday and investingit at 6% interest or receiving $6000 on your 21st birthday. Which choice gives you more money atage 21?

Write a plan of how to answer this question.

Follow your plan. Show your calculations below.

T� p ( l � r ) t

r � _______________, p � _______________, t � _______________,

Write your answer:

Math Journal 13. Monomials are called like terms if they have the same variable to the same power.

What are like terms when you are using algebra tiles? Describe how you combine like terms withpolynomials and with tiles.


The Factoring FarmerAt the Computer

Factoring Trinomials with Algebra Tiles1. Record four polynomials that you modeled. Sketch the algebra tiles and label

the length and width.

__________ � ( )( ) __________ � ( )( )

__________ � ( )( ) __________ � ( )( )

2. Explain how the area of the tiles models the product of two binomials.


Using Factoring Worksheet 9999NAME DATE

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Using Factoring (continued)Worksheet 9999

Modeling Farm Fields3. How many chains equal 1 mile? __________ chains

How many square chains equal 1 square mile? __________ square chains

How many acres are there in 1 square mile? __________ acres

Polynomials and Farm AreaRecord the following:

4. Current size of Farmer Álvarez’s farm ____________________

Desired size ____________________

The equation for the Álvarez farm ____________________

The number of chains, x, decrease in each side of the farm ____________________

5. Current size of Farmer Bogowitz’s farm ____________________

Desired size ____________________

The equation for the Bogowitz farm ____________________

The number of chains, x, increase in each side of the farm ____________________

Polynomials and Volume6. Write the polynomial expression for the volume of a cube with dimensions

(x � 2), (x � 3), and (x � 4).

7. Based on the video, explain why computer programmers use factoring and simplifyingpolynomials.


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After the Computer Session8. Solve the area problem on page 3 of the CD-ROM. Find the value for x.

(x � 7)(x � 4) � 238 x � 7

Area of Rectangle � 238

x � 4

Factors of �210 Sum of Factors

Math Journal9. Describe how to use algebra tiles to factor trinomials. Does this method work on every trinomial?

Explain why or why not.

10. Describe how to factor trinomials without using algebra tiles.


Using Factoring (continued)Worksheet 9999NAME DATE

Quadratics and Fireworks:A Perfect Match!At the Computer

Maximum Height 1. Based on the Explore demonstration, which of the cannon balls has the highest maximum height?

(fast, medium, or slow)

lnitial Velocity and Height 2. Record data for three fireworks with different initial velocities.

Slow Medium FastMaximum Height (ft) Total Time (sec)

Sketch the graphs.

Slow Medium Fast

3. Describe how these graphs are alike and different.

4. Suppose you increase the initial velocity.

How does the maximum height change?

How does the length of time the firework is in the air change?

Describe how the graph shows these changes.

NAME DATE

Exploring Quadratic and Exponential Functions Worksheet 11110000


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CD-ROM Page 2

A Quadratic Function5. Record the name for the shape of graph created by the firework’s time and height.

6. Record the quadratic function H(t) and what each letter represents.

H(t) �

H is ____________________ V is ____________________

a is ____________________ k is ____________________

t is ____________________

Finding a Quadratic Function 7. Record the function that fits the data.

8. Sketch the graph of the function.Find and record the coordinates of the points listed below.

Maximum point ____________________

y-intercept ____________________

intersection of graph and the x-axis ____________________

9. Show that the coordinates of the maximum point make your quadratic function a true statement.(Your results may not be exact, since the coordinates come from the graph).

10. Use the quadratic formula to find the time when the dummy firework hits the ground. Compare this with the corresponding point on the graph.

Quadratic formula coefficients: a � _______ b � _______ c � _______

Quadratics and Engineering 11. Describe how the civil engineer in the video uses quadratic equations in her

work.


Exploring Quadratic and Exponential Functions(continued)


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NAME DATE

Exploring Quadratic and Exponential Functions(continued)

Worksheet 11110000


Math Journal 12. Explain why the graph of height and time for a firework or a ball launched straight up is

a parabola instead of a line.

13. Describe how changing the initial velocity, V, changes the graph of the quadratic function, H(t).

14. Describe how changing the platform height, k, changes the graph of the quadratic function H(t).


Mathematics in the MoviesAt the Computer

Measurement and Movie Stunts 1. Draw a diagram of the movie set. Label the variables A, D, and L.

2. Record the name for the longest side of a right triangle.

3. Record the equation for the Pythagorean theorem. In your own words, explain what it means.

4. Explain how the equation L � A2 � D2 comes from the equation L2 � A2 � D2.

5. Record your measured values of D and A and your calculated value of L for one of your shoots that is a “take.”


Exploring Radical Expressions and Equations Worksheet 11111111NAME DATE

CD-ROM Page 2

��

NAME DATE

Exploring Radical Expressions and Equations(continued)

Worksheet 11111111

6. Suppose the camera moves farther from the starting point. How should the length of the wire change?

Graphing Distance and Length7. Describe the graph of L(D), wire length, as a function of distance.

Functions to Model Distance8. Which distance are you trying to find? Describe it in terms of the movie set.

9. Record the quadratic function that best fits the points on the graph.

10. Record the square root function that best fits the points on the graph.

11. Sketch both function graphs and label them. Label the axes.

12. Which function is a better fit to these data?


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CD-ROM Page 3

13. As stunt coordinator, where should you stand?


Math Journal14. In this movie set scenario, the stunt coordinator stayed in the same position. How would the wire

length change if the stunt coordinator moved to a different position?

15. Suppose a graph of several data points looks curved. What type(s) of functions might fit thepoints? Explain your answer and give examples.

16. In this activity, you found that a square root function fit the data better than a quadratic function.Explain why this is or is not surprising. Consider the equation for the length of the hypotenuse in a right triangle.


Exploring Radical Expressions and Equations(continued)


NAME DATE

Exploring Rational Expressions and Equations Worksheet 11112222

Investigating Underwater SoundAt the Computer

Underwater Sound1. After you listen to the video, list three ways that whales use sound.

Sound lntensity and Surface Area2. In your own words, define sound intensity.

3. Record the formula for the surface area of a sphere.

4. Sketch the graphs of sound intensity and of surface area. Be sure to label the axes.

Sound Intensity Surface Area

5. Describe each graph.

Sound Intensity Graph Surface Area Graph

________________________ ________________________

________________________ ________________________

________________________ ________________________


3000

2000

1000

0 5 10 15 20

3000

2000

1000

0 5 10 15 20

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6. How does the sound intensity value change when you change the distance?

How does the surface area of the sphere change when you change the radius?

A Rational Equation7. Record the equation for sound intensity. Record the meaning of each variable.

I is

P is

r is

A Rational Function as a Model8. Sketch the graph of the function. Label the axes.

Label the coordinates of at least three data points.

9. Record the sound intensity function that fits your data. Be sure to include the value for P. Use the variable r.

200

150

100

50

0 2 4 6 8 10 12


Exploring Rational Expressions and Equations(continued)


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NAME DATE

Exploring Rational Expressions and Equations(continued)

Worksheet 11112222

After the Computer Session10. Use the sound intensity function. Suppose that the known value for P for a species of whale is

20,000. Your listening device measures an intensity level of 1000. How far away is this whale fromyour listening device?

11. Suppose you want to detect these whales within 5 miles of your research ship. What is theminimum sound intensity that your equipment must be able to detect?

Math Journal12. Explain why a rational function is a better mathematical model for underwater sound intensity

than a linear function. Include a description of how the sound intensity changes as you move awayfrom the source. Sketch graphs to illustrate your reasons.



Answer Key


Troubleshooting Guide/WindowsWhen I double-click the Algebra start-up icon, nothing happens.

1. Make sure the desired CD-ROM is inserted into the CD-ROM drive.

2. Quit any other programs that are running, including screen savers.

3. Try launching an entirely different CD program (not a Glencoe CD) todetermine if there is a hardware problem.

4. Go to your CD-ROM drive (probably D: or E:). Then double-click thedesired file in your file listing.

The program takes a long time to launch.

Approximately one minute of wait time is normal. The performance ofthe program has been increased by loading as much information aspossible at the beginning. (See suggestions above under “The programwill not launch . . .”)

The video and/or audio sputters during playback.

1. Quit all other programs that may be running, including screen savers.

2. Check that QuickTime for Windows 2.0 or higher appears in ProgramManager as a program group or within the Accessories program group.

Note: Although the video on this CD-ROM is high-quality, video playedfrom any CD-ROM application will not play as smoothly as it would onvideotape.

The playback sound is too loud or too soft.

1. If you have speakers, be sure they are plugged in and turned up.

2. If you are using headphones, check that they are plugged in.

3. Check that your machine’s software volume control is at an appropriatesetting.

4. Go to the Program Group for your Audio Card within ProgramManager.

5. Adjust the slider to an appropriate volume level.

The printer is not working.

1. Be sure your printer is plugged in and turned on.

2. Try printing from another application to learn if the problem might behardware or cabling.

3. Contact your system administrator or hardware technician to be surethe correct print drivers for your system have been installed.

Certain colors look incorrect in the graphic images in Windows 95.

If you have customized your desktop colors in Windows 95, set themback to the default settings.


Troubleshooting Guide/MacintoshThe following extensions are required for Glencoe Language Products:

The CD-ROM icon does not appear on the desktop.

1. Check your Extensions folder in the System folder to be sure that therequired extensions are not missing or turned off.

2. If they are not missing or turned off, check your SCSI connections ifyou have an external CD-ROM drive.

3. Go to your hard disk and find a utility program that checks SCSIdevices (such as SCSI Probe or FWB Toolkit).

4. Scan your SCSI chain with the program to see what devices (CD,external hard drives, etc.) are connected.

5. If your CD-ROM drive appears from within the utility program, selectthe Mount command.

If the steps listed above do not remedy the issue, reinstall the CD-ROMsoftware drivers from your System installation disk.

The program will not launch on my computer when I double-click the start-up icon.

1. Make sure the CD-ROM is inserted into your CD-ROM drive.

2. Quit all other programs that may be running, including screen savers.

3. Check all cabling to your hardware.

4. Confirm that you have enough free RAM:Go to the Finder. (Apple icon at the upper left corner of the Screen.)Pull down the Apple menu and select About this Macintosh. Checkthe largest unused block. If the computer does not have at least5,085K, you need more RAM.

5. If you do not have enough free RAM, you may be able to add to it bydisabling Extensions that automatically load when you start your Mac.See the special section at the end of the Troubleshooting Guide.

6. Try launching an entirely different CD program (not a Glencoe CD).

• Apple CD-ROM (or the CD-ROM extension for your non-Apple CD drive)

• Apple Multimedia Tuner

• QuickTime 2.0 or greater

• QuickTime PowerPlug (for Power Macs only)

• Sound Manager

• General Controls

• Any printer extension yourparticular printer needs

• Network extension (if the system is on a network)


Troubleshooting Guide/Macintosh

The program takes a long time to launch.

1. Approximately one minute of wait time is normal. The performance ofthe program has been increased by loading as much information aspossible at the beginning.

2. Make sure you have enough free RAM.

The video and/or audio sputters during playback.

1. Check that the Extensions folder within your System folder includesQuickTime 2.1 or higher, Indeo Video, and Intel Raw Video.

2. Quit all other programs that may be running, including Screen savers.

3. Make sure that you have enough free RAM. (See suggestions in thespecial section at the end of this section.)

Note: Although the video on this CD-ROM is high-quality, video playedfrom any CD-ROM application will not play as smoothly as it would onvideotape.

The playback sound is too soft or too loud.

1. If you are using speakers or headphones, be sure they are plugged inand set at an appropriate volume.

2. Check that your machine’s software volume control is at an appropriatesetting:

Pull down the Apple menu. Select Control Panels. Double-clickSound. A Sound window will display. Choose Volumes from itsinternal pulldown menu. Adjust the slider to an appropriatevolume.

The printer is not working.

1. Be sure your printer is plugged in and turned on.

2. Try printing from some other application to learn if the problemmight be hardware or cabling.

3. Contact your system administrator or hardware technician to be surethe correct print drivers for your system have been installed.


Troubleshooting Guide/Macintosh

For Macintosh users only:If you do not have enough free RAM, it is possible to make slightly more available by disabling unusedextensions. This is tricky business, because it may affect other programs you run. It is recommendedthat you have your system administrator or hardware technician help you.

For users of System 7.0 or 7.1

1. Open the System folder on your hard drive.

2. Find and duplicate your Extensions folder. Rename it “My OriginalExtensions.”

3. Create a new folder and name it “Extensions Disabled.” Open theExtensions folder and move all extensions except those required for theGlencoe Algebra Products to the “Extensions Disabled” folder. You canfind a list of required extensions on page 98.

4. Restart your Macintosh.

Once again, the process outlined above will affect other programs you runon your machine. Before launching another program, move the itemsfrom your “Extensions Disabled” folder back into your Extensions folder,throw away the “My Original Extensions” folder, and restart yourMacintosh.

If you have any trouble, throw away the “Extensions” and “ExtensionsDisabled” folders, but do not empty the trash. Rename “My OriginalExtensions” to “Extensions.” Restart your Macintosh and then empty thetrash.

For users of System 7.5 or those with the Extensions Manager Program

1. Select the Apple pulldown menu.

2. Select Control Panels and Extensions Manager.

3. Save the current set of extensions by choosing Save Set from thepulldown menu under “Sets.” For example, you might call the set “MyOriginal Extensions.”

4. Select All Off from the pulldown menu under “Sets.”

5. Click to select only those extensions listed on page 98.

6. Save the new set and name it “Glencoe Algebra Products.”

7. Restart your Macintosh.

8. Remember to activate your original set of extensions from the “Sets”pulldown menu and restart your Macintosh before launching any otherprograms.


Customer Service GuideNeed Help?As with all Glencoe technology products, assistance—should you need it—is only a phone call away.Contact customer service at 1-800-334-7344 or the technology support hotline at 1-800-437-3715.

Algebra 1 - Glencoe

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Transcript of Algebra 1 - Glencoe