Applied Algebra I h h
Doug Gardner
h
RoguehCommunityhCollege
RoguehCommunityhCollegeh334
5hRedwoodhHighwayhGrantshPa
ss,hORh97527-
9298hwww.roguecc.edu
(541)h956-7500
An Innovative Math in CTE Curriculum:
h h h h h
FundedhbyhanhATEhgranthfromhthehNationalhSciencehFoundation:h
PrincipalhInvestigators:
DoughGardnerhSeren
ahOtahSt.hClair
rd
3 hEditionhFallh2014
, Chapter Objectives
h
Chapterh1:h ToolshofhAlgebrah(pageh5) Chapterh3:h RighthTrianglehGeometryh(pageh85)
Sectionh1.1:hOperationshwithhRealhNumbers Sectionh3.1:hPythagoreanhTheorem
• +,-,x,÷h FractionshandhDecimals • Findhthehhypotenusehinhahrighthtriangle
• +,-,x,÷h NegativehNumbers • Findhahleghinhahrighthtriangle
• Solvehpracticalhproblems
Sectionh1.2:hMeasurement
• Measurehwithhcm,hmm,handhinches Sectionh3.2:hAngles
• Converthfractionshtohdecimals • Estimatehandhmeasurehangleshinhdegrees
• Converthdecimalshtohfractions • Angleshwithhdegrees,hminutesh&hseconds
• Roundhdecimalhmeasureshtohfractions • Solvehpracticalhproblems
• Converthfeet-inch-
Sectionh3.3:hTrigonometry
fractionhmeasurementshtohincheshandh
• Usehsine,hcosineh&htangenthtohfindhmissing
decimals
hsideshandhangleshinhrighthtriangles
Sectionh1.3:hRatio,hProportionh&hPercent • Solvehpracticalhproblems
• Sethuphandhsolvehproportionhproblems
Chapterh4:h QuantitativehGeometryh(pageh113)
• Converthfractionshandhdecimalshto
hpercents Sectionh4.1:hAreah&hPerimeter
• Converthpercentshtohfractionshand • Findhthehperimeterhofhpolygonshandhcircles
hdecimals • Findhthehareahofhpolygonshandhcircles
• Solvehpercentagehproblems • Solvehpracticalhproblems
Sectionh1.4:hDimensionalhAnalysis Sectionh4.2:hSurfaceharea
• Converthtohdifferenthunitshofhmeasure: • Findhthehsurfacehareahofhsolids
hlength,harea,hvolume,h&hweight • Converthtohdifferenthunitshofhmeasure
• Converthfromhmetrichtohstandardhunits • Solvehpracticalhproblems
• Converthfromhstandardhtohmetrichunits Sectionh4.3:hVolume
Sectionh1.5:hOrderhofhOperations • Findhthehvolumehofhsolids
• Understandhmeaninghofhanhexponent • Converthtohdifferenthunitshofhmeasure
• Applyhorderhofhoperationshwithhformulas • Solvehpracticalhproblems
Chapterh2:h Formulas/Equationsh(pageh63) Appendix:
Sectionh2.1:hSolvinghsimplehequations • AbbreviationshandhSymbols
• Solvinghequationshwithhaddition,hsubtra • Conversions
ction,hmultiplication,handhdivision • AreahandhPerimeterhFormulas
• VolumehandhSurfacehAreahFormulas
Sectionh2.2:hSolvinghforhdifferenthVariables
• Decimal/FractionhConversions
• Solvinghformulashforhdifferenthletters
• SteelhDesignhTable
Sectionh2.3:hSolvinghcomplexhequations
• Solvinghequationshwithhexponents
Legendhofhassignmenthicons:
Manufacturingh
h h Electronicsh h Constructionh h Automotiveh hWeldingh h Health
,2
, Introduction
About this Book:
h h
Thishbookhishdesignedhtohbehread.h Somehhumorhandhstorieshofhmyhpersonalhjourneyhinhunderstandinghandh
applyinghthishbeautifulhlanguageharehincludedhtohkeephithinteresting.h Thereharehnohshortcuts,hhowever!h Ifhyou
harehtohunderstandhthehmaterialhdeeplyhenoughhtohapplyhithtohallhthehrichhproblemshthathlifehpresents,hyouhwill
hneedhtohaddhahconsiderablehamounthofhyourhownhthoughthandhdedicationhtohthehprocess.h Thehbiggesthproble
mhmathhstudentshhavehishattemptinghtohmemorizehstepshtohsolvehproblems.h Thishguaranteeshthathyouhwillhno
thrememberhithwellhenough,horhknowhithdeeplyhenough,htohapplyhit.h Allhmathematicshcanhbehunderstoodhbyhan
yhstudenthwillinghtohinvesththehtimehtohaskhquestions,hthinkhandhscribbleh(andhsometimeshthrowhthings).hYourh
goalhshouldhbehtoh“own”hthehmaterialhratherhthanhmerelyh“borrow”hit.h Owninghithmeanshthathyouhcarryhthehk
nowledgehwithhyou,hlikehahcarpenterhcarrieshhishorhherhtools,hreadyhtohusehthemhashneeded.h Ownership,hhow
ever,hcomeshathahcosthandhthehamounthyouhmusthpayhishdependenthonhyourhnaturalhability,hinteresthandhthehti
mehyouhhavehtohstudy.h Remember,hifhithwashasheasyhashdigginghahditch,heveryonehcouldhdohithandhyouhwouldhn
othgethpaidhextrahforhknowinghit.
Afterhahbriefhintroduction,heachhsectionhwillhoffer rate,handhthehtimehithtakeshtohpayhoffhthehloan.h If
hexampleshtohintroducehnewhconceptshandhshow heitherhthehcar’shpricehorhthehinteresthratehgohup,
hhowhtheyhcanhbehapplied.h Thehexamplesharehno hsohwillhthehmonthlyhpayment.h Onhthehotherhha
thintendedhtohprovidehahstep-by- nd,hifhyouhincreasehthehtimehperiodhoverh whichh
stephprocedurehforhyouhtohcopyhwhenhyouhsolveh youhwillhpayhoffhthehloan,hthehmonthlyhpaymenth
thehproblemshinhthehassignment.h Inhfact,hyouhwil willhdecrease.h Withouththehalgebraichformula,hh
lhfindhthaththehassignedhproblemshmayhnothevenh owever,htherehwouldhbehnohwayhtohfigurehouthw
resemblehthehexamples.h Real- haththehmonthlyhpaymenthshouldhbe.h Thehform
lifehproblems,hsuchhashthoseh thatharisehinhthehw ulahthathexpresseshthishrelationshiphpreciselyhis:
orkplace,harehsohvariedhthathyouhcannothexpectht
PRIT
ohfollowhahmemorizedhsethofhstepshtohsolvehthe Mh=
12(IT−1)
m.
WherehMh=hmonthlyhpayment,hPh=hpricehofhthehca
Algebrahis,hultimately,hahusefulhmethodhforhexpr R
r,hRh=hannualhpercentagehrateh(APR),hIh=h1h+h
essinghrelationshipshinhthehworldhthathpeoplehus 12
(thehmodifiedhinteresthratehrepresentinghmonthl
eheveryhday.h Everyhsectionhofhthish bookhishdevot
yhgrowth),handhTh=htimehtohpayhoffhthehloanhinhm
edhtohexposinghyouhto,handhincreasinghyourhskillh
onths.
with,hformulash(numericalhrelationships).h Ofhco
ursehthereharehrelationshipshinhthehworldhthathyo Thoughhthishishahdauntinghformula,hcompletehwit
uhmayhfindhmorehinteresting,hbuthyouharehproba hhmultiplication,hdivision,haddition,hsubtraction,h
blyhreadinghthishbecausehyouhhavehalreadyhdisco exponentshandhparenthesis,hindeed,heveryhopera
veredhthathyouhcannothlivehonhlovehalone. tionhthathwillhbehstudiedhinhthishcourse,hthehmea
ninghandhorderhofhoperationshcanhbehunderstood
Considerhthehcommonhexperiencehofhmakinghahc
hbyhanyonehwillinghtohinvesththehtimehnecessaryht
arhpayment.h Youhunderstandhthaththerehishahrel
ohspeakhthishmosthinterestinghandhusefulhlanguag
ationshiphbetweenhyourhmonthlyhcarhpaymenth
ehcalledhalgebra.
andhthehpricehofhthehcar,hthehinterest
4
Doug Gardner
h
RoguehCommunityhCollege
RoguehCommunityhCollegeh334
5hRedwoodhHighwayhGrantshPa
ss,hORh97527-
9298hwww.roguecc.edu
(541)h956-7500
An Innovative Math in CTE Curriculum:
h h h h h
FundedhbyhanhATEhgranthfromhthehNationalhSciencehFoundation:h
PrincipalhInvestigators:
DoughGardnerhSeren
ahOtahSt.hClair
rd
3 hEditionhFallh2014
, Chapter Objectives
h
Chapterh1:h ToolshofhAlgebrah(pageh5) Chapterh3:h RighthTrianglehGeometryh(pageh85)
Sectionh1.1:hOperationshwithhRealhNumbers Sectionh3.1:hPythagoreanhTheorem
• +,-,x,÷h FractionshandhDecimals • Findhthehhypotenusehinhahrighthtriangle
• +,-,x,÷h NegativehNumbers • Findhahleghinhahrighthtriangle
• Solvehpracticalhproblems
Sectionh1.2:hMeasurement
• Measurehwithhcm,hmm,handhinches Sectionh3.2:hAngles
• Converthfractionshtohdecimals • Estimatehandhmeasurehangleshinhdegrees
• Converthdecimalshtohfractions • Angleshwithhdegrees,hminutesh&hseconds
• Roundhdecimalhmeasureshtohfractions • Solvehpracticalhproblems
• Converthfeet-inch-
Sectionh3.3:hTrigonometry
fractionhmeasurementshtohincheshandh
• Usehsine,hcosineh&htangenthtohfindhmissing
decimals
hsideshandhangleshinhrighthtriangles
Sectionh1.3:hRatio,hProportionh&hPercent • Solvehpracticalhproblems
• Sethuphandhsolvehproportionhproblems
Chapterh4:h QuantitativehGeometryh(pageh113)
• Converthfractionshandhdecimalshto
hpercents Sectionh4.1:hAreah&hPerimeter
• Converthpercentshtohfractionshand • Findhthehperimeterhofhpolygonshandhcircles
hdecimals • Findhthehareahofhpolygonshandhcircles
• Solvehpercentagehproblems • Solvehpracticalhproblems
Sectionh1.4:hDimensionalhAnalysis Sectionh4.2:hSurfaceharea
• Converthtohdifferenthunitshofhmeasure: • Findhthehsurfacehareahofhsolids
hlength,harea,hvolume,h&hweight • Converthtohdifferenthunitshofhmeasure
• Converthfromhmetrichtohstandardhunits • Solvehpracticalhproblems
• Converthfromhstandardhtohmetrichunits Sectionh4.3:hVolume
Sectionh1.5:hOrderhofhOperations • Findhthehvolumehofhsolids
• Understandhmeaninghofhanhexponent • Converthtohdifferenthunitshofhmeasure
• Applyhorderhofhoperationshwithhformulas • Solvehpracticalhproblems
Chapterh2:h Formulas/Equationsh(pageh63) Appendix:
Sectionh2.1:hSolvinghsimplehequations • AbbreviationshandhSymbols
• Solvinghequationshwithhaddition,hsubtra • Conversions
ction,hmultiplication,handhdivision • AreahandhPerimeterhFormulas
• VolumehandhSurfacehAreahFormulas
Sectionh2.2:hSolvinghforhdifferenthVariables
• Decimal/FractionhConversions
• Solvinghformulashforhdifferenthletters
• SteelhDesignhTable
Sectionh2.3:hSolvinghcomplexhequations
• Solvinghequationshwithhexponents
Legendhofhassignmenthicons:
Manufacturingh
h h Electronicsh h Constructionh h Automotiveh hWeldingh h Health
,2
, Introduction
About this Book:
h h
Thishbookhishdesignedhtohbehread.h Somehhumorhandhstorieshofhmyhpersonalhjourneyhinhunderstandinghandh
applyinghthishbeautifulhlanguageharehincludedhtohkeephithinteresting.h Thereharehnohshortcuts,hhowever!h Ifhyou
harehtohunderstandhthehmaterialhdeeplyhenoughhtohapplyhithtohallhthehrichhproblemshthathlifehpresents,hyouhwill
hneedhtohaddhahconsiderablehamounthofhyourhownhthoughthandhdedicationhtohthehprocess.h Thehbiggesthproble
mhmathhstudentshhavehishattemptinghtohmemorizehstepshtohsolvehproblems.h Thishguaranteeshthathyouhwillhno
thrememberhithwellhenough,horhknowhithdeeplyhenough,htohapplyhit.h Allhmathematicshcanhbehunderstoodhbyhan
yhstudenthwillinghtohinvesththehtimehtohaskhquestions,hthinkhandhscribbleh(andhsometimeshthrowhthings).hYourh
goalhshouldhbehtoh“own”hthehmaterialhratherhthanhmerelyh“borrow”hit.h Owninghithmeanshthathyouhcarryhthehk
nowledgehwithhyou,hlikehahcarpenterhcarrieshhishorhherhtools,hreadyhtohusehthemhashneeded.h Ownership,hhow
ever,hcomeshathahcosthandhthehamounthyouhmusthpayhishdependenthonhyourhnaturalhability,hinteresthandhthehti
mehyouhhavehtohstudy.h Remember,hifhithwashasheasyhashdigginghahditch,heveryonehcouldhdohithandhyouhwouldhn
othgethpaidhextrahforhknowinghit.
Afterhahbriefhintroduction,heachhsectionhwillhoffer rate,handhthehtimehithtakeshtohpayhoffhthehloan.h If
hexampleshtohintroducehnewhconceptshandhshow heitherhthehcar’shpricehorhthehinteresthratehgohup,
hhowhtheyhcanhbehapplied.h Thehexamplesharehno hsohwillhthehmonthlyhpayment.h Onhthehotherhha
thintendedhtohprovidehahstep-by- nd,hifhyouhincreasehthehtimehperiodhoverh whichh
stephprocedurehforhyouhtohcopyhwhenhyouhsolveh youhwillhpayhoffhthehloan,hthehmonthlyhpaymenth
thehproblemshinhthehassignment.h Inhfact,hyouhwil willhdecrease.h Withouththehalgebraichformula,hh
lhfindhthaththehassignedhproblemshmayhnothevenh owever,htherehwouldhbehnohwayhtohfigurehouthw
resemblehthehexamples.h Real- haththehmonthlyhpaymenthshouldhbe.h Thehform
lifehproblems,hsuchhashthoseh thatharisehinhthehw ulahthathexpresseshthishrelationshiphpreciselyhis:
orkplace,harehsohvariedhthathyouhcannothexpectht
PRIT
ohfollowhahmemorizedhsethofhstepshtohsolvehthe Mh=
12(IT−1)
m.
WherehMh=hmonthlyhpayment,hPh=hpricehofhthehca
Algebrahis,hultimately,hahusefulhmethodhforhexpr R
r,hRh=hannualhpercentagehrateh(APR),hIh=h1h+h
essinghrelationshipshinhthehworldhthathpeoplehus 12
(thehmodifiedhinteresthratehrepresentinghmonthl
eheveryhday.h Everyhsectionhofhthish bookhishdevot
yhgrowth),handhTh=htimehtohpayhoffhthehloanhinhm
edhtohexposinghyouhto,handhincreasinghyourhskillh
onths.
with,hformulash(numericalhrelationships).h Ofhco
ursehthereharehrelationshipshinhthehworldhthathyo Thoughhthishishahdauntinghformula,hcompletehwit
uhmayhfindhmorehinteresting,hbuthyouharehproba hhmultiplication,hdivision,haddition,hsubtraction,h
blyhreadinghthishbecausehyouhhavehalreadyhdisco exponentshandhparenthesis,hindeed,heveryhopera
veredhthathyouhcannothlivehonhlovehalone. tionhthathwillhbehstudiedhinhthishcourse,hthehmea
ninghandhorderhofhoperationshcanhbehunderstood
Considerhthehcommonhexperiencehofhmakinghahc
hbyhanyonehwillinghtohinvesththehtimehnecessaryht
arhpayment.h Youhunderstandhthaththerehishahrel
ohspeakhthishmosthinterestinghandhusefulhlanguag
ationshiphbetweenhyourhmonthlyhcarhpaymenth
ehcalledhalgebra.
andhthehpricehofhthehcar,hthehinterest
4
