EnglishbytheNumbers教学提纲.docx
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EnglishbytheNumbers教学提纲.docx
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EnglishbytheNumbers教学提纲
EnglishbytheNumbers~Unit1
1.Numbers,Decimalsand
Fractions
Hundreds
Thousands
Fractions&Decimals
Quiz
ThisUnitpreparesstudentstounderstandand
clearlyexpresssmallandlargenumbers,aswell
asfractions,decimalsandpercents.
SampleLanguage
numbers
fivehundredandeighteen(518),sixty-threethousand
fourhundredandtwelve(63,412),sevenhundredand
seventythousand(770,000)
decimals
fiveone-thousandths(.005),onepointzerofive
(1.05),pointeightfivepercent(.85%)
fractions
one-fifth(1/5),twelveandaneighth(121/8),three-
fiftieths(3/50)
KeySentences&Examples
Thesenumbersareallgreaterthanonehundredandless
thanonethousand.
Becarefulnottoconfuse'teen'numberssuchasthirteen
with'ty'numberssuchasthirty.
Fivehundredeighteen.Threehundredeighty.
Thesenumbersareallgreaterthanonethousandandless
thanonemillion.
Ninethousandsevenhundredforty-three.Ninety-seven
thousandfourhundredthirty-six.Ninehundredseventy-
fourthousand,threehundredandsixty-one.
Sometimesthenumberninethousandsevenhundred
forty-threeisreadasninety-sevenhundredandforty-
three.
Herearesomefractions.One-half,one-third,one-fourth.
One-fiftieth,one-hundredth,one-thousandth.
Herearesomedecimalfractionsandpercents.Point
five.Onepointzerofive.Zeropointonepercent.
Forverysmallnumbers,suchas0.00001,youcanreadit
asonepointzerotimestentotheminusfifth.
EnglishbytheNumbers~Unit2
2.NumericalOperationsand
Relations
NumericalOperations
NumericalRelations
Quiz
ThisUnitpreparesstudentstounderstandand
clearlyexpresssmallandlargenumbers,aswell
asfractions,decimalsandpercents.
SampleLanguage
numericaloperations
aplusbequalsc,adividedbyb,thenthrootofx,x
squared,twicethesumofaandb,fiftypercentmore
thanfour
numericalrelations
thesecondlargestnumber,thethirdsmallestnumber,the
differencebetweenthetwolargestnumbers,halfthesum
ofthesmallestandlargestnumbers
KeySentences&Examples
Thesumofaandbisc;oraplusbequalsc.The
differenceofcandbisa;orcminusbisequaltoa.
Herewehaveatimesbequalsx;oramultipliedbybis
x.Inthisexample,wehavethesumofaandb
multipliedbyc.Inthisexample,aisdividedbyb;ora
overb.Thisisthenthrootofx.Forexample,thesquare
rootoffouristhesecondrootoffour,whichistwo.
Herewehavethecuberootofeight,orthethirdrootof
eight,whichistwo.Thisisxtothenth.Fornequalto
two,wesayxsquared.Fornequaltothree,wesayx
cubed,orxtothethird.
Takethesumoftwoplussixanddivideitbytwo.
Multiplythesumofaplusbbyfifteenanddividethe
resultbyatimesb.Whatnumberisthesumofeighty-
fiveandfive?
Whatistwotothefourth?
Whatistwenty
percentmorethanten?
Ifxisfiftypercentmorethan
four,whatisx?
Whichofthesefivenumbersisthe
smallest?
Whichnumbersarethetwolargestnumbers?
Whichnumberistenpercentofthelargestnumber?
Whichnumberisequaltothedifferencebetweenthe
largestandsmallestnumbers?
EnglishbytheNumbers~Unit3
3.RelatedChanges
Part1
HomeBuyers
SampleGraphs
SampleLanguage
Graphs
remainedfairlyconstant,didn’tchange,rise,increased,
wentup,madesteadygains,getsweaker,decreases,
wentdown,declined,dropped
relatedchanges
Xremainedfairlyconstant,butyincreasedsignificantly.
Asthepriceofanaveragehouseincreased,the
percentageofU.S.familiesabletobuyanewhouse
decreased.
Part2
Speed&Distance
LanguageLearning
BloodPressure
Quiz
ThisUnitpreparesstudentstodescribehowone
quantitycorrelatestoanother.Sometimesthere
isnorelationship.Sometimesachangeinone
quantitycausesachangeorinanother.
KeySentencesandExamples
ThisgraphshowsthepercentageofUSfamiliesableto
buyanaverage-pricednewhome.Asthepriceofan
averagehouseincreased,thepercentageofU.S.families
abletobuyanewhousedecreased.Between1970and
1976,theaveragepriceofanewhouserosefrom
$23,400to$44,200.Asaresult,fewerU.S.families
wereabletobuynewhouses.Inthisgraph,bothXand
Yareincreasing.Inthisgraph,XisincreasingwhileY
isdecreasing.HerewearelookingatchangesinXand
Yduringtheten-yearperiodfrom1978to1988.During
thatperiod,wheneverYincreased,Xdecreased,and
wheneverYwentdown,Xwentup.Inthiscase,as
exports,X,wentup,unemployment,Y,declined.While
Xstayedaboutthesame,Yincreased.Xremainedfairly
constant,butYincreasedsignificantly.Xincreased
rapidlyatfirst,butthenitfelleventhoughYcontinued
toclimb.Asthedollargetsweaker,thenumberof
AmericanworkersemployedbyJapanesefirms
continuestoclimb.Anincreaseinthevalueofthe
Japaneseyenisgenerallyfollowedbyanincreasein
Japaneseproductivity.
Goals:
Tobeabletoaskandanswerquestionsabout
howonefactorrelatestoanother.
Tobeabletoexpressanopinionaboutone
quantityisrelatedtoanother.
EnglishbytheNumbers~Unit4
4.LineGraphs
Part1
Autosales
ForeignShareofSteelMarket
UnemploymentRate
HomeBuyers
AverageFamilySize
SampleLanguage&LearningPoints
linegraphs
salesdeclinedtoalowofaround300,000,sales
increasedsteadily,saleswerearound900,000units,sales
atUnionMotorssurpassedsalesatFederalMotors,the
numberofpotentialfirst-timehomebuyerspeaked,the
largestshareofthemarket,changesinthe
unemploymentrate
presentperfect(have+V(n))
saleshavestoppedtheirdecline,haveremainedfairly
steady,thenumberofpotentialfirsttimebuyershas
changed,thenumberhasbeendropping…
Part2
CityGovernmentApproval
PopulationGrowth
WorldEnergyConsumption
PassengerCarExports
TrafficFatalities
KeySentencesandExamples:
ThisfirstexampleshowshowautosalesatUnionMotors
havechangedsince1960.In1960,saleswereabout
500,000units.From1960,salesdeclinedtoalowof
around300,000in1965.From1965,salesincreased
steadilyuntiltheyreachedahighofaround900,000in
1974.Then,becauseofincreasingimports,salesbegana
longdecline,toalowofaround500,000units.Since
1980,saleshavestoppedtheirdeclineandhaveremained
fairlysteady.
ThisgraphshowshowtheforeignshareoftotalUSsteel
saleschangedduringtheperiodfrom1965through1985.
Between1970and1980,thelowestforeignshareofthe
marketwasabout12%.Thelargestshareofthemarket
before1970wasabout17%,in'68.
Thisgraphshowshowthenumberofpotentialfirsttime
homebuyershaschanged.Thenumberofpotentialfirst-
timehomebuyerspeakedataround45millionattheend
ofthe'80s.Sincethebeginningof1990,thenumberhas
beendropping.
Thisgraphshowsthedecreaseinaveragefamilysizein
theUS.USfamiliesin1989averagedonly3.16people,
thesmallestsizesince1940.Thisdropisprimarilythe
resultoflowerbirthratesandcontinuedincreasesinthe
numberofsingle-parentfamilies.Thisgraphindicates
thattheaveragefamilyhasbeengettingsmaller.
Part2
Thislinegraphshowshowthevoterapprovalratingfora
citygovernmenthaschangedduringthepast12months.
Notethattheapprovalratingwasatitshighestduringthe
first3monthsandatitslowestinmonth8.Itreachedits
lowestpointinmonth8.Duringmonth8,60%ofthe
votersdisapprovedofthegovernment'sperformance.
Thisgraphsshowstherateofpopulationgrowthin
severalcountries.Italsoshowstheliteracyrateineach
ofthecountries.Theadultliteracyrateisthepercentage
ofadultswhocanreadandwrite.Theaxisontheleft
givesthepercentagegrowthrate,andtheaxisonthe
Quiz
ThisUnitpreparesstudentstopresentdatafrom
alinegraph,especiallychangesovertime.
Goals:
Tobeabletousethepresentperfect(have
+V(n))toexpresschange.
rightgivestheliteracyrate.Forexample,the
percentageannualgrowthrateofBrazilisabout
1.4%.Itsliteracyrateis0.83or83%.Forthese
countries,thegraphsuggeststhatcountrieswitha
higherliteracyratehavealowerrateofpopulation
growth.
Thisgraphshowshowtheworld'sconsumptionof
energyisincreasing.Thescaleontheleftisinunits
ofquadrillionBTUsorBritishThermalUnits.In
1983,theworld'senergyconsumptionwas283
quadrillionBTUs.Theworld'senergyconsumption
in1990was347quadrillionBTUs.
Thisgraphshowshowpassengercarexportschanged
inthe5yearperiodendingin2003Itshowsthevalue
ofexportsinbillionsofdollarsforsevenexporting
countries.
Thisgraphgivesthecausesoftrafficfatalitiesbased
on4000separateaccidents.Eachbarshowsthe
numberoffatalitiesforeachcause.Theaxisonthe
rightgivesthepercentage.Forexample,about1200
deathswereduetospeed.Thelinegraphabovethe
bargraphshowsthecumulativepercentageof
fatalitiesduetoeachcause.Itshowsthat72.3percent
ofthetrafficfatalitieswereduetotwocauses,lane
changesandunsafespeed.
SampleQuestions:
Whendidtheapprovalratingreach50%?
Whendidtheapprovalratingreachitslowestpoint?
Whathashappenedtotheapprovalratingduringthe
past4months?
(a)Ithasstayedflat.(b)Ithasimproved.(c)Ithas
gottenworse.
Whatpercentofvotersdisapprovedofthe
government'sperformanceduringmonth8?
Whatconclusioncanbedrawnfromthisgraph?
Whichcountryhasanegativegrowthrate?
Whichcountryhasthehighestgrowthrate?
Ofthesecountries,whichcountryhasthelowestrate
ofliteracy?
AboutwhatisVietnam'sliteracyrate?
Whatwastheworld'senergy
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