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Somethingstoknow:1. Lotsofinfoat2. HWyup.Youknowyouloveit!Bepreparedtopresent.3. Content:

4. GradingUltimately,youneedtopasstheIBexam!Presentations,quizzes,tests(80%),Projectdraft(20%)

5. Bring:Notebooks($3!),pencil(s),calculator,andyou!

www.aleimath.blogspot.com

Welcome to IB Math Studies Year 1

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Topic Hours

Topic1 Number&Algebra 20

Topic2 DescriptiveStatistics 12

Topic3 Logic,Sets&Probability 20

Topic4 StatisticalApplications 17

Topic5 Geometry&Trig 18

Topic6 MathematicalModels 20

Topic7 Calculus 18

Project 25

SyllabusOverview

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Fornow,wewillfocusonthefollowing:SumDifferenceProductQuotientFactorDivisorDividend

Butwhatabout72?and(7)2?

Trythese:

Let'sseewhatthecalculatordoeswiththem.Hmmm....whyaretheydifferent?

Anumberthatdividesevenlyintoanothernumberiscalledafactorofthatnumber.

TheFundamentalTheoremofArithmetic

SummaryofFactoringPrimeNumbers:Areonlydivisibleby1anditselfCompositeNumbers:Aretheproductoftwoormoreprimesinadditionto1Factorisation:WritinganumberasaproductoftwoormoreothernumbersPrimeFactorisation:Writinganumberasaproductoftwoormoreprimenumbers

Boxesthatare12inchestallarebeingstackednexttoboxesthatare18inchestall.Whatistheshortestheightatwhichthetwostackswillbethesameheight?

Findingfactors,primefactors

Commonfactors

Thereare40girlsand32boyswhowanttoparticipatein6thgradeintramurals.Ifeachteammusthavethesamenumberofgirlsandthesamenumberofboys,whatisthegreatestnumberofteamsthatcanparticipateinintramurals?

Commonmultiples

Threeclocksstartchimingatexactlythesameinstant.Onechimesevery3hours,oneevery4hours,andtheothereverysixhours.Whenwilltheynextchimetogether?

Review1A:#112(Numberproperties)

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Becareful,it'skindoflikebase60(infact,that'swhereitcamefromBabylonians)Sometimesit'seasy/convenienttoconverttodecimaltime(computers)

Numberisintheformax10kwhere1a

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Giveexamplesofwordsusedinmathematicsyoudon'tnecessarilyhavetoknowwhattheymean(butmakeaguessifyoudon'tknow!)

1A:#111(Vocabulary)

Fornow,wewillfocusonthefollowing:SumDifferenceProductQuotientFactorDivisorDividend

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Butwhatabout72?and(7)2?

Trythese:

Theexponentoperatesonthesymbolthatimmediatelyprecedesit!

Let'sseewhatthecalculatordoeswiththem.Hmmm....whyaretheydifferent?

Let'slookatsomeotherpropertiesofexponents.

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Usingyourunderstandingofexponents,writedownanequivalentpowerforeachproduct.

Usingyourunderstandingofexponents,writedownanequivalentpowerforeachpower.

Usingyourunderstandingofexponents,writedownanequivalentpowerforeachpower.

Canyourunderstandingofexponentshelpyouevaluate?

meansmultiply1bya,ntimes

meansdivide1bya,ntimes

Usingyourunderstandingofexponents,writedownanequivalentpowerforeachquotient.

Usingyourunderstandingofexponents,writedownanequivalentpowerforeachpower.

+1

+11

1

1

1

1

1

1

1

1

Thedefinitionofexponentsalongwithpropertiesofmultiplicationandadditionleadtosomepatternsthatwecanuseasshortcutswhenworkingwithexpressionsinvolvingexponents.

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Fornow,wewillrestrictourselvesto integer exponents.Moreonthatnextme...

ProperesofExponents

Letaandbberealnumbersandmandnbeintegers.Then:

Therearealotofusefulproperes. Donotmemorizethem!Understandthem!

Thistakespracce...

1B.1:#1,24def,58(Exponents)1B.2:#1ijkl,2efgh(ExponentsBase

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TheFundamentalTheoremofArithmetic

SummaryofFactoringPrimeNumbers:Areonlydivisibleby1anditselfCompositeNumbers:Aretheproductoftwoormoreprimesinadditionto1Factorisation:WritinganumberasaproductoftwoormoreothernumbersPrimeFactorisation:Writinganumberasaproductoftwoormoreprimenumbers

Anumberthatdividesevenlyintoanothernumberiscalledafactorofthatnumber.

Consideraregulardeckofcards.Howmanypeoplecanplayagamethatrequiresyoutodealthesamenumberofcardstoeachplayerwithoutanyleftovercards?Findasmanyanswersasyoucan.

Youneverknowhowmanyofyour5friendsarecomingovertoyourhousefortheFridaynightcardgamebutyouwanttodesignagamesothatnomatterhowmanyarrive,everyonewouldgetthesamenumberofcardswhenyoudealthewholedeck.Howmanycardsshouldyouputinthedeckyoudesign?

Numbersthathaveafactorof2arecalled: EvenNumbersNumbersthatdonothaveafactorof2arecalled: OddNumbers

Canyouwriteageneralmathematicaldescriptionofanevennumber? 2n

Whataboutanoddnumber? 2n+1

Note:Theletternisoftenusedtodescribeanarbitraryinteger(withnofractionordecimal)

So,let'slookat60: Evenorodd? PrimeorComposite?

Canyoufindallthewaystowrite60asaproductoffactors?(Thisiscalledfactorising)Besystematic!

Letslookfurtherat60as3x20.Noticethatwecanalsofactorise20sinceitis4x5.Sowecouldwrite60as:

60=3x20=3x4x5Onceagain,weseethat4canbefactorisedinto2x2.So:

60=3x20=3x4x5=3x4x5=3x2x2x5Atthispointallthefactorswehave,2,3,and5,cannotbefactoredfurtherexceptusing1(whichisreallypointless).We'redone!Thisiscalledprimefactorisation.Usuallywewritethefactorsfromsmalltolarge.

60=2x2x3x5Thereareseveralsystematicwaystodothis.Herearetwo:

FactorTree FactorLadder

Numbersthathavenofactorsotherthan1anditselfarecalled: PrimeNumbers

Noticethatallthefactorsofanumbercanbewrittenasproductsoftheprimefactorsofthatnumber.Take60forexample:

SummaryofFactoringPrimeNumbers:Areonlydivisibleby1anditselfCompositeNumbers:Aretheproductoftwoormoreprimesinadditionto1Factorisation:WritinganumberasaproductoftwoormoreothernumbersPrimeFactorisation:Writinganumberasaproductoftwoormoreprimenumbers

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CommonFactorsAnumber,a,thatisafactorofbothnandmiscalledacommonfactorofnandm.ThelargestnumberwiththispropertyiscalledtheGreatestCommonFactor(GCF)orHighestCommonFactor(HCF)ofofnandm

1C.1:#17(Factors)1C.2:#1,2cd,3cde,4(Factors)1C.3:#12(CommonFactors)

Thereare40girlsand32boyswhowanttoparticipatein6thgradeintramurals.Ifeachteammusthavethesamenumberofgirlsandthesamenumberofboys,whatisthegreatestnumberofteamsthatcanparticipateinintramurals?

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Hotdogscomeinpackagesof6,bunscomeinpackagesof8.Howmanypackagesofeachdoyouneedtobuytogetthesamenumberofhotdogsandbuns?

Boxesthatare12inchestallarebeingstackednexttoboxesthatare18inchestall.Whatistheshortestheightatwhichthetwostackswillbethesameheight?

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Attachments

QuadraticsMaster.gsp

SMART Notebook

Page 1: WelcomePage 2: Prior LearningPage 3: OverviewPage 4: 9/4 Ch 1 allPage 5: 9/9 Ch 2 allPage 6: 1A VocabularyPage 7: 1B ExponentsPage 8: Develop PropertiesPage 9: Exponent Summary & PracticePage 10: 1C FactorsPage 11: Common FactorsPage 12: 1D MultiplesPage 13: 2 MeasurementAttachments Page 1