Prerequisite Level Skills List...6.NS.3 Decimal Division × When there is a decimal in the divisor,...

CrossroadsMath--SummerCurriculum

Rising7thGraders--YaleCohort

Belowyouwillfindascheduleofwhatshouldbestudied,practiced,ANDMASTEREDeachweekoverthe summer.Weeks1-3focusonensuringfoundationalstandardsaremastered,whileweeks4-8focusonthefirst standardsofthe7thgradecurriculumthatwillbeassessedduringthefirstweeksoftheschoolyear.

● “DailyMemorization”-Creatingflashcards(canbemadebycuttingupblankpaper)isrecommended tohelpinmemorizing.Reviewingthesefor10minuteseachdayishighlyencouraged.

● KhanAcademy.orgisanexcellentresourcewith“howto”videosandmultiplepracticetypesperskill. ● Tokeeporganized,usethisfront&backcoverpageasachecklistofwhatyouhavemastered. ● Thispacketismerelyaguide.Studentsareresponsibleforfullyunderstandingeachstandardlisted.

Forsomethispacketwillbeenoughinstructionandpractice,butforotherstheywillneedto supplementinstructionwithvideosonlineandfindadditionalpracticeonlineaswell.

PrerequisiteLevelSkillsList ⇨⇨⇨QUIZON2ndDAYOFSCHOOL:Wednesday,September4th,2019⇦⇦⇦

Week DailyMEMORIZATION StandardstoLearn&Practice Mastery?

week

1

Pages 3-8

6.RP.3 EquivalentFraction,Decimal, Percentvalues:Tenths&Fifths

110

210

310

410

510

610

710

810

910 10

10 0.10.20.30.40.50.60.70.80.91.0 10%20%30%40%50%60%70%80%90%100%

51

52

53

54

55

0.20.40.60.81.0 20%40%60%80%100%

NumberSystem:Decimals � 6.NS.3-DecimalOperations

❏ Add ❏ Subtract ❏ Multiply ❏ Divide

week

2

Pages 9-13

6.RP.3 EquivalentFraction,Decimal, Percentvalues:Eighths,

Fourths,Halves 8

183

85

87

0.1250.3750.6250.875 12.5%36.7%62.5%87.5%

and 21

22

41

42

43

44

0.51.00.250.50.751.0 50%100%25%50%75%100%

NumberSystem:Fractions 5.NF.1-AddingandSubtractingFractionsand MixedNumberswithUNlikeDenominators

❏ 4.NFB.3c-AddingandSubtractingFractions andMixedNumberswithLIKEDenominators

week

3

Pages 14-19

6.RP.3 EquivalentFraction,Decimal, Percentvalues:Thirds& Convertingbetweenany fraction,decimal,percent

=0. =33. %31 3 3 =0. =66. %3

2 6 6

NumberSystem/Expressions&Equations 6.EE.1-OrderofOperations&Exponents

❏ Withwholenumbers ❏ WithDecimals&Fractions

YOUWILLHAVEAQUIZONTHESESTANDARDSONTHE2ndDAYOFSCHOOL! Thisquizwillnotcounttowardyourquarteronemathgrade;however,alloftheseskills

foundationallysupporttheseventhgradecurriculumandmasteryof7thgradematerialwillbe incrediblychallengingwithoutthisfoundation.

Questions?Call/TextMrs.Jones443-390-6673before8pm 1

7thGradeMathStandardsList ⇨⇨⇨MASTERYQUIZ2ndweekFriday,September13th,2019on7.NS.1-3⇦⇦⇦ ⇨⇨⇨MASTERYQUIZ3rdweekFriday,September20th,2019on7.SP.3&7.SP.4⇦⇦⇦ ⇨⇨⇨MASTERYQUIZ4thweekFriday,September27th,2019on7.EE.1&7.EE.4⇦⇦⇦

Week DailyMEMORIZATION StandardstoLearn&Practice Mastery?

week

4

Pages 18-24

7.NS.2-Integer Multiplication/Division

Maketwosetsofcards#1-12,one setofpositivesandonesetof

negatives.Shufflethemtogetherand choosetwotocreateamultiplication

facttopractice.

Statistics 7.SP.3-Assessthedegreeofoverlapof twodatasets,measuredifferences betweenthemeasuresofcentersasa multipleofameasureofvariability

week

5

Pages 25-29

7.NS.1-Integer Addition/Subtraction

Maketwosetsofcards#1-12,one setofpositivesandonesetof

negatives.Shufflethemtogetherand choosetwotocreateanadditionor

subtractionfacttopractice.

Statistics 7.SP.4-Usemeasuresofcenterand measuresofvariabilityfornumericaldata fromrandomsamplestodrawinformal comparativeinferencesabouttwo populations

week

6

Pages 30-35

7.NS.1-Integer Addition/Subtraction

ContinueAddition/SubtractionFacts

withnegativesfromweek5

Expressions&Equations 7.EE.1-Applypropertiesofoperationsto add,subtract,factor,andexpandlinear expressionswithrationalcoefficients.

❏ CombiningLikeTerms ❏ Distributiveproperty ❏ AdditiveInverseproperty

week

7

Pages 36-41

7.NS.1-RationalNumbers Addition/Subtraction

Nowaddinsomepracticewith AddingandSubtractingwith

negativesthatincludefractionsand decimals.YoucanuseKhanAcademy orGoogleaworksheettopractice.

Expressions&Equations 7.EE.4-Usevariablestorepresent quantitiesinareal-worldormathematical problem,andconstructsimpleequations andinequalitiestosolveproblemsby reasoningaboutthequantities.

week

8

Pages 42-47

7.NS.1-RationalNumbers Multiplication&Division

Nowaddinsomepracticewith AddingandSubtractingwith

negativesthatincludefractionsand decimals.YoucanuseKhanAcademy orGoogleaworksheettopractice.

NumberSystem 7.NS.1-Add&SubtractRational NumbersandAdditiveInverseProperty 7.NS.2-Multiply&DivideRational Numbers

� 7.NS.3-RationalNumbersOperationsin Context

YOUWILLHAVEAMASTERYQUIZONTHESESTANDARDS!! Eachstandardwillcountasanindividualmasteryquizgradeforquarterone.

Wewillbequicklyreviewingandpracticingtheseskillsduringthefirstthreeweeksofschool.

Pages48-50areANSWERKEYStoPractice(Forstudenttouseregularlytogaugeprogress.) Pages51-52aretheANSWERKEYStoQUIZZES(ForFamilyMemberholdontotocheck)


WEEK1 ____________________________________________________________________________________________________________________________________________________________________________________

DailyMemorization 6.RP.3-EquivalentPercents,Decimals,Fractions

Tenths&Fifths ____________________________________________________________________________________________________________________________________________________________________________________

-Youwillneedtohavethesebenchmarkfractions,decimals,percentsmemorizedthisweek.

-Thebestwaytomemorizetheseistocreateflashcardsandpracticethemfor10minuteseachday.

-Youcanalsohavesomeonequizyouwiththemtomakesureyouhavemasteredthem!

MEMORIZEtheequivalentdecimal&percentforeachfractionbelow:


WEEK1 ____________________________________________________________________________________________________________________________________________________________________________________

6.NS.3-DecimalOperations Fluentlyadd,subtract,multiply,anddividemulti-digitdecimalsusingthestandardalgorithmfor

eachoperation. ____________________________________________________________________________________________________________________________________________________________________________________ KhanAcademy:https://www.khanacademy.org/commoncore/grade-6-NS#6.NS.B.3

____________________________________________________________________________________________________________________________________________________________________________________ Reminder:Youmustdemonstratefullconceptualunderstandingofthestandard

inadditiontoproceduralmasteryoftheskill. ____________________________________________________________________________________________________________________________________________________________________________________ NOTES:

6.NS.3DecimalAdditionandSubtraction

LINEUPTHEDECIMALS!!inordertoaligntheplacevaluesofdigits Hint:Treatdecimalslikemoney. $5=$5.00

6.NS.3DecimalMultiplication ×

1. Removethedecimalsfromeachfactor 2. Countthetotaldecimalplacevaluesremoved 3. Multiplylikenormal 4. Placethedecimalbackintotheproductusingthetotalnumberof decimalplacevaluesremoved

6.NS.3DecimalDivision ÷

Whenthereisadecimalinthedivisor,youmustmakesomechangesto alignyourdecimalbeforedividing.

1. Movethedecimalinthedivisortomakeitawholenumber 2. Countthenumberofdecimalplacevaluejumpsandmovethe decimalinthedividendthesamenumberoftimesasthedivisor

3. Movethedecimalupintothequotient 4. Dividelikeusinglongdivisionalgorithm


https://www.khanacademy.org/commoncore/grade-6-NS#6.NS.B.3

WEEK1 ____________________________________________________________________________________________________________________________________________________________________________________

6.NS.3-DecimalOperations ____________________________________________________________________________________________________________________________________________________________________________________ SKILLPRACTICE

Adding 1) 2.4+3.3=

2) 12.7+2.8=

3) 6.72+5=

4) 245.987+16.204=

5) 34.69+72.507=

---------------------------------------------------------------------------------------------------- Subtracting 1) 7.4-3.3=

2) 15.7-2.8=

3) 6.79-5=

4) 45.53-16.69=

5) 94.609-72.517=


WEEK1 ____________________________________________________________________________________________________________________________________________________________________________________

6.NS.3-DecimalOperations ____________________________________________________________________________________________________________________________________________________________________________________ SKILLPRACTICE Multiplying

1) 2.4x0.3=

2) 12.7x0.05=

3) 6.72x10=

4) 0.024x0.62=

5) 4.8x5.9=

----------------------------------------------------------------------------------------------------

Dividing

1) 0.24÷0.3=

2) 0.125÷0.5=

3) 68.5÷10=

4) 12.4÷1.2=

5) 4.8÷0.04=


WEEK1 ____________________________________________________________________________________________________________________________________________________________________________________

6.NS.3-DecimalOperations ____________________________________________________________________________________________________________________________________________________________________________________ STANDARDPRACTICE

1) Supposeyoubuy5poundsofapplesfor$1.29 perpound.Howmuchmoneywouldyouspend ontheapples?

2) Inordertotrainfora5k,youhavedecidedto doapracticerunof3.1milesandhavealready run1.56miles.Howmanymoremilesdoyou needtorun?

3) Mrs.Joneswantstohiketwotrails.Thelength ofonetrailis6.706km.Thelengthoftheother trailis9.0704km.Whatisthetotallengthofthe twotrails?

4) WholeFoodshadpineapplesonsalefor$1.20 perpound.Tonyspent$5.28onpineapples. Howmanypoundsofpineapplesdidhebuy?

5) Ahatcosts$10.95andaT-shirtcosts$14.20. Howmuchchangewillyoureceiveifyoupay forbothitemswitha$50bill?

6) AshelfusedtostoreDVDsis60.96cmwide.If eachDVDis1.5cmwide,whatisthemaximum numberofDVDsthatcanbestoredonthe shelf?

7) Atoyboatcosts$3.88andaballcosts$1.29.If Jabrebuys2toyboatsand3balls,howmuch totalmoneywillshespend?

8) Tomhad$84.50andthenspent$12.25fora musicCD,$17.85foragift,and$15.45for gasoline.Howmuchdidhehaveleft?


WEEK1 ____________________________________________________________________________________________________________________________________________________________________________________

6.NS.3-DecimalOperations ____________________________________________________________________________________________________________________________________________________________________________________ PRACTICEQUIZ Thetableshowstheaveragepriceofgold(indollarsperounce)forseveralyears.

1.Findthequotientoftheaveragespricesofgoldin2010and1970.Whatdoesthequotientmean? 2.Aminerfoundthreepiecesofgoldinanundergroundminein1970. Thepiecesweighed0.080ounce,0.122ounce,and0.096ounce.

2a.Findthetotalweightofthegoldthatwasfoundintheundergroundminein1970.

2b.Findthetotalvalue(indollars)ofthegoldwhenitwasmined.

2c.Abouthowmuchmorewasthegoldworthin2010thanin1970?


WEEK2 ____________________________________________________________________________________________________________________________________________________________________________________


Eighths&Fourths&Halves ____________________________________________________________________________________________________________________________________________________________________________________

-Youwillneedtohavethesebenchmarkfractions,decimal,percentsmemorizedthisweek.





WEEK2 ____________________________________________________________________________________________________________________________________________________________________________________

5.NF.1-Add&SubtractFractionswithUNlikeDenominators Addandsubtractfractionswithunlikedenominators(includingmixednumbers)byreplacinggiven fractionswithequivalentfractionsinsuchawayastoproduceanequivalentsumordifferenceof fractionswithlikedenominators.Forexample,2/3+5/4=8/12+15/12=23/12.(Ingeneral,a/b+

c/d=(ad+bc)/bd.) ____________________________________________________________________________________________________________________________________________________________________________________ KhanAcademy:https://www.khanacademy.org/commoncore/grade-5-NF#5.NF.A.1


inadditiontoproceduralmasteryoftheskill. ____________________________________________________________________________________________________________________________________________________________________________________ NOTES: **FIRST,changeanymixednumberstoimproperfractions** Generaltechnique: “Trick”technique: 1.FindLeastCommonDenomination(orLCM) Google:“Butterflyfraction”addition 2.Makeequivalentfractionsusingnewdeno 3.Addthenumerators,denominatorsstaythesame


https://www.khanacademy.org/commoncore/grade-5-NF#5.NF.A.1

WEEK2 ____________________________________________________________________________________________________________________________________________________________________________________

5.NF.1-Add&SubtractFractionswithUnlikeDenominators ____________________________________________________________________________________________________________________________________________________________________________________ SKILLPRACTICE


WEEK2 ____________________________________________________________________________________________________________________________________________________________________________________

5.NF.1-Add&SubtractFractionswithUNlikeDenominators ____________________________________________________________________________________________________________________________________________________________________________________ STANDARDPRACTICE

1) Dinaaddedfive-sixthsofabagofsoiltohergarden.HerneighborNatashaadded eleven-eighthsbagsofsoiltohergarden.HowmuchmoresoildidNatashaaddthanDina?

2) IttookNickfive-thirdsofanhourtocompletehismathhomeworkonMonday,three-fourths ofanhouronTuesday,andfive-sixthsofanhouronWednesday.Howmanyhoursdidhetake tocompletehishomeworkaltogether?

3) Dylanreadhisbookaboutanimalsfor22/3hoursthisweek.Hissister,Faith,readher footballbookfor11/5hoursthisweek.HowmuchlongerdidDylanreadhisbookthanFaith readhers?

4) Therewere cratesoftomatoesinthebarnbut cratesoftomatoeswererottenandhad42 41 7 5

3

tobethrownout.Joesold cratesandcanned cratesoftomatoes.Howmanycratesof8 31 7 6

5 tomatoeswereleft?


WEEK2 ____________________________________________________________________________________________________________________________________________________________________________________

5.NF.1-Add&SubtractFractionswithUNlikeDenominators ____________________________________________________________________________________________________________________________________________________________________________________ PRACTICEQUIZ Haileyhas3cats:Bonnie,MuffinandBaby.

1.HaileyfeedsthemCatCookiesbrandcatfood. EachdayBonnieeats ofthebox,Muffineats oftheboxandBabyeats of2

181

41

thebox.Whatfractionofawholeboxdothecatseat,inall,eachday? 2.MuffinandBabyspendmuchofeachdaysleeping. Muffinsleepsfor ofthedayandBabysleepsfor oftheday.5

3 710

Whichofthetwocatssleepsforlonger?Howmuchlongerdoesitsleepeachday? 3.Hailey’scatsoftenshareacartonofcatmilk.Bonniealwaysdrinks ofthecarton,Muffinalways3

1

drinks ofthecarton,andBabyalwaysdrinks ofthecarton.512 6

1 Whatfractionofthecartonofcatmilkisleftover? 4.Hailey’scatslovetojumpinandoutoftheircatdoor.Yesterdaythecatdoorwasused100times byhercats.Bonnieuseditfor ofthetimesandMuffinuseditfor ofthetimes.Howmanytimes4

1 310

didBabyusethecatdoor?Explainhowyoufigureditout.


WEEK3 ____________________________________________________________________________________________________________________________________________________________________________________


Thirds&Convertingbetweenanyfraction,decimal,percent ____________________________________________________________________________________________________________________________________________________________________________________

-Youwillneedtohavethesebenchmarkfractions,decimal,percentsmemorizedthisweek.




KhanAcademy.orghasatonofpracticewith“Percent,fraction,decimalconversions”


WEEK3 ____________________________________________________________________________________________________________________________________________________________________________________

6.EE.1-OrderofOperations&Exponents Writeandevaluatenumericalexpressionsinvolvingwhole-numberexponents.

____________________________________________________________________________________________________________________________________________________________________________________ KhanAcademy:https://www.khanacademy.org/commoncore/grade-6-EE#6.EE.A.1




https://www.khanacademy.org/commoncore/grade-6-EE#6.EE.A.1

WEEK3 ____________________________________________________________________________________________________________________________________________________________________________________

6.EE.1-OrderofOperations&Exponents ____________________________________________________________________________________________________________________________________________________________________________________

SKILLPRACTICE WholeNumbers 1) 36x3+(56÷7)–65

2) 6×[(34–26)+3] 3) 26x3+[(56÷7)–5]

4) [(14+7)+(66÷6)]÷4

WholeNumberswithExponents 5) 8x(13-2)-32

6) (9-2)2+(10÷2)

7) (8-4)2+(12-15÷5)

8) (6x9+32)+3


WEEK3 ____________________________________________________________________________________________________________________________________________________________________________________

6.EE.1-OrderofOperations&Exponents ____________________________________________________________________________________________________________________________________________________________________________________

SKILLPRACTICE IntegerswithExponents 9) 6-[10÷5]3•9

10) 8-[14÷7]2•11

11) [(-11)•(-2)2-(-2)]+(-11)

12) [(-42)÷(-7)]2-(-2)•5

RationalNumberswithExponents 13) (8.2+ 1.9))2 ( 2.7) ÷

14) ( 3.7)x( 2.9) ( 9.4)2

15) ( )( 31 2 6

1) ÷ 31

16) x (( 51)2 5

2 + 51) ( 8

7)


WEEK3 ____________________________________________________________________________________________________________________________________________________________________________________

6.EE.1-OrderofOperations&Exponents ____________________________________________________________________________________________________________________________________________________________________________________ PRACTICEQUIZ

1) x (( 0) )1 + 2 ( )7 ( )( 3 2÷ 9)

2) .7 ( .1) (0.5) 6 4 2

3) (( 31) 6

5)2 ÷ ( 95)

4) ( .5)1 ÷ ( 1 3

1) + ( .5)1 2


PRACTICEQUIZ ____________________________________________________________________________________________________________________________________________________________________________________

DailyMemorization--Weeks1-3 6.RP.3-EquivalentPercents,Decimals,Fractions

____________________________________________________________________________________________________________________________________________________________________________________

Fraction *SIMPLESTFORMONLY*

Decimal Percent

30%

41

710

60%

0.8

52

20%

85

83

87

81

32

0.75 75%

5%

1.05


WEEK4 ____________________________________________________________________________________________________________________________________________________________________________________

DailyMemorization 7.NS.2-RationalOperationsMultiplication&Division

MultiplyandDividewithnegatives KhanAcademy:https://www.khanacademy.org/commoncore/grade-7-NS#7.NS.A.2

____________________________________________________________________________________________________________________________________________________________________________________

7.NS.2-Integer:Multiplication&Division MULTIPLICATION&DIVISIONONLY Hint:Ifthereisanoddnumberofnegatives,itwillbenegative.

KhanAcademy.orghasatonofpracticewithOperationswithNegativesunder7.NS.2


https://www.khanacademy.org/commoncore/grade-7-NS#7.NS.A.2

WEEK4 ____________________________________________________________________________________________________________________________________________________________________________________

7.SP.3-Measurethedifferencesbetweenthemeasuresofcenterasa multipleofameasureofvariability

Informallyassessthedegreeofvisualoverlapoftwonumericaldatadistributionswithsimilar variabilities,measuringthedifferencebetweenthecentersbyexpressingitasamultipleofa

measureofvariability. Forexample,themeanheightofplayersonthebasketballteamis10cmgreaterthanthemean

heightofplayersonthesoccerteam,abouttwicethevariability(meanabsolutedeviation)oneither team;onadotplot,theseparationbetweenthetwodistributionsofheightsisnoticeable.

____________________________________________________________________________________________________________________________________________________________________________________ KhanAcademy:https://www.khanacademy.org/commoncore/grade-7-SP#7.SP.B.3



MeasuresofCenter Mean-1.Addupallthenumbers2.Dividebythenumberofaddends Median-1.Orderdataleasttogreatest2.Findthemiddlenumber

(3.If2middlenumbers,findthemeanofthem)

Mode-Numberthatoccursthemost(canhavezero,one,ormultiplemodes)


https://www.khanacademy.org/commoncore/grade-7-SP#7.SP.B.3

WEEK4 ____________________________________________________________________________________________________________________________________________________________________________________


____________________________________________________________________________________________________________________________________________________________________________________ SKILLPRACTICE


WEEK4 ____________________________________________________________________________________________________________________________________________________________________________________


____________________________________________________________________________________________________________________________________________________________________________________ STANDARDPRACTICE


WEEK4 ____________________________________________________________________________________________________________________________________________________________________________________


____________________________________________________________________________________________________________________________________________________________________________________ PRACTICEQUIZ


WEEK5 ____________________________________________________________________________________________________________________________________________________________________________________

DailyMemorization 7.NS.1-RationalOperationsAddition&Subtraction

Add&Subtractwithnegatives KhanAcademy:https://www.khanacademy.org/commoncore/grade-7-NS#7.NS.A.1

____________________________________________________________________________________________________________________________________________________________________________________

7.NS.1-Integer:Addition

7.NS.1-Integer:Subtraction ChangeittoanadditionproblembyusingtheAdditiveInverseProperty Tosubtractintegers: “Addtheopposite”

1. Keep1stnumberthesame,always. 2. Changesubtractiontoaddition. 3. Change2ndnumbertoitsopposite/additiveinverse.



WEEK5 ____________________________________________________________________________________________________________________________________________________________________________________

7.SP.4-CompareTwoPopulationsusingMeasuresofCenter&Variability Usemeasuresofcenterandmeasuresofvariabilityfornumericaldatafromrandomsamplesto

drawinformalcomparativeinferencesabouttwopopulations. Forexample,decidewhetherthewordsinachapterofaseventh-gradesciencebookare

generallylongerthanthewordsinachapterofafourth-gradesciencebook. ____________________________________________________________________________________________________________________________________________________________________________________ KhanAcademy:https://www.khanacademy.org/commoncore/grade-7-SP#7.SP.B.4




https://www.khanacademy.org/commoncore/grade-7-SP#7.SP.B.4

WEEK5 ____________________________________________________________________________________________________________________________________________________________________________________

7.SP.4-CompareTwoPopulationsusingMeasuresofCenter&Variability ____________________________________________________________________________________________________________________________________________________________________________________ SKILLPRACTICE


WEEK5 ____________________________________________________________________________________________________________________________________________________________________________________

7.SP.4-CompareTwoPopulationsusingMeasuresofCenter&Variability ____________________________________________________________________________________________________________________________________________________________________________________ STANDARDPRACTICE


WEEK5 ____________________________________________________________________________________________________________________________________________________________________________________

7.SP.4-CompareTwoPopulationsusingMeasuresofCenter&Variability ____________________________________________________________________________________________________________________________________________________________________________________ PRACTICEQUIZ


WEEK6 ____________________________________________________________________________________________________________________________________________________________________________________


Add&Subtractwithnegatives CONTINUED

KhanAcademy:https://www.khanacademy.org/commoncore/grade-7-NS#7.NS.A.1 ____________________________________________________________________________________________________________________________________________________________________________________ Seenotesfromweek5

Findeachsum. Findeachdifference.

KhanAcademy.orghasatonofpracticewithOperationswithNegativesunder7.NS.1



WEEK6 ____________________________________________________________________________________________________________________________________________________________________________________

7.EE.1-Applypropertiesofoperationsasstrategiestoadd,subtract, factor,andexpandlinearexpressionswithrationalcoefficients.

____________________________________________________________________________________________________________________________________________________________________________________ KhanAcademy:https://www.khanacademy.org/commoncore/grade-7-EE#7.EE.A.1




https://www.khanacademy.org/commoncore/grade-7-EE#7.EE.A.1

WEEK6 ____________________________________________________________________________________________________________________________________________________________________________________


____________________________________________________________________________________________________________________________________________________________________________________ SKILLPRACTICE Add/Subtract


WEEK6 ____________________________________________________________________________________________________________________________________________________________________________________


____________________________________________________________________________________________________________________________________________________________________________________ SKILLPRACTICE FactorExpressions Factorthefollowingalgebraicexpressions:

9)6x+24 10)8x2−4x 11)6xy+10x2y 12)m4−3m2

13)6x2+8x+12yx Expand/Simplify


WEEK6 ____________________________________________________________________________________________________________________________________________________________________________________


____________________________________________________________________________________________________________________________________________________________________________________ STANDARDPRACTICE 1. Whichexpressionrepresentsthesumof(2x–5y)and(x+y)?

2. Inthefollowingequation,aandbarebothintegers.a(3x–8)=b–18x

a. Whatisthevalueofa? b. Whatisthevalueofb?

3. Writetheexpressioninstandardform: (2d) e ) 3d ) 3 + ( 5 + 6 + ( e

4. When issubtractedfrom ,theresultis______x8

5 + 1 31 x 1 4

1 5 61


WEEK6 ____________________________________________________________________________________________________________________________________________________________________________________


____________________________________________________________________________________________________________________________________________________________________________________ PRACTICEQUIZ 1) Writethesumof and instandardform.x 5 7 + 6 x 4 + 3

2) Writethedifferenceof and instandardform.x 5 7 + 6 x 4 + 3

3) Writethefollowingexpressioninstandardformbyexpandingandcollectinglike terms: (4a ) (a 0) 3 + 6 + 2 1

4) Writethefollowingexpressioninstandardform:

( b) 12 ) 3 • 2 • a + 5 7 + ( • c • 4


WEEK7 ____________________________________________________________________________________________________________________________________________________________________________________


Add&Subtractwithnegatives INCLUDINGDECIMALS&FRACTIONS

KhanAcademy:https://www.khanacademy.org/commoncore/grade-7-NS#7.NS.A.1 ____________________________________________________________________________________________________________________________________________________________________________________ Continuepracticingwithadditionandsubtraction,nowusingrationalnumbers(fractions/decimals)



WEEK7 ____________________________________________________________________________________________________________________________________________________________________________________

7.EE.4-ConstructEquations&InequalitiestoSolveProblems Usevariablestorepresentquantitiesinareal-worldormathematicalproblem,andconstruct simpleequationsandinequalitiestosolveproblemsbyreasoningaboutthequantities.

7.EE.4.A--Solvewordproblemsleadingtoequationsoftheformpx+q=randp(x+q)=r,wherep,q,andrare specificrationalnumbers.Solveequationsoftheseformsfluently.Compareanalgebraicsolutiontoanarithmetic

solution,identifyingthesequenceoftheoperationsusedineachapproach. Forexample,theperimeterofarectangleis54cm.Itslengthis6cm.Whatisitswidth?

7.EE.4.B--Solvewordproblemsleadingtoinequalitiesoftheformpx+q>rorpx+q<r,wherep,q,andrarespecific rationalnumbers.Graphthesolutionsetoftheinequalityandinterpretitinthecontextoftheproblem.

Forexample:Asasalesperson,youarepaid$50perweekplus$3persale.Thisweekyouwantyourpaytobeatleast $100.Writeaninequalityforthenumberofsalesyouneedtomake,anddescribethesolutions.

____________________________________________________________________________________________________________________________________________________________________________________ KhanAcademy:https://www.khanacademy.org/commoncore/grade-7-EE#7.EE.B.4

https://www.khanacademy.org/commoncore/grade-7-EE#7.EE.B.4a https://www.khanacademy.org/commoncore/grade-7-EE#7.EE.B.4b


inadditiontoproceduralmasteryoftheskill. ____________________________________________________________________________________________________________________________________________________________________________________ NOTES: AndDon’tCallMeAfterMidnight!

(AdditiveInverse) 1. DistributiveProperty 2. CombineLikeTerms 3. Movevariabletooneside 4. UndoanyAddition/Subtraction 5. UndoanyMultiplication/Division

*Changesubtractiontoadditiveinverse(“addtheopposite”) *Eliminatefractionsbymultiplyingeverythingbythedenominator


https://www.khanacademy.org/commoncore/grade-7-EE#7.EE.B.4

https://www.khanacademy.org/commoncore/grade-7-EE#7.EE.B.4a

https://www.khanacademy.org/commoncore/grade-7-EE#7.EE.B.4b

WEEK7 ____________________________________________________________________________________________________________________________________________________________________________________

7.EE.4-ConstructEquations&InequalitiestoSolveProblems ____________________________________________________________________________________________________________________________________________________________________________________ SKILLPRACTICE Equations


WEEK7 ____________________________________________________________________________________________________________________________________________________________________________________

7.EE.4-ConstructEquations&InequalitiestoSolveProblems ____________________________________________________________________________________________________________________________________________________________________________________ SKILLPRACTICE Inequalities


WEEK7 ____________________________________________________________________________________________________________________________________________________________________________________

7.EE.4-ConstructEquations&InequalitiestoSolveProblems ____________________________________________________________________________________________________________________________________________________________________________________ STANDARDPRACTICE 1.Atthezoo,thereare3fewerferretsthantwice thenumberoftigers.Ifthereare21ferrets, what’sanequationforthenumberoftigersat thezoo? 2.Jennaboughtenoughlattesforallherfriends. Eachlattewas$3.50andshegavethebarista a$20bill,whothengaveherback$2.50in change.Writeanequationmodelingthis,with xasthecostperlatte.Howmanylattesdidshe buy? 3.Theperimeterofasquareis15feet.What’s anequationforfindingthelengthofoneofits sides(s)?Howlongiseachside? 4.Yvettecanspendnomorethan$100atherlocal armorythisweek.Shespends$35onpotionsandwants tospendtherestonswords.If eachswordcosts$5,writeaninequalityforthe numberofswordsshecanbuy. 5.Barbaramade$310.05thisweek,andshe’s readytospenditall.Shebuys45kittensand stillhas$3.60leftover.Howmuchwaseach kitten?Whatequationdidyouusetosolve this?

6.Solve50x−18<7andgraphthesolutionona numberline. 7.IfJohnbuys8jacketsatxdollarsapieceand2 movieticketsat$11apiece,what’sthemosthe canspendoneachjacketifhistotalbudgetis $200? 8.Laurasellsusedcars,andshereallyneedsto makeatleast$1055atherjobthismonthto coverherbills.Ifshegetsamonthlysalaryof $600,plus$45.50foreachcarshesells,what’s aninequalitythatshowsthis?Willshebe okayifshesells8cars? 9.Thesumofthreeconsecutiveoddnumbersis 21.What’sanequationrepresentingthis? 10.Usingtheinformationfromthepreviousproblem, whatarethethreenumbers?


WEEK7 ____________________________________________________________________________________________________________________________________________________________________________________

7.EE.4-ConstructEquations&InequalitiestoSolveProblems ____________________________________________________________________________________________________________________________________________________________________________________ PRACTICEQUIZ

1. IsBenny’sargumentreasonable?Explainwhyorwhynot.

2. DeterminethenumberofpeopleforwhichGutterGuysislessexpensivethanStrikeForce.Setupequationsor inequalitiesbasedontheinformationprovidedandthensolvetheproblem.Showallofyourwork.

3. InterpretyoursolutionfrompartCintermsofthecontextoftheproblem.WhenisGutterGuysthebetterdeal? WhenisStrikeForcethebetterdeal?WhichbowlingalleycostslessforBenny’sparty?


WEEK8 ____________________________________________________________________________________________________________________________________________________________________________________

DailyMemorization 7.NS.2-RationalOperationsMultiplication&Division

MultiplyandDividewithnegatives INCLUDINGDECIMALS&FRACTIONS

KhanAcademy:https://www.khanacademy.org/commoncore/grade-7-NS#7.NS.A.2

____________________________________________________________________________________________________________________________________________________________________________________ PracticeofMultiplication/DivisionwithRationalNumbers(fractions/decimals)



WEEK8 ____________________________________________________________________________________________________________________________________________________________________________________

7.NS.1-Add/SubtractRationalNumbers Apply&extendpreviousunderstandingsofadditionandsubtractiontoadd&subtractrational numbers;representaddition&subtractiononahorizontalorverticalnumberlinediagram.

7.NS.1.A-Describesituationsinwhichoppositequantitiescombinetomake0.Forexample,ahydrogenatomhas0chargebecause itstwoconstituentsareoppositelycharged. 7.NS.1.B-Understandp+qasthenumberlocatedadistance|q|fromp,inthepositiveornegativedirectiondependingonwhether qispositiveornegative.Showthatanumberanditsoppositehaveasumof0(areadditiveinverses).Interpretsumsofrational numbersbydescribingreal-worldcontexts. 7.NS.1.C-Understandsubtractionofrationalnumbersasaddingtheadditiveinverse,p-q=p+(-q).Showthatthedistancebetween tworationalnumbersonthenumberlineistheabsolutevalueoftheirdifference,andapplythisprincipleinreal-worldcontexts. 7.NS.1.D-Applypropertiesofoperationsasstrategiestoadd&subtractrationalnumbers.Usevariablestorepresentquantitiesina real-worldormathematicalproblem,&constructsimpleequations&inequalitiestosolveproblemsbyreasoningaboutthequantities.

7.NS.2-Multiply/DivideRationalNumbers Applyandextendpreviousunderstandingsofmultiplicationanddivisionandoffractionsto

multiplyanddividerationalnumbers. 7.NS.2.A-Understandthatmultiplicationisextendedfromfractionstorationalnumbersbyrequiringthatoperationscontinueto satisfythepropertiesofoperations,particularlythedistributiveproperty,leadingtoproductssuchas(-1)(-1)=1andtherulesfor multiplyingsignednumbers.Interpretproductsofrationalnumbersbydescribingreal-worldcontexts. 7.NS.2.B-Understandthatintegerscanbedivided,providedthatthedivisorisnotzero,andeveryquotientofintegers(withnon-zero divisor)isarationalnumber.Ifpandqareintegers,then-(p/q)=(-p)/q=p/(-q).Interpretquotientsofrationalnumbersbydescribing real-worldcontexts. 7.NS.2.C--Applypropertiesofoperationsasstrategiestomultiplyanddividerationalnumbers. 7.NS.2.D--Convertarationalnumbertoadecimalusinglongdivision;knowthatthedecimalformofarationalnumberterminatesin 0soreventuallyrepeats.

7.NS.3-SolveRationalOperationsinContext Solvereal-worldandmathematicalproblemsinvolvingthefouroperationswithrationalnumbers.

Computationswithrationalnumbersextendtherulesformanipulatingfractionstocomplexfractions. ____________________________________________________________________________________________________________________________________________________________________________________

KhanAcademy:https://www.khanacademy.org/commoncore/grade-7-NS ____________________________________________________________________________________________________________________________________________________________________________________

Reminder:Youmustdemonstratefullconceptualunderstandingofthestandard inadditiontoproceduralmasteryoftheskill.

____________________________________________________________________________________________________________________________________________________________________________________ NOTES:


https://www.khanacademy.org/commoncore/grade-7-NS

WEEK8 ____________________________________________________________________________________________________________________________________________________________________________________

7.NS.3-SolveRationalOperationsinContext ____________________________________________________________________________________________________________________________________________________________________________________ SKILLPRACTICE

1. Determinethedifference. a.2–6 b.2–(-6) c.-2–6 d.-2–(-6)

a. a+1 b. b+(-1) c. a+(-2) d. a+(-a) e. a+b

3.Evaluate,thendescribeyourstrategyforcalculatingdifferencesinproblemsinvolvingdecimals.

a.2–6.3 b.2–(-6.3)

4.Louiseclaimsthatsubtractinganegativenumberisequivalenttoaddingthatnumber.For example,2.3–(-4)=2.3+4.DoyouagreewithLouise?Justifyyourresponsemathematicallyusing apictureoranumberline. 5.Decidewhetherthefollowingexpressionsareequal.

a.-4–12=12–(-4) b.3–10=10–3

c.5–(-2)=-2–5 6.Isitpossiblefora–btoequalb–a?Explainyourreasoning.


WEEK8 ____________________________________________________________________________________________________________________________________________________________________________________

7.NS.3-SolveRationalOperationsinContext ____________________________________________________________________________________________________________________________________________________________________________________ STANDARDPRACTICE

1) Atnoonthetemperaturewas-3°C.Overthenextfourhoursthetemperaturedropped another15degrees.Theneveryhouruntil7:00thetemperaturerose2degrees.Whatwasthe temperatureat7:00?

2) Paigewasplayingatriviagamewhereyougainedpointsforcorrectanswersandlostpoints forincorrectanswers.Atthestartofround3shewasat-700points.Duringtheroundshe answeredeight400pointquestionscorrectandsheanswerednine600pointsquestions incorrect.Whatwasherscoreattheendoftheround?

3) Racheland4friendsweregoingtothemovies.Eachticketcost$11andthentheybought2 popcornsat$3.5apieceandtheneachpersonboughttheirownsodaat$3.75each.How muchmoneydidtheyspendtotalfortheirtriptothemovies?

4) Arestaurantchefwasorderingsupplies.Heordered4poundsofbeefat9.25perpound,6 poundsofpotatoesat$6.96apoundand5poundsofcarrotsat$9.81perpound.He estimatesthatthiswillmake28meals.Ifhecharges48.32permealhowmuchprofitwillhe make?


WEEK8 ____________________________________________________________________________________________________________________________________________________________________________________

7.NS.3-SolveRationalOperationsinContext ____________________________________________________________________________________________________________________________________________________________________________________ PRACTICEQUIZ

1) Suzygetsontheelevatoronthegroundfloor.Shegoesup3floors,down2floors,up7 floors,up2floors,down5floorsandup8floors.Whatfloorissheon?

2) Mt.Everest,thehighestelevationinAsia,is29,028feetabovesealevel.TheDead Sea,thelowestelevation,is1312feetbelowsealevel.Whatisthedifferencebetweenthese twoelevations?

3) Asubmarinewassituated800ftbelowsealevel.Ifitascends250ft,descends300ftand ascends75ft,whatisitsnewposition?

4) ThehighestrecordedtemperatureonEarthis136℉.Thelowestis−129℉.Whatisthe differencebetweenthesetemperatures?

5) Acompanyhasaprofitof$150aweekfor9weeks.Itthenhasalossof$65aweekfor25 weeks.Attheendof34weekswhatisthecompany’sprofitorloss?


PRACTICEQUIZ ____________________________________________________________________________________________________________________________________________________________________________________

DailyMemorization--Weeks4-8 7.NS.1-Add/SubtractRationalNumbers 7.NS.2-Multiply/DivideRationalNumbers

____________________________________________________________________________________________________________________________________________________________________________________ a)2+(−7)=__________ b)0−(−4)=_________ c)56÷(−8)=__________ d)−63÷9=__________ e)-5×-6=__________ f)60÷(-10)=__________ g)-9–(-10)=__________ h)-7×-8=__________ i)56÷-8=__________ j)7+(-8)=__________


ANSWERKEY#1 ____________________________________________________________________________________________________________________________________________________________________________________

Skill/StandardPractice+DailyMemorization ____________________________________________________________________________________________________________________________________________________________________________________ WEEK1//6.NS.3

SKILL Add 1)5.7 2)15.5 3)11.72 4)262.191 5)107.197 Subtract 1)4.1 2)12.9 3)1.79 4)28.84 5)22.092 Multiply 1)0.72 2)0.635 3)67.2 4)0.01488 5)28.32 Divide 1)0.8 2)0.25 3)6.85 4) 0.31 5)120

STANDARD 1)Multiply $6.45 2)Subtract 1.54miles 3)Add 15.7764km 4)Divide 4.4pounds 5)Add,thenSubtract $24.85 6)Divide,thenround 40DVDs(cost$40.46) 7)Multiply,thenAdd $11.63total(2boats=$7.76and3balls=$3.87) 8)Add,thenSubtract $38.95left

WEEK2//5.NF.1 SKILL

1) 320

2) =455 3 1 4

3

3) =67 1 6

1

4) =455 3 1 4

3

5) =2435 1 24

11

6) =861 7 8

5

7) 1413

8) =1138 3 5

11

STANDARD 1) 24

13

2) =1239 3 4

1

3) =1522 1 7

15

4) 6029

WEEK3//6.EE.1 SKILL

WholeNumbers 1)51 2)66 3)81 4)8

WholeNumberswithExponents 5)79 6)54 7)25 8)66

IntegerswithExponents 9)-66 10)-36 11)-53 12)46

RationalNumberswithExponents 13)-14.7 14)-77.63 15) 6

1 16) 750

WEEK4//DailyMemorization//7.NS.2Multiply/DivideIntegers


WEEK4//7.SP.3 SKILL

Q12)C Q4)Top:CompanyCMiddle:CompanyABottom:CompanyB

STANDARD Q10)a.Greaterthanb.Lessthan Q2)5

WEEK5//DailyMemorization//7.NS.1Add/SubIntegers

WEEK5//7.SP.4

SKILL Q1)Median=75Range=45 // Q18)Mean=52MAD=15 STANDARD Q4)a.Mitch’sclass/b.Bothclassesthesame/c.Can’ttellfromthisgraph Q11)D

WEEK6//DailyMemorization//7.NS.1Add/SubtractIntegers

WEEK6//7.EE.1

SKILLPRACTICE Add/Subtract

1) 8x+3 2) x2+8 3) 2x+3 4) 12x-2 5) p+12 6) -n+5 7) -15r+1 8) 6r-13

FactorExpressions 9)6(x+4) 10)4x(2x−1) 11)2xy(3+5x) 12)m2(m2−3) 13)2x(3x+4+6y)

Expand/Simplify 15)-28x-11 16)-10+2n 17)45b-56 18)2p-1 19)-11+20n 20)-5k+56 21)8-21b 22)-53+40

STANDARDPRACTICE 1) 3x-4y 2) a=-6b=48 3) d e 3 6 + 6

4) x 85 6 2

1


WEEK7//DailyMemorization//7.NS.1Add/SubtractRationalNumbers 1)-0.8 2)-15.5 3)4.6 4) 7

125) =4

13 3 41 6) =9

17 1 98 7)4

8)8.8 9)0.5 10) 524 11) =28

29 1 128 12)-3.4 13) =5

26 5 51 14)-9.1

WEEK7//7.EE.4 SKILL

Equations 1) a = 1 98 2)x=1 3) x = 1 9

114)k=5

5) 2 m = 1 6)m=-8 7) r = 7112 8)x=-6

Inequalities 1) closeddot,shadedleft. n ≤ 5 2) opendot,shadedright x > 9

3) closeddot,shadedleft y ≤ 9 4) closeddot,shadedright x ≥ 5

5) opendot,shadedright*whenyoumultiply/dividebyanegativeyoufliptheinequality* x > 8

STANDARD 1)2t−3=21 2)20−3.5x=2.5,whichmeansx=5lattes. 3)equation:4s=15,sos=3.75ft 4)inequality:5s+35≤100,ors≤13 5)equation:45k+3.6=310.05,eachkittencost$6.81 6)Thesolutionisx<0.5(opendot,shadeleft) 7)Nomorethan$22.25perJacket($22.25orless) 8)inequality:45.5c+600≥1055,soc≥10.Thatmeanssheneedstosellatleast10

cars,so8won’tquitegetherenoughmoney. 9)Oddnumbersincreaseby2everytime,soourequationisx+(x+2)+(x+4)=21,or

3x+6=21,wherexisthefirstnumber. 10)Thenumbersare5,7,and9.

WEEK8//DailyMemorization//7.NS.2Multiply/DivideRationalNumbers 1)26.785 2)−3.57 3)−0.32 4)−5.27 5)33.12 6)68.7648 7) = 5

27 5 52 8) 9

209) = 5

12 2 52 10) = 7

12 1 75 11) 25

24 12) 98

WEEK8//7.NS.3 SKILL 1a)-4 1b)8 1c)-8 1d)4 2a)negative 2b)positive 2c)negative 2d)equaltozero(additiveinverse) 2e)positive 3a)-4.3 3b)8.3 4)Yesthisistrue.Youchangesubtractiontoaddtheopposite,andtheoppositeofanegative numberisapositivenumber.Onanumberlineyouwouldtakeawayanegativeamount, whichisthesameasgettingpositiveback.

5a)no 6 = 6) ( 1 / 1 5b)no = ) ( 7 / 7 5c)no = ) ( 7 / 7

6)Itisonlypossiblewhenbothaandbareequal .a ) ( = b Forexample,ifa=5andb=5then5-5=0and5-5=0. Howeveritotherwiseisnottrueasorderissignificantinsubtraction.

STANDARD 1)-3+(-1×15)+((7-4)×2)=451.52 2)-700+(8×400)+(9×600×-1)=-12 3)(11×(4+1))+(2×3.5)+(3.75×(4+1))=-2,900 4)=11,225.15


ANSWERKEY#2 ____________________________________________________________________________________________________________________________________________________________________________________

PRACTICEQUIZZES ____________________________________________________________________________________________________________________________________________________________________________________ WEEK1//6.NS.3

1.Divide.Goldpricein2010isabout34timesthepricein1974. 2a.Add.0.298oz 2b.Multiply.$10.73 2c.Subtract.$354.18

WEEK2//5.NF.1 1. 8

7 2.Babyby ofaday110 3. 1

12 4.45times WEEK3//6.EE.1

1)-1 2)-27.72 3) 2 920

4) 3 83

WEEK4//7.SP.3 Q8)B

WEEK5//7.SP.4 Q7)B,C,F

WEEK6//7.EE.1 1. -2x-7y+2 2. -8x+3 3. 14a-2 4. -6a-35b+48c

WEEK7//7.EE.4 Asamplelevel4responsefollows.

Part1:"Benny'sexpressionsworkaslongasyouaretalkingabout20ormorepeople.ButGutterGuyscharges a$200flatrateforupto20people,sothemodeldoesnotalwayswork.Benny'sconclusionisaboutfewerthan 20people,butthemodelisnotcorrectforthatmanypeople.Also,Bennymademistakesinhiscalculations,so hisconclusionisbasedonfaultymathematicalreasoning.Ironically,ithappenstobetruethatGutterGuysis lessexpensivefor18people,because200<80+8(18)=80+80+64=224."

Part2,sampleresponse: "Acompletesolutionneedstwoinequalities,oneforwhenx<20andoneforwhenx>20.

Whenx≤20:200<80+8x→120<8x→15<x. Whenx>20:200+10(x–20)<80+8x→200+10x–200<80+8x→10x<80+8x→2x<80→x<40.

GutterGuysislessexpensivefor15<x<40.Toconfirm,dosometestcases..

Part3,sampleresponse:"GutterGuysisthebetterdealformorethan15peopleandfewerthan40people. StrikeForceisthebetterdealformorethan40peopleorfewerthan15people.SinceBennyisinviting18 people,and18isgreaterthan15butlessthan40,GutterGuyscostslessforBenny'sparty."

WEEK8//7.NS.3 1)3+(-2)+7+2+(-5)+8=13thfloor 2)29,028−(-1312)=30,340ft 3)-800+250+(-300)+75=−775ft 4)136−(-129)=265℉ 5)150(9)+(-65)(25)=−275socompanyhadalossof$275


ANSWERKEY#2 ____________________________________________________________________________________________________________________________________________________________________________________

PRACTICEQUIZZES DailyMemorization

____________________________________________________________________________________________________________________________________________________________________________________ MEMORIZATIONWEEKS1-3//PDFs MEMORIZATIONWEEKS4-8//Operationsw/Negatives


Prerequisite Level Skills List...6.NS.3 Decimal Division × When there is a decimal in the divisor,...

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Transcript of Prerequisite Level Skills List...6.NS.3 Decimal Division × When there is a decimal in the divisor,...