foundations for algebra winter student enrichment...
TRANSCRIPT
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Foundations for Algebra
Winter Student Enrichment Packet
Detroit Public Schools Community District Department of Curriculum and Instruction
Office of Mathematics
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NOTE TO THE STUDENT
This Winter Student Enrichment Packet has been compiled to complement middle school mathematics classroom instruction aligned to the Michigan Standards for Mathematics. The packet is intended to be used for review and practice of previously taught and new concepts. We strongly encourage you to work diligently to complete the activities for the choice board. You may experience some difficulty with some activities in this packet, but we encourage you to think critically and creatively and complete them to the best of your ability.
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FoundationsforAlgebraWinterEnrichmentChoiceBoard:Three‐CourseMeal
Completethespecifiednumberofappetizers,maindishes,anddessertsasindicatedbelow.
Appetizers(Select2)
Identifyifthegivenfunctionislinearornonlinear.Classifythesolutionstolinearequationsashavingonesolution,nosolution,orinfinitelymanysolutions.Solveeachinequalityandgraphitssolution.
MainDishes(CompleteAll)
Writeequationsinslope‐interceptformgivengraphsofthelinesonthecoordinategrid.Equationsandfunctionsmixedpractice.Writeasystemofequationstomatchareal‐worldsituation.
Desserts(Select1)
PuzzleTime:Solvethesolutionofthesystemsofequationsusingmultiplicationwiththeadditionmethod(equationsarenotnecessarilyinstandardform).
CrosswordPuzzle:Solvethepuzzleinrelationtolinearfunctions.
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Appetizer1:IdentifyingLinearorNonlinearFunctionsDirections:Identifyifthefunctionislinearornonlinear.Writetheletterofyouranswerintheappropriateboxbelow.
N.Thegraphshowsafunction. R.Thegraphshowsafunction.IsthefunctionIsthefunctionlinearornonlinear?linearornonlinear?O.Isthefunctiony=3x+2 Y.Isthefunctiony=–8linearornonlinear?linearornonlinear?
B.Isthefunction 6 E.Thetableshowsafunction.
linearornonlinear?Isthefunctionlinearornonlinear? R.Thetableshowsafunction.Isthefunctionlinearornonlinear?
T.Thegraphshowsafunction.Isthe
functionlinearornonlinear?
D.Isthefunction √
linearornonlinear?
Linear
Nonlinear
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Appetizer2:ClassifyingSolutionstoLinearEquationsDirections: 1.Putacheck()markontheblankbeforetheitemnumberiftheequationhasonesolution.2.Putanmarkontheblankbeforetheitemnumberiftheequationhasnosolution.3.Putapound(#)markontheblankbeforetheitemnumberiftheequationhasinfinitelymanysolutions.
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______1.6x–3=5x+5
______2.8x–3=8x+5
______3.3x–3=–3+3x
______4.11x–2x+15=8+7+9x
______5.3(x–14)+1=–4x+5
_______6.–3x+32–7x=–2(5x+10)
______7.21(8x+26)=13+4x
______8.18x+21=6(3x+25)
______9.8–9x=15x+7+3x
_____10.5(x+9)=5x+45
_____11.6x+1=1+6x
_____12.–2x–4=–2x+4
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Appetizer3:SolvingInequalitiesandGraphingSolutions
Directions:Solveeachinequalityandgraphitssolution.Showyourwork. Graphofsolution
1.18≥3x +8 1.
2.x–2x+3>6 2.3.–4+3x –8 3.4.–4x–6 –18 4.5.28 3–5x 5.
6.32 x+7 –3 6.
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MainDish1:WritingEquationsinSlope‐InterceptForm Directions:Writetheequationofthelineshownineachgraphinslope‐interceptform.Notethat
eachgridlineisequivalentto1unit.Writeeachanswerintheblank.1.______________________________2.__________________________3._____________________________
4.______________________________ 5.__________________________ 6.____________________________
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MainDish2:EquationsandFunctionsMixedPractice
MultipleChoice:Circlethecorrectansweroranswersforeachproblem.1.WhichofthefollowingcouldNOTbethegraphofafunction?Selectallthatapply.
a. b. c. d.
2.Worriedaboutgoingoverhisstoragelimit,Kennethmonitoredthenumberofundeletedvoicemailmessagesstoredonhisphoneeachday.
Accordingtothegraph,whatwastherateofchangebetweenThursdayandFriday?
a. –3voicemailmessagesperday
b. –2voicemailmessagesperday
c. 3voicemailmessagesperday
d. 2voicemailmessagesperday
3.ThisgraphshowshowthetotalnumberofstampsMariahasinhercollectionisrelatedtotheamountofmoneyshespendsonadditionalstamps.
With$60tospendonnewstamps,howmanytotalstampscanMariahaveinhercollection?
a.60stamps b.20stampsc.80stamps d.50stamps
4.Cristellestartedmakingthistableofvaluestoshowtherelationshipbetweenthenumberofscarvesshesells,x,andtheprofit,y,indollars,sheearnsinherbusiness.
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x 1 2 3 4 5y ? –110 –90 –70 –50
Whatisthemissingvalueinthistable? a.–100 b.–120 c.–130 d.–1505.Staceyenteredtheamountshechargedonhercreditcardeachmonthintoaspreadsheet.
Accordingtothetable,whatwastherateofchangebetweenAprilandMay?
a.–$8permonthb.$8permonthc.$150permonthd.–$150permonth6.Howistheequationy=‐4x+1writteninfunctionnotation? a.f(x)=–4f+1 b.f(x)=–4x+1 c.f(x)=–4y+1 d.f(x)=–4f(x)+17.Sophiawalksataspeedof2.5milesperhour.Whichequationmodelsthisunitrate? a.x=2.5y b.x=2.5+y
c.y=2.5x d.y=2.5+x8.Whichnumberlinebelowcorrectlyshowsthesolutionsetfortheinequality 4 16x ?a. b.
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c.d.
9.TriangleMNPissimilartotriangleQRS. Whichsideshavethesameslope? a. and b. and c. and d. and
10.Whatisthesolutiontothesystemofequationsshownonthisgraph?
a.(1,4) b.(–1,4) c.(4,1) d.(4,–1)
11.Inspectthesystemofequationsshownbelow.
3 12 6 2
Howmanysolutionsdoesthissystemoflinearequationshave?a.0 b.exactly2c.exactly1 d.infinitelymany
12.Staceywantstographthissystemofequations:
3 4
2 3 6
Whichchoicebelowshowshowsheshouldrewritetheseequationsinslope‐interceptform?
a.3 4
2 b.3 4
3
c.3 4
2 d.3 4
3
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MainDish3:WritingSystemsofEquationsSystemsofequationscanbeusedtorepresentmanyreal‐worldsituations.AnexampleofsystemsofequationsappliedinaUniformMotionProblemisshownbelow.Problem:Flyingwiththewind,aplanecanfly750milesin3hours.Againstthewind,theplanecanflythesamedistancein5hours.Writeasystemofequationstorepresentthesituation.
Strategy1.Chooseonevariabletorepresenttheplaneinacalmconditionandasecondvariabletorepresent
therateofthewindorcurrent. let p=therateoftheplaneincalmair w=rateofthewindsothat p+w=rateoftheplanetravelingwiththewind p‐w=rateoftheplanetravelingagainstthewind2. Usetheexpressionsfromstep1,aswellasthetimetraveledwithandagainstthewind,toget
expressionsforthedistancestraveledwithandagainstthewind.Recall:Rate Time Distance isusedtodeterminetheexpressionforthedistancetraveled.Organizethedatainatable.
Trip Rate Time = Distance
Withthewind =
Againstthewind =
3. Writeasystemofequationsthatmodelstheproblem.
Trip Rate Time = Distance
Withthewind (p+w) 3 = 750
Againstthewind (p–w) 5 = 750
So,thesystemofequationswouldbe:3 7505 750
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WritingSystemsofEquationsActivity
Directions:Writeasystemofequationstorepresenteachsituationthatcouldbeusedtodeterminetheanswertothequestionintheproblem.Donotfindthesolutiontothesystem.
1. Flyingwiththewind,anairplanemadea708‐miletripin3hours.Flyingagainstthewindtomakethesametrip,theplanetook4hours.Whatisthespeedofthewindandhowfastwouldtheplanetravelinstillair?
2. Afieldgoalis3pointsandtheextrapointafteratouchdownis1point.Tobegintheseason,akickersuccessfullymadeatotalof30kicksforatotalof56points.Howmanyfieldgoalsandhowmanyextrapointsdidthekickermake?
3. Arestauranthasonepriceforadultsandanotherpriceforchildrentoeatatitsbuffet.Twofamiliesateatthebuffet.TheTraymorefamilyhastwoadultsandthreechildrenandtheirbillwas$49.50.TheWillisfamilyhasthreeadultsandonechildandtheirbillwas$44.50.Whatisthecostforanadulttoeatatthebuffetandwhatisthecostofachildtoeatatthebuffet?
4. Astudentissellingpizzasfor$6andsubsandwichesfor$4forafundraiser.Thestudentsold13moresubsandwichesthanpizzasandcollectedatotalof$262.Howmanypizzasandhowmanysubsandwichesdidthestudentsell?
5. Thelibraryishavingabooksale.Hardcoverbooksaresellingfor$5eachandpaperbackbooksaresellingfor$3each.Mrs.Smithspent$51tobuy13books.HowmanyofeachtypeofbookdidMrs.Smithpurchase?
6. Atastore,allshirtsarepricedthesameandalljeansarepricedthesame.Amyboughtfourshirtsandthreepairsofjeansfor$150.Briannaboughtoneshirtandtwopairsofjeansfor$70.Whatisthecostofashirtatthestore?Whatisthecostforapairofjeansatthestore?
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Dessert
1 PuzzleTime(AdaptedfromAlgebrawithPizzazz!)
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Dessert2LinearFunctionsCrosswordPuzzle
Across:
3.The__________linetestthatallowsyoutodiscovervisuallywhetherarelationisafunction.
5.Thefirstcoordinatesinasetoforderedpairs.
7.Asetoforderedpairs.
8.Anorderedpairthatmakesanequationwithtwovariablestrue.
9.Amathematicalphrasethatusesvariables,numbers,andoperations.
10.Theratioofriseoverrun.
Down:
1.Arelationshipinwhicheachmemberofthedomainispairedwithexactlyonememberofthe
range.
2.A(n)________________equationisanequationwhosegraphisaline.
4.Amathematicalsentencewithanequalsign.
6.Aletterstandsforanumber.
7.Thesecondcoordinatesinasetoforderedpairs.