7thMath:Entering8th2017SummerPracticePart1:SUNGLASSESCalculatorsokayifnecessaryWhodoesn'tliketowearsunglassesinthesummer?Thinkaboutthemathinvolvedinthedesign,construction,andbusinessofmakingandsellingasimplepairofsunglasses.Acompanyneedstothinkaboutfashion,materials,eyeprotection,sizing,advertising,andofcoursethebottomline.Thinkaboutbuyingsunglassesandhowmuchtheycost.Completetheseproblemsbythepoolwithyourcoolestpairofshades.1.)Supposethat1/3ofthepopulationofthecityofTulsabuysnewsunglassesinJuneand1/8ofthosepeoplebuyapairofblackRay-Bans.a.)WhatfractionofthepopulationbuystheblackRay-Bans?b.)FindthepopulationofthecityofTulsa.UsethefractionstofindhowmanypeoplebuynewsunglassesinJuneandhowmanybuytheblackRay-Bans.Thinkhowtosensiblyexpressyouranswer;itrepresentsnumbersofpeople.

PopulationofTulsa:

Numberofsunglassbuyers: NumberofRay-Banbuyers:2.)Sunglassescomeindifferentsizes,andtherearedifferentpartstomeasure.Chooseapairofsunglassesatyourhouse.Measureseveralofthedimensionsofthesunglassesininchesandfractionsofaninchtothenearestfourth.(Forexample,3¼inches).Makeyourownsketchofthesunglasseswithlabeleddimensionsorjustlabelthissketch.(Whichdimensions,youmayask.Uptoyou.Whichdimensionsmakesensetomeasure?)Your6year-oldcousinwantsapairjustlikeyours,buttheyneedtobethree-fourthsthesize.Whatwouldthosedimensionsbe?Makeasketchlabelingthesmallerdimensions.

3.)Evensmallchangesindesigncanmakebigchangesintheamountofmaterialusedinmanufacturing.Adesignchangesavesacompany0.32gramsofplasticperpairofsunglasses.Howmuchplasticwouldbesavedin5yearsif25,000pairsofsunglassesweremanufacturedeachyear?Showthinking,ofcourse.4.)AstyleofsunglassesdesignedintheUSisgoingtobemanufacturedinEurope.MachinesintheUSuseinchesanddecimalfractionsofinches.MachinistsinEuropeusethemetricsystem,sothedesigndimensionsmustbechanged.Converteachmeasurementtomillimeters.Thinkbeforeyoudothisproblem.Whatconversionfactordoyouneed?Showyourthinking;no"one-number"answersintheboxes,please.Partmeasured Measurement

(ininches)Measurement(inmillimeters)

a.)Lenssize 2.5in.by2in.rectangle

b.)Temple-to-ear 7.12inches

c.)Pupil-to-pupil 2.84inches

5.)a.)Pleasewatchthisshortvideoanddescribethesituationitshows.http://threeacts.mrmeyer.com/doublesunglasses/act1/act1.movb.)Whatquestiondoyouhave?Writeyourquestionclearlyandcompletely.c.)Answeryourquestion;showyourthinking.6.)Asunglassescompanyearns64centsprofitoneach$1insales.Howmuchprofitdotheymakeon$2.5millioninsales?Showyourproportion.(Makesuretowrite2.5millioncorrectly!)

7.)Somedesignsaremoredifficulttomanufacturethanothers,whichmaymeanstherearemorerejectsfromthemanufacturingprocess.(Rejectsareproductsthatdonotpassinspectionsandcannotbesold.)Supposeacompanysetsalimitof7%rejectsonmanufacturing.Onemonththeyproduce16,000sunglasses;thereare1240rejects.Tellwhetherornottheyexceededthelimit;supportyouranswer.8.)Thistableshowsresultsofasurveyonproductpreferenceforfourdifferentstyles,with41%ofthosesurveyedchoosingnottobuyanyofthefourstylesshown. StyleA

StyleB StyleC StyleD

Percentofpeoplewhopreferthestyle

12% 8% 24% 15%

Numberpeopleoutof50,000whowouldbuythestyle

Profitonstyleperpairsold

$10 $12 $4 $8.50

Totalprofitonstylegivennumbersold.

9.)TheseOakleysunglassesareonsale!Whatisthepercentdiscount?Showthinking.

10.)Ibuyacoolpairofsunglassesfor$25.95.Salestaxis8.5%.Whatistheamountoftax?HowmuchdoIpayintotal?Showthinking. 11.)Lastyear,thesunglassesIlikedcost$25.50.Thisyear,theycost$29.00.Whatisthepercentincreasefromlastyeartothisyear?Roundtonearesttenthofapercent,please.Remember,percentchangeistheratio(new-old)/old. 12.)Thisgraphicshows%markupsforsometypesofdesignerfashion.(http://www.businessinsider.com/products-high-markups-2014-7)Eyeglassframeshaveaverylargemarkup-muchhigherthanmarkupsweusedinproblemswedidinclass.Usethegraphictoanswerthesequestions.a.)Writethemarkup%foreyeglassframesasadecimal.b.)Supposeitcosts$7.50tomanufactureapairofframes.Findtheamountofmarkup. Remember?markupamount=cost*percentofmarkupc.)Findthesellingpricebyaddingthemarkupamounttothecost.d.)Thispricedoesnotevenincludelenses!Doyouthinkdesignersunglassesareworthit?Tellwhyorwhynotinatleasttwocompletesentences.

13.)Whatistheareaofacircularlenswitharadiusof2.5centimeters? Whatlengthofwirewouldbeneededtogoaroundonelens? Showthinking,ofcourse!14.)CompanyresearchshowssalesofStyleAtoStyleBaretypicallyina2:5ratio.TheTulsastoresells2450pairsthismonth,andthestore'ssalesfollowthetypicalstyleratio.a.)Fillinthetabletoshowhowmanyofeachstylesold.Style Ratio TulsaStoreSales

A

B

TOTAL

b.)TheOKCstoreclaimstheircustomerslikeaviatorglasses(styleA)waymorethanpeopleinthetypicalstore.Theysold1200pairsofStyleAand1600pairsofStyleB.Dothesenumberssupporttheclaim?Supportyouranswerwithratiothinking.15.)a.)Amanufacturersellssunglassestodepartmentstoresatapriceof$10each,andeachpaircosts$2.48tomanufacture.Whatistheamountofprofitforthemanufacturerperpairofsunglasses?(Note:profitisrevenueminuscost)b.)Themanufacturerspent$220,000inthedesignprocessandplanstospend$750,000inadvertising.Basedontheprofitforeachpaircalculatedinparta,howmanypairsofsunglasseswouldthecompanyhavetosellinordertorecoverthoseinitialcosts?

16.)ThewordSUNGLASSESiswritteninarow8timeslikethis:SUNGLASSESSUNGLASSESSUNGLASSESSUNGLASSESSUNGLASSESSUNGLASSESSUNGLASSESSUNGLASSESThenthatrowofwordsisrepeated120timesaroundthegym.Worksmarter,nothardertoanswerthesequestions.Whatfractionofthelettersarevowels(insimplestform)? WhatpercentofthelettersistheletterS?17.)Thisscatterplotshowsadvertisingdollarsandsalesforabigsunglasscompany.Whichistheindependentvariable? _______________

Whichisthedependentvariable? ________________

Advertisingspendingof$250,000,helpstogeneratehowmuchinsales?________

Writeonesentencedescribingtherelationshipbetweenspendingonadvertisingandsales.

SunglassSales

7thMathEntering8th2016SummerPracticePart2:SkillsNOCalculators,Please.Showallthinkingandwork.Circleanswers,please.SignedNumbers/FractionsFind the sum or difference: 1.) -58 + 82 2.) -64 + 37 3.) -14 + 9 4.) 5 - (-25) 5.) -5 - (-25) 6.) 6 - 28 7.) -14 + (-9) 8.) 15 + (-42) 9.) -15 + 42 10.) 27 + (-27) 11.) -27 - 27 12.) -27 - (-27) 13.) Circle the problem with a negative sum. Think; do not calculate. a.) -8.5 + 9.73 b.) -9 + -1.5 c.) 30 + (-9.2) 14.) Circle the problem with a different answer than the others. Think; do not calculate. a.) 26.6 - 80 b.) 80 - 26.6 c.) 80 + (-26.6) 15.) Show on a number line. Clearly show the start place, what direction you moved, and the ending place. a.) -3 + 6 b.) -2 - 3

16.) Find the product: a.) −47 ∙ 5.8 b.) −4.37 ∙ (−52) 17.) Find the quotient: a.) 32.5 / −13 b.) −52.2 / −0.6 18.) Find the perimeter AND the area of this right triangle. (measurements are inches; please label units) 3/4

5/6

19.) One serving of chicken noodle soup is 1 !! cups. The cafeteria makes 65 cups of

soup. How many servings do they have?

7/8

20.) I ran 2 ½ times around a 4 ⅔ mile trail. How many miles did I run?

21.) Right now there are 5 !! gallons in my car's gas tank. The tank can hold 11 !

!

gallons of gasoline. How much more gas is needed to fill the tank?

22.) Fill in each blank with a possible number that makes the sentence true. a.) !

!of _________ = a whole number b.) !

!of __________ = NOT a whole number

23.) Fill in >, <, = by using number sense. No computation needed! a.) 8 ÷ 2 _____ 8 ÷ ½ b.) 6 ÷ ½ _____ 6 x 2 24.) My garden takes up 1/3 of my yard; I plant tomatoes in 1/2 of the garden. Write and solve the equation shown by the diagram to tell what fraction of my yard is tomatoes. Computation: 25.) − !

!+ (− !

!) 26.) − !

! + !

! 27.) 5 !

!+ 3 !

!

28.) 15− 8 !

!" 29.) 3 !

! ÷ 1 !

!" 30.) 1 !

! × 4 !

!

Evaluate the expressions following order of operations. 31.) 20 - 4 + 2 ÷ 2 ! 3 32.) (-5 + 2)3 + 3 Evaluate the expressions when x = 4 and y = -8. Show substitutions. 33.) 𝑥 + 𝑥𝑦 34.) 𝑦 + 3(𝑥 − 6) Write the sentence as an equation. Then solve the equation with proper steps. 35.) Three-fourths more than a number n is equal to two and three-eighths. 36.) Nine less than a number n equals negative two. Solve each equation with proper steps. Circle answer, please. 37.) 3.4𝑥 = 20.4 38.) !

!!.!= 21

39.) 2𝑥 − 5.4 = −10 40.) −3𝑥 − 3 = 54