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7thPre-Algebra: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.Fillinthetable. StyleA
StyleB StyleC StyleD
Percentofpeoplewhopreferthestyle
12% 8% 24% 15%
Numberpeopleoutof50,000whowouldbuythestyle
Profitonstyleperpairsold
$10 $12 $4 $8.50
Totalprofitonstylegivennumbersold.
9.)TheseOakleysunglassesareonsale!Whatistheoriginalprice?Showthinking.
10.)Acoolpairofsunglassesis35%offtheoriginalpriceof$54.95.Salestaxis8.5%.HowmuchdoIpayintotal?Showthinking. 11.)Lastyear,thesunglassesIlikedcost$25.50.Thisyear,theycost$29.00.Whatisthepercentincreasefromlastyeartothisyear?Roundtonearesttenthofapercent,please. 12.)Thisgraphicshows%markupsforsometypesofdesignerfashion.(http://www.businessinsider.com/products-high-markups-2014-7)Eyeglassframeshaveaverylargemarkup-muchhigherthanmarkupsweusedinproblemswedidinclass.Usethegraphictoanswerthesequestions.a.)Writethemarkup%foreyeglassframesasadecimal.b.)Supposeitcosts$7.50tomanufactureapairofframes.Usethe%markuptofindthesellingprice. c.)Supposethesellingpriceforapairofframesis$175.Usethepercentmarkuptofindthecosttomanufacturetheframes.Challenge:Thinkcarefullyonthisone!d.)Thesepricesdonotevenincludelenses!Doyouthinkdesignersunglassesareworthit?Tellwhyorwhynotinatleasttwocompletesentences.
13.)a.)Whatistheareaofacircularlenswitharadiusof2.5centimeters? b.)Whatlengthofwirewouldbeneededtogoaroundonelens? Showthinking,ofcourse!14.)CompanyresearchshowssalesofStyleAtoStyleBaretypicallyina2:5ratio.TheTulsastoresells2450pairsthismonth,andthestore'ssalesfollowthetypicalstyleratio.a.)Fillinthetabletoshowhowmanyofeachstylesold.Style Ratio TulsaStoreSales
A
B
TOTAL
b.)TheOKCstoreclaimstheircustomerslikeaviatorglasses(styleA)muchmorethanpeopleinthetypicalstore.Theysold1200pairsofStyleAand1600pairsofStyleB.Dothesenumberssupporttheclaim?Supportyouranswerwithratiothinking.15.)a.)Amanufacturersellssunglassestodepartmentstoresatapriceof$10each,andeachpaircosts$2.48tomanufacture.Whatistheamountofprofitforthemanufacturerperpairofsunglasses?(Note:profitisrevenueminuscost)b.)Themanufacturerspent$220,000inthedesignprocessandplanstospend$750,000inadvertising.Basedontheprofitforeachpaircalculatedinparta,howmanypairsofsunglasseswouldthecompanyhavetosellinordertorecoverthoseinitialcosts?Showthinkingplease.
16.)ThewordSUNGLASSESiswritteninarow8timeslikethis:SUNGLASSESSUNGLASSESSUNGLASSESSUNGLASSESSUNGLASSESSUNGLASSESSUNGLASSESSUNGLASSESThenthatrowofwordsisrepeated120timesaroundthegym.Worksmarter,nothardertoanswerthesequestions.Whatfractionofthelettersarevowels(insimplestform)? WhatpercentofthelettersistheletterS?17.)Thistableshowshowthethicknessofthelinesofonekindofmaterialaffectsthepercentofvisiblelightthatistransmittedbythematerial.Independentvariable:______________Dependentvariable:_______________Asthelensthicknessincreases,the%ofvisiblelight_______________Plotthesenumbersonthiscoordinategrid.YouMUSThavetitles,axislabels,andchooseanappropriatescale.Isthisalinearfunction?Howdoyouknow?___________________________________Whattransmissionpercentwouldyouexpectforathicknessof0.9mm?______1.9mm?____
Lensthickness(mm)
%visiblelighttransmitted
1.0 50%1.1 45%1.2 41%1.3 36%1.4 33%1.5 30%1.6 27%1.7 24%1.8 22%
7thPre-AlgebraEntering8th2016SummerPracticePart2:SkillsNOCalculators,Please.Showallthinkingandwork.Circleanswers,please.FractionApplications1.) Find the LCM and the GCF. Use any method.
a.) 28 and 29 b.) 120 and 84 2.) It takes 4/5 of a yard of fabric to make a play costume. How many costumes can be made from 52 yards? 3.) Heights of students at a school vary from 2 !!
!" feet to 5 !
! feet. Find the range of the
heights, expressed in feet. (no decimals). 4.) Find the area of this right triangle. All measurements are in inches. 2 !! 5 !
!"
4 !
!
5.) I used !
! of a 5 !
! pound bag of apples to make a pie.
a.) How many pounds did I use? b.) How many pounds are left?
6.) Fill in >, < or = Use number sense - no computation needed! a.) ⅓ + ⅓ ____ 2(⅓) b.) ½ of 64 _____ ¼ of 128 c.) ¼ • 8 ____ 8 ÷ 4 d.) ⅗ • ⅖ _____ ⅗ + ⅖ e.) ¾ ÷ ⅓ _____ 1 f.) 6 x 5______ 6 ÷ ⅕ Fraction Computation 7.) −5 !
!− 9 !
! 8.) !"
!" − !"
!"
9.) − !
!"÷ 32 10.) 1 !
! − 4 !
!"
11.) !!
!" • !"
!!" 12.) −3 !
! • 1 !"
!"
13.) 5÷ 2 !
! ∙ 2 !
! 14.) 6 !
! ÷ 3 !
! ∙ !
!
Algebraic Expressions and Equations 15.) Evaulate the expressions following order of operations.
a.) (9 − 15)! + 3 ÷ 3 b.) 90 − 12 ÷ 0.3 ÷ 2! 16.) The perimeter of a rectangular garden is 30 feet.
The length is 3 more than twice the width.
a.) Label the rectangle with variable expressions for its width and length.
b.) Write and then solve an equation to find the width AND length of the garden.
Solve equation below; write answers here: width = ______ ft length = ______ ft Solve these equations. Show all thinking. 17.) 5𝑥 + 3 𝑥 − 14 = 8 18.) 5𝑥 − 𝑥 − 5 + 7 = 15
19.) !!𝑥 − !
!+ !
!= 6 20.) !
!𝑥 − !
!+ !
! = 6
21.) 3𝑥 − 8 = 8𝑥 − 12 22.) −7 − 6𝑥 = −10 − 2𝑥
Linear Equations / Slope 23.) Which is steeper, the boat ramp or a road with a 12% grade? Support your answer by reasoning about slope. 24.)Make a table of values following our guidelines (three x values: pos, zero, neg). Graph the equation. 𝒚 = − 𝟏
𝟑𝒙 + 𝟒
25.)Find the slope of the line passing through each pair of points. No graph. Support your answer with the slope formula. A(-2, 3) B( -4, -1) 26.) Find the slope of each line from the graph. a.) b.) 27.) Solve for y to express in slope-intercept form; then use the slope-intercept form to graph the equation. No table of values.
4x + 2y = 6
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