7th Math: Entering 8th 2017 Summer Practice Part 1: SUNGLASSES · Summer Practice Part 1:...
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7 th Math: Entering 8 th 2017 Summer Practice Part 1: SUNGLASSES Calculators okay if necessary Who doesn't like to wear sunglasses in the summer? Think about the math involved in the design, construction, and business of making and selling a simple pair of sunglasses. A company needs to think about fashion, materials, eye protection, sizing, advertising, and of course the bottom line. Think about buying sunglasses and how much they cost. Complete these problems by the pool with your coolest pair of shades. 1.) Suppose that 1/3 of the population of the city of Tulsa buys new sunglasses in June and 1/8 of those people buy a pair of black Ray-Bans. a.) What fraction of the population buys the black Ray-Bans? b.) Find the population of the city of Tulsa. Use the fractions to find how many people buy new sunglasses in June and how many buy the black Ray-Bans. Think how to sensibly express your answer; it represents numbers of people. Population of Tulsa: Number of sunglass buyers: Number of Ray-Ban buyers: 2.) Sunglasses come in different sizes, and there are different parts to measure. Choose a pair of sunglasses at your house. Measure several of the dimensions of the sunglasses in inches and fractions of an inch to the nearest fourth. (For example, 3 ¼ inches). Make your own sketch of the sunglasses with labeled dimensions or just label this sketch. (Which dimensions, you may ask. Up to you. Which dimensions make sense to measure?) Your 6 year-old cousin wants a pair just like yours, but they need to be three-fourths the size. What would those dimensions be? Make a sketch labeling the smaller dimensions.
Transcript of 7th Math: Entering 8th 2017 Summer Practice Part 1: SUNGLASSES · Summer Practice Part 1:...
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
