7thMath:Entering8th2017
SummerPracticePart1:SUNGLASSES
Calculatorsokayifnecessary
Whodoesn'tliketowearsunglassesinthesummer?Thinkaboutthemathinvolvedinthe
design,construction,andbusinessofmakingandsellingasimplepairofsunglasses.A
companyneedstothinkaboutfashion,materials,eyeprotection,sizing,advertising,andof
coursethebottomline.Thinkaboutbuyingsunglassesandhowmuchtheycost.Complete
theseproblemsbythepoolwithyourcoolestpairofshades.
1.)Supposethat1/3ofthepopulationofthecityofTulsabuysnewsunglassesinJuneand1/8
ofthosepeoplebuyapairofblackRay-Bans.
a.)WhatfractionofthepopulationbuystheblackRay-Bans?
b.)FindthepopulationofthecityofTulsa.Usethefractionstofindhowmanypeoplebuynew
sunglassesinJuneandhowmanybuytheblackRay-Bans.Thinkhowtosensiblyexpressyour
answer;itrepresentsnumbersofpeople.
PopulationofTulsa: Numberofsunglassbuyers:
NumberofRay-Banbuyers:
2.)Sunglassescomeindifferentsizes,andtherearedifferentpartstomeasure.
Chooseapairofsunglassesatyourhouse.Measureseveralofthedimensionsofthesunglasses
ininchesandfractionsofaninchtothenearestfourth.(Forexample,3¼inches).
Makeyourownsketchofthesunglasseswithlabeleddimensionsorjustlabelthissketch.
(Whichdimensions,youmayask.Uptoyou.Whichdimensionsmakesensetomeasure?)
Your6year-oldcousinwantsapairjustlikeyours,buttheyneedtobethree-fourthsthesize.
Whatwouldthosedimensionsbe?Makeasketchlabelingthesmallerdimensions.
3.)Evensmallchangesindesigncanmakebigchangesintheamountofmaterialusedin
manufacturing.Adesignchangesavesacompany0.32gramsofplasticperpairofsunglasses.
Howmuchplasticwouldbesavedin5yearsif25,000pairsofsunglassesweremanufactured
eachyear?Showthinking,ofcourse.
4.)AstyleofsunglassesdesignedintheUSisgoingtobemanufacturedinEurope.Machinesin
theUSuseinchesanddecimalfractionsofinches.MachinistsinEuropeusethemetricsystem,
sothedesigndimensionsmustbechanged.Converteachmeasurementtomillimeters.
Thinkbeforeyoudothisproblem.Whatconversionfactordoyouneed?
Showyourthinking;no"one-number"answersintheboxes,please.
Partmeasured
Measurement
Measurement
(ininches)
(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.mov
b.)Whatquestiondoyouhave?Writeyourquestionclearlyandcompletely.
c.)Answeryourquestion;showyourthinking.
6.)Asunglassescompanyearns64centsprofitoneach$1insales.Howmuchprofitdothey
makeon$2.5millioninsales?Showyourproportion.(Makesuretowrite2.5millioncorrectly!)
7.)Somedesignsaremoredifficulttomanufacturethanothers,whichmaymeansthereare
morerejectsfromthemanufacturingprocess.(Rejectsareproductsthatdonotpass
inspectionsandcannotbesold.)Supposeacompanysetsalimitof7%rejectson
manufacturing.Onemonththeyproduce16,000sunglasses;thereare1240rejects.Tell
whetherornottheyexceededthelimit;supportyouranswer.
8.)Thistableshowsresultsofasurveyonproductpreferenceforfourdifferentstyles,with
41%ofthosesurveyedchoosingnottobuyanyofthefourstylesshown.
StyleA
StyleB
StyleC
StyleD
Percentofpeople
12%
8%
24%
15%
whopreferthestyle
Numberpeopleout
of50,000who
wouldbuythestyle
Profitonstyleper
pairsold
Totalprofitonstyle
givennumbersold.
$10
$12
$4
$8.50
9.)TheseOakleysunglassesareonsale!Whatisthepercentdiscount?Showthinking.
10.)Ibuyacoolpairofsunglassesfor$25.95.Salestaxis8.5%.
Whatistheamountoftax?HowmuchdoIpayintotal?Showthinking.
11.)Lastyear,thesunglassesIlikedcost$25.50.Thisyear,theycost$29.00.Whatisthe
percentincreasefromlastyeartothisyear?Roundtonearesttenthofapercent,please.
Remember,percentchangeistheratio(new-old)/old.
12.)Thisgraphicshows%markupsforsometypesof
designerfashion.
(http://www.businessinsider.com/products-high-markups-2014-7)
Eyeglassframeshaveaverylargemarkup-muchhigher
thanmarkupsweusedinproblemswedidinclass.
Usethegraphictoanswerthesequestions.
a.)Writethemarkup%foreyeglassframesasadecimal.
b.)Supposeitcosts$7.50tomanufactureapairofframes.
Findtheamountofmarkup. Remember?markupamount=cost*percentofmarkup
c.)Findthesellingpricebyaddingthemarkupamounttothecost.
d.)Thispricedoesnotevenincludelenses!Doyouthinkdesignersunglassesareworthit?Tell
whyorwhynotinatleasttwocompletesentences.
13.)Whatistheareaofacircularlenswitharadiusof2.5centimeters? Whatlengthofwirewouldbeneededtogoaroundonelens? Showthinking,ofcourse!
14.)CompanyresearchshowssalesofStyleAtoStyleBaretypicallyina2:5ratio.TheTulsa
storesells2450pairsthismonth,andthestore'ssalesfollowthetypicalstyleratio.
a.)Fillinthetabletoshowhowmanyofeachstylesold.
Style
Ratio
TulsaStoreSales
A
B
TOTAL
b.)TheOKCstoreclaimstheircustomerslikeaviatorglasses(styleA)waymorethanpeoplein
thetypicalstore.Theysold1200pairsofStyleAand1600pairsofStyleB.Dothesenumbers
supporttheclaim?Supportyouranswerwithratiothinking.
15.)a.)Amanufacturersellssunglassestodepartmentstoresatapriceof$10each,andeach
paircosts$2.48tomanufacture.Whatistheamountofprofitforthemanufacturerperpairof
sunglasses?(Note:profitisrevenueminuscost)
b.)Themanufacturerspent$220,000inthedesignprocessandplanstospend$750,000in
advertising.Basedontheprofitforeachpaircalculatedinparta,howmanypairsofsunglasses
wouldthecompanyhavetosellinordertorecoverthoseinitialcosts?
16.)ThewordSUNGLASSESiswritteninarow8timeslikethis:
SUNGLASSESSUNGLASSESSUNGLASSESSUNGLASSESSUNGLASSESSUNGLASSESSUNGLASSESSUNGLASSES
Thenthatrowofwordsisrepeated120timesaroundthegym.
Worksmarter,nothardertoanswerthesequestions.
Whatfractionofthelettersarevowels(insimplestform)? WhatpercentofthelettersistheletterS?
17.)Thisscatterplotshowsadvertisingdollarsandsalesforabigsunglasscompany.
Whichistheindependentvariable? _______________
Whichisthedependentvariable? ________________
Advertisingspendingof$250,000,helpstogeneratehowmuchinsales?________
Writeonesentencedescribingtherelationshipbetweenspendingonadvertisingandsales.
SunglassSales
7thMathEntering8th2016
SummerPracticePart2:Skills
NOCalculators,Please.Showallthinkingandwork.Circleanswers,please.
SignedNumbers/Fractions
Find 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
7/8
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?
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.)
− ! + (− !)
28.)
15 − 8 !"
!
!
26.)
−! +
29.)
3
!
!
!
!
÷1
!
!"
!
27.)
5
30.)
1! × 4!
!
!
+ 3
!
!
!
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.)
39.)
3.4𝑥 = 20.4
2𝑥 − 5.4 = −10
38.)
40.)
!
!!.!
= 21
−3𝑥 − 3 = 54