7thPre-Algebra: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.Fillinthetable.
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!Whatistheoriginalprice?Showthinking.
10.)Acoolpairofsunglassesis35%offtheoriginalpriceof$54.95.Salestaxis8.5%.
HowmuchdoIpayintotal?Showthinking.
11.)Lastyear,thesunglassesIlikedcost$25.50.Thisyear,theycost$29.00.Whatisthe
percentincreasefromlastyeartothisyear?Roundtonearesttenthofapercent,please.
12.)Thisgraphicshows%markupsforsometypesof
designerfashion.
(http://www.businessinsider.com/products-high-markups-2014-7)
Eyeglassframeshaveaverylargemarkup-muchhigher
thanmarkupsweusedinproblemswedidinclass.
Usethegraphictoanswerthesequestions.
a.)Writethemarkup%foreyeglassframesasadecimal.
b.)Supposeitcosts$7.50tomanufactureapairofframes.
Usethe%markuptofindthesellingprice. c.)Supposethesellingpriceforapairofframesis$175.Usethepercentmarkuptofindthe
costtomanufacturetheframes.Challenge:Thinkcarefullyonthisone!
d.)Thesepricesdonotevenincludelenses!Doyouthinkdesignersunglassesareworthit?Tell
whyorwhynotinatleasttwocompletesentences.
13.)a.)Whatistheareaofacircularlenswitharadiusof2.5centimeters? b.)Whatlengthofwirewouldbeneededtogoaroundonelens? Showthinking,ofcourse!
14.)CompanyresearchshowssalesofStyleAtoStyleBaretypicallyina2:5ratio.TheTulsa
storesells2450pairsthismonth,andthestore'ssalesfollowthetypicalstyleratio.
a.)Fillinthetabletoshowhowmanyofeachstylesold.
Style
Ratio
TulsaStoreSales
A
B
TOTAL
b.)TheOKCstoreclaimstheircustomerslikeaviatorglasses(styleA)muchmorethanpeoplein
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?Showthinkingplease.
16.)ThewordSUNGLASSESiswritteninarow8timeslikethis:
SUNGLASSESSUNGLASSESSUNGLASSESSUNGLASSESSUNGLASSESSUNGLASSESSUNGLASSESSUNGLASSES
Thenthatrowofwordsisrepeated120timesaroundthegym.
Worksmarter,nothardertoanswerthesequestions.
Whatfractionofthelettersarevowels(insimplestform)? WhatpercentofthelettersistheletterS?
17.)Thistableshowshowthethicknessofthelinesofonekindofmaterialaffectsthepercent
ofvisiblelightthatistransmittedbythematerial.
Independentvariable:______________Dependentvariable:_______________
Asthelensthicknessincreases,the%ofvisiblelight_______________
Plotthesenumbersonthiscoordinategrid.
YouMUSThavetitles,axislabels,andchooseanappropriatescale.
Isthisalinearfunction?Howdoyouknow?___________________________________
Whattransmissionpercentwouldyouexpectforathicknessof0.9mm?______1.9mm?____
Lens
%visible
thickness
(mm)
light
transmitted
1.0
1.1
1.2
1.3
1.4
1.5
1.6
1.7
1.8
50%
45%
41%
36%
33%
30%
27%
24%
22%
7thPre-AlgebraEntering8th2016
SummerPracticePart2:Skills
NOCalculators,Please.Showallthinkingandwork.Circleanswers,please.
FractionApplications
1.) 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.)
!
!!
!"
•
!"
!"
!
10.) 1 ! − 4 !"
!"
!
!"
12.) −3 ! • 1 !"
!!"
!
−
!
9.) − !" ÷ 32
11.)
!"
!"
!
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:
Solve these equations. Show all thinking.
17.) 5𝑥 + 3 𝑥 − 14 = 8
19.)
!
𝑥−
!
!
+
!
!
=6
!
21.) 3𝑥 − 8 = 8𝑥 − 12
width = ______ ft
length = ______ ft
18.) 5𝑥 − 𝑥 − 5 + 7 = 15
20.)
!
𝑥−
!
!
+
!
!
!
=6
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.
𝟏
𝒚 = −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