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GeorgeMasonUniversityCOMPLETEMath©2015
ASplashofColor
CreatedbyKateBeckSpring2016
TheTaskCreateacolorfuldesignforyouriPhonescreen.Usethecharttohelpyouchooseyourcolorsandbesuretoincludeatleast8differentcolors.LabeleachcomponentofyourdesignwiththeRGBvalueaswellasthehexadecimal#RRGGBBvalue.Finally,coloryourdesign!
BigIdeas• Placevalueinapositionalnumbersystem.
StandardsofLearningforGrades3-4-5
3.1aReadandwrite6-digitnumeralsandidentifytheplacevalueandvalueofeachdigit.
4.1aIdentifyorallyandinwritingtheplacevalueforeachdigitinawholenumberexpressedthroughmillions.
StandardsofLearningforGrades6-7-86.5Investigateanddescribeconceptsofpositive
exponents.7.10Determinetheprobabilityofcompoundevents,
usingtheFundamentalCountingPrinciple.
ProcessGoals• ProblemSolvingandReasoning–Studentswillapplyanunderstandingofbase10placevaluetomake
senseofthebase16hexadecimalsystem.• ConnectionsandRepresentations–Studentswillrecognizeandusemathematicalconnectionsto
extendandgeneralizepatternsinapositionalnumbersystem.Theywilluseavarietyofrepresentationsastheyexplorebase16andcommunicatetheirthinking.
• Communication–Studentswilljustifytheirfindingsandpresenttheirresultstotheclasswithprecisemathematicallanguage.
RelatedTask–OutofthisWorldYourmissionistomakesenseoftheWoop/Zoobie/GlimnumbersystemandpresentittothemathematiciansonEarth.Youmusthelpthemunderstandthisnewwayofcounting.Peaceinoursolarsystemdependsonit!
RelatedTask–MayanMathStudytheMayancountingsystem.Completethefollowingtasks:
• DeterminethenumberthattheMayancountingsystemisbasedon.• MakeaplacevaluechartfortheMayansystem.• Chooseanumberthatfitseachcategorybelowinbase10andrecordtheequivalentnumberinthe
Mayansystem.*Anumberbetween40and100.*Anumberbetween100and500.*Anumberbetween500and1,000.*Anumberbetween1,000and10,000.
*Anumbergreaterthan10,000.
GeorgeMasonUniversityCOMPLETEMath©2015
ASplashofColorLessonPlan
CreatedbyKateBeck
Spring2016
TheTaskCreateacolorfuldesignforyouriPhonescreen.Usethecharttohelpyouchooseyourcolorsandbesuretoincludeatleast8differentcolors.LabeleachcomponentofyourdesignwiththeRGBvalueaswellasthehexadecimal#RRGGBBvalue.Finally,coloryourdesign!
Materials• CopiesoftheSupplementalMaterialsforeach
student• Copiesofthetaskforeachstudentorpair• CopiesoftheRGBColorChartorthe
HexadecimalColorChartforeachstudentorpair
• Blankpaper• Chartpaper• Markers• Calculator
FacilitatingTaskNote:• Youmayconsiderexploringthesupplemental
materialswithyourstudents.ThesematerialswillwalkyourstudentsthroughanintroductiontothehexadecimalsystemandtheRGBcolorsystem.Thismaybedoneinalessonpriortothetaskoritmaybedoneatthestartofthetask.
• ChoosewhetheryouwantstudentstocompletethetaskbyconvertinghexadecimalvaluestoRGB(base10)valuesorRGB(base10)valuestohexadecimalvaluesandincludetheappropriatechartwiththetask.*Thesechartsarenotcorrelated.Simplychoosetheoneyouwilluse,anddonotincludetheotherwhendistributingthetasktothestudents.
• Studentscanworkindividuallyorinpairs.Giveeachstudentorpairacopyofthetask.
• Readthetasktogetherandanswerclarifyingquestions.
• Eachstudentorpairmaycreateitsdesigndirectlyonthetaskpaperoronalargechartpaperforpresentingtotheclass.
• Allow10minutesattheendofthelessonforpresentationsanddiscussion.Studentsorpairswillsharetheirdesignswiththeclass.
• Afterstudentshaveshared,discussthechallengesofconvertingbetweenbase10andthehexadecimalsystem.(Seeprompts/questionsbelow.)
Misconceptions• Thestudentsmaythinkthatthefirsttwo
columnsinthehexadecimalsystemarethesameasbase10(tensandones).
• ThestudentsmaygetconfusedbythehexadecimalRGBformat(#RRGGBB).Theymaythinkthatthesixnumbersrepresentsixplaceswithinthehexadecimalsystemratherthanthreetwodigithexadecimalnumbers.
SuggestedPromptsorQuestions• Whatpatternsdidyounoticeasyouconverted
betweenbase10andthehexadecimalsystem?• Howarebasetenandthehexadecimalsystem
thesame?• Howaretheydifferent?• Whatdidyoufindtrickiestaboutworkingwithin
eachsystem?• Hasanythingbecomecleareraboutbaseten
afterworkinginthehexadecimalsystem?
GeorgeMasonUniversityCOMPLETEMath©2015
ASplashofColor Name Date CreateacolorfuldesignforyouriPhonescreen.Usethecharttohelpyouchooseyourcolorsandbesuretoincludeatleast8differentcolors.LabeleachcomponentofyourdesignwiththeRGBvalueaswellasthehexadecimal#RRGGBBvalue.Finally,coloryourdesign!
GeorgeMasonUniversityCOMPLETEMath©2015
Extension:
*Whatisthehighestcolorvalueinthe#RRGGBBhexadecimalsystem?UsethisinformationtofigureouthowmanyRGBcolorsexist.
GeorgeMasonUniversityCOMPLETEMath©2015
ASplashofColor Name Date Computerprogrammersuseahexadecimalnumbersystemwhenassigningcolorstoobjectsonthescreen.
What’sahexadecimalsystem?It’sanumbersystembasedon16.
Belowarethedigitsusedinthehexadecimalsystem:
0,1,2,3,4,5,6,7,8,9,A,B,C,D,E,F
whereAisthedigitthatstandsforthevalue10,Bfor11,andsoonuptoFfor15.
Justasourbase10numbersystemisapositionalnumbersystembasedon10,
theHexadecimalsystemisbasedonthenumber16.
Workwithyourgrouptoconvertthefollowinghexadecimalnumberstobaseten.
42166C16FE16
Now,convertthesebasetennumberstohexadecimals.
64 100 255
101=10100=1
tens ones
161=16160=1
sixteensones
GeorgeMasonUniversityCOMPLETEMath©2015
It’stimetogetcolorful!
WeusetheRGBcolormodeltolabelcolors.R(red),G(green),andB(blue).Thesethreecolorsworktogethertocreatenewcolors.EachcolorhasanRvalue,aGvalue,andaBvalue.Thesevaluesareinwritteninbase10.
Forexample,
• RedhasanRGBvalueof255,0,0.
• YellowhasanRGBvalueof255,255,0.
• PinkhasanRGBvalueof255,192,203.
Whencodingwebpages,computerprogrammersusethehexadecimalsystemtotellthecomputerwhatcolortouse.Theywritethenumbersusingthisformat:
#RRGGBB
Let’sconvertpink’sRGBvaluetoit’shexadecimalequivalentsowecanaddittoapictureonourwebpage.
Givenpink’sRGBvalueof255,192,203,canyouconvertpinktoitshexadecimalequivalent?
Theredvalueinbase16.
Thegreenvalueinbase16.
Thebluevalueinbase16.
GeorgeMasonUniversityCOMPLETEMath©2015
RGBColorChart
Reminder:Thenumbersonthischartarewritteninbase10.
GeorgeMasonUniversityCOMPLETEMath©2015
HexadecimalColorChart
GeorgeMasonUniversityCOMPLETEMath©2015
GeorgeMasonUniversityCOMPLETEMath©2015
Extension:
*Whatisthehighestcolorvalueinthe#RRGGBBhexadecimalsystem?UsethisinformationtofigureouthowmanyRGBcolorsexist.
Solution:
Thehighestcolorvalueis#FFFFFFwhichcorrelatestotheRGBvalueof255255255.Sincethevaluesrangefrom0to255,thereare256possiblevalueseachforred,green,andblue.
Usingthefundamentalcountingprinciple,wecanfindthenumberofRGBcolorsthatexistbysolving:256x256x256=16,777,216possiblecolorcombinations.
GeorgeMasonUniversityCOMPLETEMath©2015
GeorgeMasonUniversityCOMPLETEMath©2015