DeficienciesandMegadoses / TEACHERNAME / PROGRAMNAME
[UnitTitle]
AlgebraandPatterns / NRSEFL(s)
3–6 / TIMEFRAME
120minutes
Instruction / ABE/ASEStandards–Mathematics
Numbers(N) / Algebra(A) / Geometry(G) / Data(D)
NumbersandOperation / N.3.26
N.3.19 / Operations andAlgebraicThinking / GeometricShapesandFigures / MeasurementandData
TheNumberSystem / ExpressionsandEquations / A.3.8
A.4.3 / Congruence / StatisticsandProbability
Ratios andProportionalRelationships / Functions / A.4.13
A.6.6
A.4.15
A.6.9 / Similarity,RightTriangles.AndTrigonometry / Benchmarks identified in RED are priority benchmarks. To view a complete list of priority benchmarks and related Ohio ABLE lesson plans, please see the Curriculum Alignments located on the Teacher Resource Center (TRC).
Numberand Quantity / GeometricMeasurementand Dimensions
ModelingwithGeometry
S
sevidenceofstudent
teachershouldactivelylistenionsforsignsof
fmisconceptions.Ifstudents
,theteachershouldhavetloudas theysolvethe
owstudentstheopportunitytonsbasedonwhattheylearnerspresenttheirsolutions.
eRDAis90mgandtheTUILrgydrinkcontains1000mgoff broccolicontains90mg.1.numberofenergydrinksand
havetostaybetweentheheinequality.
INSTRUCTIONALACTIVITIES1.Review(orintroduce)theconceptofscientificnotation.Reviewbasicnumberlineproblemssuchas3≤x≤6and3≤x6,makingsuretoemphasizethedifferencebetweenanopendot(<or>)andacloseddot(≤or≥).
2.Gooversystemsofequations.Startwithasimpleexamplelikex+y=4,x– y=2andthenmoveontomorechallengingexamples.Presentthesubstitutionmethod(solveforxoryinoneequationandthenplugitintotheotherequation)andthesynthesismethod(multiplyoneorbothequationssothatavariablehasoppositecoefficientsandthenaddtheequations).Forexample,usingthesynthesismethodtosolve2x+3y=7,5x-2y=-1.5,youcouldmultiplythefirstequationby5andthesecondequationby-2andthenaddthetwoequations toget19y=38.Thus,y=2andx=(1/2).Afteryousolvethesystem,plotbothlinesontheX-Yplaneandask whattheintersectionrepresents(itshouldbethepoint(1/2,2)that youjustfound).
3.Keepthesametwooriginalequationsontheboard,butchangetheequalssignsintogreaterthanorequals.(e.g.,2x +3y≥7,5x-2y≥
-1.5).Ask ifanyonehasanyideas onsolvingthisnewsystemofequations.Showhowyoucansolveforeitherxoryineachequationandthenshadeabove(yisgreaterthan),below(yislessthan),totheleft(xislessthan),ortotheright(xisgreaterthan)oftheline.IfBOTHequationsmustbesatisfied,thentheanswerwillbetheregionoftheX-Yplanethatisshadedtwice.DiscusshowthismeansthattheanswerisaregioninsteadofapointlikeinStep2.
4.Putthefollowingproblemontheboard:3≤ 2x+5y≤7.Ask forideasonhowstudentswouldapproachthisproblem.Showhowthiscanbebrokenupintotwoinequalities(3≤2x +5yand2x+5y / RESOURCES
StudentcopiesofVitaminDhandout(attached)StudentcopiesofVitaminEhandout(attached)StudentcopiesofFolicAcidhandout(attached)TeacherAnswerSheet(attached)
VocabularySheet(attached)
≤7)andthensolvedasinStep3.Makesureyouplotthisonagraph.Ask studentstolistatleastoneintegerpairsolutionintheshadedregion(e.g.,(0,1)).
5.Introducethecontext.Tellyourstudentsaboutthegeneralconceptofdeficienciesandmegadoses(basicallythatourbodiesaresensitivetotoomuchandtoolittleofmanyimportantvitaminsandminerals).Thiscangetcomplicatedbecauseavitamincanbepresentindifferentforms,eachofwhichmayhaveadistinctpotencylevel.ExplainthatscientistshavederivedameasurementunitnamedIU(InternationalUnit)tohandlethisproblem.ThelowerlimitofIUofaparticularvitaminormineralthatnutritionistsrecommendforeachpersonistheRecommendedDailyAllowance(RDA).TheupperlimitconsideredtobesafeistheTolerableUpperIntakeLimit(TUIL).Tellstudentsthatthecontentsofthislessonarebasedonthemostaccurateinformationavailable,butthatthatthislessondoesnottaketheplaceofofficialmedicaladvice.CertainpeoplehavehealthconditionsthatwillrequiretakinglessthantheRDAormorethantheTUILofavitaminandsostudentsshouldconsulttheirdoctorbeforemakinganychangestotheirdiet.
6.(Ido)Teachermodelsthe solutionprocessontheVitaminDhandout.SpendafewminutesbecomingfamiliarwithVitaminDasagroupbeforegoingthroughthetaskquestions.UsetheTalkAloudprocedureasyouworkthrougheachofthefirstfourquestions.(Optionforadvancedgroups:WhenyoucreatethenumberlineforQuestion#2,createandlabelintermediateplacesonthelinealso.Forexample,theIUsideofthelinecouldbelabeledatevery1,000IU,andthenthemicrogram sidewouldbelabeledatevery25micrograms).
7.(Wedo)TeacherandstudentscollaborativelyworkthroughtheVitaminEtask.BeginwiththeVitaminEsourcechartanddiscusswhetherstudentsareeatingnaturalsourcesofVitaminE.Then
readthroughthebenefits,aswellasthedangersofdeficiencyandmegadoses.Whenyouget totheconversions,thiswillbethefirsttimemostofthestudentswillhaveencounteredasplitconversion.RemindstudentsthatthisiswhymostnutritionlabelsuseIUforvitaminsandmineralsinsteadofastandardweight(inotherwords,theIUgiveusasinglemeasureforcomparingdifferentsourcesofVitaminEwithdifferentpotencylevels).Questions#1and#2areverysimilartowhatstudentswatched youdointheVitaminDtask,sotrytoseeiftheycanhandlethesesteps(withthehelpofyourpromptswhennecessary).AsyouaretalkingthroughQuestions#3and#4,makesure youpointoutthat#3isanequationand#4isaninequality.For#4,makesureyouworkthrougha2-variableinequality(inotherwords,considerthetwotogetherinsteadofseparately–seetheTeacherAnswerSheetforanexampleofthis).
8.(Youdo)StudentsindependentlyworkthroughtheFolicAcidhandout.Dependingonyourclassdynamics,eitherpartnerstudentstogetherorhavethemworkindividually.Beforeyoupassoutthetask,explainthat youwantthestudentstotacklethisproblemasindependentlyaspossible.Afterpassingoutthehandouts,walkaroundtheroomsilentlymonitoringthestudents’progress.Whenyouseethem runintodifficulties,trynottoanswertheirquestionsdirectly;instead,remindthemofsimilarsituationsfrom thefirsttwotasks.Question#4isthemostdifficult.ReferthemtogobackthroughQuestion#4from theVitaminEtaskbeforepromptingthemwithanswers.
9.Haveeachstudent(orpair)shareboththeprocesstheyusedandtheirfinalcomparisons.Encouragestudentstodiscusstheprosandconsofalternativeapproachestaken.Inthiscase,thereisonly onecorrectanswerforeachquestion,althoughstudentsmayhavedifferentrepresentationsfor#4.Whenstudentsdisagree,donotimmediatelyprovidethecorrectanswer;alloweachstudentorpairtotrytoconvincetheotherfirst.
10.Makingitrelevant.Havestudentsbrainstormspecificvitaminsormineralsthattheywanttoinvestigateintheirdiet(see“NextSteps”belowforanoptionalassignment).
DIFFERENTIATION
Reflection / TEACHERREFLECTION/LESSONEVALUATION
ADDITIONALINFORMATION
NEXTSTEPS
Ifstudentstakeanysupplements,havethem researchtheRDAandTUILforeachone,andthenestimatetheiraveragedailyintake.Iftheyarenotalreadytakingsupplements,havethem researchacommononelikeVitaminCorCalcium andseehowtheirnaturaldailyintakecomparestothedesirablerange.Seewebsitesbelowforresearchstartingpoints.
TECHNOLOGYINTEGRATION
Thisarticleprovidesamorethoroughdiscussionabouttheconceptofdeficienciesandmegadoses: world.ThisfollowinglinktakesstudentstotheVitaminEinformationpage,buttheycaneasilysearchforothervitaminsormineralsinthesearchbox: e/NS_patient-vitamine/DSECTION=dosing
PURPOSEFUL/TRANSPARENT
Studentsareconcernedabouttheirhealth,butdonot(andshouldnot)alwaystrustthemessagestheyaregivenabouthowmuchvitaminstheyneed.Inthislesson,studentslearntocalculateappropriatevitamindosagesbyusingalgebraicinequalities.
CONTEXTUAL
Thislessonhitsondosagesofvitaminsandminerals,oneofthefewtopicsapplicabletoeveryone’slife.Theissuebecomesevenmoreimportantgiventheubiquitouspresenceofenergydrinks,energybars,fortifiedfoods,andsupplements.
BUILDINGEXPERTISE
Thislessonbuildsonstudents’abilitytoreadanumberline,understandasimpleinequality,andsolveabasicsystemofequations.Studentsmustcombinethesethreeskillstosolvesystemsofinequalities.Thefinalstepofplottingthegraphsforgesconnectionsbetweenalgebraicandgraphicalrepresentations.
NOTE:ThecontentintheAdditionalInformationboxexceedswhatisrequiredfortheOBRApprovedLessonPlanTemplate.Thisinformationwasprovidedduringtheinitialdevelopmentofthelesson,priortothecreationoftheOBRApprovedLessonPlanTemplate.FeelfreetoremovefromoraddtotheAdditionalInformationboxtosuit yourlessonplanningneeds.
Deficiencies andMegadoses:VocabularySheet
Algebraic equation– anequationthatincludesatleast one unknown variable.
Deficiency– a problematic conditionwhere thebodyis not receivinganadequate amount ofaspecific vitamin or mineral.
Integer pair– acoordinate on theX-Y plane,where both thex-value andy-value are integers.Forexample, (2,-7) would beaninteger pair, but (0.5,3) would not.
Megadose – aproblematic conditionwhere thebodyis receivingtoo muchofa specific vitamin ormineral.
Number line– alineon whicheach point represents a realnumber.
Scientific notation– a numeric format where thebase number, which is greater thanorequal to oneandlessthan 10, is multipliedtimes a power often.
Systemofequations– a set of atleasttwoalgebraic equationswith thesame value for eachvariable.