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$By: Melissa Hanel Math B/Grade 11 5 Day Unit Plan Technologies ...$

COMETS ANDCONIC5 ECTIQt\l5(From Kepler's discovery (see "Hep" KepZer Didn't Go Around In CircZes) we knowthat each planet's orbit is an ellipse. Ellipses belong to a special group of curvesknown as the conic sections. These curves have interested mathematicians and astronomersfor years.A conic section is the curve of intersectionbetween a hollow cone and a plane that cuts throughit. The pictures show some conic sections.i,, /,,--d~\lPERBOLA, '" , ", ,,//', , ,,,,, ,,PARABOLAWhy do the planets have e111ptica1 orbits? Newtondiscovered that ::he gravitational pull of the sun onthe planets causes their orbits to be elliptical. Hethen wondered whether comets were affected by thegravitational pull of the sun·and if so he predictedthat their orbits would be conic sections. In particularif the comets had nearly circular orbits thevwould be visi~le at regular and somewhat frequentintervals. Edmund Ha1iey supported Newton's beliefby discovering; that the comet he was observing wasthe same one that was seen 75 years earlier.Halley's comet· last appeared:f,n 1910 and is dueagain about the spring of 1986.---Cb-~'-,\/---HYPE.RBOLA~ ~~GO1980 1970TIll: ORBIT Of" WALU:VS COMET(We now know that the orbit of a comet will be anellipse, a parabola or one branch of a hyperbola asshown in the bottom figure. It is believed that mostcomets travel on elliptical orbits but that the orbitsare so stretched out that the portion we can seeappears like a parabola.ELLIPSE• SU~PARABOLAI-lYPtRlOOLAThe following two pages describe methods that canbe used to draw ellipses, parabolas and hyperbolas. (114
1) A Method for Drawing EllipsesCOMETS ANDCONICSECTIONS(PAGE: '2-)a) Make or obtain apage of concentriccircles (circleshaving the samecenter).b) Draw a large circle on a piece ofpaper and pick a point P insidethe circle (not the center).c) Using the page of concentriccircles, arrange a circle sothat it passes through P andis tangent to (just touches)the large circle you drew.See the dotted circle in thefigure to the right. Markthe center of the dottedcircle." ...... ~-~ ............ ,, . ,, '\',P ,,/..... _--_ .... '", "'Cd) Repeat (c) with several differentsizes of circles. Connect thecenters to form a smooth curve asshown in the figure to the left.The curve is an ellipse.115
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MATHEMATICS INSCIENCE AND SOCIETYPl
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DIDACTICSTEACHING FOR TRANSFERthan
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DIDACTICSTEACHING FOR TRANSFEREmpha
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DIDACTICSTEACHING FOR TRANSFER1. Wh
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DIDACTICSTEACHING FOR TRANSFER14. I
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DIDACTICSTEACHING VIA PROBLEM SOLVI
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MATHEMATICS INSCIENCE AND SOCIETYPl
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DIDACTICSTEACHING VIA LAB APPROACHE
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Page 46 and 47: DIDACTICSTEACHING VIA PROELEM SOLVI
Page 48 and 49: INTRODUCTIONMATHEMATICS AND ASTRONO
Page 50 and 51: (TITLEPAGETOPICMATHTYPEMaking Waves
Page 52 and 53: We all know that the Sun gives off
Page 54 and 55: TRACK RECORDS IN SPACE??? ---YOU WI
Page 56 and 57: MEA8UI2\NG BYTf2IAtJGULAlI0NHow can
Page 58: Angle measurements and scale drawin
Page 61 and 62: .. ~(CONT'>-lUe:O)3.In the city of
Page 63 and 64: \S THE SUMWITHIN RANGE?(PACOC 2.) D
Page 65 and 66: We can use a base line on the Earth
Page 67 and 68: , ,,,B. II,,,,, ,,, ,,EI\12T\-l1T
Page 69 and 70: 2. The diagrams below represent two
Page 71 and 72: 2. To construct a scale model of th
Page 73 and 74: In It's A Long Shot triangulation i
Page 75 and 76: (PAGE: 2.)f. Repeat steps b through
Page 77 and 78: A HVGE"CHUN\
Page 79 and 80: THATS A MODELI CAf\J I2ELATE TOe,AT
Page 81 and 82: One of two movies, Powers of Tenor
Page 83 and 84: ~~t:P'The actual orbits of most ofh
Page 85 and 86: .KepIeY3Jaw( COt..lTlt-)UE,D )secon
Page 87 and 88: Exercises:1. An object is in an orb
Page 89: c. The average speed of Alpha is 8
Page 93 and 94: Our ancestors spent much time study
Page 95 and 96: The polar chart to the right can be
Page 97 and 98: C£OJSA2Yalternate interior angles.
Page 99 and 100: ASTRONOMYGLOSSARYmer-surmeridian (o
Page 101 and 102: NUM££ZCAL I1ATA1. Cons tants11 ""
Page 103 and 104: to MATHEMATICS AND BIOLOGYBiology--
Page 105 and 106: MATHEMATICS AND BIOLOGYTITLEPAGETOP
Page 110 and 111: 1. Your body contains 206 bones.1Ab
Page 112 and 113: ,1.1) Keep your fingers together an
Page 114 and 115: Tape a strip of butcher paper to th
Page 116 and 117: This activity will see how quickly
Page 118 and 119: .''Y07.(f2 IfEfiJ2r15.Jt. ELDOD;GOO
Page 120 and 121: ~ ~My HEARTTHRO S~OR Yo~Materials N
Page 122 and 123: 144III.IDEA FROM:(COWl"INU£O)Simpl
Page 124 and 125: I. Does a person's body temperature
Page 126 and 127: I. To measure your angle of periphe
Page 128 and 129: ·"ltll•• oRLOSING(PAGE. 2)(.",
Page 130 and 131: GAI.I•• oRLOSING ~(PAGE. 4)(Cal
Page 132 and 133: GAI.I•• oeLOSINGc::rJ:f§3(PAG
Page 134 and 135: V:hoi's YOUQ TYPE1. Weigh yourself
Page 136 and 137: ~1AGN IFI EDARE DRAWN Te SCALE.spoR
Page 138 and 139: A fly can sit on the surface of wat
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( ,An earthworm absorbs oxygen for
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(CO~TIIJl>('O)(I4YBRID BROWt-.lBbB
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ANAlYZ\NG1RA\T£(PAGE: 2.)I(o -t-II
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a mode! 50r!nhQfitanc8/(, ,For this
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WItAT TVPEARE YOII ?(CONTINUE:O)(\S
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JUST LIKE PEASI~A~nD( COt-lTIt-JUED
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BIOLOGY GLOSSARYlun-villung capacit
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INTRODUCTIONENVIRONMENTThe pages in
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(\What America is doing to reclaim
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((,(180
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~NVIQONMtNTSCOQtPut a check in the
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[DMPUT~O~ DNDTW~~NVIODNM~NT(COIVTII
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(TITLEPAGETOPICMATHTYPELet's Go Cou
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(TITLE PAGE TOPIC MATH TYPEMATHEMAT
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P~DPLb-[DUNTIN~ DQT~~'J1"-lE:'EEtU,
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Percent ofPopulation total Land are
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This table gives thepopulation of t
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0CE) ~:;<
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Choose your own colors.o -1 million
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IF PEOPLtW~Q~ LITTLtQDr. Igorovichs
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(p [ill ~ [ill [b [mu0[ill ~[p~[Q]J
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"City Has A Million Rats""2,500,000
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oSome chemicals do a good job of ki
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PAIZTfCULA£POLLUTANTSTl-\(:Y USED
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[RLLINCRLL [ARSToo many cars can ca
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Do a lot of cars and bikes travel n
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_28CITYCIRCUM5TRNCE5SGSPENDED PAR'l
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,/Needed:Watch, radio, metre stickC
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1. There has been a concern by envi
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MY WATER USE (one day)1) On the ave
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FI X TfiAT L(AK~ t t ~ ~Materials N
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WATER POLLUTION, MAJOR DRAINAGE ARE
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WRlERFigure VIII-14 - COMMERCIAL FI
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Recent surveys continue to show tha
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How much garbage, rubbish and junk
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~\JNNING~V7?(Unless more is found,t
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· ~.; '. '" ~ : .... (Erosion is n
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L~ND ~NDR~~OURC~£PROJbCTS1) What m
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Needed:HOW MRNYHORStS IWatch with s
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PULL FORPDOLINC~.~(Make plans to ta
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(Both the car and the driver contri
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((This includes several ideas from
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ENVIRONMENT GLOSSARYgra-watgram. A
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(Materials are available without oh
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SOURCESENVIRONMENTThe Population Co
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INTRODUCTION MATHEMATICS AND MUSICM
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Listen to the Students~ TO STUOCt\l
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(PAGE '2»(Ask students to look for
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(TITLEPAGETOPICMATHTYPEYou'd Better
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(----:--0-=---- APPEAREDWHOIN =----
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(Materials Needed:Record player wit
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PRE.5'2>URE: I~ GIVE./-.l l"l 'ORee
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Many musical terms have prefixes wh
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(Select aproject onthese or your ow
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INSTQUM~NTSWIT~ CLRSSClassification
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INST~UMtNTSWIT~CLRSS(PAGE 3) (After
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INSTRUMtNTSWIT~ [LRSS(PAGE: 5)(GUIT
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(A GAME IN RECOGNIZING ATTRIBUTES O
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(Materials:Playing board with 2 lar
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284NOTtS,~£STS'-tiD r~l1CrrONS(COI
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I~::::::::========-- ('(286
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lbTTbU[CJUf\JT fJI\j IT! (Counting
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Besides being fun to figure out, sy
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(Reflections do occur in music, bot
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Background for Student Page:(Studen
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(Background for Student Page:The no
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Background for Student Page:(Combin
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I. Water MusicMaterials:Activity:1.
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,.(Many people recognize a composer
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AdvertisementSolving Musical Myster
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(Material:RESTBlank music paperThre
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THETWtLVt- TONEM[T~OO(1.All twelve
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THETWtL Vt- TDNtM[T/-{OO(PAGE 3)(VI
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( .V. Most people can tell a differ
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-~r:Jb Wb ON TWb, !:~Mb ~Ql:OUbN[l,
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~U&1nI[I§F~15g~~g5(PAGE 2)The huma
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318Loud musicmay cause• •migraI
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(Select some of the following proje
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(1) How does sound travel? Howfast
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MUSIC GLOSSARYfif-notfifth.firstsca
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MUSIC GLOSSARYtern-wootempo. The ra
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INTRODUCTIONMATHEMATICS AND PHYSICS
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TITLEPAGE'fOPICMATHTYPEArchimedes K
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Above every person is a tall column
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Materials Needed:ISet up a pendulum
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(Materials Needed:2 metre sticks, s
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IVGraphing the results.(COl\llIlJUE
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Have a student bring a 5 or 10 spee
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(Materials Needed:An inclined plane
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BEING \tJTHE: MCDOL.E:Of: THINGS (I
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Materials Needed:REW.ii~W~EXPEj;2IE
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The following activities investigat
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~~lt~~ ~NDHALF-LIFE/,Materials Need
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QJ~t~Ur! RNDHALF-LIFE (Nuclear reac
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Albert A. Michelson (1852 - 1931),
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RtFLECTIONS2~OITJ3J13R(Two figures
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MIRROR, MIPPOQON TI-I[; WHLL(Materi
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IV~~~~~~( CONl"lNUED)Making some me
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(Materials Needed:Magnifying mirror
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(To project an image using a concav
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Step DBENDING OF LIGHT?![r(7?7CrIGN
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BENDING OF LIGHT?![(?!?{CrIL1N(COIV
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PHYSICS GLOSSARYref-weireflection,
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INTRODUCTIONMATHEMATICS AND SPORTSI
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World swim championships(Men(PRELIM
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Certainillustrationscan be used ast
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(PAGE
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(\TITLEPAGETOPICMATHTYPEOlympics -
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Each of the following numbers is as
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The time of day, the temperature an
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R 7(COIJTIIIlUW)(\___ 3HREZ I-lR11-
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Find a soccer ball. The Physical Ed
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( COI\lTllJUE.D)5E5The following qu
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3925.This activity consists of ten
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(PERSONAL RECORD OF CLASSROOM DECAT
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Most sporting activities involve an
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(Numerous ads to eat wisely and exe
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vvhors YOUQ TYPE1. Weigh yourself a
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AnRRI; L,JOUPW~~I[~LLWr=IT'?interes
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SHUTTLERUNTwo blocks of wood, 2"x2"
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The table to the right shows the fi
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(meanS 3 mi nutesI10 secondsWORLD R
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WORLD TRACK RECORDS-RUNNING EVENTS-
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(Rules for bowling with dice:1) Rol
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1) A bowling ball can have a circum
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YOU WILL NEED AN ALMANAC.BASEBALL A
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.j>.I\.)o"U (f)~'"03 c
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FLICHT"rTHE"/,E88(In most classes a
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Vet Moyer in the waySullivan slates
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IfnMOUf nTIILETEf PUZlLE I(Born in
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Have a student bring a 5 or 10 spee
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Use the chart to answer these quest
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SPORTS GLOSSARY ope-wor 2open frame
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BIBLIOGRAPHY MATHEMATICS IN SCIENCE
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BIBLIOGRAPHYMATHEMATICS IN SCIENCE
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BIBLIOGRAPHYMATHEMATICS AND MUSIC.
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BIBLIOGRAPHYOLD OREGON.1975.97403)M
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BIBLIOGRAPHYMATHEMATICS IN SCIENCE
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BIBLIOGRAPHYFILMSMATHEMATICS IN SCI
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Page Number3 It would be at its ori
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Page Number245 (1) .e1ectric train;
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Page NumberIII (1) Yes «2) Using t
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Page Number388 (a) pentagons and he
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