friday mar 13 slides from class - washburn high school
TRANSCRIPT
Takeoutyournotebookfortoday'swarm-up!
FridayMar13,2015
Testing Season is coming soon.... remember your Miller Pride and DO YOUR BEST!
HW#11wsAreaChallengeProblems-dueFriMar13EXT#3-FactoringPractice-isdueonFridayMar13
TESTonPOLYGONS nextTuesdayMar17th!!
Richard Sudo Friday, March 13, 2015 3:10:14 PM CT 00:19:e3:4a:d2:21
LearningTargets
Richard Sudo Friday, March 13, 2015 3:10:14 PM CT 00:19:e3:4a:d2:21
LT5.2:Icandescribe,compareandcontrastpropertiesofpolygons.
LT5.3:Icansolveproblemsandjustifymyresultsusingpropertiesofcongruentandsimilarpolygons
LT5.1:Icancomposeanddecomposepolygons.
LT5.4:Icanusecoordinategeometrytomeasureandclassifypolygons.
LT2.6I can apply the properties of special right triangles to solve problems and logically justify my results.LT2.7I can use coordinate geometry to translate, reflect and rotate triangles and analyze the result.
LT2.5I can apply the Pythagorean Theorem and its converse to solve problems and logically justify my results.
Richard Sudo Friday, March 13, 2015 3:10:14 PM CT 00:19:e3:4a:d2:21
Warm-up
Richard Sudo Friday, March 13, 2015 3:10:14 PM CT 00:19:e3:4a:d2:21
Warmup3-13-15
1. 2. Aregularn-gonhasaninteriorangleof157.50Howmanysidesdoesithave?
Richard Sudo Friday, March 13, 2015 3:10:14 PM CT 00:19:e3:4a:d2:21
1.
Richard Sudo Friday, March 13, 2015 3:10:14 PM CT 00:19:e3:4a:d2:21
1.
Richard Sudo Friday, March 13, 2015 3:10:14 PM CT 00:19:e3:4a:d2:21
2. Aregularn-gonhasaninteriorangleof157.50Howmanysidesdoesithave?
Richard Sudo Friday, March 13, 2015 3:10:14 PM CT 00:19:e3:4a:d2:21
2. Aregularn-gonhasaninteriorangleof157.50Howmanysidesdoesithave?
Richard Sudo Friday, March 13, 2015 3:10:14 PM CT 00:19:e3:4a:d2:21
"lattice"points
onesquareunit
Whataboutpolygonsthataren't"regular"polyons-IsthereaFORMULA??????
Richard Sudo Friday, March 13, 2015 3:10:14 PM CT 00:19:e3:4a:d2:21
Richard Sudo Friday, March 13, 2015 3:10:14 PM CT 00:19:e3:4a:d2:21
Richard Sudo Friday, March 13, 2015 3:10:14 PM CT 00:19:e3:4a:d2:21
Richard Sudo Friday, March 13, 2015 3:10:14 PM CT 00:19:e3:4a:d2:21
Richard Sudo Friday, March 13, 2015 3:10:14 PM CT 00:19:e3:4a:d2:21
Richard Sudo Friday, March 13, 2015 3:10:14 PM CT 00:19:e3:4a:d2:21
Richard Sudo Friday, March 13, 2015 3:10:14 PM CT 00:19:e3:4a:d2:21
Notes
Richard Sudo Friday, March 13, 2015 3:10:14 PM CT 00:19:e3:4a:d2:21
π day???
3-14-2015
Richard Sudo Friday, March 13, 2015 3:10:14 PM CT 00:19:e3:4a:d2:21
Richard Sudo Friday, March 13, 2015 3:10:14 PM CT 00:19:e3:4a:d2:21
3/14/2015
3/14/15926:53:58
Wemisseditby423yrs
Richard Sudo Friday, March 13, 2015 3:10:14 PM CT 00:19:e3:4a:d2:21
Only13911moreyears togo
Richard Sudo Friday, March 13, 2015 3:10:14 PM CT 00:19:e3:4a:d2:21
πisanirrational number !!Inmathematics,anirrational numberisalnumberthatcannotbeexpressedasaratioa/b,whereaandbareintegersandbisnon-zero.Inotherwords,thismeansthatanirrational numberlikePicannot berepresented asasimple fraction.
Richard Sudo Friday, March 13, 2015 3:10:14 PM CT 00:19:e3:4a:d2:21
πisirrational!!!(cannotberepresentedasafraction)
Wedefinitelywon'tcelebratelikethis
Richard Sudo Friday, March 13, 2015 3:10:14 PM CT 00:19:e3:4a:d2:21
InthisclasswewillnotdisrespectPibyeatingsomecheapsugaryconfection!
Richard Sudo Friday, March 13, 2015 3:10:14 PM CT 00:19:e3:4a:d2:21
ST.PATRICKSDAYISMarch17
Richard Sudo Friday, March 13, 2015 3:10:14 PM CT 00:19:e3:4a:d2:21
ST.PATRICKSDAYISMarch17
Richard Sudo Friday, March 13, 2015 3:10:14 PM CT 00:19:e3:4a:d2:21
HaikuPoetry:
5
7
5
Falling to the ground,
I watch a leaf settle down
In a bed of brown.
Richard Sudo Friday, March 13, 2015 3:10:14 PM CT 00:19:e3:4a:d2:21
πPiKuπ
3
1
4
radius
twice
diameter!
Sudois
right.
Nopietoday!
MyBestClassYay!Geometry
radiustwicediameter!
Heystudents!
LEARN...
helpyourselfgrowRichard Sudo Friday, March 13, 2015 3:10:14 PM CT 00:19:e3:4a:d2:21
EatingPIEisatemporarythrillwhichcanleadtoindigestion
WhereasPIismorelikePoetry3.14159265358979323...
Richard Sudo Friday, March 13, 2015 3:10:14 PM CT 00:19:e3:4a:d2:21
Richard Sudo Friday, March 13, 2015 3:10:14 PM CT 00:19:e3:4a:d2:21
Thefirst calculation ofpiwasdonebyArchimedesofSyracuse(287–212BC),oneofthegreatestmathematiciansoftheancientworld.Archimedesapproximatedtheareaofacirclebyusing thePythagorean Theoremtofind theareasoftworegularpolygons:thepolygoninscribedwithinthecircleandthepolygonwithinwhichthecirclewascircumscribed.Sincetheactualareaofthecircleliesbetweentheareasoftheinscribedandcircumscribedpolygons,theareasofthepolygonsgaveupperandlowerboundsfortheareaofthecircle.Archimedesknewthathehadnotfoundthevalueofpibutonlyanapproximationwithinthoselimits.Inthisway,Archimedesshowedthatpiisbetween31/7and310/71.
Richard Sudo Friday, March 13, 2015 3:10:14 PM CT 00:19:e3:4a:d2:21
Archemedes
Hmmmm....
Piisbetween
3 and317
1071 3=3.1428
3=3.1408π =3.14159
171071
Richard Sudo Friday, March 13, 2015 3:10:14 PM CT 00:19:e3:4a:d2:21
circumscribedcircle
inscribedcircle
radius
apothem
side
Richard Sudo Friday, March 13, 2015 3:10:14 PM CT 00:19:e3:4a:d2:21
AsimilarapproachwasusedbyZuChongzhi(429–501),abrilliantChinesemathematicianandastronomer.ZuChongzhiwouldnothavebeenfamiliarwithArchimedes’method—butbecausehisbookhasbeenlost,littleisknownofhiswork.Hecalculatedthevalueoftheratioofthecircumferenceofacircletoitsdiametertobe355/113.Tocomputethisaccuracyforpi,hemusthavestartedwithaninscribed regular24,576-gonandperformedlengthycalculationsinvolvinghundredsofsquarerootscarriedoutto9decimalplaces
Richard Sudo Friday, March 13, 2015 3:10:14 PM CT 00:19:e3:4a:d2:21
Homework
Richard Sudo Friday, March 13, 2015 3:10:14 PM CT 00:19:e3:4a:d2:21
DueonFridayMar13
210.44cm2
337.2cm2
120.71cm2
Richard Sudo Friday, March 13, 2015 3:10:14 PM CT 00:19:e3:4a:d2:21
Richard Sudo Friday, March 13, 2015 3:10:14 PM CT 00:19:e3:4a:d2:21
Richard Sudo Friday, March 13, 2015 3:10:14 PM CT 00:19:e3:4a:d2:21
Richard Sudo Friday, March 13, 2015 3:10:14 PM CT 00:19:e3:4a:d2:21
Richard Sudo Friday, March 13, 2015 3:10:14 PM CT 00:19:e3:4a:d2:21
Richard Sudo Friday, March 13, 2015 3:10:14 PM CT 00:19:e3:4a:d2:21
Richard Sudo Friday, March 13, 2015 3:10:14 PM CT 00:19:e3:4a:d2:21
Richard Sudo Friday, March 13, 2015 3:10:14 PM CT 00:19:e3:4a:d2:21
Richard Sudo Friday, March 13, 2015 3:10:14 PM CT 00:19:e3:4a:d2:21
Richard Sudo Friday, March 13, 2015 3:10:14 PM CT 00:19:e3:4a:d2:21
Homework
Richard Sudo Friday, March 13, 2015 3:10:14 PM CT 00:19:e3:4a:d2:21
Richard Sudo Friday, March 13, 2015 3:10:14 PM CT 00:19:e3:4a:d2:21
Richard Sudo Friday, March 13, 2015 3:10:14 PM CT 00:19:e3:4a:d2:21
Richard Sudo Friday, March 13, 2015 3:10:14 PM CT 00:19:e3:4a:d2:21
Richard Sudo Friday, March 13, 2015 3:10:14 PM CT 00:19:e3:4a:d2:21
Richard Sudo Friday, March 13, 2015 3:10:14 PM CT 00:19:e3:4a:d2:21
1250
Richard Sudo Friday, March 13, 2015 3:10:14 PM CT 00:19:e3:4a:d2:21
98 82 90 94
Richard Sudo Friday, March 13, 2015 3:10:14 PM CT 00:19:e3:4a:d2:21
Richard Sudo Friday, March 13, 2015 3:10:14 PM CT 00:19:e3:4a:d2:21
Richard Sudo Friday, March 13, 2015 3:10:14 PM CT 00:19:e3:4a:d2:21
Richard Sudo Friday, March 13, 2015 3:10:14 PM CT 00:19:e3:4a:d2:21
Richard Sudo Friday, March 13, 2015 3:10:14 PM CT 00:19:e3:4a:d2:21
Richard Sudo Friday, March 13, 2015 3:10:14 PM CT 00:19:e3:4a:d2:21
Richard Sudo Friday, March 13, 2015 3:10:14 PM CT 00:19:e3:4a:d2:21