Upload
others
View
3
Download
0
Embed Size (px)
Citation preview
Geom.–Ch.2.1InductiveReasoning&Counterexamples
Mr.Deyo
HomeWork1‐2‐3:1)StormCheckPastedinNotebook?
NEWUnitTableofContents!2)Section______ 3)Section______RFM/RTProblems_________ NotesCopiedinNotebook?Pasted&SolvedinNotebook?
Learning Target
Studentswillapplyinductivereasoningtoidentifypatterns,makeconjectures,andfindcounterexamplestodisproveconjectures.
Studentswillshowthisbycompletingagraphicorganizerandsolvinginductivereasoningproblemsinapairactivity.
Storm Check (Think, Write, Discuss, Report) Questions on which to ponder and answer: 1. How are the two pictures similar? 2. How are they different? 3. How can these two pictures be related to math?
1) Conjecture2) Counterexample
3) Hypothesis4) Conclusion
Vocabulary 1. Teachersaystheword.
• ALLStudentsrepeattheword.
2. Teachercountsoutsyllablesass/hesaystheword.
• ALLstudentsrepeatsyllablecountastheysaytheword.
3. Studentteamscreateaphysicalrepresentationoftheword.
• ClasschoosesonephysicalrepresentationforALLstudents.
4. Studentteamscreateafriendlydefinitionfortheword.
• Classchoosesonefriendlydefinitionfortheword.
DAY 3 and/or DAY 4 1. Review the word
¨ Friendly Definition ¨ Physical Representation
2. Show how the word works ¨ Synonyms/antonym ¨ Word Problems ¨ Related words/phrases ¨ Example/non-example
Friendly Definition Sketch
Wordwork Sentence
DAY 2 1. Review word
¨ Friendly Definition ¨ Physical Representation
2. Draw a sketch
DAY 5 1. Review the word
¨ Friendly definition ¨ Physical Representation
3. Write a sentence at least 2 rich words (1 action) correct spelling correct punctuation correct subject/predicate agreement clear and clean writing
DAY 1 1. Use Visuals
2. Introduce the word ¨ Friendly Definition ¨ Physical Representation
3. Use Cognates
4. Write friendly definition
5. Physical Representation
WordList1. 2. 3. 4.
Notes:
Whenseveralexamplesformapatternandyouassumethepatternwillcontinue,youareapplyinginductivereasoning.
Inductivereasoningistheprocessofreasoningthataruleorstatementistruebecausespecificcasesaretrue.
Youmayuseinductivereasoningtodrawaconclusionfromapattern.
Astatementyoubelievetobetruebasedoninductivereasoningiscalledaconjecture.
A‐BProblemAnotes:
1)Findthenextiteminthepattern. January,March,May,...
2)Findthenextiteminthepattern. 7,14,21,28,…
A‐BProblemACheck:
1)Findthenextiteminthepattern. January,March,May,...
ThenextmonthisJuly.
Alternatingmonthsoftheyearmakeupthepattern.
2)Findthenextiteminthepattern. 7,14,21,28,…
Thenextmultipleis35.
Multiplesof7makeupthepattern.
A‐BProblemBSOLVE!!
3)Findthenextiteminthepattern.
4) Findthenextiteminthepattern:
0.4,0.04,0.004,…
A‐BProblemBCheck!!
3)Findthenextiteminthepattern. Inthispattern,thefigurerotates90°counter‐clockwiseeachtime.
Thenextfigureis.
4)Findthenextiteminthepattern0.4,0.04,0.004,…Whenreadingthepatternfromlefttoright,thenextiteminthepatternhasonemorezeroafterthedecimalpoint.
Thenextitemwouldhave3zerosafterthedecimalpoint,or0.0004.
StormCheck(Think,Write,Discuss,Report)
Inyourownlife,givemetwoexampleswhereyoulookforpatternsandmakeconjectures?
OneexampleinmylifewhereIusepatternsand
makeconjecturesis______________________.
Anotherexampleis______________________
_______________________________________.
Notes:
InductiveReasoning
1.Lookforapattern.
2.Makeaconjecture.
3.Provetheconjectureorfindacounterexample.
Notes:
Toshowthataconjectureisfalse,youhavetofindonlyoneexampleinwhichtheconjectureisnottrue.Thiscaseiscalledacounterexample.Acounterexamplecanbeadrawing,astatement,oranumber.
Toshowthataconjectureisalwaystrue,youmustproveit.
A‐BProblemAnotes:
Theproductoftwooddnumbersis?.
1)Completetheconjecture(Testexamplesfirst).
4)Makeaconjectureaboutthelengthsofmaleandfemalelionsbasedonthedata.
Average Lion Lengths Length of Female (ft) 4.5 5.1 5.0 4.8 4.9 4.7 Length of Male (ft) 4.7 4.9 5.4 5.2 5.3 4.8
A‐BProblemACheck:
Theproductoftwooddnumbersis?.
1)Completetheconjecture(Testexamplesfirst).
Theproductoftwooddnumbersisodd.
Listsomeexamplesandlookforapattern. 1x1=13x3=95x7=35
4)Makeaconjectureaboutthelengthsofmaleandfemalelionsbasedonthedata.
In5ofthe6pairsofnumbersabovethemaleislonger.
Male lions are longer than female lions.
Average Lion Lengths Length of Female (ft) 4.5 5.1 5.0 4.8 4.9 4.7 Length of Male (ft) 4.7 4.9 5.4 5.2 5.3 4.8
A‐BProblemBSOLVE!!
3)Completetheconjecture(Testexamplesfirst). Thesumoftwopositivenumbersis?.
4)Makeaconjectureaboutthelengthsofmaleandfemalewhalesbasedonthedata.
Average Whale Lengths Length of Female (ft) 49 51 50 48 51 47 Length of Male (ft) 47 45 44 46 48 48
A‐BProblemBCheck!!
3)Completetheconjecture(Testexamplesfirst).
Thesumoftwopositivenumbersis?. Thesumoftwopositivenumbersispositive.
Listsomeexamples&lookforapattern.
1+1=2 3.14+0.01=3.15
3,900+1,000,017=1,003,917
4)Makeaconjectureaboutthelengthsofmaleandfemalewhalesbasedonthedata.
In5ofthe6pairsofnumbersabovethefemaleislonger.
Female whales are longer than male whales.
Average Whale Lengths Length of Female (ft) 49 51 50 48 51 47 Length of Male (ft) 47 45 44 46 48 48
StormCheck(Think,Write,Discuss,Report)
Inyourownwords,howwouldyoudefineaconjectureandacounterexample?
Aconjectureis__________________________.
Acounterexampleis_____________________.
Howdoaconjectureandacounterexamplerelatetoeachother?
Theyrelatetoeachotherbecause____________
________________________________________.
1) Conjecture2) Counterexample
3) Hypothesis4) Conclusion
Vocabulary Review 1. Teachersaystheword.
• ALLStudentsrepeattheword.
2. Teachercountsoutsyllablesass/hesaystheword.
• ALLstudentsrepeatsyllablecountastheysaytheword.
3. Studentteamscreateaphysicalrepresentationoftheword.
• ClasschoosesonephysicalrepresentationforALLstudents.
4. Studentteamscreateafriendlydefinitionfortheword.
• Classchoosesonefriendlydefinitionfortheword.
Learning Target
Studentswillapplyinductivereasoningtoidentifypatterns,makeconjectures,andfindcounterexamplestodisproveconjectures.
Studentswillshowthisbycompletingagraphicorganizerandsolvinginductivereasoningproblemsinapairactivity.
2)Section______ 3)Section______RFM/RTProblems_________ NotesCopiedinNotebook?Pasted&SolvedinNotebook?
HomeWork1‐2‐3:1)StormCheckPastedinNotebook?
NEWUnitTableofContents!
Ticket OUT.
Findthenextitemineachpattern.
1.0.7,0.07,0.007,… 2.
Determineifeachconjectureistrue.Iffalse,giveacounterexample.3.Thequotientoftwonegativenumbersisapositivenumber. 4.Twosupplementaryanglesarenotcongruent.
Ticket OUT.
Findthenextitemineachpattern.
1.0.7,0.07,0.007,… 2.
0.0007
Determineifeachconjectureistrue.Iffalse,giveacounterexample.3.Thequotientoftwonegativenumbersisapositivenumber. 4.Twosupplementaryanglesarenotcongruent.
true
false;90°and90°