geom. – ch. 2.3 deductive reasoning - mr. deyo's...
TRANSCRIPT
Geom.–Ch.2.3DeductiveReasoning
Mr.Deyo
HomeWork1‐2‐3:1)StormCheckPastedinNotebook?
2)Section______ 3)Section______RFM/RTProblems_________ NotesCopiedinNotebook?Pasted&SolvedinNotebook?
Learning Target
StudentswillapplytheLawofDetachmentandtheLawofSyllogismindeductivereasoning.
Studentswillshowthisbycompletingagraphicorganizerandsolvingdeductivereasoningproblemsinapairactivity.
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) Inductive2) Deductive3) Detachment
4) Syllogism
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:
Deductivereasoningistheprocessofusinglogictodrawconclusionsfromgivenfacts,definitions,andproperties.
Indeductivereasoning,ifthegivenfactsaretrueandyouapplythecorrectlogic,thentheconclusionmustbetrue.TheLawofDetachmentisonevalidformofdeductivereasoning.
LawofDetachment
Ifpqisatruestatementandpistrue,thenqistrue.
A‐BProblemAnotes:
IdentifytheHypothesisandConclusioninthegivenconditional.Then,determineiftheconjectureisvalidbytheLawofDetachment. Given:IntheWorldSeries,ifateamwinsfourgames,thentheteamwinstheseries.
Statement:TheRedSoxwonfourgamesinthe2004WorldSeries.
Conjecture:TheRedSoxwonthe2004WorldSeries.
A‐BProblemACheck:
Identifythehypothesisandconclusioninthegivenconditional.
IntheWorldSeries,ifateamwinsfourgames,thentheteamwinstheseries.
Thestatement“TheRedSoxwonfourgamesinthe2004WorldSeries”matchesthehypothesisofatrueconditional.
BytheLawofDetachment,theRedSoxwonthe2004WorldSeries.Theconjectureisvalid.
A‐BProblemBSOLVE!!
IdentifytheHypothesisandConclusioninthegivenconditional.Then,determineiftheconjectureisvalidbytheLawofDetachment.
Given:Ifastudentpasseshisclasses,thestudentiseligibletoplaysports.
Statement:Ramonpassedhisclasses.
Conjecture:Ramoniseligibletoplaysports.
A‐BProblemBCheck!!
Identifythehypothesisandconclusioninthegivenconditional.
Ifastudentpasseshisclasses,thenthestudentiseligibletoplaysports.
Thestatement“Ramonpassedhisclasses”matchesthehypothesisofatrueconditional.
BytheLawofDetachment,Ramoniseligibletoplaysports.Theconjectureisvalid.
StormCheck(Think,Write,Discuss,Report)
Inyourownlife,givemeanexamplewhereyourfriend’sargument/claimwasbasedonfalselogic?
OneexampleinmylifewhereIcouldtellthat
myfriendwasusingfalselogicwas__________
_______________________________________
_______________________________________.
Notes:
AnothervalidformofdeductivereasoningistheLawofSyllogism.Itallowsyoutodrawconclusionsfromtwoconditionalstatementswhentheconclusionofoneisthehypothesisoftheother.
LawofSyllogism
Ifpqandqraretruestatements,thenprisatruestatement.
IFalldogsaremammals,
ANDIFallmammalsarewarm‐bloodedcreatures,
THEN,alldogsarewarm‐bloodedcreatures.
A‐BProblemAnotes:
DetermineiftheconjectureisvalidbytheLawofSyllogism.
Given:Ifafigureisakite,thenitisaquadrilateral.Ifafigureisaquadrilateral,thenitisapolygon.
Conjecture:Ifafigureisakite,thenitisapolygon.
A‐BProblemACheck:
Letp,q,andrrepresentthefollowing.
p:Afigureisakite.
q:Afigureisaquadrilateral.
r:Afigureisapolygon.
Youaregiventhatpqandqr.
Sinceqistheconclusionofthefirstconditionalandthehypothesisofthesecondconditional,youcanconcludethatpr.TheconjectureisvalidbyLawofSyllogism.
A‐BProblemBSOLVE!!
DetermineiftheconjectureisvalidbytheLawofSyllogism.
Given:Ifanumberisdivisibleby2,thenitiseven.
Ifanumberiseven,thenitisaninteger.
Conjecture:
Ifanumberisaninteger,thenitisdivisibleby2.
A‐BProblemBCheck!!
Letx,y,andzrepresentthefollowing.
x:Anumberisdivisibleby2.y:Anumberiseven.z:Anumberisaninteger.
Youaregiventhatxyandyz.TheLawofSyllogismcannotbeusedtodeducethatzx.Theconclusionisnotvalid.
Why?ARationalNumber(Decimalorfraction)canbedivisibleby2,butnotnecessarilyEVEN(WholeNumber)
StormCheck(Think,Write,Discuss,Report)
Inyourownwords,howwouldyouexplaintheLawofSyllogism?
TheLawofSyllogismis_____________________
________________________________________.
Inyourownwords,howwouldyouexplaintheLawofDetachment?
TheLawofDetachmentis___________________
________________________________________.
Vocabulary Review 1. Teachersaystheword.
• ALLStudentsrepeattheword.
2. Teachercountsoutsyllablesass/hesaystheword.
• ALLstudentsrepeatsyllablecountastheysaytheword.
3. Studentteamscreateaphysicalrepresentationoftheword.
• ClasschoosesonephysicalrepresentationforALLstudents.
4. Studentteamscreateafriendlydefinitionfortheword.
• Classchoosesonefriendlydefinitionfortheword.
1) Inductive2) Deductive3) Detachment
4) Syllogism
Learning Target
StudentswillapplytheLawofDetachmentandtheLawofSyllogismindeductivereasoning.
Studentswillshowthisbycompletingagraphicorganizerandsolvingdeductivereasoningproblemsinapairactivity.
2)Section______ 3)Section______RFM/RTProblems_________ NotesCopiedinNotebook?Pasted&SolvedinNotebook?
HomeWork1‐2‐3:1)StormCheckPastedinNotebook?
Ticket OUT.
Is the conclusion a result of inductive or deductive reasoning?
At Reagan High School, students must pass Geometry before they take Algebra 2. Emily is in Algebra 2, so she must have passed Geometry.
Ticket OUT.
Is the conclusion a result of inductive or deductive reasoning?
At Reagan High School, students must pass Geometry before they take Algebra 2. Emily is in Algebra 2, so she must have passed Geometry.
deductivereasoning