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