2.8h the wow factor - mr. lemon's math...
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SECONDARY MATH II // MODULE 2
STRUCTURES OF EXPRESSIONS – 2.8H
Mathematics Vision Project
Licensed under the Creative Commons Attribution CC BY 4.0 mathematicsvisionproject.org
2.8H The Wow Factor
A Solidify Understanding Task
Optima’sQuiltssometimesgetsordersforblocksthataremultiplesofagivenblock.Forinstance,
Optimagotanorderforablockthatwasexactlytwiceasbigastherectangularblockthathasaside
thatis1”longerthanthebasicsize,!, andonesidethatis3”longerthanthebasicsize.1.Drawandlabelthisblock.Writetwoequivalentexpressionsfortheareaoftheblock.
2.Ohdear!Thisorderwasscrambledandthepiecesareshownhere.Putthepiecestogetherto
makearectangularblockandwritetwoequivalentexpressionsfortheareaoftheblock.
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SECONDARY MATH II // MODULE 2
STRUCTURES OF EXPRESSIONS – 2.8H
Mathematics Vision Project
Licensed under the Creative Commons Attribution CC BY 4.0 mathematicsvisionproject.org
3.Whatdoyounoticewhenyoucomparethetwoequivalentexpressionsinproblems#1and#2?
4.Optimahasalotofneworders.Usediagramstohelpyoufindequivalentexpressionsforeachof
thefollowing:
a. 5!! + 10!
b. 3!! + 21! + 36
c. 2!! + 2! − 4
d. 2!! − 10! + 12
e. 3!! − 27
Becausesheisagreatbusinessmanager,Optimaoffershercustomerslotsofoptions.Oneoptionis
tohaverectanglesthathavesidelengthsthataremorethanone!.Forinstance,Optimamadethiscoolblock:
5. Writetwoequivalentexpressionsforthisblock.Usethedistributivepropertytoverifythat
youransweriscorrect.
SECONDARY MATH II // MODULE 2
STRUCTURES OF EXPRESSIONS – 2.8H
Mathematics Vision Project
Licensed under the Creative Commons Attribution CC BY 4.0 mathematicsvisionproject.org
6. Herewehavesomepartialorders.Wehaveoneoftheexpressionsfortheareaoftheblock
andweknowthelengthofoneofthesides.Useadiagramtofindthelengthoftheothersideand
writeasecondexpressionfortheareaoftheblock.Verifyyourtwoexpressionsfortheareaofthe
blockareequivalentusingalgebra.
a. Area: 2!! + 7! + 3 Side: (! + 3)
Equivalentexpressionforarea:
b. Area: 5!! + 8! + 3 Side: (! + 1)
Equivalentexpressionforarea:
c. Area: 2!! + 7! + 3 Side: (2! + 1)
Equivalentexpressionforarea:
7. Whataresomepatternsyouseeinthetwoequivalentexpressionsforareathatmighthelp
youtofactor?
SECONDARY MATH II // MODULE 2
STRUCTURES OF EXPRESSIONS – 2.8H
Mathematics Vision Project
Licensed under the Creative Commons Attribution CC BY 4.0 mathematicsvisionproject.org
8. Businessisbooming!Moreandmoreordersarecomingin!Usediagramsornumber
patterns(orboth)towriteeachofthefollowingordersinfactoredform:
a. 3!! + 16! + 5
b. 2!! − 13! + 15
c. 3!! + ! − 10
d. 2!! + 9! − 5
9. InThe !Factor,youwrotesomerulesfordecidingaboutthesignsinsidethefactors.Dothoserulesstillworkinfactoringthesetypesofexpressions?Explainyouranswer.
10. ExplainhowOptimacantelliftheblockisamultipleofanotherblockorifonesidehasa
multipleof!inthesidelength.
SECONDARY MATH II // MODULE 2
STRUCTURES OF EXPRESSIONS – 2.8H
Mathematics Vision Project
Licensed under the Creative Commons Attribution CC BY 4.0 mathematicsvisionproject.org
11. There’sonemoretwistonthekindofblocksthatOptimamakes.Thesearethetrickiestof
allbecausetheyhavemorethanone!inthelengthofbothsidesoftherectangle!Here’sanexample:
Writetwoequivalentexpressionsforthisblock.Usethedistributivepropertytoverifythatyour
answeriscorrect.
12. Allright,let’strythetrickyones.Theymaytakealittlemessingaroundtogetthefactored
expressiontomatchthegivenexpression.Makesureyoucheckyouranswerstobesurethat
you’vegotthemright.Factoreachofthefollowing:
a. 6!! + 7! + 2
b. 10!! + 17! + 3
c. 4!! − 8! + 3
d. 4!! + 4! − 3
e. 9!! − 9! − 10
12. Writea“recipe”forhowtofactortrinomialsintheform,!"! + !" + !.