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’s Quilts sometimes gets orders for blocks that are multiples of a given block. For instance, Optima got an order for a block that was exactly twice as big as the rectangular block that has a side that is 1” longer than the basic size, !, and one side that is 3” longer than the basic size. 1. Draw and label this block. Write two equivalent expressions for the area of the block. 2. Oh dear! This order was scrambled and the pieces are shown here. Put the pieces together to make a rectangular block and write two equivalent expressions for the area of the block. CC BY Paul Inkles https://flic.kr/p/dxn5FU
Transcript of 2.8H The Wow Factor - Mr. Lemon's Math...
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,!"! + !" + !.
