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.

CC

BY

Pau

l Ink

les

http

s://f

lic.k

r/p/

dxn5

FU

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,!"! + !" + !.