Download 4. 3 Solving Equations Literally

Survey
yes no Was this document useful for you?
   Thank you for your participation!

* Your assessment is very important for improving the work of artificial intelligence, which forms the content of this project

Document related concepts

List of important publications in mathematics wikipedia, lookup

Mathematics of radio engineering wikipedia, lookup

Line (geometry) wikipedia, lookup

System of polynomial equations wikipedia, lookup

Elementary algebra wikipedia, lookup

Recurrence relation wikipedia, lookup

History of mathematical notation wikipedia, lookup

System of linear equations wikipedia, lookup

History of algebra wikipedia, lookup

Algebra wikipedia, lookup

Partial differential equation wikipedia, lookup

Secondary School Mathematics Curriculum Improvement Study wikipedia, lookup

Analytical mechanics wikipedia, lookup

Transcript
10
CC BY https://flic.kr/p/ayDEGr
SECONDARY MATH I // MODULE 4
EQUATIONS AND INEQUALITIES – 4.3
4. 3 Solving Equations Literally
A Practice Understanding Task
Solveeachofthefollowingequationsforx:
1.
3x + 2
=7
5
2.
3x + 2y
=7
5
3.
4x
− 5 = 11
3
4.
4x
− 5y = 11
3
5.
2
(x + 3) = 6
5
6.
2
(x + y) = 6
5
7.
2(3x + 4) = 4 x + 12
8.
2(3x + 4 y) = 4 x + 12y
Writeaverbaldescriptionforeachstepoftheequationsolvingprocessusedtosolvethefollowing
equationsforx.Yourdescriptionshouldincludestatementsabouthowyouknowwhattodonext.
Forexample,youmightwrite,“FirstI__________________,because_______________________...”
9.
ax + b
−d=e
c
Mathematics Vision Project
Licensed under the Creative Commons Attribution CC BY 4.0
mathematicsvisionproject.org
10.
r⋅
mx
+s=t
n
SECONDARY MATH I // MODULE 4
EQUATIONS AND INEQUALITIES – 4.3
4. 3 Solving Equations Literally – Teacher Notes
A Practice Understanding Task
Purpose:Thistaskprovidespracticeforsolvinglinearequationsinonevariable,solvinglinear
equationsintwovariablesforoneofitsvariables,andsolvingliteralequations.Theprocessfor
solvingmultivariableequationsforoneofitsvariablesbecomesmoreapparentwhenjuxtaposed
withsimilarly-formattedequationsinonevariable.Theonlydifferenceinthesolutionprocessis
theabilitytocarryoutnumericalcomputationstosimplifytheexpressionsintheone-variable
equations.
CoreStandardsFocus:
A.REI.1Explaineachstepinsolvingasimpleequationasfollowingfromtheequalityofnumbers
assertedatthepreviousstep,startingfromtheassumptionthattheoriginalequationhasasolution.
Constructaviableargumenttojustifyasolutionmethod.
A.REI.3Solvelinearequationsandinequalitiesinonevariable,includingequationswith
coefficientsrepresentedbyletters.
RelatedStandards:
StandardsforMathematicalPracticeofFocusintheTask:
SMP7–Lookandmakeuseofstructure
SMP8-Lookforandexpressregularityinrepeatedreasoning
AdditionalResourcesforTeachers:
Ananswerkeyforthequestionsinthetaskcanbefoundasaseparatepageattheendofthese
teachernotes.Itisrecommendedthatyouworkthroughthetaskyourselfbeforeconsultingthe
answerkeytodevelopabettersenseofhowyourstudentsmightengageinthetask.
Mathematics Vision Project
Licensed under the Creative Commons Attribution CC BY 4.0
mathematicsvisionproject.org
SECONDARY MATH I // MODULE 4
EQUATIONS AND INEQUALITIES – 4.3
TheTeachingCycle:
Launch(WholeClass):
Encouragestudentstonotethesimilaritiesintheirworkonthepairsofproblemsinquestions1-8.
Alsopointoutthattheyaretowritedetailedexplanationsoftheirsolutionstrategyonproblems9
and10.Onewaytofacilitatethiswouldbetohavestudentsfoldapieceofpaperinhalflengthwise.
Ontheleftsideofthepapertheywriteouttheiralgebrasteps,andontherightsidetheywriteout
theirjustifications.
Explore(SmallGroup):
Monitorstudentswhileworkingontheseproblemsandofferappropriatefeedback,asnecessary.
Someoftheproblemshavealternativestrategies,suchas#5whereyoucandistributethe2/5first,
ormultiplybothsidesoftheequationsby5/2first.
Helpstudentsrecognizethedifferencebetweenchangingtheformofanexpressionononesideof
anequation,vs.writinganequivalentequationbyapplyingthesameoperationtobothsides.
Ifstudentsarehavingdifficultieswith#9or#10,havethemwritearelatedequationinwhichthey
replaceallletterswithnumbersexceptforthex.Seeiftheycansolvetherelatedequationforxand
ifthatworkcanhelpthemsolvetheoriginalliteralequation.Problem10involvesasquarerootin
ordertoemphasizethatoneofthekeyissuesinsolvinganequationisto“un-do”anoperationby
applyingtheinverseoperationtobothsides.Helpstudentsthinkabouthowthatwouldplayoutin
problem10.Thatis,howmightthey“un-do”asquareroot?
Discuss(WholeClass):
Havestudentspresenttheirsolutionprocessforanyproblemsthatmayhavebeendifficultfora
numberofstudents.Youmightalsowanttohavestudentscritiqueeachother’sexplanationson
problems9and10byhavingstudentsexchangepapers.Theyshouldfoldtheirpartner’spaperin
half,sothatonlytherightsidewiththewrittenexplanationisshowing.Onaseparatesheetof
papertheyshouldwrite-outthealgebrastepstheywouldtaketosolveeachproblem,basedonlyon
thewordingoftheirpartners’explanation.Theyshoulddiscussanyexplanationsthatareunclear
withtheirpartner.
AlignedReady,Set,Go:EquationsandInequalities4.3
Mathematics Vision Project
Licensed under the Creative Commons Attribution CC BY 4.0
mathematicsvisionproject.org
11
SECONDARY MATH I // MODULE 4
4.3
SOLVING EQUATIONS AND INEQUALITIES – 4.3
READY, SET, GO!
Name
PeriodDate
READY
Topic:SolvingInequalities.
Usetheinequality−9 < 2tocompleteeachrowinthetable.
Applyeachoperationtotheoriginal
Result
Istheresulting
inequality−9 < 2
inequalitytrueorfalse?
Example:Add3tobothsides
-9+3<2+3→-6<5
True
1.Subtract7frombothsides.
2.Add15tobothsides.
3.Add-10tobothsides.
4.Multiplybothsidesby10.
5.Dividebothsidesby5.
6.Multiplybothsidesby-6.
7.Dividebothsidesby-3.
8.Whatoperationswhenperformedonaninequality,reversetheinequality?
(Beveryspecific!)
SET
Topic:Solveliteralequationsthatrequiremorethanonestep.
Solvefortheindicatedvariable.Showyourwork!!!
9.Solveforh.
! = 25!ℎ
10.Solveforh.
! = !! ! ℎ
11.Solveform.! = 7! + 6
12.Solveform.! = !" + !
13.Solveforz. ! = ! + 7 3
14.Solveforz. ! = ! + 7 !
15.Solveforx.
!!!
!
!!!!
= 4
16.Solveforx.
− 9 = 6
18.Solveforx.
!!
20.Solveforx.
!
!
= 4
!!
17.Solveforx.
!
!
− 9! = 6
19.Solveforx.
!
!
! − 2 = 12
Mathematics Vision Project
Licensed under the Creative Commons Attribution CC BY 4.0
mathematicsvisionproject.org
!
! − 2! = 12
12
SECONDARY MATH I // MODULE 4
4.3
SOLVING EQUATIONS AND INEQUALITIES – 4.3
GO
Topic:Identifyingx-interceptsandy-intercepts
Locatethex-interceptandy-interceptinthetable.Writeeachasanorderedpair.
21.
22.
23.
!
!
!
!
!
!
-4
12
0
-6
-3
10
-3
10
3
-5
-2
8
-2
8
6
-4
-1
6
-1
6
9
-3
0
4
0
4
12
-2
1
2
1
2
15
-1
2
0
2
0
18
0
3
-2
x–intercept:
x–intercept:
x–intercept:
y–intercept:
y–intercept:
y–intercept:
Locatethex-interceptandthey-interceptinthegraph.Writeeachasanorderedpair.
24.
25.
x–intercept:
x–intercept:
y–intercept:
y–intercept:
Mathematics Vision Project
Licensed under the Creative Commons Attribution CC BY 4.0
mathematicsvisionproject.org
13
SECONDARY MATH I // MODULE 4
4.3
SOLVING EQUATIONS AND INEQUALITIES – 4.3
Solveeachequationforx.Providethejustificationsforeachstep.Seethefirstexampleasa
reminderforthetypesofjustificationsthatmightbeused.
Example:
26.
4x–10=2
Justification
3x–6=15
Justification
+6+6
AdditionProperty
ofequality
3x=21
DivisionProperty
33
ofequality
x=7
27.
28.
–16=3x+11
Justification
6–2x=10
Justification
29.
6x+3=x+18
30.
Justification
3x–10=2x+12
Justification
31.
32.
X(B+7)=9
Justification
12x+3y=15
Justification
Mathematics Vision Project
Licensed under the Creative Commons Attribution CC BY 4.0
mathematicsvisionproject.org