Download Algebra II Curriculum

AlgebraIICurriculum
PASSAICCOUNTYTECHNICALINSTITUTE
45ReinhardtRoad
Wayne,NewJersey
REVISED2016
AlgebraIICurriculum
AlgebraIIOverview–Buildingontheunderstandingoflinear,quadraticandexponentialfunctions
fromAlgebraI,thiscoursewillextendfunctionconceptstoincludepolynomial,rational,andradical
functions.Thestandardsinthiscoursecontinuetheworkofmodelingsituationsandsolving
equations.
Unit1standardswillbuildonthestudents’previousknowledgeoffunctions,trigonometricratiosandcirclesin
geometrytoextendtrigonometrytomodelperiodicphenomena.Standardwillcontinuewithanalyzationof
trigonometricidentities.
Unit2willextendstudent’salgebraknowledgeofpolynomials.Standardwillcontinuewithfactoring,solvingand
graphingpolynomials,focusingontransformationsofgraphs.
Unit3willextendstudent’salgebraknowledgeofrational,radical,andexponentialfunctions.Standardwill
continuewithlogarithmicfunctions.Thegraphsofallthefunctionsinunit3willbemodeledandtheir
transformationswillbeanalyzed.
Unit4willinvestigateinversefunctions,usingcompositions.Theunitwillcontinuewithrelationandvisual
displaysandsummarystatisticslearnedinpriorcoursestodifferenttypesofdataandtoprobabilitydistributions.
Samples,surveys,experimentsandsimulationswillbeusedasmethodstocollectdata.
PCTIMATHEMATICSDEPARTMENT
COURSE:AlgebraII
UNIT:1
UNITNAME:TRIGONOMETRY
TOPICS Green
Book
Blue
Book
Obj.
#
STUDENTLEARNINGOBJECTIVES
CCSScode
0.SummerPacketReview(10days)
10days
1
Reviewkeyconceptsfromalgebra1withinthesummerpacket.
I. TRIGONOMETRICRATIOSANDFUNCTIONS(35days)
7days
9.2
10.3
1
Understandtheradianmeasureofanangleasthelengthofthearcontheunitcircle
subtendedbytheangle.
F.TF.1
7days
9.2;9.3
10.3
2
Explainhowtheunitcircleinthecoordinateplaneenablestheextensionof
trigonometricfunctionstoallrealnumbers.
F.TF.2
7days
10.1
11.1;
11.2
3
Graphtrigonometricfunctions,showingperiod,midline,andamplitude.
F.IF.4,F.IF.7E,
F.BF.3
7days
10.2
11.1;
11.2
4
Choosetrigonometricfunctionstomodelperiodicphenomenawithspecified
amplitude,frequency,andmidline.**
F.TF.5
7days
10.3
11.3
5
VerifyreciprocaltrigonometricandPythagoreanidentities.
F.TF.8
**TaughtinApps/NotConceptsorResource
TECHNOLOGYSTANDARDS
I.1.Understandtheradianmeasureofanangleasthelengthofthearcontheunitcirclesubtendedbytheangle.
https://www.youtube.com/watch?v=cwL3uktPLEs
https://www.youtube.com/watch?v=sw5QNMLpep0
13.2–DefineGeneralAnglesandUseRadianMeasure.ppt
http://www.youtube.com/watch?v=vlSb74Gk8yc
http://www.youtube.com/watch?v=N6Lsjb4s5Ak
http://ceemrr.com/Geometry2/GeneralAngles/GeneralAngles_print.html
13_2Notes.doc-MiraCostaHighSchool
I.2.Explainhowtheunitcircleinthecoordinateplaneenablestheextensionoftrigonometricfunctionstoallreal
numbers.
http://www.youtube.com/watch?v=cNjzynK5QqE
http://cims.nyu.edu/~kiryl/Precalculus/Section_6.3Trigonometric%20Functions%20of%20Angles/Trigonometric%20Functions%20of%20Angles.pdf
http://www.youtube.com/watch?v=Cg70E506maw
http://www.youtube.com/watch?v=zFvxHQtUHrQ
http://www.youtube.com/watch?v=sb9oZZeBNhg
I.3.Graphtrigonometricfunctions,showingperiod,midline,andamplitude.
http://www.mathsisfun.com/algebra/trig-sin-cos-tan-graphs.html
http://www.analyzemath.com/unitcircle/unit_circle_applet.html
http://www.youtube.com/watch?v=pxFZCTAl9G8
http://exchange.smarttech.com/search.html?q=%22Sine%20%20Cosine%22
http://youtu.be/yR7y8hyOpDU
http://youtu.be/c1VD_LEs5ZY
I.4.Choosetrigonometricfunctionstomodelperiodicphenomenawithspecifiedamplitude,frequency,andmidline.**
TranslateandReflectTrigonometricGraphs-MiraCostaHighSchool
10-2TranslateandReflectTrigonometricGraphs
http://youtu.be/CuvO9-Zk2Xc
http://youtu.be/0KxVA7NWZiM
I.5.Verifyreciprocaltrigonometricandpythagoreanidentities.
ProvingTrigonometricIdentities-Purplemath
Verifyingtrigonometricidentities-SlideShare
http://youtu.be/vA6451TpSig
http://youtu.be/TCdhf9iVkYc
http://youtu.be/q8k-sS7qRts
http://youtu.be/mAnw4ImaPK0
http://youtu.be/a70-dYvDJZY
KEY
VOCABULARY
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
Sine
Cosine
Tangent
Cosecant
Secant
Cotangent
Initialside
Terminalside
Standardposition
Coterminal
Radian
Sector
Centralangle
Unitcircle
Quadrantalangle
Referenceangle
Amplitude
Periodicfunction
Cycle
Period
Frequency
Translation
Reflection
Amplitude
Period
Trigonometric
identity
SelectedOpportunitiesforConnectionsto
MathematicalPractices
1.
2.
3.
4.
5.
6.
7.
8.
Makesenseofproblemsandpersevereinsolvingthem.
Reasonabstractlyandquantitatively.
Constructviableargumentsandcritiquethereasoningofothers.
Modelwithmathematics.
Useappropriatetoolsstrategically.
Attendtoprecision.
Lookforandmakeuseofstructure.
Lookforandexpressregularityinrepeatedreasoning.
Unit1-LinkstoOpenEndedProblems
RelatedtotheStandards
F.TF.2
F.TF.3
F.IF.7
F.TF.5
F.TF.8
CCSS
Code
F.TF.1
F.TF.2
F.IF.7.E
F.BF.3
F.TF.5
F.TF.8
CCSSCodeDESRCIPTION
Understandradianmeasureofanangleasthelengthofthearcontheunitcirclesubtendedbytheangle.
Explainhowtheunitcircleinthecoordinateplaneenablestheextensionoftrigonometricfunctionstoallrealnumbers,interpretedasradian
measuresofanglestraversedcounterclockwisearoundtheunitcircle.
Graphexponentialandlogarithmicfunctions,showinginterceptsandendbehavior,andtrigonometricfunctions,showingperiod,midline,and
amplitude.
Identifytheeffectonthegraphofreplacingf(x)byf(x)+k,kf(x),f(kx),andf(x+k)forspecificvaluesofk(bothpositiveandnegative);findthe
valueofkgiventhegraphs.Experimentwithcasesandillustrateanexplanationoftheeffectsonthegraphusingtechnology.Includerecognizing
evenandoddfunctionsfromtheirgraphsandalgebraicexpressionsforthem.
Choosetrigonometricfunctionstomodelperiodicphenomenawithspecifiedamplitude,frequency,andmidline.*
ProvethePythagoreanidentitysin$ 𝜃 + cos $ 𝜃 = 1anduseittofindsin(θ),cos(θ),ortan(θ)givensin(θ),cos(θ),ortan(θ)andthequadrantofthe
angle.
PCTIMATHEMATICSDEPARTMENT
COURSE:AlgebraII
UNIT:2
UNITNAME:POLYNOMIALS
TOPICS Green
Book
II.
Blue
Book
Obj.
#
STUDENTLEARNINGOBJECTIVES
POLYNOMIALS(45days)
7days
1.7,1.8
2.3,2.4,
2.6
1
Solvequadraticequationswithrealcoefficientsthathavecomplexsolutions.
A.REI.4.b
5days
1.6
2.9
2
UsePropertiesofoperationstoadd,subtract,andmultiplycomplexnumbers.
N.CN.1,2,7
6days
1.2
2.1
3
GraphQuadraticFunctionsInVertexandInterceptForm.
A.SSE.3a,F.IF.4,
7,F.BF.3
5days
2.3
3.1-3.2
4
Performingarithmeticoperationsonpolynomials.
A.APR.4
5days
2.5
3.3,3.4
5
Usetheremainderandfactortheorems.
A.APR.2
7days
2.4
3.4
6
Useanappropriatefactoringtechniquetofactorexpressionscompletely.
A.SSE.2,A.APR.3
5days
2.7
3.6
7
KnowtheFundamentalTheoremofAlgebra;showthatitistrueforquadratic
polynomials.
N.CN.9
5days
2.2,2.8
3.7
8
Interpretkeyfeaturesofpolynomialgraphsintermsofthequantities,andsketch
graphsshowingkeyfeaturesgivenaverbaldescriptionoftherelationship.
F.IF.4,F.BF.3
**TaughtinApps/NotConceptsorResource
CCSScode
TECHNOLOGYSTANDARDS
II.1.Solvequadraticequationswithrealcoefficientsthathavecomplexsolutions.
http://www.webgraphing.com/quadraticequation_completingthesquare.jsp
https://www.khanacademy.org/math/algebra/quadratics/completing_the_square/v/solving-quadratic-equations-bysquare-roots
https://www.khanacademy.org/math/algebra/quadratics/quadratic_formula/v/using-the-quadratic-formula
http://www.webgraphing.com/quadraticequation_quadraticformula.jsp
http://www.mathplanet.com/education/algebra-1/exponents-and-exponential-functions/properties-of-exponents
II.2.UsePropertiesofoperationstoadd,subtract,andmultiplycomplexnumbers.
http://www.purplemath.com/modules/complex2.htm
http://www.youtube.com/watch?v=MEuPzvh0roM
II.3.GraphQuadraticFunctionsInVertexandInterceptForm.
https://www.desmos.com/calculator
http://www.youtube.com/watch?v=y99lNRqLjBA
http://vimeo.com/47178923
II.4.Performingarithmeticoperationsonpolynomials.
http://www.virtualnerd.com/algebra-1/polynomials-and-factoring/add-subtract/
http://www.virtualnerd.com/algebra-1/polynomials-and-factoring/multiply-divide/
II.5.Usetheremainderandfactortheorems.
http://www.virtualnerd.com/algebra-1/polynomials-and-factoring/factoring-strategy-solving-equations/choosingstrategy-grouping/
http://www.youtube.com/watch?v=_IPqCaspZOs
II.6.Useanappropriatefactoringtechniquetofactorexpressionscompletely.
http://www.virtualnerd.com/algebra-1/polynomials-and-factoring/factoring-strategy-solving-equations/solvingequations/
http://www.virtualnerd.com/algebra-1/polynomials-and-factoring/factoring-strategy-solving-equations/choosingstrategy-grouping/
II.7.KnowtheFundamentalTheoremofAlgebra;showthatitistrueforquadraticpolynomials.
http://www.mathsisfun.com/algebra/fundamental-theorem-algebra.html
http://www.youtube.com/watch?v=ox3zyPKRnlM
II.8.Interpretkeyfeaturesofpolynomialgraphsintermsofthequantities,andsketchgraphsshowingkeyfeatures
givenaverbaldescriptionoftherelationship.
http://www.youtube.com/watch?v=Vl4pBa_XroE
http://www.youtube.com/watch?v=-LJ5Bt8UwCo
KEYVOCABULARY
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
Complexconjugates
Constantterm
Factorbygrouping
Factoredcompletely
Irrationalconjugates
Leadingcoefficient
Liketerms
Localmaximum
Localminimum
Polynomiallongdivision
Quadraticform
Repeatedsolution
ScientificNotation
Syntheticdivision
Zeroofafunction
Complexconjugates
Constantterm
Factorbygrouping
Factoredcompletely
Irrationalconjugates
Leadingcoefficient
Liketerms
Localmaximum
Localminimum
Polynomiallongdivision
Quadraticform
Repeatedsolution
ScientificNotation
Syntheticdivision
Zeroofafunction
SelectedOpportunitiesforConnectionsto
MathematicalPractices
1.
2.
3.
4.
5.
6.
7.
8.
Makesenseofproblemsandpersevereinsolvingthem.
Reasonabstractlyandquantitatively.
Constructviableargumentsandcritiquethereasoningofothers.
Modelwithmathematics.
Useappropriatetoolsstrategically.
Attendtoprecision.
Lookforandmakeuseofstructure.
Lookforandexpressregularityinrepeatedreasoning.
CCSS
Code
Unit2-LinkstoOpenEndedProblems
RelatedtotheStandards
A.REI.4
N.CN.1
N.CN.2
N.CN.7
A.SSE.3a
F.IF.4
F.IF.7
A.APR.1
A.APR.2
A.APR.3
A.APR.4
A.SSE.1
A.SSE.2
A.SSE.4
CCSSCodeDESRCIPTION
A.REI.4
Solve quadratic equations in one variable.
Use the method of completing the square to transform any quadratic equation in x into an equation of the form 𝑥 − 𝑝 $ = 𝑞 that has the same solutions.
A.REI.4.A
Derive the quadratic formula from this form.
Solve quadratic equations by inspection (e.g., for 𝑥 $ = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate
A.REI.4.B
to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as a ± bi for real numbers a and b.
N.CN.1
Know there is a complex number i such that 𝑖 $ = −1, and every complex number has the form a + bi with a and b real.
N.CN.2
Use the relation 𝑖 $ = −1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers.
N.CN.7
Solve quadratic equations with real coefficients that have complex solutions.
A.SSE.3.A Factor a quadratic expression to reveal the zeros of the function it defines.
For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs
showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing,
F.IF.4
positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity.*
Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.*
F.IF.7
F.IF.7.A
Graph linear and quadratic functions and show intercepts, maxima, and minima.
F.IF.7.B
Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions.
Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and
multiplication; add, subtract, and multiply polynomials.
Know and apply the Remainder Theorem: For a polynomial p(x) and a number a, the remainder on division by x - a is p(a), so p(a) = 0 if and only if (x - a)
is a factor of p(x).
Identify zeros of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the function defined by the
polynomial.
Prove polynomial identities and use them to describe numerical relationships. For example, the polynomial identity 𝑥 $ + 𝑦 $ $ = 𝑥 $ − 𝑦 $ $ + 2𝑥𝑦 $ can
be used to generate Pythagorean triples.
Interpret expressions that represent a quantity in terms of its context.*
A.APR.1
A.APR.2
A.APR.3
A.APR.4
A.SSE.1
A.SSE.1.A Interpret parts of an expression, such as terms, factors, and coefficients.
Identify zeros of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the function defined by the
A.SSE.2
polynomial.
A.SSE.4
Derive the formula for the sum of a finite geometric series (when the common ratio is not 1), and use the formula to solve problems. For example,
calculate mortgage payments.*
PCTIMATHEMATICSDEPARTMENT
COURSE:AlgebraII
UNIT:3
UNITNAME:RATIONAL,RADICAL,EXPONENTIAL,ANDLOGARITHMICFUNCTIONS
TOPICS Green
Book
III.
Blue
Book
Obj.
#
PerformarithmeticoperationswithRationalExpressions.
Rewritesimplerationalexpressionsindifferentformsusinginspection,longdivision,
or,forthemorecomplicatedexamples,acomputeralgebrasystem.**
A.APR.7
3
SolveRationalEquations.
A.REI.1,
A.REI.2
5.4
4
Interpretkeyfeaturesofsimpleandgeneralrationalgraphsintermsofthequantities,
andsketchgraphsshowingkeyfeaturesgivenaverbaldescriptionoftherelationship.
F.IF.4,F.BF.3
3.1,3.2
5.6
5
Usepropertiesofintegerexponentstoexplainandconvertbetweenexpressions
involvingradicalsandrationalexponents,usingcorrectnotation.
N.RN.1,N.RN.2
3.6
5.8
6
SolveRadicalEquations.
A.REI.1,
A.REI.2
7
InterpretkeyfeaturesofSquareRootFunctionandCubeRootgraphsintermsofthe
quantities,andsketchgraphsshowingkeyfeaturesgivenaverbaldescriptionofthe
relationship.
F.IF.4,F.BF.3
5.4,5.5
5.2,5.3
1
4days
5.2Ext
2
5days
5.6
5.5
3days
5.2,5.3
2days
5days
IV.
CCSS
code
RATIONALANDRADICALFUNCTIONS(27days)
5days
3days
STUDENTLEARNINGOBJECTIVES
3.5
5.7
A.APR.6
EXPONENTIALANDLOGARITHMICFUNCTIONSRATIONALANDRADICALFUNCTIONS(18days)
2days
2.1
1
Chooseandproduceequivalentexpressionsforexponentialfunctionsusingthe
propertiesofexponents.
A.SSE.3
2days
4.1,4.2
4.1
2
Usepropertiesofexponentstorewriteafunctioninanequivalentformtorevealand
explaindifferentpropertiesoftheexponentialfunction.
F.IF.8b
2days
4.1,4.2
4.1
3
Graphexponentialfunctionsexpressedsymbolicallyorverballyandshowkey
featuresofthegraph.
F.IF.4,F.BF.3
2days
4.3
4.6
4
UseFunctionsInvolvinge.
F.IF.4,7,8,
F.BF.3
3days
2days
3days
4.4
4.5
4.6
4.3
4.4
4.5-4.6
5
6
7
RewritingExponentialEquationsinLogarithmicForm.
ApplyPropertiesofLogarithms.
SolveExponentialandLogarithmicEquations.
InterpretkeyfeaturesofLogarithmicFunctionsgraphsintermsofthequantities,and
2days
4.4
4.7
8
sketchgraphsshowingkeyfeaturesgivenaverbaldescriptionoftherelationship.
**TaughtinApps/NotConceptsorResource
F.IF.4,7,8
F.LE.4
F.LE.4
F.IF.4,F.BF.3
TECHNOLOGYSTANDARDS
III.1.PerformarithmeticoperationswithRationalExpressions.
http://www.youtube.com/watch?v=z4Hssd_oiDQ
http://www.youtube.com/watch?v=WbvLjmK4Kmc
http://www.youtube.com/watch?v=d3xr5a4cln0
http://www.youtube.com/watch?v=r_mkzOlfQOo
http://www.youtube.com/watch?v=8_2x1kktEPc
http://www.youtube.com/watch?v=SyVq0-ObQdA
III.2.Rewritesimplerationalexpressionsindifferentformsusinginspection,longdivision,or,forthemorecomplicated
examples,acomputeralgebrasystem.**
https://www.youtube.com/watch?v=-DUMVzvu7-g
III.3.SolveRationalEquations
http://www.youtube.com/watch?v=JkhePJajfEc
http://www.youtube.com/watch?v=f9QBU4v0X2U
http://www.youtube.com/watch?v=r9LYqfqssS0
III.4.Interpretkeyfeaturesofsimpleandgeneralrationalgraphsintermsofthequantities,andsketchgraphsshowing
keyfeaturesgivenaverbaldescriptionoftherelationship.
https://www.youtube.com/watch?v=-DUMVzvu7-g
http://www.purplemath.com/modules/grphrtnl.htm
III.5.Usepropertiesofintegerexponentstoexplainandconvertbetweenexpressionsinvolvingradicalsandrational
exponents,usingcorrectnotation.
http://www.youtube.com/watch?v=PpuKD2_OfFk
http://www.youtube.com/watch?v=NCEB8x-lYBM
http://www.youtube.com/watch?v=pafRsMuHNOQ
http://www.youtube.com/watch?v=-T1punCdxas
III.6.SolveRadicalEquations.
http://www.youtube.com/watch?v=hkF8ej72NAg
http://www.youtube.com/watch?v=8EOGx68kdwo
http://www.youtube.com/watch?v=Ef2gOQbDv7M
http://www.youtube.com/watch?v=QCnPnV4mE8g
III.7.InterpretkeyfeaturesofSquareRootFunctionandCubeRootgraphsintermsofthequantities,andsketchgraphs
showingkeyfeaturesgivenaverbaldescriptionoftherelationship.
http://www.youtube.com/watch?v=xQ6DTxjUA7w
http://www.youtube.com/watch?v=17rEN-fVPvE
IV.1.Chooseandproduceequivalentexpressionsforexponentialfunctionsusingthepropertiesofexponents.
http://www.mathplanet.com/education/algebra-1/exponents-and-exponential-functions/properties-of-exponents
IV.2.Usepropertiesofexponentstorewriteafunctioninanequivalentformtorevealandexplaindifferentpropertiesof
theexponentialfunction.
http://www.youtube.com/watch?v=c6pcRR5Uy6w
http://www.youtube.com/watch?v=4vmR8XMvQ_I
http://www.youtube.com/watch?v=f-3QDswUc8o
http://www.youtube.com/watch?v=sf8KdpN67Sk
http://www.youtube.com/watch?v=XJlawwoGhxQ
IV.3.Graphexponentialfunctionsexpressedsymbolicallyorverballyandshowkeyfeaturesofthegraph.
http://www.youtube.com/watch?v=c6pcRR5Uy6w
KEYVOCABULARY
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
nthrootofa
Indexofaradical
Simplestformofa
radical
Likeradicals
PowerFunction
Composition
Inverserelation
InverseFunction
Radicalequation
Extraneous
solution
Exponential
Function
Exponentialgrowth
GrowthFactor
Asymptote
RationalFunction
Domain
Range
Asymptote
EndBehavior
RationalFunction
Simplifiedformofa
rationalexpression
Reciprocal
ComplexFraction
Crossmultiplying
Extraneous
solution
Increasing
Decreasing
Oddfunction
Evenfunction
http://www.youtube.com/watch?v=4vmR8XMvQ_I
http://www.youtube.com/watch?v=f-3QDswUc8o
http://www.youtube.com/watch?v=sf8KdpN67Sk
http://www.youtube.com/watch?v=XJlawwoGhxQ
IV.4.UseFunctionsInvolvinge.
http://www.youtube.com/watch?v=SNZgbj3UaRE
http://www.youtube.com/watch?v=gvwXYc7Qa9E
http://www.youtube.com/watch?v=Yo-UN392NDc
IV.5.RewritingExponentialEquationsinLogarithmicForm.
https://www.youtube.com/watch?v=fjBZCEZpISQ
http://www.youtube.com/user/learnmathtutorials?v=wfYsiJcVWy0
http://www.youtube.com/watch?v=REPqXHu7gXc&feature=c4-overview-vl&list=PLBFAE01DF8EA66352
http://www.youtube.com/watch?v=mUfXkwTQB8o&feature=c4-overview-vl&list=PLBFAE01DF8EA66352
http://www.youtube.com/watch?v=Fo0pciptGWs
IV.6.ApplyPropertiesofLogarithms.
http://www.youtube.com/watch?v=eLapHtvQbFo
http://www.youtube.com/watch?v=kXYbrOjm9D8
http://www.youtube.com/watch?v=dLJAuL_dveQ
IV.7.SolveExponentialandLogarithmicEquations.
http://www.youtube.com/watch?v=CqYDBfoiwOc
http://www.youtube.com/watch?v=QMesv6cJxtI
http://www.youtube.com/watch?v=Fo0pciptGWs
IV.8.InterpretkeyfeaturesofLogarithmicFunctionsgraphsintermsofthequantities,andsketchgraphsshowingkey
featuresgivenaverbaldescriptionoftherelationship.
https://www.youtube.com/watch?v=fjBZCEZpISQ
http://www.youtube.com/user/learnmathtutorials?v=wfYsiJcVWy0
http://www.youtube.com/watch?v=REPqXHu7gXc&feature=c4-overview-vl&list=PLBFAE01DF8EA66352
http://www.youtube.com/watch?v=mUfXkwTQB8o&feature=c4-overview-vl&list=PLBFAE01DF8EA66352
http://www.youtube.com/watch?v=Fo0pciptGWs
SelectedOpportunitiesforConnectionsto
MathematicalPractices
1.
2.
3.
4.
5.
6.
7.
8.
Makesenseofproblemsandpersevereinsolvingthem.
Reasonabstractlyandquantitatively.
Constructviableargumentsandcritiquethereasoningofothers.
Modelwithmathematics.
Useappropriatetoolsstrategically.
Attendtoprecision.
Lookforandmakeuseofstructure.
Lookforandexpressregularityinrepeatedreasoning.
Unit3-LinkstoOpenEndedProblems
RelatedtotheStandards
A.APR.6
A.APR.7
A.REI.1
A.REI.2
A.REI.6
A.REI.7
F.IF.4
F.BF.3
N.RN.1
N.RN.2
A.SSE.3
F.IF.7
F.IF.8
F.LE.4
CCSS
Code
A.APR.6
A.APR.7
A.REI.1
A.REI.2
A.REI.6
A.REI.7
F.IF.4
F.BF.3
N.RN.1
CCSSCodeDESRCIPTION
Rewritesimplerationalexpressionsindifferentforms;writea(x)/b(x)intheformq(x)+r(x)/b(x),wherea(x),b(x),q(x),andr(x)arepolynomialswith
thedegreeofr(x)lessthanthedegreeofb(x),usinginspection,longdivision,or,forthemorecomplicatedexamples,acomputeralgebrasystem.
(+)Understandthatrationalexpressionsformasystemanalogoustotherationalnumbers,closedunderaddition,subtraction,multiplication,and
divisionbyanonzerorationalexpression;add,subtract,multiply,anddividerationalexpressions.
Explaineachstepinsolvingasimpleequationasfollowingfromtheequalityofnumbersassertedatthepreviousstep,startingfromtheassumption
thattheoriginalequationhasasolution.Constructaviableargumenttojustifyasolutionmethod.
Solvesimplerationalandradicalequationsinonevariable,andgiveexamplesshowinghowextraneoussolutionsmayarise.
Solvesystemsoflinearequationsexactlyandapproximately(e.g.,withgraphs),focusingonpairsoflinearequationsintwovariables.
Solveasimplesystemconsistingofalinearequationandaquadraticequationintwovariablesalgebraicallyandgraphically.Forexample,findthe
pointsofintersectionbetweentheliney=-3xandthecircle𝑥 $ + 𝑦 $ = 3.
Forafunctionthatmodelsarelationshipbetweentwoquantities,interpretkeyfeaturesofgraphsandtablesintermsofthequantities,andsketch
graphsshowingkeyfeaturesgivenaverbaldescriptionoftherelationship.Keyfeaturesinclude:intercepts;intervalswherethefunctionisincreasing,
decreasing,positive,ornegative;relativemaximumsandminimums;symmetries;endbehavior;andperiodicity.*
Identifytheeffectonthegraphofreplacingf(x)byf(x)+k,kf(x),f(kx),andf(x+k)forspecificvaluesofk(bothpositiveandnegative);findthevalue
ofkgiventhegraphs.Experimentwithcasesandillustrateanexplanationoftheeffectsonthegraphusingtechnology.Includerecognizingevenand
oddfunctionsfromtheirgraphsandalgebraicexpressionsforthem.
Explainhowthedefinitionofthemeaningofrationalexponentsfollowsfromextendingthepropertiesofintegerexponentstothosevalues,allowing
foranotationforradicalsintermsofrationalexponents.Forexample,wedefine5
so 5
7
7
7 tobethecuberootof5becausewewant
5
6
7
7
=5
6
7
8
tohold,
mustequal5.
N.RN.2
Rewriteexpressionsinvolvingradicalsandrationalexponentsusingthepropertiesofexponents.
A.SSE.3
Chooseandproduceanequivalentformofanexpressiontorevealandexplainpropertiesofthequantityrepresentedbytheexpression.*
Graphfunctionsexpressedsymbolicallyandshowkeyfeaturesofthegraph,byhandinsimplecasesandusingtechnologyformorecomplicated
cases.*
Graphexponentialandlogarithmicfunctions,showinginterceptsandendbehavior,andtrigonometricfunctions,showingperiod,midline,and
amplitude.
Writeafunctiondefinedbyanexpressionindifferentbutequivalentformstorevealandexplaindifferentpropertiesofthefunction.
Usethepropertiesofexponentstointerpretexpressionsforexponentialfunctions.Forexample,identifypercentrateofchangeinfunctionssuchasy
=(1.02)ᵗ,y=(0.97)ᵗ,y=(1.01)12ᵗ,y=(1.2)ᵗ/10,andclassifythemasrepresentingexponentialgrowthordecay.
Forexponentialmodels,expressasalogarithmthesolutiontoabct=dwherea,c,anddarenumbersandthebasebis2,10,ore;evaluatethe
logarithmusingtechnology.
F.IF.7
F.IF.7.E
F.IF.8
F.IF.8.B
F.LE.4
6
6
PCTIMATHEMATICSDEPARTMENT
COURSE:AlgebraII
UNIT:4
UNITNAME:INVERSEFUNCTIONS,SEQUENCES&SERIES,ANDDATA&STATISTICS
TOPICS Green
Book
V.
Blue
Book
Obj.
#
3.3
6.5
1
5days
3.4
6.6
2
5days
8.7
12.7
3
5days
4
PerformFunctionComposition.
Determinetheinversefunctionforasimplefunctionthathasaninverseandwritean
expressionfortheinverse.
Solvesystemsoflinearequationsandsimplesystemsconsistingofalinearanda
quadraticequationintwovariables,algebraicallyandgraphically.
Findapproximatesolutionsfortheintersectionsoffunctionsandexplainwhythexcoordinatesofthepointswherethegraphsoftheequationsy=f(x)andy=g(x)
intersectarethesolutionsoftheequationf(x)=g(x)involvinglinear,polynomial,
rational,absolutevalue,logarithmicandexponentialfunctions.
7.1-7.3,
7.5
9.1-9.4
1
7days
7.4
9.5
2
Writearithmeticandgeometricsequencesbothrecursivelyandwithanexplicit
formula,usethemtomodelsituations,andtranslatebetweenthetwoforms.
Derivetheformulaforthesumofafinitegeometricseries(whenthecommonratiois
not1),andusetheformulatosolveproblems.Forexample,calculatemortgage
payments.
F.BF.4
A.REI.6,A.REI.7
A.REI.11
F.BF.2
A.SSE.4
ANALYZEDATAANDSTATISTICS(10days)
Identifydifferentmethodsandpurposesforconductingsamplesurveys,experiments,
andobservationalstudiesandexplainhowrandomizationrelatestoeach.**
Usedatafromarandomizedexperimenttocomparetwotreatmentsanduse
5days
6.5EXT 8.3
2
simulationstodecideifdifferencesbetweenparametersaresignificant;evaluate
reportsbasedondata.**
**TaughtinApps/NotConceptsorResource
5days
F.BF.4
SEQUENCEANDSERIES(14days)
7days
VII.
CCSScode
INVERSEFUNCTIONSANDFUNCTIONSYSTEMS(21days)
6days
VI.
STUDENTLEARNINGOBJECTIVES
6.4-6.5
8.2
1
S.IC.3
S.IC.5,S.IC.6
TECHNOLOGYSTANDARDS
V.1.PerformFunctionComposition.
http://www.youtube.com/watch?v=LM_NyH4R6yw
http://www.youtube.com/watch?v=Gl_0MhsuyO8
http://www.youtube.com/watch?v=v8JgEEimO7w
V.2.Determinetheinversefunctionforasimplefunctionthathasaninverseandwriteanexpressionfortheinverse.
http://www.youtube.com/watch?v=nSmFzOpxhbY
http://www.youtube.com/watch?v=DsaJKV4M-vk
V.3.Solvesystemsoflinearequationsandsimplesystemsconsistingofalinearandaquadraticequationintwovariables,
algebraicallyandgraphically.
http://www.youtube.com/watch?v=TSRhRbuL7E8
http://mathnmind.com/PDF%20Files/Algebra%202/chap09/section07/notetaking.pdf
V.4.Findapproximatesolutionsfortheintersectionsoffunctionsandexplainwhythex-coordinatesofthepointswhere
thegraphsoftheequationsy=f(x)andy=g(x)intersectarethesolutionsoftheequationf(x)=g(x)involvinglinear,
polynomial,rational,absolutevalue,logarithmicandexponentialfunctions.
http://www.youtube.com/watch?v=TSRhRbuL7E8
http://mathnmind.com/PDF%20Files/Algebra%202/chap09/section07/notetaking.pdf
VI.1.Writearithmeticandgeometricsequencesbothrecursivelyandwithanexplicitformula,usethemtomodel
situations,andtranslatebetweenthetwoforms.
http://mathnmind.com/PDF%20Files/Algebra%202/chap10/section01/notetaking.pdf
http://www.virtualnerd.com/algebra-2/sequences-series
http://www.youtube.com/watch?v=oDQmXsXzNn0
http://www.youtube.com/watch?v=W561_exZn2k
http://www.youtube.com/watch?v=lj_X9JVSF8k
http://prezi.com/htshzbfuhzyi/122-analyze-arithmetic-sequences-and-series/
http://www.youtube.com/watch?v=rtsk8caxbr4
http://www.virtualnerd.com/algebra-2/sequences-series/geometric/geometric-sequences
http://www.youtube.com/watch?v=k-ygvxR47Fc
http://www.youtube.com/watch?v=NEZuM5itx7o
http://www.youtube.com/watch?v=y6QIro3Cdig
http://www.youtube.com/watch?v=-XVIMMjtAmI
VI.2.Derivetheformulaforthesumofafinitegeometricseries(whenthecommonratioisnot1),andusetheformulato
solveproblems.Forexample,calculatemortgagepayments.
http://www.youtube.com/watch?v=i6zeKlXYgE8
http://www.youtube.com/watch?v=mcnblnEsf98
http://www.youtube.com/watch?v=Ocd1iQyN-qk
VII.1.Identifydifferentmethodsandpurposesforconductingsamplesurveys,experiments,andobservationalstudiesand
explainhowrandomizationrelatestoeach.**
http://www.slideserve.com/kiet/7-5-purple-select-and-draw-conclusions-from-samples
Download6.4-SelectandDrawConclusions
Lesson14.4ADrawingConclusionsfromSamples,Surveys-CORD...
7.5selectanddrawconclusionsfromsamples
http://www.youtube.com/watch?v=wnNapKDGQH4
VII.2.Usedatafromarandomizedexperimenttocomparetwotreatmentsandusesimulationstodecideifdifferences
betweenparametersaresignificant;evaluatereportsbasedondata.**
http://www.slideserve.com/kiet/7-5-purple-select-and-draw-conclusions-from-samples
KEYVOCABULARY
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
Composition
Inverserelation
InverseFunction
Focus
Directrix
Parabola
Vertex
Quadraticsystem
biasedquestions
biasedsample
controlgroup
controlled
experiment
experiment
marginoferror
observationalstudy
Population
randomized
comparative
experiment
sample
treatmentgroup
unbiasedsample
Arithmeticsequence
Commondifference
Arithmeticseries
Geometricsequence
Commonratio
Geometricseries
Explicitrule
Recursiverule
Iteration
Download6.4-SelectandDrawConclusions
Lesson14.4ADrawingConclusionsfromSamples,Surveys-CORD...
7.5selectanddrawconclusionsfromsamples
http://www.youtube.com/watch?v=wnNapKDGQH4
SelectedOpportunitiesforConnectionsto
MathematicalPractices
Unit4-LinkstoOpenEndedProblems
9. Makesenseofproblemsandpersevereinsolvingthem.
10. Reasonabstractlyandquantitatively.
11. Constructviableargumentsandcritiquethereasoningofothers.
12. Modelwithmathematics.
13. Useappropriatetoolsstrategically.
14. Attendtoprecision.
15. Lookforandmakeuseofstructure.
16. Lookforandexpressregularityinrepeatedreasoning.
CCSS
Code
F.BF.4
RelatedtotheStandards
F.BF.4
A.REI.6
A.REI.7
A.REI.11
F.BF.2
A.SSE.4
S.IC.3
S.IC.5
S.IC.6
CCSSCodeDESRCIPTION
F.BF.4.B
Findinversefunctions.
Solveanequationoftheformf(x)=cforasimplefunctionfthathasaninverseandwriteanexpressionfortheinverse.Forexample,f(x)=2x3or
f(x)=(x+1)/(x-1)forx≠1.
(+)Verifybycompositionthatonefunctionistheinverseofanother.
F.BF.4.C
(+)Readvaluesofaninversefunctionfromagraphoratable,giventhatthefunctionhasaninverse.
F.BF.4.D
(+)Produceaninvertiblefunctionfromanon-invertiblefunctionbyrestrictingthedomain.
F.BF.4
Findinversefunctions.
A.REI.6
Solvesystemsoflinearequationsexactlyandapproximately(e.g.,withgraphs),focusingonpairsoflinearequationsintwovariables.
F.BF.4.A
A.REI.7
A.REI.11
F.BF.2
Solveasimplesystemconsistingofalinearequationandaquadraticequationintwovariablesalgebraicallyandgraphically.Forexample,find
thepointsofintersectionbetweentheliney=-3xandthecircle𝑥 $ + 𝑦 $ = 3.
Explainwhythex-coordinatesofthepointswherethegraphsoftheequationsy=f(x)andy=g(x)intersectarethesolutionsoftheequationf(x)
=g(x);findthesolutionsapproximately,e.g.,usingtechnologytographthefunctions,maketablesofvalues,orfindsuccessiveapproximations.
Includecaseswheref(x)and/org(x)arelinear,polynomial,rational,absolutevalue,exponential,andlogarithmicfunctions.*
Writearithmeticandgeometricsequencesbothrecursivelyandwithanexplicitformula,usethemtomodelsituations,andtranslatebetween
thetwoforms.*
A.SSE.4
Derivetheformulaforthesumofafinitegeometricseries(whenthecommonratioisnot1),andusetheformulatosolveproblems.For
example,calculatemortgagepayments.*
S.IC.3
Recognizethepurposesofanddifferencesamongsamplesurveys,experiments,andobservationalstudies;explainhowrandomizationrelatesto
each.
S.IC.5
Usedatafromarandomizedexperimenttocomparetwotreatments;usesimulationstodecideifdifferencesbetweenparametersare
significant.
S.IC.6
Evaluatereportsbasedondata.