PA Core Standards for Mathematics
2.1 Numbers and Operations PreK-12
Grade
Pre-K
Pre-K
BigIdea
Mathematicalrelationships
amongnumberscanbe
represented,compared,and
communicated.
Mathematicalrelationships
amongnumberscanbe
represented,compared,and
communicated.
Patternsexhibitrelationships
thatcanbeextended,
described,andgeneralized.
K
Howismathematicsusedtoquantify,
compare,represent,andmodel
numbers?
Howcanmathematicssupport
effectivecommunication?
Howismathematicsusedtoquantify,
compare,represent,andmodel
numbers?
Concepts
Numerical
Sequence
Object
Quantity
Howcanmathematicssupport
effectivecommunication?
Howcanpatternsbeusedtodescribe
relationshipsinmathematical
situations?
Mathematicalrelationships
amongnumberscanbe
represented,compared,and
communicated.
Howismathematicsusedtoquantify,
compare,represent,andmodel
numbers?
Howcanmathematicssupport
effectivecommunication?
Number
Comparison
Mathematicalrelationships
amongnumberscanbe
represented,compared,and
communicated.
Numericalquantities,
calculations,and
measurementscanbe
estimatedoranalyzedby
usingappropriatestrategies
andtools.
Howismathematicsusedtoquantify,
compare,represent,andmodel
numbers?
Howcanmathematicssupport
effectivecommunication?
Whatdoesitmeantoestimateor
analyzenumericalquantities?
Numerical
Sequence
Pre-K
EssentialQuestions
Competencies
Standard
Eligible
Content
Rotecountto20.
Namenumeralsupto10.
Representanumberofobjects
withawrittennumeral0-10.
Recognizesmallquantitiesupto
6.
Useaone-to-one
correspondencewhencounting
to10.
Statethetotalnumberof
objectscounted,demonstrating
understandingthatthat
numbernamedtellsthe
numberofobjectscounted.
Identifywhetherthenumberof
objectsinonegroupisgreater
than,lessthanorequaltothe
numberofobjectsinanother
groupupto10.
Comparetwonumbers
between1and5when
presentedaswrittennumerals.
Rotecountto100.
Countforwardbeginningfroma
givennumberwithintheknown
sequence(insteadofhavingto
beginat1).
Namenumerals0–20.
Representanumberofobjects
withawrittennumeral0-20.
CC.2.1.PREK.A.1
CC.2.1.PREK.A.2
CC.2.1.PREK.A.3 CC.2.1.K.A.1
Vocabulary
Above
Addition
Below
Beside
Between
Circle
Cone
Cube
Cylinder
Equal
Greaterthan
Length
Lessthan
Measure
Numeral
Rectangle
Sphere
Square
Subtraction
Threedimensional
shapes
Triangle
Twodimensional
shapes
Weight
Addition
Area
Capacity
Circle
Cone
Corners(vertices)
Cube
Cylinder
Digit
Equal
Greaterthan
1
OCT 2016
PA Core Standards for Mathematics
2.1 Numbers and Operations PreK-12
Grade
BigIdea
EssentialQuestions
K
Mathematicalrelationships
amongnumberscanbe
represented,compared,and
communicated.
Patternsexhibitrelationships
thatcanbeextended,
described,andgeneralized.
Howismathematicsusedtoquantify,
compare,represent,andmodel
numbers?
Howcanmathematicssupport
effectivecommunication?
Howcanpatternsbeusedtodescribe
relationshipsinmathematical
situations?
Object
Quantity
K
Mathematicalrelationships
amongnumberscanbe
represented,compared,and
communicated.
Numericalquantities,
calculations,and
measurementscanbe
estimatedoranalyzedby
usingappropriatestrategies
andtools.
Number
Comparison
K
Mathematicalrelationships
amongnumberscanbe
represented,compared,and
communicated.
Patternsexhibitrelationships
thatcanbeextended,
described,andgeneralized.
Howismathematicsusedtoquantify,
compare,represent,andmodel
numbers?
Howcanmathematicssupport
effectivecommunication?
Whenisitisappropriatetoestimate
versuscalculate?
Whatmakesatooland/orstrategy
appropriateforagiventask?
Howismathematicsusedtoquantify,
compare,represent,andmodel
numbers?
1
Mathematicalrelationships
amongnumberscanbe
represented,compared,and
Concepts
Standard
Eligible
Content
Usesone-to-one
correspondencewhencounting
to20.
Statethetotalnumberof
objectscounted,demonstrating
understandingthatthatlast
numbernamedtellsthe
numberofobjectscounted.
Understandthateach
successivenumbernamerefers
toaquantitythatisonelarger.
Identifywhetherthenumberof
objectsinonegroupisgreater
than,lessthan,orequaltothe
numberofobjectsinanother
group,e.g.,byusingmatching
andcountingstrategies.
Comparetwonumbers
between1and10presentedas
writtennumerals.
CC.2.1.K.A.2
CC.2.1.K.A.3
PlaceValue
Composeanddecompose
numbersupto19intotenand
onesbyusingobjectsor
drawings,andrecordeach
compositionordecomposition
byadrawingorequation.
CC.2.1.K.B.1
Numerical
Sequence
Countto120,startingatany
numberlessthan120.
CC.2.1.1.B.1
Howcanmathematicssupport
effectivecommunication?
Howcanrecognizingrepetitionor
regularityassistinsolvingproblems
moreefficiently?
Howismathematicsusedtoquantify,
compare,represent,andmodel
numbers?
Competencies
Vocabulary
Length
Lessthan
Ones
Placevalue
Quantity
Rectangle
Sides
Sphere
Square
Subtraction
Tens
Total
Triangle
Weight
Addend
Addition
Analog
2
OCT 2016
PA Core Standards for Mathematics
2.1 Numbers and Operations PreK-12
Grade
1
2
BigIdea
communicated.
Mathematicalrelationships
canberepresentedas
expressions,equationsand
inequalitiesinmathematical
situations.
Numericalquantities,
calculations,and
measurementscanbe
estimatedoranalyzedby
usingappropriatestrategies
andtools.
Mathematicalrelationships
amongnumberscanbe
represented,compared,and
communicated.
Mathematicalrelationships
canberepresentedas
expressions,equationsand
inequalitiesinmathematical
situations.
Numericalquantities,
calculations,and
measurementscanbe
estimatedoranalyzedby
usingappropriatestrategies
andtools.
Patternsexhibitrelationships
thatcanbeextended,
described,andgeneralized.
Mathematicalrelationships
amongnumberscanbe
represented,compared,and
EssentialQuestions
Concepts
Howcanmathematicssupport
effectivecommunication?
Howarerelationshipsrepresented
mathematically?
Whatdoesitmeantoestimateor
analyzenumericalquantities?
Whatmakesatooland/orstrategy
appropriateforagiventask?
Howismathematicsusedtoquantify,
compare,represent,andmodel
numbers?
Howcanmathematicssupport
effectivecommunication?
Howarerelationshipsrepresented
mathematically?
Standard
Eligible
Content
Readandwritenumeralsupto
120andrepresentanumberof
objectswithawrittennumeral.
PlaceValue
Whatdoesitmeantoestimateor
analyzenumericalquantities?
Whatmakesatooland/orstrategy
appropriateforagiventask?
Howcanrecognizingrepetitionor
regularityassistinsolvingproblems
moreefficiently?
Howismathematicsusedtoquantify,
compare,represent,andmodel
numbers?
Competencies
PlaceValue
Comparetwotwo-digit
numbersbasedonmeaningsof
thetensandonesdigits,
recordingtheresultsof
comparisonswiththesymbols
>,=,and<.
Addwithin100,including
addingatwo-digitnumberand
aone-digitnumber,andadding
atwo-digitnumberanda
multipleof10usingconcrete
modelsordrawings.Relatethe
strategytoawrittenmethod
andexplainthereasoningused.
Subtractmultiplesof10inthe
range10-90,usingconcrete
modelsordrawings.Relatethe
strategytoawrittenmethod
andexplainthereasoningused.
Understandthatthethreedigits
ofathree-digitnumber
representamountsof
CC.2.1.1.B.2
CC.2.1.1.B.3
CC.2.1.2.B.1
CC.2.1.2.B.2
Vocabulary
Circle
Compare
compose/
Cone
Countingon
Cube
Cylinder
Data
decompose
Equalto
Fourths
Fractions–
Greaterthan
Halfcircles
Half-hour
Halves
Hour
Length
Lessthan
Makingten
Ones
Placevalue
Quarter-circles
Quarters
Rectangle
RectangularPrism
Square
Subtraction
Sum
Tens
Trapezoids
Triangle
A.M.
Addend
Analog/digital
3
OCT 2016
PA Core Standards for Mathematics
2.1 Numbers and Operations PreK-12
Grade
2
BigIdea
EssentialQuestions
communicated.
Mathematicalrelationships
canberepresentedas
expressions,equationsand
inequalitiesinmathematical
situations.
Numericalquantities,
calculations,and
measurementscanbe
estimatedoranalyzedby
usingappropriatestrategies
andtools.
Patternsexhibitrelationships
thatcanbeextended,
described,andgeneralized.
Mathematicalrelationships
amongnumberscanbe
represented,compared,and
communicated.
Mathematicalrelationships
canberepresentedas
expressions,equationsand
inequalitiesinmathematical
situations.
Numericalquantities,
calculations,and
measurementscanbe
estimatedoranalyzedby
usingappropriatestrategies
andtools.
Howcanmathematicssupport
effectivecommunication?
Howarerelationshipsrepresented
mathematically?
Whatdoesitmeantoestimateor
analyzenumericalquantities?
Whatmakesatooland/orstrategy
appropriateforagiventask?
Howcanrecognizingrepetitionor
regularityassistinsolvingproblems
moreefficiently?
Howismathematicsusedtoquantify,
compare,represent,andmodel
numbers?
Concepts
Competencies
Standard
Eligible
Content
hundreds,tens,andones.
Comparetwothree-digit
numbersbasedonmeaningsof
thehundreds,tens,andones
digits,using>,=,and<symbols
torecordtheresultsof
comparisons.
Countwithin1000;skip-count
by5s,10s,and100s.
Readandwritenumbersto
1000usingbase-tennumerals,
numbernames,andexpanded
form.
Additionand
Subtraction
Howcanmathematicssupport
effectivecommunication?
Howarerelationshipsrepresented
mathematically?
Whatdoesitmeantoestimateor
analyzenumericalquantities?
Whatmakesatooland/orstrategy
appropriateforagiventask?
Adduptofourtwo-digit
numbersusingstrategiesbased
onplacevalueandpropertiesof
operations.
Addandsubtractwithin1000.
Understandthatinaddingor
subtractingthree-digit
numbers,oneaddsorsubtracts
hundredsandhundreds,tens
andtens,onesandones;and
sometimesitisnecessaryto
composeordecomposetensor
hundreds.
Explainwhyadditionand
subtractionstrategieswork,
usingplacevalueandthe
propertiesofoperations.
CC.2.1.2.B.3
Vocabulary
Angles
Bargraph
Centimeter
Compose
Decompose
Dime
Dollar
Equation
Equivalent
Estimate
Even
Expandedform
Faces
Feet
Fractions–Thirds
Hexagon
Hundreds
Inch
Lineplot
Meter
Money
Nickel
Odd
P.M.
Penny
Pentagon
Picturegraph
Placevalue
Quadrilateral
Quarter
Sum
4
OCT 2016
PA Core Standards for Mathematics
2.1 Numbers and Operations PreK-12
Grade
3
3
BigIdea
EssentialQuestions
Concepts
Competencies
Mathematicalrelationships
amongnumberscanbe
represented,compared,and
communicated.
Mathematicalrelationships
canberepresentedas
expressions,equationsand
inequalitiesinmathematical
situations.
Numericalquantities,
calculations,and
measurementscanbe
estimatedoranalyzedby
usingappropriatestrategies
andtools.
Patternsexhibitrelationships
thatcanbeextended,
described,andgeneralized.
Mathematicalrelationships
amongnumberscanbe
represented,compared,and
communicated.
Mathematicalrelationships
canberepresentedas
expressions,equationsand
inequalitiesinmathematical
situations.
Numericalquantities,
calculations,and
measurementscanbe
estimatedoranalyzedby
usingappropriatestrategies
andtools.
Howismathematicsusedtoquantify,
compare,represent,andmodel
numbers?
Howcanmathematicssupport
effectivecommunication?
Howarerelationshipsrepresented
mathematically?
Whatdoesitmeantoestimateor
analyzenumericalquantities?
Whatmakesatooland/orstrategy
appropriateforagiventask?
Whenisitisappropriatetoestimate
versuscalculate?
Howcanpatternsbeusedtodescribe
relationshipsinmathematical
situations?
Howismathematicsusedtoquantify,
compare,represent,andmodel
numbers?
PlaceValue
and
Propertiesof
Operations
Performmulti-digitarithmetic.
Demonstratefluencyof
additionandsubtraction.
Roundwholenumberstothe
nearesttenorhundred.
CC.2.1.3.B.1
Fractions
Developanunderstandingof
fractionsasnumbers.
Representfractionsona
numberline.
Representandgenerate
equivalentfractions.
Comparefractionswiththe
samenumeratororsame
denominator.
CC.2.1.3.C.1
Howcanmathematicssupport
effectivecommunication?
Howarerelationshipsrepresented
mathematically?
Whatdoesitmeantoestimateor
analyzenumericalquantities?
Standard
Eligible
Content
Vocabulary
M03.A-T.1.1.1
Area
M03.A-T.1.1.2 Denominator
M03.A-T.1.1.3Division
M03.A-T.1.1.4 Equivalentfractions
Estimate
Fraction
Linear
LiquidVolume
Mass
Numerator
Pattern
Pentagon
Perimeter
Pictograph
Polygon
Quadrilateral
Rhombus
Round
SquareUnit
TallyChart
Temperature
M03.A-F.1.1.1
M03.A-F.1.1.2
M03.A-F.1.1.3
M03.A-F.1.1.4
M03.A-F.1.1.5
Whatmakesatooland/orstrategy
appropriateforagiventask?
5
OCT 2016
PA Core Standards for Mathematics
2.1 Numbers and Operations PreK-12
Grade
4
4
4
BigIdea
EssentialQuestions
Concepts
Competencies
Mathematicalrelationships
amongnumberscanbe
represented,compared,and
communicated.
Mathematicalrelationships
canberepresentedas
expressions,equationsand
inequalitiesinmathematical
situations.
Numericalquantities,
calculations,and
measurementscanbe
estimatedoranalyzedby
usingappropriatestrategies
andtools.
Patternsexhibitrelationships
thatcanbeextended,
described,andgeneralized.
Howismathematicsusedtoquantify,
compare,represent,andmodel
numbers?
Howcanmathematicssupport
effectivecommunication?
Howarerelationshipsrepresented
mathematically?
Whatdoesitmeantoestimateor
analyzenumericalquantities?
Whenisitisappropriatetoestimate
versuscalculate?
Whatmakesatooland/orstrategy
appropriateforagiventask?
Howcanpatternsbeusedtodescribe
relationshipsinmathematical
situations?
Howismathematicsusedtoquantify,
compare,represent,andmodel
numbers?
PlaceValue
and
Propertiesof
Operations
Demonstrateanunderstanding
ofmulti-digitwholenumbers.
Compareandroundmulti-digit
numbers.
Performmulti-digitarithmetic.
CC.2.1.4.B.1
CC.2.1.4.B.2
M04.A-T.1.1.1
M04.A-T.1.1.2
M04.A-T.1.1.3
M04.A-T.1.1.4
M04.A-T.2.1.1
M04.A-T.2.1.2
M04.A-T.2.1.3
M04.A-T.2.1.4
Fractions
Demonstrateanunderstanding
offractionequivalence.
Compareandorderfractions.
Solveproblemsinvolving
fractionsandmixednumbers.
CC.2.1.4.C.1
CC.2.1.4.C.2
M04.A-F.1.1.1
M04.A-F.1.1.2
M04.A-F.2.1.1
M04.A-F.2.1.2
M04.A-F.2.1.3
M04.A-F.2.1.4
M04.A-F.2.1.5
M04.A-F.2.1.6
M04.A-F.2.1.7
Decimals
Usedecimalnotationfor
CC.2.1.4.C.3
M04.A-F.3.1.1
Mathematicalrelationships
amongnumberscanbe
represented,compared,and
communicated.
Mathematicalrelationships
canberepresentedas
expressions,equationsand
inequalitiesinmathematical
situations.
Numericalquantities,
calculations,and
measurementscanbe
estimatedoranalyzedby
usingappropriatestrategies
andtools.
Mathematicalrelationships
Howcanmathematicssupport
effectivecommunication?
Howarerelationshipsrepresented
mathematically?
Standard
Eligible
Content
Vocabulary
AcuteAngle
Angle
Decimal
DecimalFraction
Equivalence
Factor
Line
Lineofsymmetry
LineSegment
MixedNumber
Multiple
ObtuseTriangle
Point
Ray
RightAngle
Symmetry
UnitFraction
Weight
Whatdoesitmeantoestimateor
analyzenumericalquantities?
Whatmakesatooland/orstrategy
appropriateforagiventask?
Howismathematicsusedtoquantify,
6
OCT 2016
PA Core Standards for Mathematics
2.1 Numbers and Operations PreK-12
Grade
5
BigIdea
amongnumberscanbe
represented,compared,and
communicated.
Mathematicalrelationships
canberepresentedas
expressions,equationsand
inequalitiesinmathematical
situations.
Numericalquantities,
calculations,and
measurementscanbe
estimatedoranalyzedby
usingappropriatestrategies
andtools.
Mathematicalrelationships
amongnumberscanbe
represented,compared,and
communicated.
Mathematicalrelationships
canberepresentedas
expressions,equations,and
inequalitiesinmathematical
situations.
Numericalquantities,
calculations,and
measurementscanbe
estimatedoranalyzedby
usingappropriatestrategies
andtools.
Patternsexhibitrelationships
thatcanbeextended,
described,andgeneralized.
EssentialQuestions
Concepts
compare,represent,andmodel
numbers?
Competencies
Standard
decimalfractions.
Comparedecimalfractions.
Comparedecimals.
Howcanmathematicssupport
effectivecommunication?
Eligible
Content
Vocabulary
M04.A-F.3.1.2
M04.A-F.3.1.3
Howarerelationshipsrepresented
mathematically?
Whatdoesitmeantoestimateor
analyzenumericalquantities?
Whatmakesatooland/orstrategy
appropriateforagiventask?
Howismathematicsusedtoquantify,
compare,represent,andmodel
numbers?
Howcanmathematicssupport
effectivecommunication?
Howarerelationshipsrepresented
mathematically?
Whatdoesitmeantoestimateor
analyzenumericalquantities?
Whenisitisappropriatetoestimate
versuscalculate?
Whatmakesatooland/orstrategy
appropriateforagiventask?
Howcanpatternsbeusedtodescribe
relationshipsinmathematical
situations?
PlaceValue
and
Propertiesof
Operations
Demonstrateanunderstanding
ofroundingasitpertainsto
wholenumbersanddecimals.
CC.2.1.5.B.1
Read,writeandcompare
decimals.
Usewholenumbersand
decimalstocompute
accurately.
CC.2.1.5.B.2
M05.A-T.1.1.1
M05.A-T.1.1.2
M05.A-T.1.1.3
M05.A-T.1.1.4
M05.A-T.1.1.5
M05.A-T.2.1.1
M05.A-T.2.1.2
M05.A-T.2.1.3
Braces
Brackets
CoordinatePlane
CubicUnits
DecimalPlaceValue
(throughthousandths)
MeasurementSystems
MeasurementUnits
NumericalExpressions
OrderofOperations
Origin
Parentheses
Scaling(resizing)
UnitFraction
Volume
X-axis
X-coordinate
Y-axis
Y-coordinate
7
OCT 2016
PA Core Standards for Mathematics
2.1 Numbers and Operations PreK-12
Grade
5
5
6
BigIdea
Mathematicalrelationships
amongnumberscanbe
represented,compared,and
communicated.
Mathematicalrelationships
canberepresentedas
expressions,equations,and
inequalitiesinmathematical
situations.
Numericalquantities,
calculations,and
measurementscanbe
estimatedoranalyzedby
usingappropriatestrategies
andtools.
Mathematicalrelationships
amongnumberscanbe
represented,compared,and
communicated.
Mathematicalrelationships
canberepresentedas
expressions,equations,and
inequalitiesinmathematical
situations.
Numericalquantities,
calculations,and
measurementscanbe
estimatedoranalyzedby
usingappropriatestrategies
andtools.
Mathematicalrelationships
amongnumberscanbe
represented,compared,and
communicated.
EssentialQuestions
Concepts
Competencies
Add,Subtract,Multiplyand
Dividefractionstosolve
problems.
Standard
Eligible
Content
Howismathematicsusedtoquantify,
compare,represent,andmodel
numbers?
Howcanmathematicssupport
effectivecommunication?
Howarerelationshipsrepresented
mathematically?
Whatdoesitmeantoestimateor
analyzenumericalquantities?
Whatmakesatooland/orstrategy
appropriateforagiventask?
Fractions
CC.2.1.5.C.1
M05.A-F.1.1.1
CC.2.1.5.C.2
M05.A-F.2.1.1
M05.A-F.2.1.2
M05.A-F.2.1.3
M05.A-F.2.1.4
Howismathematicsusedtoquantify,
compare,represent,andmodel
numbers?
Howcanmathematicssupport
effectivecommunication?
Howarerelationshipsrepresented
mathematically?
Whatdoesitmeantoestimateor
analyzenumericalquantities?
Whenisitisappropriatetoestimate
versuscalculate?
Decimals
Read,writeandcompare
decimals.
Usewholenumbersand
decimalstocompute
accurately.
CC.2.1.5.B.2
M05.A-T.2.1.1
M05.A-T.2.1.2
M05.A-T.2.1.3
Howismathematicsusedtoquantify,
compare,representandmodel
numbers?
Ratios,
Proportions,
andPercent
Representratiorelationshipsin
variousforms.
Determineunitratesincontext.
CC.2.1.6.D.1
M06.A-R.1.1.1
M06.A-R.1.1.2
M06.A-R.1.1.3
M06.A-R.1.1.4
Explainoperationsasthey
pertaintofractions.
Vocabulary
Absolutevalue
Algebraicexpressions
Boxandwhiskerplots
Coefficient
8
OCT 2016
PA Core Standards for Mathematics
2.1 Numbers and Operations PreK-12
Grade
6
6
BigIdea
EssentialQuestions
Mathematicalrelationships
canberepresentedas
expressions,equationsand
inequalitiesinmathematical
situations.
Numericalquantities,
calculations,and
measurementscanbe
estimatedoranalyzedby
usingappropriatestrategies
andtools.
Patternsexhibitrelationships
thatcanbeextended,
described,andgeneralized.
Mathematicalrelationships
amongnumberscanbe
represented,compared,and
communicated.
Numericalquantities,
calculations,and
measurementscanbe
estimatedoranalyzedby
usingappropriatestrategies
andtools.
Howcanmathematicssupport
effectivecommunication?
Howarerelationshipsrepresented
mathematically?
Howcanexpressions,equationsand
inequalitiesbeusedtoquantify,solve,
modeland/oranalyzemathematical
situations?
Whatmakesatooland/orstrategy
appropriateforagiventask?
Howcanpatternsbeusedtodescribe
relationshipsinmathematical
situations?
Howismathematicsusedtoquantify,
compare,represent,andmodel
numbers?
Howcanmathematicssupport
effectivecommunication?
Whatdoesitmeantoestimateor
analyzenumericalquantities?
Whatmakesatooland/orstrategy
appropriateforagiventask?
Howismathematicsusedtoquantify,
compare,represent,andmodel
numbers?
Howcanmathematicssupport
effectivecommunication?
Howarerelationshipsrepresented
mathematically?
Mathematicalrelationships
amongnumberscanbe
represented,compared,and
communicated.
Mathematicalrelationships
canberepresentedas
expressions,equationsand
inequalitiesinmathematical
situations.
Concepts
Competencies
Standard
Interpretandcompute
CC.2.1.6.E.1
quotientsoffraction.
Solveproblemsusingratioand
ratereasoning.
Convertmeasurementunits
usingequivalentratios.
Eligible
Content
M06.A-R.1.1.5
M06.A-R.1.1.3
M06.A-R.1.1.4
M06.A-R.1.1.5
M06.A-N.1.1.1
Number
Theory
Conceptsand
Operations
Solveproblemsandcompute
CC2.1.6.E.2
M06.A-N.2.1.1
fluentlywithwholenumbers
M06.A-N.2.2.1
anddecimals.
CC.2.1.6.E.3
M06.A-N.2.2.1
Findcommonmultiplesand
M06.A-N.2.2.2
factorsincludinggreatest
commonfactorandleast
commonmultiple.
Usethedistributivepropertyto
expressasumoftwonumbers.
Integersand
Other
Rational
Numbers
Usepositiveandnegative
CC.2.1.6.E.4
M06.A-N.3.1.1
numberstorepresent
M06.A-N.3.1.2
quantitiesinrealworld
M06.A-N.3.1.3
contexts.
M06.A-N.3.2.1
M06.A-N.3.2.2
Plotintegersandotherrational
M06.A-N.3.2.3
numbersonanumberlineand
onacoordinategraph.
Interprettheoppositeand
Vocabulary
Compoundpolygon
Dependentvariable
Distributiveproperty
Dotplots
Exponent
GreatestCommon
Factor
Independentvariable
Inequality
Integer
Interquartilerange
IrregularPolygon
LeastCommon
Multiple
Mean
Meanabsolute
deviation
9
OCT 2016
PA Core Standards for Mathematics
2.1 Numbers and Operations PreK-12
Grade
7
7
BigIdea
EssentialQuestions
Numericalquantities,
calculations,and
measurementscanbe
estimatedoranalyzedby
usingappropriatestrategies
andtools.
Mathematicalrelationships
amongnumberscanbe
represented,compared,and
communicated.
Mathematicalrelationships
canberepresentedas
expressions,equationsand
inequalitiesinmathematical
situations.
Numericalquantities,
calculations,and
measurementscanbe
estimatedoranalyzedby
usingappropriatestrategies
andtools.
Patternsexhibitrelationships
thatcanbeextended,
described,andgeneralized.
Howcanexpressions,equationsand
inequalitiesbeusedtoquantify,solve,
modeland/oranalyzemathematical
situations?
Whatmakesatooland/orstrategy
appropriateforagiventask?
Howismathematicsusedtoquantify,
compare,represent,andmodel
numbers?
Howcanmathematicssupport
effectivecommunication?
Howarerelationshipsrepresented
mathematically?
Howcanexpressions,equationsand
inequalitiesbeusedtoquantify,solve,
modeland/oranalyzemathematical
situations?
Whatdoesitmeantoestimateor
analyzenumericalquantities?
Whatmakesatooland/orstrategy
appropriateforagiventask?
Howcanrecognizingrepetitionor
regularityassistinsolvingproblems
moreefficiently?
Howcanmathematicssupport
effectivecommunication?
Howarerelationshipsrepresented
mathematically?
Howcanexpressions,equationsand
Mathematicalrelationships
amongnumberscanbe
represented,compared,and
communicated.
Mathematicalrelationships
canberepresentedas
Concepts
Competencies
Standard
Eligible
Content
Vocabulary
absolutevalueofanintegeras
itsdistancefromzeroona
numberline
Compareandorderrational
numbers.
Ratios,
Proportions,
andPercent
Computeunitratesassociated
withratiosoffractions.
Recognizeandrepresent
proportionalrelationships
betweenquantities.
Useproportionalrelationships
tosolvemultistepratioand
percentproblems.
CC.2.1.7.D.1
Rational
Numbers
Solvereal-worldand
mathematicalproblems
involvingthefouroperations
withrationalnumbers.
CC.2.1.7.E.1
M07.A-R.1.1.1
M07.A-R.1.1.2
M07.A-R.1.1.3
M07.A-R.1.1.4
M07.A-R.1.1.5
M07.A-R.1.1.6
Acutetriangle
Adjacentangles
Alternateexterior
angles
Alternateinterior
angles
Chanceevent
Circumference
Complementaryangles
Compoundevent
Correspondingangles
Datadistribution
decrease
Equallylikely
Equilateraltriangle
Independentevent
Isoscelestriangle
Likelyevent
Linearexpression
Obtusetriangle
Outcome
Percentincreaseand
Population
Probability
M07.A-N.1.1.1 Processofchance
M07.A-N.1.1.2 Proportion
M07.A-N.1.1.3 Randomsample
Relativefrequency
Repeatingdecimal
Scaledrawing
Scalenetriangle
10
OCT 2016
PA Core Standards for Mathematics
2.1 Numbers and Operations PreK-12
Grade
8
BigIdea
EssentialQuestions
expressions,equationsand
inequalitiesinmathematical
situations.
Numericalquantities,
calculations,and
measurementscanbe
estimatedoranalyzedby
usingappropriatestrategies
andtools.
Patternsexhibitrelationships
thatcanbeextended,
described,andgeneralized.
inequalitiesbeusedtoquantify,solve,
modeland/oranalyzemathematical
situations?
Whatdoesitmeantoestimateor
analyzenumericalquantities?
Whatmakesatooland/orstrategy
appropriateforagiventask?
Howcanrecognizingrepetitionor
regularityassistinsolvingproblems
moreefficiently?
Howismathematicsusedtoquantify,
compare,represent,andmodel
numbers?
Howcanmathematicssupport
effectivecommunication?
Howarerelationshipsrepresented
mathematically?
Howcanexpressions,equationsand
inequalitiesbeusedtoquantify,solve,
modeland/oranalyzemathematical
situations?
Whatdoesitmeantoestimateor
analyzenumericalquantities?
Whatmakesatooland/orstrategy
appropriateforagiventask?
Howcanpatternsbeusedtodescribe
relationshipsinmathematical
situations?
Mathematicalrelationships
amongnumberscanbe
represented,compared,and
communicated.
Mathematicalrelationships
canberepresentedas
expressions,equationsand
inequalitiesinmathematical
situations.
Numericalquantities,
calculations,and
measurementscanbe
estimatedoranalyzedby
usingappropriatestrategies
andtools.
Patternsexhibitrelationships
thatcanbeextended,
described,andgeneralized.
Concepts
Rational
Numbersand
Irrational
Numbers
Competencies
Distinguishbetweenrational
andirrationalnumbersusing
theirproperties.
Convertaterminatingor
repeatingdecimalintoa
rationalnumber.
Userationalapproximationsof
irrationalnumberstocompare
thesizeofirrationalnumbers.
Standard
CC.2.1.8.E.1
CC.2.1.8.E.4
Eligible
Content
Vocabulary
M08.A-N.1.1.1
M08.A-N.1.1.2
M08.A-N.1.1.3
M08.A-N.1.1.4
M08.A-N.1.1.5
Bivariatedata
Clustering
Coefficient
Cone
Congruence
Congruentfigures
Cuberoot
Cylinder
Dilations
Function
Irrationalnumber
Lineofbestfit
Linearassociation
Linearequation
Negativecorrelation
Non-Linearassociation
Outlier
Perfectcube
Perfectsquare
Positivecorrelation
Pythagoreantheorem
Rateofchange
Rationalnumber
Reflection
11
OCT 2016
PA Core Standards for Mathematics
2.1 Numbers and Operations PreK-12
Grade
ALG1
BigIdea
EssentialQuestions
Concepts
Mathematicalrelationships
amongnumberscanbe
represented,compared,and
communicated.
Mathematicalrelationships
canberepresentedas
expressions,equationsand
inequalitiesinmathematical
situations.
Numericalquantities,
calculations,and
measurementscanbe
estimatedoranalyzedby
usingappropriatestrategies
andtools.
Patternsexhibitrelationships
thatcanbeextended,
described,andgeneralized.
Howismathematicsusedtoquantify, Rationaland
compare,represent,andmodel
Irrational
numbers?
Numbers
Howcanmathematicssupport
effectivecommunication?
Howarerelationshipsrepresented
mathematically?
Whatdoesitmeantoestimateor
analyzenumericalquantities?
Howcanexpressions,equationsand
inequalitiesbeusedtoquantify,solve,
modeland/oranalyzemathematical
situations?
Whatmakesatooland/orstrategy
appropriateforagiventask?
Howcanpatternsbeusedtodescribe
relationshipsinmathematical
situations?
Competencies
Standard
Eligible
Content
Representand/orusenumbers
inequivalentforms(integers,
fractions,decimals,percent’s,
squareroots,exponents).
CC.2.1.HS.F.1
CC.2.1.HS.F.2
A1.1.1.1.1
A1.1.1.1.2
A1.1.1.3.1
Vocabulary
Relation
Rotation
Scatterplot
Scientificnotation
Similarity
Simultaneouslinear
equations
Slope
Sphere
Squareroot
Transformation
Translation
Two-waytable
y-intercept
AdditiveInverse
AdditivePropertyof
Equality
Algorithm
ArithmeticSequence
AssociativeProperty
Asymptote
BarGraph
Binomial
BivariateData
BoundaryLine
BoundedRegion
CircleGraph
Coefficient
CommutativeProperty
CompositeNumber
CompoundEvent
CompoundInequality
Degree(ofpolynomial)
DependentEvents
Domain(ofRelationor
Function)
Equivalent
EstimationStrategy
12
OCT 2016
PA Core Standards for Mathematics
2.1 Numbers and Operations PreK-12
Grade
ALG1
BigIdea
Mathematicalrelationships
amongnumberscanbe
represented,compared,and
communicated.
Mathematicalrelationships
canberepresentedas
expressions,equationsand
inequalitiesinmathematical
situations.
Numericalquantities,
calculations,and
measurementscanbe
estimatedoranalyzedby
usingappropriatestrategies
andtools.
Mathematicalrelationships
amongnumberscanbe
represented,compared,and
communicated.
ALG1
Mathematicalrelationships
canberepresentedas
expressions,equationsand
inequalitiesinmathematical
situations.
Numericalquantities,
calculations,and
measurementscanbe
estimatedoranalyzedby
usingappropriatestrategies
andtools.
EssentialQuestions
Concepts
Competencies
Standard
Eligible
Content
Howismathematicsusedtoquantify,
compare,represent,andmodel
numbers?
Howcanmathematicssupport
effectivecommunication?
Howarerelationshipsrepresented
mathematically?
Howcanexpressions,equationsand
inequalitiesbeusedtoquantify,solve,
modeland/oranalyzemathematical
situations?
Whatdoesitmeantoestimateor
analyzenumericalquantities?
Whatmakesatooland/orstrategy
appropriateforagiventask?
Howismathematicsusedtoquantify,
compare,represent,andmodel
numbers?
Howcanmathematicssupport
effectivecommunication?
Howarerelationshipsrepresented
mathematically?
Howcanexpressions,equationsand
inequalitiesbeusedtoquantify,solve,
modeland/oranalyzemathematical
situations?
Whatmakesatooland/orstrategy
appropriateforagiventask?
RealNumber
System
Applyandextendthe
propertiesofexponentsto
solveproblemswithrational
exponents.
Applynumbertheoryconcepts
toshowrelationshipsbetween
realnumbersinproblemsolvingsettings.
Useexponents,roots,and/or
absolutevaluestosolve
problems.
CC.2.1.HS.F.1
CC.2.1.HS.F.2
CC.2.1.HS.F.3
A1.1.1.1.1
A1.1.1.1.2
A1.1.1.3.1
A1.1.2.1.1
A1.1.2.1.2
A1.1.2.1.3
A1.2.1.2.1
A1.2.1.2.2
Equations
and
Inequalities
Interpretsolutionstolinear
equationsandinequalities.
Interpretsolutionstolinear
systemsofequationsand
inequalities.
CC.2.1.HS.F.3
CC.2.1.HS.F.4
CC.2.1.HS.F.5
A1.1.2.1.1
A1.1.2.1.2
A1.1.2.1.3
A1.2.1.2.1
A1.2.1.2.2
A1.1.2.2.1
A1.1.2.2.2
A1.1.3.1.1
A1.1.3.1.2
A1.1.3.1.3
A1.1.3.2.1
A1.1.3.2.2
Vocabulary
ExponentialEquation
ExponentialExpression
ExponentialFunction
Exponential
Growth/Decay
Extrapolate
Frequency
Function
GeometricSequence
GreatestCommon
Factor
Half-Plane
IndependentEvents
IndependentVariable
Index
Interpolate
InterquartileRange
Inverse(ofaRelation)
InverseOperation
MaximumValue(ofa
Graph)
MeasureofCentral
Tendencies
MeasureofDispersion
MinimumValue(ofa
Graph)
MultiplicativeInverse
MultiplicativeProperty
ofEquality
MultiplicativeProperty
ofZero
MutuallyExclusive
(rationalv.irrational)
MutuallyExclusive
Event
NegativeExponent
Odds
Outlier
Point-SlopeForm
PolynomialFunction
13
OCT 2016
PA Core Standards for Mathematics
2.1 Numbers and Operations PreK-12
Grade
BigIdea
ALG2
Mathematicalrelationships
amongnumberscanbe
represented,compared,and
communicated.
Mathematicalrelationships
canberepresentedas
expressions,equationsand
inequalitiesinmathematical
EssentialQuestions
Howismathematicsusedtoquantify,
compare,represent,andmodel
numbers?
Howcanmathematicssupport
effectivecommunication?
Howarerelationshipsrepresented
mathematically?
Concepts
Complex
Number
System
Competencies
Representand/oruseimaginary
numbersinequivalentforms.
Simplify/evaluateexpressions
involvingimaginarynumbers.
Performarithmeticoperations
andapplytocomplexnumbers.
Standard
CC.2.1.HS.F.6
CC.2.1.HS.F.7
Eligible
Content
A2.1.1.1.1
A2.1.1.1.2
A2.1.1.2.1
A2.1.1.2.2
Vocabulary
PositiveExponents
Probabilityof
CompoundEvents
Quadrants
QuadraticFunctions
Quartile
RadicalExpression
Range(ofData)
Range(ofRelationor
Function)
Rate(ofChange)
Relation
RepeatingDecimal
Scatterplot
SimpleEvent
Simplestform(ofan
Expression)
Slope-InterceptForm
StandardForm(ofa
LinearEquation)
SubstitutionMethod
SystemsofLinear
Equations
SystemsofLinear
Inequalities
TerminatingDecimal
TestPoint
Trinomial
UnboundedRegion
Asymptote
Binomial
Combination
CommonLogarithm
Complex
Number
System
CompoundEvents
Dependent/Independe
ntEvents
14
OCT 2016
PA Core Standards for Mathematics
2.1 Numbers and Operations PreK-12
Grade
BigIdea
situations.
Numericalquantities,
calculations,and
measurementscanbe
estimatedoranalyzedby
usingappropriatestrategies
andtools.
ALG2
ALG2
Mathematicalrelationships
amongnumberscanbe
represented,compared,and
communicated.
Mathematicalrelationships
canberepresentedas
expressions,equationsand
inequalitiesinmathematical
situations.
Numericalquantities,
calculations,and
measurementscanbe
estimatedoranalyzedby
usingappropriatestrategies
andtools.
Mathematicalrelationships
amongnumberscanbe
represented,compared,and
communicated.
Mathematicalrelationships
canberepresentedas
expressions,equationsand
inequalitiesinmathematical
EssentialQuestions
Howcanexpressions,equationsand
inequalitiesbeusedtoquantify,solve,
modeland/oranalyzemathematical
situations?
Whatdoesitmeantoestimateor
analyzenumericalquantities?
Whatmakesatooland/orstrategy
appropriateforagiventask?
Howismathematicsusedtoquantify,
compare,represent,andmodel
numbers?
Howcanmathematicssupport
effectivecommunication?
Howarerelationshipsrepresented
mathematically?
Howcanexpressions,equationsand
inequalitiesbeusedtoquantify,solve,
modeland/oranalyzemathematical
situations?
Whatmakesatooland/orstrategy
appropriateforagiventask?
Howismathematicsusedtoquantify,
compare,represent,andmodel
numbers?
Howcanmathematicssupport
effectivecommunication?
Howarerelationshipsrepresented
mathematically?
Concepts
Competencies
Standard
Eligible
Content
Polynomial
andRational
Expressions
Performarithmeticoperations
onpolynomials.
Understandtherelationship
betweenzerosandfactorsof
polynomials.
Rewriterationalexpressions.
Simplify/factorexpressions
involvingpolynomials.
CC.2.1.HS.F.1
CC.2.1.HS.D.1
CC.2.1.HS.D.2
CC.2.1.HS.D.3
CC.2.1.HS.D.4
CC.2.1.HS.D.5
CC.2.1.HS.D.6
A2.1.2.1.2
A2.1.3.1.2
A2.1.2.2.1
A2.1.2.2.2
Equations
and
Inequalities
Createand/orsolveequations
(includingliteral,polynomial,
rational,radical,exponential,
andlogarithmic)both
algebraicallyandgraphically.
Useand/orexplainreasoning
whilesolvingequations,and
justifythesolutionmethod.
CC.2.1.HS.F.1
CC.2.1.HS.D.1
CC.2.1.HS.D.2
A2.1.2.1.3
A2.1.2.1.4
A2.1.2.2.2
A2.1.3.1.1
A2.1.3.1.3
A2.1.3.1.4
A2.1.3.2.1
A2.1.3.2.2
A2.2.2.1.2
Vocabulary
Dilation
Exponential
ExponentialDecay
ExponentialFunction
ExponentialGrowth
Expression
GeometricSequence
ImaginaryNumber
Intervals
Intercept
Logarithm
NaturalLogarithm
NegativeExponents
ObservationalStudy
Outcomes
Perfect
Square
Trinomial
Permutation
Polynomial
PolynomialIdentity
Probability
QuadraticFormula
QuadraticFunction
RadicalFunctions
RationalFunctions
Reflection
RegressionModels
RootFunctions
SampleSurvey
Scatterplot
StandardDeviation
StatisticalExperiment
Transformation
Translations
Trinomial
UnitCircle
15
OCT 2016
PA Core Standards for Mathematics
2.1 Numbers and Operations PreK-12
Grade
BigIdea
situations.
Numericalquantities,
calculations,and
measurementscanbe
estimatedoranalyzedby
usingappropriatestrategies
andtools.
EssentialQuestions
Howcanexpressions,equationsand
inequalitiesbeusedtoquantify,solve,
modeland/oranalyzemathematical
situations?
Whatmakesatooland/orstrategy
appropriateforagiventask?
Concepts
Competencies
Determinehowachangeinone
variablerelatestoachangeina
secondvariable.
Useexponents,roots,and/or
absolutevaluestorepresent
equivalentformsortosolve
problems.
Standard
Eligible
Content
Vocabulary
A2.2.2.1.3
16
OCT 2016