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Page 1: Academic Standards for Mathematics...The Co=on Core Standards in Mathematics in grades PreK-5 lay a solid foundation in whole numbers, addition, subtraction, multiplication, division,

Academic Standards for Mathematics

Grades PreK-High School January 2013

Pennsylvania Department ofEducation

Pennsylvania Core Standards Mathematics

INTRODUCTION

The Co=on Core Standards in Mathematics in grades PreK-5 lay a solid foundation in whole numbers addition subtraction multiplication division fractions and decimals Taken together these elements support a students ability to learn and apply more demanding math concepts and procedures The middle school and high school standards call on students to practice applying mathematical ways ofthinking to real world issues and challenges they prepare students to think and reason mathematically Additionally they set a rigorous definition of college and career readiness by demanding that students develop a depth ofunderstanding and ability to apply mathematics to novel situations as college students and employees regularly do Although the standards are not a curriculum or a prescribed series of activities school entities will use them to develop a local school curriculum that will meet local students needs

This document includes PA Core Standards for Mathematical Content and Mathematical Practice The mathematics standards define what students should understand and be able to do Mathematical Practice Standards describes the habits ofmind required to reach_a level ofmathematical

proficiency

PA Core Standards

Standards for Mathematical Practice 1

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January 2013

Pennsylvania Core Standards Mathematics

Standards cannot be viewed or addressed in isolation as each standard depends upon or may lead into multiple standards across grades thus it is imperative that educators are familiar with both the standards that come before and those that follow a particular grade level These revised standards reflect instructional shifts that cannot occur without the integrated emphasis on content and practice

Standards are overarching statements ofwhat a proficient math student should know and be able to do The Pennsylvania Assessment Anchors and Eligible Content closely align with the revised standards and are an invaluable source for greater detail

Key Points in Mathematics

bull The standards stress both procedural skills and conceptual understanding to ensure students are learning and applying the critical information they need to succeed at higher levels

bull K-5 standards which provide students with a solidfoundation in whole numbers addition subtraction multiplication division fractions and decimals help young students build the foundation to successfully apply more demanding math concepts and procedures and move into application They also provide detailed guidance to teachers on how to navigate their way through topics such as fractions negative numbers and geometry and do so by maintaining a continuous progression from grade to grade

bull Having built a strong foundation at K-5 students can do hands-on learning in geometry algebra and probability and statistics Students who have mastered the content and skills through the seventh grade will be well-preparedfor algebra in grade 8

bull High school standards emphasize practicing applying mathematical ways ofthinking to real world issues and challenges

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Pennsylvania Core Standards Mathematics

The PA Core Standards for Mathematics detail four standard areas Numbers and Operations Algebraic Concepts Geometry and Measurement Data and Probability These standard areas are reflective ofthe reporting categories in the PA Core Assessment Anchors and Eligible Content The middot intent of this document is to provide a useful tool for designing curriculum instruction and assessment The grade level curriculum and instructional shifts in mathematics cannot occur without the integrated emphasis on content and practice The chart below illustrates the four standard areas and the development and progression of the strands with an understanding that all is framed around the Standards for Mathematical Practice

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Pennsylvania Core Standards Mathematics

21 Numbers and Operations The Standards ofMathematical Practices

Make sense ofproblems and persevere in solving them Reason abstractly and quantitatively Construct viable arguments and critique the reasoning ofothers Model with mathematics Use appropriate tools strategically Attend to precision Look for and make use ofstructure

GradePreK GradeK Z1PreK Z1K

Gradel Z11

GradeZ Z1Z

Look for and exnress re~laritv in repeated reasonin1

Grade3 Grade4 Z13 Z14

Grades Z15

Pennsylvanias public schools shall teach challenge andsupporteverystudent to realize his orhermaximum potential and to acquire the Jmowledge andskills needed to CCZ1PreKA1 ccz1KA1 Know number names Know number names and and the =Cunt sequence write and recite the count olt eshy

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cC2Tia3middot----------middot Use place-value concepts and properties of operations to add and subtrattwithin 100

ccz1zs1 Use place-value concepts to represent amoWltS of tens and ones and to compare three digit numbers

CC21ZBZ Use place-value concepts to read write and skip count to 1000

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Pennsylvania Core Standards Mathematics

CCZ13C1 CCZ14C1 ccz1sc1 Explore and develop an Extend the Use the understanding of unde=ndingof unde=ndingof equivalency to add and fractions as numbers fractions to show snbtract fractions

equivalence and M03A-F1ll ordering MOSA-Flll M03AmiddotF1l2 M03A-Fll3 M04A-Fltl M03A-F1l4 M04A-Fll2

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21 Numbers and Operations

The Standards ofMathematical Practices Make sense ofproblems and persevere in solving them Reason abstractly and quantitatively Construct viable arguments and critique the reasoning ofothers Model with mathematics Use appropriate tools strategically Attend to precision Look for and make use ofstructure Look for and bull=ress reltgtuJaritv in ren eated reasonin

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Grades Z15

Pennsylvanias public schools shall teach challenge and support every student to realize his orher maximum potentialand to acquire the knowledge and skills needed to

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Pennsylvania Core Standards Mathematics

CCZ2lreKA1 CC22KA1 CC221A1 CCZ22A1 CC223A1 CC2Z4A1 CC22SA1 Understand addition as Extend the concepts of Representand solve Represent and solve Represent and solve Represent and solve Interpretand evaluate putting together and putting together and problems involviDg problems involving problems involving problems involving tbt numerical expressions adding to and taking apart to add and addition and subtraction addition and multiplication and four operations using order ofoperations understand subtraction subtract Within 10 Within20 subtraction Within 100 division astakingapartand M04ll-011l MOSJl011l taking from M03ll-Oll1 M04ll-0l12 MOSllmiddotOl12

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22 Algebraic Concepts

The Standards ofMathematical Practices Make sense ofproblems and persevere in solVingthem Reason abstractly and quantitatively Construct viable arguments and critique the reasoning of others Model with mathematics Use appropriate tools strategically Attend to precision Look for and make use ofstructure Look for and Pvnress rerulari -v in reoeated reasonini

GradePreK GradeK Gradel Grade2 Grade3 Grade4 Grades 22PreK 22K 221 Z22 223 224 225

Pennsylvanias public schools shall teach challenge andsupport every student to realize his orher maximum potentialand to acquire the knowledge andskiIfs needed to

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January 2013

23 Geometry

Pennsylvania Core Standards Mathematics

The Standards of Mathematical Practices Make sense ofproblems and persevere in solving them Reason abstractly and quantitatively Construct viable arguments and critique the reasoning ofothers Model with mathematics Use appropriate tools strategically Attend to precision Look for and make use ofstructure Look for and exuress regularitv in reueated reasonin

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Grades 235

Pennsylvanias public schools shall teach challenge andsupport everystudent to realize his orhermaximum potential and to acquire the lmowledge andskills needed to

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CC23KA1 Identify and descnbe two- and three-dimensional shapes

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CCZ31A1 Compose and distinguish between ruro- and three-shydimensional shapes based on their attrihutes

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CC232A1 Analyze and draw two-and threeffimensional shapes having specified attnOutes

middotce2s2A2 middot----shy --shy -shyUse the understanding offractions to partition shapes into halves quarters and thirds

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CC233A1 Identifycolllpareand classifyshapes and their attributes

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CC234A1 Draw lines and angles and identify these in tvvo-dimensional figures

M04C-G111

-ci3-4Ai___ --shy --shy --shy-Classifytwo-dimensional figures by properties oftheir llnes and angles

M04C-G112

middotccii4-Ar----------shyRecognize symmetric shapes and draw lines of symmetry

CC235A1 Graph points in the first quadranton the coordinate plane and interpret these points when solving real world and mathematical problems

MOSC-G111 _1P_~f~1~--shy -------shy -shyCC23SAZ Glassey twoditnensional figures into categories based on an understanding oftheir properties

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January2013

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Pennsylvania Core Standards Mathematics

24 Measurement Data and Probability The Standards ofMathematical Practices

Make sense of problems and persevere in solving them Reason abstractly and quantitatively Construct Viable arguments and critique the reasoning of others Model with mathematics Use appropriate tools strategically Attend to precision Look for and make use of strUcture Look for and vnress reunl~ri in reoeated reasonine-

GradePreK GradeK Gradel Grade2 Grade3 Grade4 Grades 24PreK 24K 241 242 243 Z44 24S

CC24PreKA1 Describe and compare measurable attributes oflength and weight of evecyday objects

CC24KA1 Descnbe and compare attributes oflength area weight and capacity of everyday objects

CC241A1 Order Iengtbs and measure them both indirelttly and by repeating length units

CC242A1 Measure and estimate lengths in standard units using appropriate tools

CCZ43A1 Solve problems involving measurement and estimation of temperature liqUid volume mass and length

CCZ44A1 Solve problems involving measurement and conversioos from a larger unit to a smaller unit

CCZ4SA1 Solve problems using conversions within a given measurement system

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middotccZyen3u-middot----------shyTell and write time to the

M04D-M11l M04D-M112 M04D-M113 M04D-M114middotccz4u-shy --shy --shy --shyTranslate information

middotcci4s-AZ______________

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nearest half hour using both analog and digital clocks

the nearest five minutes using both analog and digital clocks

nearest minute and solve problems by calculating time intervals

from one type of data display to another

data using appropriate scale

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make change using coins and paper currency with appropriate symbols

chaDge involving money using a combination of coins and bills

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January 2013

Pennsylvania Core Standards Mathematics

24 Measurement Data and Probabilitv The Standards ofMathematical Practices

Make sense ofproblems and persevere in solving them Reason abstractly and quantitatively Construct viable arguments and crltique the reasoning of others Model with mathematics Use appropriate tools strategically Attend to precision Look for and make use of structure Look for and exnress regularitv in repeated reasoning

GradePreK Z4K Grade K Gradel Z4Z Grade 2 243 Grade 3 244middot Grade 4 Z45 Grade 5 24PreK 241

PenTI vJvanias uublic schools shall teach challenae and sunnort evp~rstudent to realize his or her maximum Dotential and to acauire the knowledae andskills needed to CCZ4PreKA4 CCZ4KA4 CCZ41A4 CCZ4ZA4 CCZ43A4 CCZ44A4 CCZ4SA4 Classify objects and Classify objects and count Representand interpret Represent and interpret Representand interpret Representand interpret Solve problems involving count the number of objects iii each category

the number ofobjects in each category

data using tablescharts data using line plots pictUre graphs and bar

data using tally charts tables pictographs line

data irivolviog fractions using informationmiddot

computation offractions using information

graphs plots and bar graphs provided in a line plot provided in a line plot

M03DmiddotMZ11 MD4IJMZ11 MOSDmiddotMZ11 M03D-M212 M04IJM212 M03DmiddotM213

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laquociyeniA6-------bull -bull -- laquoci43A6middot--shy --shy --shy --shy -cc244A6____________ MOSDmiddotM31l

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angles to solve problems lntentionalb Blank

M03D-M411 M04DmiddotM311 M04DmiddotM312

IP age 10

Januazy2013

Pennsylvania Core Standards Mathematics

21 Numbers and Operations The Standards ofMathematical Practices

Make sense ofproblems and persevere in solving them Reason abstractly and quantitatively Construct viable arguments and critique the reasoning of others Model with mathematics Use appropriate tools strategically Attend to precision Look for and make use of structure Look for and eXPress regularitv in repeated reasoning

216Grade6 I 217Grade7 I 21SGradeS I I 21HSHighSchool

Pennsylvanias public schools shall teach challenge and support every student to realize his orher maximum potentialand to acquire the lmowledge andskills needed to

- CCZ16D1 CCZ17D1 I I I CCZ1lSF1 ~ Understand ratio Analyze proportional Apply and extend the properties ofexponents to solve problems with rational exponents sect concepts and use ratio relationships and use Al1111 Al1112 A1l131 A21211 A21212 A21213 A2lZ14 t vi reasoning to solve them to modcl and solve8 sect problems real-world and CCZ1HSFZ E lt mathematicalproblems Apply properties of rational and irrational numberS to solve real world or mathematical problems0 Intentionally Blartk Al1111 Al1112 All131 Al112l o1l il M06AmiddotR1l1 M07AmiddotR1l1 ~~ M06AmiddotR112 M07AmiddotR1l2 CCZllSF3= isect M06A-Rl13 M07A-R1l3 Apply quantitative reasoning to choose and interpret units and scales in formulas graphs and data ~ M06AmiddotR114 M07AmiddotR114 displayse M06A-Rl15 M07A-R11S Al1211 Al1212 Al1Z13 A12121 A12122 A2ZZ11 A22Z12 A223l1

M07A-R116 A2Z312 CC216E1 CCZ17E1 CC21SE1 Apply and extend Apply and extend 0 CCZlHSF4Distioguisb between

Use units as avray to understand problems and to guide the solution -0fmulti-step problemsprevious understandings previous understandings rational and irrational g Al1211 Al1212 Al1Z13 Al2121 A12122 A22211 A22212 of multiplication and of-Operations with numbers usiDg their sectdivision to diVide fractions to operations properties fractions by fractions with rational nUIIlbers CCZlHSFS] Choose a level of accuracy appropriate to limitations on measurement when reporting quantitiesMOSA-Nl1l a Al1211 A11Z12 Al1Z13 Al1221 Al12Z2 Al13l1 Al1312 Al1313 M06A-N111 M07A-N111 lMOSA-Nl12

Al13 21 All3 22 A2Z311 A22312 = Ei -~~~~~t~~~----------- -~t~t~t____________ _poundg ------------------------shy CCZ1HSF6 CC216E2 sect Extend the lmowiedge of arithmetic operations and apply to complex numbers sect appropriate processes to ~ Identify and choose

A2l111 A21112 A211Z1 A2l122 S compute fluently with

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Intentionally Blank Intentionally Blank Develop mdor apply nUlDbertheoryconcepts to find common factors and multiples

M06A-N22l M06A-N222

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IP age 11

January 2013

Pennsylvania Core Standards Mathematics

21 Numbers and Operations The Standards ofMathematical Practices

Make sense ofproblems and persevere in solving them Reason abstractly and quantitatively Construct viable arguments and critique the reasoning of others Model with mathematics Use appropriate tools strategically Attend to precision Look for and make use ofstructure Look for and bullvnress reltnlaritv in reoeated reasoning

216 Grade 6 217 Grade 7 21HS High School 218 Grade 8

Pennsylvanias public schools shall teach challenge and support every studentw realize his orher maximum potential and to acquire the knowledge andskills needed W CC216E4 Apply and extend previous understandings ofnumbers to the system ofrational numbers

M06A-N311 M06A-N312 M06AmiddotN313 M06AmiddotN321 M06A-ll322 M06A-N323

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CC218E4 Estimate irrational numbers by compaing them to rational numbers

MOSAmiddotN113 MOSAmiddotN114 MOSA-N11S Al1111

[Page12

January 2013

Pennsylvania Core Standards Mathematics

22 Algebraic Concepts

The Standards ofMathematical Practices Make sense ofproblems and persevere in solvilg them Reason abstractly and quantitatively Construct viable arguments and critique the reasoning of others Model with mathematics Use appropriate tools strategically Attend to precision Look for and make use ofstructure Look for and exnress regularitvin repeated reasoning

226 Grade 6 22 7 Grade 7 228 Grade 8 22HS High School

Penn rvlvartias uublic schools shall teach challem1e and sunnort everv student to realize his orher maximum uotential and to acmrire the mowledae and skills needed to CC2Z681 CC22781 CC2ZHSD1 Apply and extend

CC2Z8B1 Apply properties of Apply concepts of radicals Interpret the structure of expressions to represent a quantity in terms of its context

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M07B-E111 Al11S1 Al1152 Al1153 AZ1211 AZ1Z12AZ1213 AZ1214 AZ1221 M06B-E111 MOSBmiddotE111 AZ1ZZ2 M06B-E112 MOSB-E112

CC22HSD3M06B-E113 MOSB-E113 Extend the knowledge of arithmetic operations and apply to polynomialsM06B-E114 MOSB-E114

_]1Qsect~~l ___________ Al11S1 Al1152 Al1153 AZl221 AZ1222 -~~J~_1__ ___ ---- --- --- -shy--~---------------------- CC22HSD4CCZ2682 CCZ28BZ

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e ~ M06B-EZ14 CC22HSD7middotcciz6iir------------ middotec2z7ii3------ -----shy middotcc-2z~S1ii middot----- ---middot---shy Create and graph equations or inequalitiesto describe numbers or relationships Represent and analyze Model and solve real- Analyze and solve linear Al1211 Al1212 Al1213 Al1Z21 Al1222 All311 Al1312 Al1313 s x

quantitative world and mathematical equations and pairs of Al1321 All322 AZl311 A21312 AZ1313 AZ13M AZ1321 AZ132Z~ problems by using andrelationships between Simultaneous linear A22211 AZ2212 AZZ213 AZ2214

dependent and connecting numerical equations CC22HS08independent variables algebraic andor Apply inverse operations to solve equations or formulas for a given variableMOSB-E311graphical Al1211 Al1Z12 Al1213 AZ1311 AZ1312 AZ1313 AZ1314M06B-E311 representations MOSB-E31Z AZl321 AZ1322M06B-E312 MOSB-E313

M07B-E211 CC22HS09MOSB-E314 Use reasooing to solve equations and justify the solution method M07B-EZZ1 MOBB-E31S

All141 Al1211 Al121Z Al1213 Al1221 Al1222 Al1311 Al13l2 M07B-EZ22 Al1211 M07B-EZ31 Al1313 AZ1311 AZ1312 AZ1313 AZ1314 AZ1321 AZ132ZAll221 A11141 CCZ2lSD10Al1222

Represent solve and interpret equationsinequalities and systems of equationsinequalities algebraically and graphically

AllZ11 Al1212 Al1213 Al1221 Al1222 Al1311 Al1312 All313 Al1321 Al1322 A21311 AZl312 A2l313 AZ13U

JPage13

January 2013

Pennsylvania Core Standards Mathematics

ZZ Algebraic Concepts

The Standards ofMathematical Practices Make sense ofproblems and persevere in solving them Reason abstractly and quantitatively Construct viable arguments and critique the reasoning of others Model with mathematics Use appropriate tools strategically Attend to precision Look for and make use ofstructure Look for and Pxnress repoundUlaritv in repeated reasoning

Z26 Grade 6 zz 7 Grade 7 Z2S Grade 8 ZZHS High School

Penm 1lvanias public schools shall teach challenae andsunnort ev~rv student to realize his orhermaximum Potential and to acm1ire the knowledae and skills needed to cc22sc1 CCZ2HSC1 Define evaluate and Use the conceptand notation offunttionsto interpretand appiythemin terrns oftheir context compare functions Al2111 Al2112 Al2113 Al2211 Al2212 AlZ213 Al2214 AZ21ll

AZ2112 AZ2113 A22114 G2221 G2222 G2223 G2224 GZ225 MOSBmiddotF111 MOSJH112 CC22HSC2 MOSBmiddotF113 Graph and analyze functions and use their properties to make connections between the different

representationsAl1211 Al2111 Al2112 Al2113 Al2121 Al2122 Al22l1 AZ1314 AZ1321

Al2121 Al2112

AZ1322 AZ2111 AZ2112 AZ2113 AZ2114 Al2122

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MOSBmiddotF211 cc22HSC4MOSBmiddotF212 Interpret the effects transformations have on functions and find the inverses of functionsAl1213 =0 Al2121 Al2122 AZ1313 AZ1314 AZ1321 AZ2211 AZ2212 AZ2213g =

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CC22HSC6 Interpret functions in terms of the situations they modeL

Al2121 Al2212 Al2213 Al2221 AZ1313AZZ1l1 AZZ112 AZ2113 AZ2114 AZ2213 AZ2214 AZ2221

CC22HSC7 Apply radian measure ofan angle and the unit circle to analyze the trigonometric functions

CC22HSC8 Choose trigonometric functions to model periodic phenomena and describe the properties of the graphs

CC22HSC9 Prove the Pythagorean identity and 11Se it to calculate trigonometric ratios

G1321 G211l G2112

JPage14

January 2013

Pennsylvania Core Standards Mathematics

CC236A1 CC237A1 CC238A1 CC23lSA1 Apply appropriate tools Solve real-world and Apply the concepts of Use geometric figures and their properties to represent transformations in the plane to solve real~world and mathematical problems volume ofcylinders cones G1311 G131Z mathematical problems involving angle and spheres to solve realshy CC23HSA2 involving area surface measure area swface world and mathematical Apply rigid transformations to determine and explain congruence area and volume area circumference problems GU11 G1312

and volume CC23HSA3 M06C-Gll1 M08C-C3ll Verify and apply geometric theorems as they relate to geometric figures M06C-GllZ M07C-G2l1 G2312 G1211 G1212 G1213 G1214 G1215 G1321 G2211 G2212 G2221 G2222 M06C-Gll3 M07C-G212 G2223 G2224 G222S M06C-G1L4 M07C-G22l CC23HS-A4 M06C-Gli5 M07C-G222 Apply the concept ofcongruence to create geometric constructions

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M07C-Gll2 MOSC-G113 CC23HSA8 M07C-Gll3 M08C-Gll4 Apply geometric theorems to veruy properties ofcircless ~M07C-Gll4 GJ211 ~ G1111 G1112 G1113 G1114 G1321 G223l

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CC23HSA11 MOSC-G211 Apply coordinate geometry to prove simple geometric theorems algebraically MOSC-G212 G2121 GZ122 G2123

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CC23llSA13 Analyze relationships between two-dimensional and three-dimensional objects

G1111 G111Z G1113 Gl114 G1211 G1212 G1213 G1214 G1215 G2321 CC23HSA14 Apply geometric concepts to model and solve real world problems

G2241 G231l G2312 GZ313

23 Geometrv The Standards ofMathematical Practices

Make sense of problems and persevere in solving them Reason abstractly and quantitatively ConstructViable arguments and critique the reasoning ofothers Model with mathematics Use appropriate tools strategically Attend to precision Look for and make use of structure Look for and evnress reUlaritv in reneated reasoniniz

Grade 6 Grade7 Grades High School Z36 237 23S Z3HS

Pennltvfvanias vublic schools shall teach challen e and sunnort evPrv student to realize his or her maximum votential and to acauire the knowledae and skills needed to

jPage15

)anuazy 2013

Pennsylvania Core Standards Mathematics

24 Measurement Data and Probabilitv The Standards ofMathematical Practices

Make sense ofproblems and persevere in solving them Reason abstractly and quantitatively Construct viable ar~ments and critique the reasoning ofothers Model with mathematics Use appropriate tools strategically Attend to precision Look for and make use ofstructure Look for and express regularity in repeated reasoning

Grade 6 246

Grade7 247

Grade3 243

High School 24HS

Pennsylvanias public schools shall teach challenge and support every student to realize his or her mt1Ximum potential and to acquire the mowedge andskills needed to

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middotcci47S3----- --- --- -shy[mrestigate cbaoce processes and develop use and evaluate probability models

CCZ48B1 Analyze andor interpret bivariate data displayed in multiple representations

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iCi4862 ----------shyUnderstand thatpatterns ofassociation can be seen in bivariate data utilizing frequencies

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CCZ4HSB2 Summarize represent and interpret data on two categorical and quantitative variables

Al21ll Al2112 A12113 Al2121 Al2122 Al2221 A2211l AZ2311 AZ2312

CCZ4HSB3 Analyze linear models to make interpretations based on the data

Al222l A1231l Al2321 Al2322 Al2323 A22311 AZ2312

CCZ4HSB4 Recognize and evaluate random processes underlying statistical experiments

Al2331 A223Z1 A2232Z A22323

CC24HSBS Make inferences and justify conclusions based on sample surveys experiments and observational studies

Al2321 Al2322 Al2323 A22321 A22322 A22323

CCZ4J5B6 Use the concepts ofindependence and conditional probability to interpret data

AZ2321 A22322 A22323

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lntentionany Blank CCZ4HSB7 Apply the rules of probability to compute probabilities ofcompound events in a uniform probability model

Al2331 A223Z1 A223ZZ A22323

[Page16

January 2013

Pennsylvania Core Standards Mathematics

Key Terms for this Document

Standards for Mathematical Content-These standards define what students should know and be able to do in their study of mathematics

Standards for Mathematical Practice-These standards describe the processes and proficiencies in which all students grades K-12 should engage Educators

must instill these standards of practice in their students so that they become habitual The standards for mathematical practice should be used as the vehicle to

deliver the standards of mathematical content

Standard Algorithm-A locally agreed upon method of computation which is conventionally taught for solving mathematical problems

Decimal Fraction-A fraction whose denominator is a power of ten (examples 2100 810) These fractions are commonly expressed as decimals

Unit Fraction-A rational number written as a fraction where the numerator is one and the denominator is a positive integer (example 120)

Bivariate Data-The data involves two variables and is usually represented as a scatter plot

Rule-A single operation (examples add 5 multiply by 2)

IP age 17

January 2013

Page 2: Academic Standards for Mathematics...The Co=on Core Standards in Mathematics in grades PreK-5 lay a solid foundation in whole numbers, addition, subtraction, multiplication, division,

Pennsylvania Core Standards Mathematics

INTRODUCTION

The Co=on Core Standards in Mathematics in grades PreK-5 lay a solid foundation in whole numbers addition subtraction multiplication division fractions and decimals Taken together these elements support a students ability to learn and apply more demanding math concepts and procedures The middle school and high school standards call on students to practice applying mathematical ways ofthinking to real world issues and challenges they prepare students to think and reason mathematically Additionally they set a rigorous definition of college and career readiness by demanding that students develop a depth ofunderstanding and ability to apply mathematics to novel situations as college students and employees regularly do Although the standards are not a curriculum or a prescribed series of activities school entities will use them to develop a local school curriculum that will meet local students needs

This document includes PA Core Standards for Mathematical Content and Mathematical Practice The mathematics standards define what students should understand and be able to do Mathematical Practice Standards describes the habits ofmind required to reach_a level ofmathematical

proficiency

PA Core Standards

Standards for Mathematical Practice 1

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IPage2

January 2013

Pennsylvania Core Standards Mathematics

Standards cannot be viewed or addressed in isolation as each standard depends upon or may lead into multiple standards across grades thus it is imperative that educators are familiar with both the standards that come before and those that follow a particular grade level These revised standards reflect instructional shifts that cannot occur without the integrated emphasis on content and practice

Standards are overarching statements ofwhat a proficient math student should know and be able to do The Pennsylvania Assessment Anchors and Eligible Content closely align with the revised standards and are an invaluable source for greater detail

Key Points in Mathematics

bull The standards stress both procedural skills and conceptual understanding to ensure students are learning and applying the critical information they need to succeed at higher levels

bull K-5 standards which provide students with a solidfoundation in whole numbers addition subtraction multiplication division fractions and decimals help young students build the foundation to successfully apply more demanding math concepts and procedures and move into application They also provide detailed guidance to teachers on how to navigate their way through topics such as fractions negative numbers and geometry and do so by maintaining a continuous progression from grade to grade

bull Having built a strong foundation at K-5 students can do hands-on learning in geometry algebra and probability and statistics Students who have mastered the content and skills through the seventh grade will be well-preparedfor algebra in grade 8

bull High school standards emphasize practicing applying mathematical ways ofthinking to real world issues and challenges

Page3

january2013

Pennsylvania Core Standards Mathematics

The PA Core Standards for Mathematics detail four standard areas Numbers and Operations Algebraic Concepts Geometry and Measurement Data and Probability These standard areas are reflective ofthe reporting categories in the PA Core Assessment Anchors and Eligible Content The middot intent of this document is to provide a useful tool for designing curriculum instruction and assessment The grade level curriculum and instructional shifts in mathematics cannot occur without the integrated emphasis on content and practice The chart below illustrates the four standard areas and the development and progression of the strands with an understanding that all is framed around the Standards for Mathematical Practice

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January 2013

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Pennsylvania Core Standards Mathematics

21 Numbers and Operations The Standards ofMathematical Practices

Make sense ofproblems and persevere in solving them Reason abstractly and quantitatively Construct viable arguments and critique the reasoning ofothers Model with mathematics Use appropriate tools strategically Attend to precision Look for and make use ofstructure

GradePreK GradeK Z1PreK Z1K

Gradel Z11

GradeZ Z1Z

Look for and exnress re~laritv in repeated reasonin1

Grade3 Grade4 Z13 Z14

Grades Z15

Pennsylvanias public schools shall teach challenge andsupporteverystudent to realize his orhermaximum potential and to acquire the Jmowledge andskills needed to CCZ1PreKA1 ccz1KA1 Know number names Know number names and and the =Cunt sequence write and recite the count olt eshy

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~ -----------------------middot CCZ1PreKA3 ~ Compare numbers

Apply one-to-one correspondence to count

_JflJtXlll2~t95~bj~middot- --shyccz1KA3 Apply the concept of magnitude to compare numbers and ouantities CCZ1KB1 Use place value to compose and decompose numbers within 19

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CC211B1 Extend the counting sequence to read and write numerals to represent objects

middotcc zi~isimiddot-- ----middotmiddot --- shyUse place-V3lue concepts to represent amounts of tens and ones and to compare two digit numbers

cC2Tia3middot----------middot Use place-value concepts and properties of operations to add and subtrattwithin 100

ccz1zs1 Use place-value concepts to represent amoWltS of tens and ones and to compare three digit numbers

CC21ZBZ Use place-value concepts to read write and skip count to 1000

CCZ13B1 Apply place-value understanding and properties ofoperations to perform multi-digit arithmetic

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CC214B1 Apply place-value concepts to show an understanding ofmulti-digit whole numbers

M04A-T1l1 M04A-Tl12 M04A-TLl3 M04A-Tll4

middotc-cziiiii---- --- --- shyUse place-value understanding and properties ofoperations to perform multi-digit arithmetic

M04A-T2ll M04A-T212 M04A-T213 191~r1

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CCZ15B1 Apply placemiddotvalue concepts to show an understanding of operations and rounding as they pertain to whole numbers and decimals

MOSA-Tlll MOSAmiddotT112 MOSA-T113 MOSA-T114 MOSAmiddotT115

middotcczis-B2middotmiddotmiddot---------shyExtend an understandiIg ofoperations with whole numbers to perform operations including decimals

MOSAmiddotTZ11 MOSA-TZlZ MOSA-TZ13

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JPageS

)anuary2013

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Pennsylvania Core Standards Mathematics

CCZ13C1 CCZ14C1 ccz1sc1 Explore and develop an Extend the Use the understanding of unde=ndingof unde=ndingof equivalency to add and fractions as numbers fractions to show snbtract fractions

equivalence and M03A-F1ll ordering MOSA-Flll M03AmiddotF1l2 M03A-Fll3 M04A-Fltl M03A-F1l4 M04A-Fll2

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middotcczi4c3middot-----middot--middot-shyConnect decimal notation to fractions and compare decimal fractions (base 10

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M04AmiddotF311 M04A-F3l2 M04AmiddotF313

21 Numbers and Operations

The Standards ofMathematical Practices Make sense ofproblems and persevere in solving them Reason abstractly and quantitatively Construct viable arguments and critique the reasoning ofothers Model with mathematics Use appropriate tools strategically Attend to precision Look for and make use ofstructure Look for and bull=ress reltgtuJaritv in ren eated reasonin

GradePreK GradeK Gradel GradeZ Grade3 Grade4 Z1PreK 21K 211 Z12 Z13 214

Grades Z15

Pennsylvanias public schools shall teach challenge and support every student to realize his orher maximum potentialand to acquire the knowledge and skills needed to

1Page6

January 2013

Pennsylvania Core Standards Mathematics

CCZ2lreKA1 CC22KA1 CC221A1 CCZ22A1 CC223A1 CC2Z4A1 CC22SA1 Understand addition as Extend the concepts of Representand solve Represent and solve Represent and solve Represent and solve Interpretand evaluate putting together and putting together and problems involviDg problems involving problems involving problems involving tbt numerical expressions adding to and taking apart to add and addition and subtraction addition and multiplication and four operations using order ofoperations understand subtraction subtract Within 10 Within20 subtraction Within 100 division astakingapartand M04ll-011l MOSJl011l taking from M03ll-Oll1 M04ll-0l12 MOSllmiddotOl12

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subtraction division

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22 Algebraic Concepts

The Standards ofMathematical Practices Make sense ofproblems and persevere in solVingthem Reason abstractly and quantitatively Construct viable arguments and critique the reasoning of others Model with mathematics Use appropriate tools strategically Attend to precision Look for and make use ofstructure Look for and Pvnress rerulari -v in reoeated reasonini

GradePreK GradeK Gradel Grade2 Grade3 Grade4 Grades 22PreK 22K 221 Z22 223 224 225

Pennsylvanias public schools shall teach challenge andsupport every student to realize his orher maximum potentialand to acquire the knowledge andskiIfs needed to

IPage7

January 2013

23 Geometry

Pennsylvania Core Standards Mathematics

The Standards of Mathematical Practices Make sense ofproblems and persevere in solving them Reason abstractly and quantitatively Construct viable arguments and critique the reasoning ofothers Model with mathematics Use appropriate tools strategically Attend to precision Look for and make use ofstructure Look for and exuress regularitv in reueated reasonin

GradePreK 23PreK

GradeK 23l(

Grade 1 Z31

GradeZ Z3Z

Grade3 233

Grade4 Z34

Grades 235

Pennsylvanias public schools shall teach challenge andsupport everystudent to realize his orhermaximum potential and to acquire the lmowledge andskills needed to

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CC23KA1 Identify and descnbe two- and three-dimensional shapes

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CCZ31A1 Compose and distinguish between ruro- and three-shydimensional shapes based on their attrihutes

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CC232A1 Analyze and draw two-and threeffimensional shapes having specified attnOutes

middotce2s2A2 middot----shy --shy -shyUse the understanding offractions to partition shapes into halves quarters and thirds

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CC233A1 Identifycolllpareand classifyshapes and their attributes

M03C-G111 M03C-G112

------------------------shyCC233AZ Use the understanding of fractionstopartition shapes into parts with equal areas and express the area ofeach microwt as a unit fraction ofthe whole

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CC234A1 Draw lines and angles and identify these in tvvo-dimensional figures

M04C-G111

-ci3-4Ai___ --shy --shy --shy-Classifytwo-dimensional figures by properties oftheir llnes and angles

M04C-G112

middotccii4-Ar----------shyRecognize symmetric shapes and draw lines of symmetry

CC235A1 Graph points in the first quadranton the coordinate plane and interpret these points when solving real world and mathematical problems

MOSC-G111 _1P_~f~1~--shy -------shy -shyCC23SAZ Glassey twoditnensional figures into categories based on an understanding oftheir properties

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M04C-G113

[Pages

January2013

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Pennsylvania Core Standards Mathematics

24 Measurement Data and Probability The Standards ofMathematical Practices

Make sense of problems and persevere in solving them Reason abstractly and quantitatively Construct Viable arguments and critique the reasoning of others Model with mathematics Use appropriate tools strategically Attend to precision Look for and make use of strUcture Look for and vnress reunl~ri in reoeated reasonine-

GradePreK GradeK Gradel Grade2 Grade3 Grade4 Grades 24PreK 24K 241 242 243 Z44 24S

CC24PreKA1 Describe and compare measurable attributes oflength and weight of evecyday objects

CC24KA1 Descnbe and compare attributes oflength area weight and capacity of everyday objects

CC241A1 Order Iengtbs and measure them both indirelttly and by repeating length units

CC242A1 Measure and estimate lengths in standard units using appropriate tools

CCZ43A1 Solve problems involving measurement and estimation of temperature liqUid volume mass and length

CCZ44A1 Solve problems involving measurement and conversioos from a larger unit to a smaller unit

CCZ4SA1 Solve problems using conversions within a given measurement system

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M03D-M121 M03D-M122 M03D-M123

middotccZyen3u-middot----------shyTell and write time to the

M04D-M11l M04D-M112 M04D-M113 M04D-M114middotccz4u-shy --shy --shy --shyTranslate information

middotcci4s-AZ______________

Represent and interpret

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nearest half hour using both analog and digital clocks

the nearest five minutes using both analog and digital clocks

nearest minute and solve problems by calculating time intervals

from one type of data display to another

data using appropriate scale

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Solve problems and

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make change using coins and paper currency with appropriate symbols

chaDge involving money using a combination of coins and bills

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P uJvanias public schools shaJJ teach chalenqe and surwort ev student to realize his or her maximum Dotential and to acauire the knowledae and skills needed to

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[Page9

January 2013

Pennsylvania Core Standards Mathematics

24 Measurement Data and Probabilitv The Standards ofMathematical Practices

Make sense ofproblems and persevere in solving them Reason abstractly and quantitatively Construct viable arguments and crltique the reasoning of others Model with mathematics Use appropriate tools strategically Attend to precision Look for and make use of structure Look for and exnress regularitv in repeated reasoning

GradePreK Z4K Grade K Gradel Z4Z Grade 2 243 Grade 3 244middot Grade 4 Z45 Grade 5 24PreK 241

PenTI vJvanias uublic schools shall teach challenae and sunnort evp~rstudent to realize his or her maximum Dotential and to acauire the knowledae andskills needed to CCZ4PreKA4 CCZ4KA4 CCZ41A4 CCZ4ZA4 CCZ43A4 CCZ44A4 CCZ4SA4 Classify objects and Classify objects and count Representand interpret Represent and interpret Representand interpret Representand interpret Solve problems involving count the number of objects iii each category

the number ofobjects in each category

data using tablescharts data using line plots pictUre graphs and bar

data using tally charts tables pictographs line

data irivolviog fractions using informationmiddot

computation offractions using information

graphs plots and bar graphs provided in a line plot provided in a line plot

M03DmiddotMZ11 MD4IJMZ11 MOSDmiddotMZ11 M03D-M212 M04IJM212 M03DmiddotM213

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Determine the area of a rectangle and apply the concept to multiplicati~n and to addition

M03D-M311

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Apply concepts ofvolume to solve problems and relate volume to multiplication and to addition

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laquociyeniA6-------bull -bull -- laquoci43A6middot--shy --shy --shy --shy -cc244A6____________ MOSDmiddotM31l

_Qsectl31~middot~___ -----middot-shy bull s Extend the concepts of Solve problems involTng Measure angles and use ~ addition and subtraction perimeters ofpolygons properties of adjacent ~ to problems involving

length-and distinguish between linear and area measures

angles to solve problems lntentionalb Blank

M03D-M411 M04DmiddotM311 M04DmiddotM312

IP age 10

Januazy2013

Pennsylvania Core Standards Mathematics

21 Numbers and Operations The Standards ofMathematical Practices

Make sense ofproblems and persevere in solving them Reason abstractly and quantitatively Construct viable arguments and critique the reasoning of others Model with mathematics Use appropriate tools strategically Attend to precision Look for and make use of structure Look for and eXPress regularitv in repeated reasoning

216Grade6 I 217Grade7 I 21SGradeS I I 21HSHighSchool

Pennsylvanias public schools shall teach challenge and support every student to realize his orher maximum potentialand to acquire the lmowledge andskills needed to

- CCZ16D1 CCZ17D1 I I I CCZ1lSF1 ~ Understand ratio Analyze proportional Apply and extend the properties ofexponents to solve problems with rational exponents sect concepts and use ratio relationships and use Al1111 Al1112 A1l131 A21211 A21212 A21213 A2lZ14 t vi reasoning to solve them to modcl and solve8 sect problems real-world and CCZ1HSFZ E lt mathematicalproblems Apply properties of rational and irrational numberS to solve real world or mathematical problems0 Intentionally Blartk Al1111 Al1112 All131 Al112l o1l il M06AmiddotR1l1 M07AmiddotR1l1 ~~ M06AmiddotR112 M07AmiddotR1l2 CCZllSF3= isect M06A-Rl13 M07A-R1l3 Apply quantitative reasoning to choose and interpret units and scales in formulas graphs and data ~ M06AmiddotR114 M07AmiddotR114 displayse M06A-Rl15 M07A-R11S Al1211 Al1212 Al1Z13 A12121 A12122 A2ZZ11 A22Z12 A223l1

M07A-R116 A2Z312 CC216E1 CCZ17E1 CC21SE1 Apply and extend Apply and extend 0 CCZlHSF4Distioguisb between

Use units as avray to understand problems and to guide the solution -0fmulti-step problemsprevious understandings previous understandings rational and irrational g Al1211 Al1212 Al1Z13 Al2121 A12122 A22211 A22212 of multiplication and of-Operations with numbers usiDg their sectdivision to diVide fractions to operations properties fractions by fractions with rational nUIIlbers CCZlHSFS] Choose a level of accuracy appropriate to limitations on measurement when reporting quantitiesMOSA-Nl1l a Al1211 A11Z12 Al1Z13 Al1221 Al12Z2 Al13l1 Al1312 Al1313 M06A-N111 M07A-N111 lMOSA-Nl12

Al13 21 All3 22 A2Z311 A22312 = Ei -~~~~~t~~~----------- -~t~t~t____________ _poundg ------------------------shy CCZ1HSF6 CC216E2 sect Extend the lmowiedge of arithmetic operations and apply to complex numbers sect appropriate processes to ~ Identify and choose

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M06A-N22l M06A-N222

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IP age 11

January 2013

Pennsylvania Core Standards Mathematics

21 Numbers and Operations The Standards ofMathematical Practices

Make sense ofproblems and persevere in solving them Reason abstractly and quantitatively Construct viable arguments and critique the reasoning of others Model with mathematics Use appropriate tools strategically Attend to precision Look for and make use ofstructure Look for and bullvnress reltnlaritv in reoeated reasoning

216 Grade 6 217 Grade 7 21HS High School 218 Grade 8

Pennsylvanias public schools shall teach challenge and support every studentw realize his orher maximum potential and to acquire the knowledge andskills needed W CC216E4 Apply and extend previous understandings ofnumbers to the system ofrational numbers

M06A-N311 M06A-N312 M06AmiddotN313 M06AmiddotN321 M06A-ll322 M06A-N323

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CC218E4 Estimate irrational numbers by compaing them to rational numbers

MOSAmiddotN113 MOSAmiddotN114 MOSA-N11S Al1111

[Page12

January 2013

Pennsylvania Core Standards Mathematics

22 Algebraic Concepts

The Standards ofMathematical Practices Make sense ofproblems and persevere in solvilg them Reason abstractly and quantitatively Construct viable arguments and critique the reasoning of others Model with mathematics Use appropriate tools strategically Attend to precision Look for and make use ofstructure Look for and exnress regularitvin repeated reasoning

226 Grade 6 22 7 Grade 7 228 Grade 8 22HS High School

Penn rvlvartias uublic schools shall teach challem1e and sunnort everv student to realize his orher maximum uotential and to acmrire the mowledae and skills needed to CC2Z681 CC22781 CC2ZHSD1 Apply and extend

CC2Z8B1 Apply properties of Apply concepts of radicals Interpret the structure of expressions to represent a quantity in terms of its context

Al1151 Al1152Al11S3 AZ1221 AZ1222previous understandings operations to generate and integer exponents to of arithmetic to algebraic equivalent expressions generate equivalent CC22HSD2 expressions expressions Write expressions in equivalent forms to solve problems

M07B-E111 Al11S1 Al1152 Al1153 AZ1211 AZ1Z12AZ1213 AZ1214 AZ1221 M06B-E111 MOSBmiddotE111 AZ1ZZ2 M06B-E112 MOSB-E112

CC22HSD3M06B-E113 MOSB-E113 Extend the knowledge of arithmetic operations and apply to polynomialsM06B-E114 MOSB-E114

_]1Qsect~~l ___________ Al11S1 Al1152 Al1153 AZl221 AZ1222 -~~J~_1__ ___ ---- --- --- -shy--~---------------------- CC22HSD4CCZ2682 CCZ28BZ

Understand the relationship between zeros and fac-ors of polynomials to make generalizations about Understand the process Understand the functions and their graphs of solving a one-variable connections between

AZ1ZZ1 AZ1222equation or inequality proportional relationshlps and apply it to real-worldg

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CC22HSOSlines1 and linear equations Use polynomial identities to solve problemsand mathematical~ Intentionally Blank Al1151 Al1152 Al1153 AZ1221 AZ1ZZ2AZl311 AZl312 AZl313 problems MOSB-E211 AZ1314MOSBmiddotE212

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MOSB-E213M06E-E211 CC22HSD6 ~

_~ M06B-EZ12 Al2122 Extend the knowledge ofrational functions to remite in equivaleztformsltg M06B-E213

B ~ Al11S1 Al1152 Al1153 AZ1311 AZ1312AZ1313 AZ1314

e ~ M06B-EZ14 CC22HSD7middotcciz6iir------------ middotec2z7ii3------ -----shy middotcc-2z~S1ii middot----- ---middot---shy Create and graph equations or inequalitiesto describe numbers or relationships Represent and analyze Model and solve real- Analyze and solve linear Al1211 Al1212 Al1213 Al1Z21 Al1222 All311 Al1312 Al1313 s x

quantitative world and mathematical equations and pairs of Al1321 All322 AZl311 A21312 AZ1313 AZ13M AZ1321 AZ132Z~ problems by using andrelationships between Simultaneous linear A22211 AZ2212 AZZ213 AZ2214

dependent and connecting numerical equations CC22HS08independent variables algebraic andor Apply inverse operations to solve equations or formulas for a given variableMOSB-E311graphical Al1211 Al1Z12 Al1213 AZ1311 AZ1312 AZ1313 AZ1314M06B-E311 representations MOSB-E31Z AZl321 AZ1322M06B-E312 MOSB-E313

M07B-E211 CC22HS09MOSB-E314 Use reasooing to solve equations and justify the solution method M07B-EZZ1 MOBB-E31S

All141 Al1211 Al121Z Al1213 Al1221 Al1222 Al1311 Al13l2 M07B-EZ22 Al1211 M07B-EZ31 Al1313 AZ1311 AZ1312 AZ1313 AZ1314 AZ1321 AZ132ZAll221 A11141 CCZ2lSD10Al1222

Represent solve and interpret equationsinequalities and systems of equationsinequalities algebraically and graphically

AllZ11 Al1212 Al1213 Al1221 Al1222 Al1311 Al1312 All313 Al1321 Al1322 A21311 AZl312 A2l313 AZ13U

JPage13

January 2013

Pennsylvania Core Standards Mathematics

ZZ Algebraic Concepts

The Standards ofMathematical Practices Make sense ofproblems and persevere in solving them Reason abstractly and quantitatively Construct viable arguments and critique the reasoning of others Model with mathematics Use appropriate tools strategically Attend to precision Look for and make use ofstructure Look for and Pxnress repoundUlaritv in repeated reasoning

Z26 Grade 6 zz 7 Grade 7 Z2S Grade 8 ZZHS High School

Penm 1lvanias public schools shall teach challenae andsunnort ev~rv student to realize his orhermaximum Potential and to acm1ire the knowledae and skills needed to cc22sc1 CCZ2HSC1 Define evaluate and Use the conceptand notation offunttionsto interpretand appiythemin terrns oftheir context compare functions Al2111 Al2112 Al2113 Al2211 Al2212 AlZ213 Al2214 AZ21ll

AZ2112 AZ2113 A22114 G2221 G2222 G2223 G2224 GZ225 MOSBmiddotF111 MOSJH112 CC22HSC2 MOSBmiddotF113 Graph and analyze functions and use their properties to make connections between the different

representationsAl1211 Al2111 Al2112 Al2113 Al2121 Al2122 Al22l1 AZ1314 AZ1321

Al2121 Al2112

AZ1322 AZ2111 AZ2112 AZ2113 AZ2114 Al2122

CCZ2lSC3middotz2samiddotmiddotmiddotmiddotmiddotmiddotmiddotmiddotmiddotmiddotmiddotmiddotmiddotmiddot Write functions or sequences that model relationships between two quantitiesUse concepts offunctions

Al1Z11 AllZ12 Al1213 Al2111 Al2112 Al2113 Al2121 Al2l22 to model relationships Al2Z13 Al2214 A21311A21312 AZ1313 AZ1314 AZ1321AZ1322betvveen quantities AZ211l AZ2112 AZ2l13 AZZ114 A22211A22212A22Z13 AZ2214

MOSBmiddotF211 cc22HSC4MOSBmiddotF212 Interpret the effects transformations have on functions and find the inverses of functionsAl1213 =0 Al2121 Al2122 AZ1313 AZ1314 AZ1321 AZ2211 AZ2212 AZ2213g =

A12111 u AZ2Z14 AZ2221uAl2122Intentionally Blank Intentionally Blank= = Al2213 CC22HSC5Al2214 G G Construct and compare linear quadratic and exponential models to solve problems

~ ~

Al2211 Al2Z12 Al2213 Al2214 A213ll A2l312 AZ1313 AZ1314 AZ2111 AZ2112 AZ2113 AZ2114 AZ22ll AZZ21Z AZ2213 AZ2214 A2222l

CC22HSC6 Interpret functions in terms of the situations they modeL

Al2121 Al2212 Al2213 Al2221 AZ1313AZZ1l1 AZZ112 AZ2113 AZ2114 AZ2213 AZ2214 AZ2221

CC22HSC7 Apply radian measure ofan angle and the unit circle to analyze the trigonometric functions

CC22HSC8 Choose trigonometric functions to model periodic phenomena and describe the properties of the graphs

CC22HSC9 Prove the Pythagorean identity and 11Se it to calculate trigonometric ratios

G1321 G211l G2112

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January 2013

Pennsylvania Core Standards Mathematics

CC236A1 CC237A1 CC238A1 CC23lSA1 Apply appropriate tools Solve real-world and Apply the concepts of Use geometric figures and their properties to represent transformations in the plane to solve real~world and mathematical problems volume ofcylinders cones G1311 G131Z mathematical problems involving angle and spheres to solve realshy CC23HSA2 involving area surface measure area swface world and mathematical Apply rigid transformations to determine and explain congruence area and volume area circumference problems GU11 G1312

and volume CC23HSA3 M06C-Gll1 M08C-C3ll Verify and apply geometric theorems as they relate to geometric figures M06C-GllZ M07C-G2l1 G2312 G1211 G1212 G1213 G1214 G1215 G1321 G2211 G2212 G2221 G2222 M06C-Gll3 M07C-G212 G2223 G2224 G222S M06C-G1L4 M07C-G22l CC23HS-A4 M06C-Gli5 M07C-G222 Apply the concept ofcongruence to create geometric constructions

MQsectt_-_G~Jsect_ --- shy -- shy -- shy ---------------------middot-middot CC23HSA5

--------------------------middotCC237A2 CC238A2 Create justifications based on transformations to establish similarity ofplane figures VlSUalize and represent Understand and apply G1311 G1312 geometric figures and congruence similarity and CC23HSA6 descnbethe geometric transformations Verify and apply theorems involving similarity as they relate to plane figures relatiooships betWeen using various tools G1311 G1312 G1321 them

CC23HSA7_ _- Intentionally Blank MOSC-C111 - Apply trigonometric ratios to solve problems involving right triangles~ sect M07C-Glll M08C-Gll2 = G21ll G21120

M07C-Gll2 MOSC-G113 CC23HSA8 M07C-Gll3 M08C-Gll4 Apply geometric theorems to veruy properties ofcircless ~M07C-Gll4 GJ211 ~ G1111 G1112 G1113 G1114 G1321 G223l

G1214 CC23HS-A9

-----------------------shy ----------------------shyG2211 Extend the concept ofsimilarity to determine arc lengths and areas ofsectors ofcircles

CCi32A3--shy -shy G1111 G1112 G1l13 G1114 G2221 G2222 G2223 G2224 G2225 G2231 Understand and apply the CC23HSA10 Pythagorean Theoremto Translate beti-veen the geometric description and the equation for a conic section solve problems A221l4 AZ221l

CC23HSA11 MOSC-G211 Apply coordinate geometry to prove simple geometric theorems algebraically MOSC-G212 G2121 GZ122 G2123

Intentionally Blank Intentionally Blank MOSC-G213 CC23HSA12 G2111 Explain volume formulas and use them to solve problems G21Zl G2311 G231Z G2313

CC23llSA13 Analyze relationships between two-dimensional and three-dimensional objects

G1111 G111Z G1113 Gl114 G1211 G1212 G1213 G1214 G1215 G2321 CC23HSA14 Apply geometric concepts to model and solve real world problems

G2241 G231l G2312 GZ313

23 Geometrv The Standards ofMathematical Practices

Make sense of problems and persevere in solving them Reason abstractly and quantitatively ConstructViable arguments and critique the reasoning ofothers Model with mathematics Use appropriate tools strategically Attend to precision Look for and make use of structure Look for and evnress reUlaritv in reneated reasoniniz

Grade 6 Grade7 Grades High School Z36 237 23S Z3HS

Pennltvfvanias vublic schools shall teach challen e and sunnort evPrv student to realize his or her maximum votential and to acauire the knowledae and skills needed to

jPage15

)anuazy 2013

Pennsylvania Core Standards Mathematics

24 Measurement Data and Probabilitv The Standards ofMathematical Practices

Make sense ofproblems and persevere in solving them Reason abstractly and quantitatively Construct viable ar~ments and critique the reasoning ofothers Model with mathematics Use appropriate tools strategically Attend to precision Look for and make use ofstructure Look for and express regularity in repeated reasoning

Grade 6 246

Grade7 247

Grade3 243

High School 24HS

Pennsylvanias public schools shall teach challenge and support every student to realize his or her mt1Ximum potential and to acquire the mowedge andskills needed to

~ E 0 0

d ilc c g ~ e

CCZ46B1 Demonstrate an understanding of statistical vaiability by displaying analyzing and summarizing distributions

M06DmiddotSlll M06DmiddotSll2 M06D-Sll3 M06D-Sll4

------------------------shy

Intentionally Blank

------------------------shy

CCZ47B1 Draw inferences about populatioos based on rardom sampling concepts

M07D-S1l1 M07D-S1l2

middotcczyen7-szmiddot----middot----- shy -Draw informal comparative inferences about two populations

M07D-S211

middotcci47S3----- --- --- -shy[mrestigate cbaoce processes and develop use and evaluate probability models

CCZ48B1 Analyze andor interpret bivariate data displayed in multiple representations

MOSD-S11l MOSDmiddotS112 MOSDmiddotS113 AlZ22l

iCi4862 ----------shyUnderstand thatpatterns ofassociation can be seen in bivariate data utilizing frequencies

MOSDmiddotS121

-------------------------shy

c a 0 0

d ltgt middotc ~ middotc g

sect

CCZ4HSB1 Summarize represent and interpret data on a single count or measurement variable

A12212 Al2311 A12321 Al2322 Al2323

CCZ4HSB2 Summarize represent and interpret data on two categorical and quantitative variables

Al21ll Al2112 A12113 Al2121 Al2122 Al2221 A2211l AZ2311 AZ2312

CCZ4HSB3 Analyze linear models to make interpretations based on the data

Al222l A1231l Al2321 Al2322 Al2323 A22311 AZ2312

CCZ4HSB4 Recognize and evaluate random processes underlying statistical experiments

Al2331 A223Z1 A2232Z A22323

CC24HSBS Make inferences and justify conclusions based on sample surveys experiments and observational studies

Al2321 Al2322 Al2323 A22321 A22322 A22323

CCZ4J5B6 Use the concepts ofindependence and conditional probability to interpret data

AZ2321 A22322 A22323

Intentionally Blunk M07D-S31l M07D-S32l M07D-S322 M07D-S323 Al2331

lntentionany Blank CCZ4HSB7 Apply the rules of probability to compute probabilities ofcompound events in a uniform probability model

Al2331 A223Z1 A223ZZ A22323

[Page16

January 2013

Pennsylvania Core Standards Mathematics

Key Terms for this Document

Standards for Mathematical Content-These standards define what students should know and be able to do in their study of mathematics

Standards for Mathematical Practice-These standards describe the processes and proficiencies in which all students grades K-12 should engage Educators

must instill these standards of practice in their students so that they become habitual The standards for mathematical practice should be used as the vehicle to

deliver the standards of mathematical content

Standard Algorithm-A locally agreed upon method of computation which is conventionally taught for solving mathematical problems

Decimal Fraction-A fraction whose denominator is a power of ten (examples 2100 810) These fractions are commonly expressed as decimals

Unit Fraction-A rational number written as a fraction where the numerator is one and the denominator is a positive integer (example 120)

Bivariate Data-The data involves two variables and is usually represented as a scatter plot

Rule-A single operation (examples add 5 multiply by 2)

IP age 17

January 2013

Page 3: Academic Standards for Mathematics...The Co=on Core Standards in Mathematics in grades PreK-5 lay a solid foundation in whole numbers, addition, subtraction, multiplication, division,

Pennsylvania Core Standards Mathematics

Standards cannot be viewed or addressed in isolation as each standard depends upon or may lead into multiple standards across grades thus it is imperative that educators are familiar with both the standards that come before and those that follow a particular grade level These revised standards reflect instructional shifts that cannot occur without the integrated emphasis on content and practice

Standards are overarching statements ofwhat a proficient math student should know and be able to do The Pennsylvania Assessment Anchors and Eligible Content closely align with the revised standards and are an invaluable source for greater detail

Key Points in Mathematics

bull The standards stress both procedural skills and conceptual understanding to ensure students are learning and applying the critical information they need to succeed at higher levels

bull K-5 standards which provide students with a solidfoundation in whole numbers addition subtraction multiplication division fractions and decimals help young students build the foundation to successfully apply more demanding math concepts and procedures and move into application They also provide detailed guidance to teachers on how to navigate their way through topics such as fractions negative numbers and geometry and do so by maintaining a continuous progression from grade to grade

bull Having built a strong foundation at K-5 students can do hands-on learning in geometry algebra and probability and statistics Students who have mastered the content and skills through the seventh grade will be well-preparedfor algebra in grade 8

bull High school standards emphasize practicing applying mathematical ways ofthinking to real world issues and challenges

Page3

january2013

Pennsylvania Core Standards Mathematics

The PA Core Standards for Mathematics detail four standard areas Numbers and Operations Algebraic Concepts Geometry and Measurement Data and Probability These standard areas are reflective ofthe reporting categories in the PA Core Assessment Anchors and Eligible Content The middot intent of this document is to provide a useful tool for designing curriculum instruction and assessment The grade level curriculum and instructional shifts in mathematics cannot occur without the integrated emphasis on content and practice The chart below illustrates the four standard areas and the development and progression of the strands with an understanding that all is framed around the Standards for Mathematical Practice

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1middotmiddotr~bull1bullmiddotli1ibullo ctmavJe~a enlOgtbullan ct1tl ue1a~emiddot -eason1n middot) middottlue ~middot~1middot~gtbull1~1middot~ 1=bullmiddot~=middot1~11middot=middot1i=---1middot~middot- r eLlvi middot bullmauie atics~-1 1~ 1middot11Jibullli1I1

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1lj[middot 1 middot ljI $eRi911na ~ oo I I 1111 I II11 flmiddot]f lt1bull 1middot llmiddoti I 1middot 1 1middot 1 middotmiddot bulliJi1 middot]llttenJ tomiddotprews1on I 1 11middot11 r-1iililiiir1i[iitiii[1middot1fii 1middot 11middot 1middot1middot ll middot ~1 bulll11~k1i-bull1_af~1f-rJiiLli=lh1Jl1b~~Jl1(l~ll1 11middot1I1J 111 11 111111 Ii 1bull1il~11 111 I 1lt11 middot middot ~ I imiddot1bullli middot lI 1+1 rl~ ~ l11 1~r1~1 1~r 1j1~111i11 j1fi-jl1 1bull1bull1 1middot1fi iJ11r1i1~~1t 11111i11 ~]11J111U ] piril 11[[ lj111111 r bullIbull-Diill L_ i ~I ii lli 111 middot_middot middot1 1 middot==1-1 1~1 =1 bull o oran -m~~iusev111 4iw1e1111bulll111-11i11 1 middot11middot 111111 middot i Imiddot I=~ - 1-middot11 middot1 middot_ 111 r1bullh _ middotl11-1middot middot11 1middotL1middot -1iJOOlmiddotitOr1~Ui-$Pressrezwan SO_middot gc11- ~~r

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1Page4

January 2013

--- ------ ---

------------------------ ------------------------ -------------------------

__________ -------------------------

Pennsylvania Core Standards Mathematics

21 Numbers and Operations The Standards ofMathematical Practices

Make sense ofproblems and persevere in solving them Reason abstractly and quantitatively Construct viable arguments and critique the reasoning ofothers Model with mathematics Use appropriate tools strategically Attend to precision Look for and make use ofstructure

GradePreK GradeK Z1PreK Z1K

Gradel Z11

GradeZ Z1Z

Look for and exnress re~laritv in repeated reasonin1

Grade3 Grade4 Z13 Z14

Grades Z15

Pennsylvanias public schools shall teach challenge andsupporteverystudent to realize his orhermaximum potential and to acquire the Jmowledge andskills needed to CCZ1PreKA1 ccz1KA1 Know number names Know number names and and the =Cunt sequence write and recite the count olt eshy

ao= middotccZipKAtbull --------~t~i=~middot--- s ccz1KAZ Count to tell the number=sect ofobjects 83

~ -----------------------middot CCZ1PreKA3 ~ Compare numbers

Apply one-to-one correspondence to count

_JflJtXlll2~t95~bj~middot- --shyccz1KA3 Apply the concept of magnitude to compare numbers and ouantities CCZ1KB1 Use place value to compose and decompose numbers within 19

= ~ s ~ = 0c Intentionally Blank 0 oil il = Intentionally Blanki s ~

Intentional(y Blank lntentional(y Blank lntentional(y Blank lntentional(y Blank lntentional(y Blank

CC211B1 Extend the counting sequence to read and write numerals to represent objects

middotcc zi~isimiddot-- ----middotmiddot --- shyUse place-V3lue concepts to represent amounts of tens and ones and to compare two digit numbers

cC2Tia3middot----------middot Use place-value concepts and properties of operations to add and subtrattwithin 100

ccz1zs1 Use place-value concepts to represent amoWltS of tens and ones and to compare three digit numbers

CC21ZBZ Use place-value concepts to read write and skip count to 1000

CCZ13B1 Apply place-value understanding and properties ofoperations to perform multi-digit arithmetic

M03A-Tl1l M03A-T1lZ M03AmiddotTll3 M03A-Tll4

Intentionally Blank

middotccziiJij ---- --- ---- ------------------------shyUse place-value understanding and Intentionally Blankproperties ofoperations to add and subtract within 1000

CC214B1 Apply place-value concepts to show an understanding ofmulti-digit whole numbers

M04A-T1l1 M04A-Tl12 M04A-TLl3 M04A-Tll4

middotc-cziiiii---- --- --- shyUse place-value understanding and properties ofoperations to perform multi-digit arithmetic

M04A-T2ll M04A-T212 M04A-T213 191~r1

Intentionally Blank

CCZ15B1 Apply placemiddotvalue concepts to show an understanding of operations and rounding as they pertain to whole numbers and decimals

MOSA-Tlll MOSAmiddotT112 MOSA-T113 MOSA-T114 MOSAmiddotT115

middotcczis-B2middotmiddotmiddot---------shyExtend an understandiIg ofoperations with whole numbers to perform operations including decimals

MOSAmiddotTZ11 MOSA-TZlZ MOSA-TZ13

ntentional(y Blank

JPageS

)anuary2013

-------------------------------------------------------------------

Pennsylvania Core Standards Mathematics

CCZ13C1 CCZ14C1 ccz1sc1 Explore and develop an Extend the Use the understanding of unde=ndingof unde=ndingof equivalency to add and fractions as numbers fractions to show snbtract fractions

equivalence and M03A-F1ll ordering MOSA-Flll M03AmiddotF1l2 M03A-Fll3 M04A-Fltl M03A-F1l4 M04A-Fll2

~ M9amp~~1~b2 bullbullbull -- shy -- shy __ middotecii4cimiddot------middotmiddotmiddotmiddotshy middoteoisomiddot-----------shy= 0 Build fractions from Apply and extend ~ unit fractions by previomicros understandings applying and extending ofmultiplication and I previous division to multiply and ~ understandings of divide fractions = 0 operations on whole

- numbers MOSA-F211f lntentionany Blank Intentionally Blank Intentionally Blank Intentionally Blank Intentionally Blank MOSA-F2lZ

M04A-FZ11 MOSA-F2130 ~ M04AmiddotFZl2 MOSA-F214

~ M04A-FZ13

M04A-F214 M04A-FZ15 z M04AmiddotF216

G -----------------------shyM04AmiddotFZ17

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middotcczi4c3middot-----middot--middot-shyConnect decimal notation to fractions and compare decimal fractions (base 10

Intentionally Blank denominator eg bttentionally Blank 19100)

M04AmiddotF311 M04A-F3l2 M04AmiddotF313

21 Numbers and Operations

The Standards ofMathematical Practices Make sense ofproblems and persevere in solving them Reason abstractly and quantitatively Construct viable arguments and critique the reasoning ofothers Model with mathematics Use appropriate tools strategically Attend to precision Look for and make use ofstructure Look for and bull=ress reltgtuJaritv in ren eated reasonin

GradePreK GradeK Gradel GradeZ Grade3 Grade4 Z1PreK 21K 211 Z12 Z13 214

Grades Z15

Pennsylvanias public schools shall teach challenge and support every student to realize his orher maximum potentialand to acquire the knowledge and skills needed to

1Page6

January 2013

Pennsylvania Core Standards Mathematics

CCZ2lreKA1 CC22KA1 CC221A1 CCZ22A1 CC223A1 CC2Z4A1 CC22SA1 Understand addition as Extend the concepts of Representand solve Represent and solve Represent and solve Represent and solve Interpretand evaluate putting together and putting together and problems involviDg problems involving problems involving problems involving tbt numerical expressions adding to and taking apart to add and addition and subtraction addition and multiplication and four operations using order ofoperations understand subtraction subtract Within 10 Within20 subtraction Within 100 division astakingapartand M04ll-011l MOSJl011l taking from M03ll-Oll1 M04ll-0l12 MOSllmiddotOl12

M03B-OllZ M04B-Oll3 M03B-Ol2l M04B-Ol14

bO -----------------------shy ------------------------shyM03Bmiddot0122

-----------------------shy -------------------------shy= middotccz~z1umiddot-middotmiddot----shy middotcci-ZzA2middotmiddotmiddotmiddotmiddotmiddotmiddotmiddot middot middotshy middotcc2z1iA2middotmiddotmiddotmiddotmiddotmiddotmiddot--middotmiddot-middot CCZ24A2ii Understand and apply Use mental strategies to Understand properties of Develop andor apply 5 properties of operations add and subtract Within multiplication and the number tbeozy concepts= E-lt and the relationship 20 relationship between to find factors and

betvveen addition and multiplication and multiplesmiddot Intentionally Blank Intentionally Blank Intentionally Blank

subtraction division

M04Bmiddot0211 ~ M03B-OZ11 M03B-0212

MQ~JQ~J middot-middot--middotmiddot bullbullbullbull= -----------------------shy ------------------------shy -----------------------shy ~----------------------- ----------------------shy ------------------------shy CCZ22A3 CCZ23A3

WorkWitb equal groups Demonstrate= s Intentionally Blank Intentionally Blank Intentionally Blank ofobjects to gain multiplication and Intentionally Blank Intentionally Blank ~ foundations for division fluency a

-----------------------shy ------------------------shy ------------------------shy PP112iPltCl~~l__ ___ ----shy ------------------------shy -----------------------shy ------------------------shy CCZ23A4 CC224A4 CC225A4 0 Solve problems involving Generate and analyze Analyze patterns and ~ s the four operations and patterns using one rule relationships using tlNo

identify and explain rules patterns in arithmetic M04B-0311

M04B-0312 MOSB-0211 Intentionally Blank Intentionally Blank Intentionally Blank Intentionally Blank M03Bmiddot0311 M04llmiddot0313 MOSB-0212

M03Bmiddot0312 M03B-03l3 M03B-0314 M03B-031S M03B-0316 M03B-0317

22 Algebraic Concepts

The Standards ofMathematical Practices Make sense ofproblems and persevere in solVingthem Reason abstractly and quantitatively Construct viable arguments and critique the reasoning of others Model with mathematics Use appropriate tools strategically Attend to precision Look for and make use ofstructure Look for and Pvnress rerulari -v in reoeated reasonini

GradePreK GradeK Gradel Grade2 Grade3 Grade4 Grades 22PreK 22K 221 Z22 223 224 225

Pennsylvanias public schools shall teach challenge andsupport every student to realize his orher maximum potentialand to acquire the knowledge andskiIfs needed to

IPage7

January 2013

23 Geometry

Pennsylvania Core Standards Mathematics

The Standards of Mathematical Practices Make sense ofproblems and persevere in solving them Reason abstractly and quantitatively Construct viable arguments and critique the reasoning ofothers Model with mathematics Use appropriate tools strategically Attend to precision Look for and make use ofstructure Look for and exuress regularitv in reueated reasonin

GradePreK 23PreK

GradeK 23l(

Grade 1 Z31

GradeZ Z3Z

Grade3 233

Grade4 Z34

Grades 235

Pennsylvanias public schools shall teach challenge andsupport everystudent to realize his orhermaximum potential and to acquire the lmowledge andskills needed to

f s 0

~ sect

CCZ3PreKA1 Identify and describe shapes

middotcczerKAz-shy------Attalyze compare create and compose shapes

----------------------shy

Intentionally Blank

CC23KA1 Identify and descnbe two- and three-dimensional shapes

-CciTKApound-----------shyAnalyze compare create and compose twomiddot and three-dimensional shapes

------------------------shy

lntentionally Blank

CCZ31A1 Compose and distinguish between ruro- and three-shydimensional shapes based on their attrihutes

(C23ii2shy--shy------shy -shyUse the understanding of fractions to partition shapes into halves and quarters

------------------------shy

Intentionally Blank

CC232A1 Analyze and draw two-and threeffimensional shapes having specified attnOutes

middotce2s2A2 middot----shy --shy -shyUse the understanding offractions to partition shapes into halves quarters and thirds

-----------------------shy

Intentionally Blank

CC233A1 Identifycolllpareand classifyshapes and their attributes

M03C-G111 M03C-G112

------------------------shyCC233AZ Use the understanding of fractionstopartition shapes into parts with equal areas and express the area ofeach microwt as a unit fraction ofthe whole

_J1Qg~j1~ailc___________

Intentionally Blank

CC234A1 Draw lines and angles and identify these in tvvo-dimensional figures

M04C-G111

-ci3-4Ai___ --shy --shy --shy-Classifytwo-dimensional figures by properties oftheir llnes and angles

M04C-G112

middotccii4-Ar----------shyRecognize symmetric shapes and draw lines of symmetry

CC235A1 Graph points in the first quadranton the coordinate plane and interpret these points when solving real world and mathematical problems

MOSC-G111 _1P_~f~1~--shy -------shy -shyCC23SAZ Glassey twoditnensional figures into categories based on an understanding oftheir properties

MOSC-G211

-------------------------middot

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M04C-G113

[Pages

January2013

------------------------- ------------------------ --------------------------

Pennsylvania Core Standards Mathematics

24 Measurement Data and Probability The Standards ofMathematical Practices

Make sense of problems and persevere in solving them Reason abstractly and quantitatively Construct Viable arguments and critique the reasoning of others Model with mathematics Use appropriate tools strategically Attend to precision Look for and make use of strUcture Look for and vnress reunl~ri in reoeated reasonine-

GradePreK GradeK Gradel Grade2 Grade3 Grade4 Grades 24PreK 24K 241 242 243 Z44 24S

CC24PreKA1 Describe and compare measurable attributes oflength and weight of evecyday objects

CC24KA1 Descnbe and compare attributes oflength area weight and capacity of everyday objects

CC241A1 Order Iengtbs and measure them both indirelttly and by repeating length units

CC242A1 Measure and estimate lengths in standard units using appropriate tools

CCZ43A1 Solve problems involving measurement and estimation of temperature liqUid volume mass and length

CCZ44A1 Solve problems involving measurement and conversioos from a larger unit to a smaller unit

CCZ4SA1 Solve problems using conversions within a given measurement system

MOSD-M111

-A O = =

----------------------shy ------------------------shy -ec21A2_______ --shy --shyTell and write time to the

-----------------------shyCC24ZAZ Tell and write time to

M03D-M121 M03D-M122 M03D-M123

middotccZyen3u-middot----------shyTell and write time to the

M04D-M11l M04D-M112 M04D-M113 M04D-M114middotccz4u-shy --shy --shy --shyTranslate information

middotcci4s-AZ______________

Represent and interpret

s Intentionally Blank Intentionally Blank

nearest half hour using both analog and digital clocks

the nearest five minutes using both analog and digital clocks

nearest minute and solve problems by calculating time intervals

from one type of data display to another

data using appropriate scale

~ s -----------------------middot ------------------------shy ------------------------shy

-cci42A3____________

Solve problems and

M03DmiddotMll1 M9-3olMmiddotJJ _____ ----__ CCZ43A3 Solve problems and make

M04D-MZ13

-----------------------shy

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-------------------------shy

IntentJdegonally Blank Intentionally Blank Intentionally Blank

make change using coins and paper currency with appropriate symbols

chaDge involving money using a combination of coins and bills

MD3D-M13l M03D-Ml3Z

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P uJvanias public schools shaJJ teach chalenqe and surwort ev student to realize his or her maximum Dotential and to acauire the knowledae and skills needed to

-------------------------------------------------middot _119301-L~bullbullbullbullbullbullbullbullbullbullbullbullbullbullbullbullbullbullbullbullbullbullbullbullbullbullbullbull bullbullbullbullbullbullbull_

[Page9

January 2013

Pennsylvania Core Standards Mathematics

24 Measurement Data and Probabilitv The Standards ofMathematical Practices

Make sense ofproblems and persevere in solving them Reason abstractly and quantitatively Construct viable arguments and crltique the reasoning of others Model with mathematics Use appropriate tools strategically Attend to precision Look for and make use of structure Look for and exnress regularitv in repeated reasoning

GradePreK Z4K Grade K Gradel Z4Z Grade 2 243 Grade 3 244middot Grade 4 Z45 Grade 5 24PreK 241

PenTI vJvanias uublic schools shall teach challenae and sunnort evp~rstudent to realize his or her maximum Dotential and to acauire the knowledae andskills needed to CCZ4PreKA4 CCZ4KA4 CCZ41A4 CCZ4ZA4 CCZ43A4 CCZ44A4 CCZ4SA4 Classify objects and Classify objects and count Representand interpret Represent and interpret Representand interpret Representand interpret Solve problems involving count the number of objects iii each category

the number ofobjects in each category

data using tablescharts data using line plots pictUre graphs and bar

data using tally charts tables pictographs line

data irivolviog fractions using informationmiddot

computation offractions using information

graphs plots and bar graphs provided in a line plot provided in a line plot

M03DmiddotMZ11 MD4IJMZ11 MOSDmiddotMZ11 M03D-M212 M04IJM212 M03DmiddotM213

S ----------------------shy ------------------------shy ------------------------shy -----------------------shy

1D_3JlMJ~4t-bullbull_ __ bull__ CCZ43A5 -----------------------shy middotca4sAs----- --middot--middot -- shy

ilt

s

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Determine the area of a rectangle and apply the concept to multiplicati~n and to addition

M03D-M311

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Apply concepts ofvolume to solve problems and relate volume to multiplication and to addition

s

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laquociyeniA6-------bull -bull -- laquoci43A6middot--shy --shy --shy --shy -cc244A6____________ MOSDmiddotM31l

_Qsectl31~middot~___ -----middot-shy bull s Extend the concepts of Solve problems involTng Measure angles and use ~ addition and subtraction perimeters ofpolygons properties of adjacent ~ to problems involving

length-and distinguish between linear and area measures

angles to solve problems lntentionalb Blank

M03D-M411 M04DmiddotM311 M04DmiddotM312

IP age 10

Januazy2013

Pennsylvania Core Standards Mathematics

21 Numbers and Operations The Standards ofMathematical Practices

Make sense ofproblems and persevere in solving them Reason abstractly and quantitatively Construct viable arguments and critique the reasoning of others Model with mathematics Use appropriate tools strategically Attend to precision Look for and make use of structure Look for and eXPress regularitv in repeated reasoning

216Grade6 I 217Grade7 I 21SGradeS I I 21HSHighSchool

Pennsylvanias public schools shall teach challenge and support every student to realize his orher maximum potentialand to acquire the lmowledge andskills needed to

- CCZ16D1 CCZ17D1 I I I CCZ1lSF1 ~ Understand ratio Analyze proportional Apply and extend the properties ofexponents to solve problems with rational exponents sect concepts and use ratio relationships and use Al1111 Al1112 A1l131 A21211 A21212 A21213 A2lZ14 t vi reasoning to solve them to modcl and solve8 sect problems real-world and CCZ1HSFZ E lt mathematicalproblems Apply properties of rational and irrational numberS to solve real world or mathematical problems0 Intentionally Blartk Al1111 Al1112 All131 Al112l o1l il M06AmiddotR1l1 M07AmiddotR1l1 ~~ M06AmiddotR112 M07AmiddotR1l2 CCZllSF3= isect M06A-Rl13 M07A-R1l3 Apply quantitative reasoning to choose and interpret units and scales in formulas graphs and data ~ M06AmiddotR114 M07AmiddotR114 displayse M06A-Rl15 M07A-R11S Al1211 Al1212 Al1Z13 A12121 A12122 A2ZZ11 A22Z12 A223l1

M07A-R116 A2Z312 CC216E1 CCZ17E1 CC21SE1 Apply and extend Apply and extend 0 CCZlHSF4Distioguisb between

Use units as avray to understand problems and to guide the solution -0fmulti-step problemsprevious understandings previous understandings rational and irrational g Al1211 Al1212 Al1Z13 Al2121 A12122 A22211 A22212 of multiplication and of-Operations with numbers usiDg their sectdivision to diVide fractions to operations properties fractions by fractions with rational nUIIlbers CCZlHSFS] Choose a level of accuracy appropriate to limitations on measurement when reporting quantitiesMOSA-Nl1l a Al1211 A11Z12 Al1Z13 Al1221 Al12Z2 Al13l1 Al1312 Al1313 M06A-N111 M07A-N111 lMOSA-Nl12

Al13 21 All3 22 A2Z311 A22312 = Ei -~~~~~t~~~----------- -~t~t~t____________ _poundg ------------------------shy CCZ1HSF6 CC216E2 sect Extend the lmowiedge of arithmetic operations and apply to complex numbers sect appropriate processes to ~ Identify and choose

A2l111 A21112 A211Z1 A2l122 S compute fluently with

CC21HSF7~ multi-digit numbers Apply concepts ofcomplex numbers in polynomial identities and quadratic equations to solve problemssect J-~~~t~i1L_________ _ A2Zl11 A22112 A22l13 A22114

Intentionally Blank Intentionally Blank Develop mdor apply nUlDbertheoryconcepts to find common factors and multiples

M06A-N22l M06A-N222

----~-1h~~L-------------------------------------------------------middot-middot------~-~--------------------------------~

IP age 11

January 2013

Pennsylvania Core Standards Mathematics

21 Numbers and Operations The Standards ofMathematical Practices

Make sense ofproblems and persevere in solving them Reason abstractly and quantitatively Construct viable arguments and critique the reasoning of others Model with mathematics Use appropriate tools strategically Attend to precision Look for and make use ofstructure Look for and bullvnress reltnlaritv in reoeated reasoning

216 Grade 6 217 Grade 7 21HS High School 218 Grade 8

Pennsylvanias public schools shall teach challenge and support every studentw realize his orher maximum potential and to acquire the knowledge andskills needed W CC216E4 Apply and extend previous understandings ofnumbers to the system ofrational numbers

M06A-N311 M06A-N312 M06AmiddotN313 M06AmiddotN321 M06A-ll322 M06A-N323

Intentionally Blank

CC218E4 Estimate irrational numbers by compaing them to rational numbers

MOSAmiddotN113 MOSAmiddotN114 MOSA-N11S Al1111

[Page12

January 2013

Pennsylvania Core Standards Mathematics

22 Algebraic Concepts

The Standards ofMathematical Practices Make sense ofproblems and persevere in solvilg them Reason abstractly and quantitatively Construct viable arguments and critique the reasoning of others Model with mathematics Use appropriate tools strategically Attend to precision Look for and make use ofstructure Look for and exnress regularitvin repeated reasoning

226 Grade 6 22 7 Grade 7 228 Grade 8 22HS High School

Penn rvlvartias uublic schools shall teach challem1e and sunnort everv student to realize his orher maximum uotential and to acmrire the mowledae and skills needed to CC2Z681 CC22781 CC2ZHSD1 Apply and extend

CC2Z8B1 Apply properties of Apply concepts of radicals Interpret the structure of expressions to represent a quantity in terms of its context

Al1151 Al1152Al11S3 AZ1221 AZ1222previous understandings operations to generate and integer exponents to of arithmetic to algebraic equivalent expressions generate equivalent CC22HSD2 expressions expressions Write expressions in equivalent forms to solve problems

M07B-E111 Al11S1 Al1152 Al1153 AZ1211 AZ1Z12AZ1213 AZ1214 AZ1221 M06B-E111 MOSBmiddotE111 AZ1ZZ2 M06B-E112 MOSB-E112

CC22HSD3M06B-E113 MOSB-E113 Extend the knowledge of arithmetic operations and apply to polynomialsM06B-E114 MOSB-E114

_]1Qsect~~l ___________ Al11S1 Al1152 Al1153 AZl221 AZ1222 -~~J~_1__ ___ ---- --- --- -shy--~---------------------- CC22HSD4CCZ2682 CCZ28BZ

Understand the relationship between zeros and fac-ors of polynomials to make generalizations about Understand the process Understand the functions and their graphs of solving a one-variable connections between

AZ1ZZ1 AZ1222equation or inequality proportional relationshlps and apply it to real-worldg

~

CC22HSOSlines1 and linear equations Use polynomial identities to solve problemsand mathematical~ Intentionally Blank Al1151 Al1152 Al1153 AZ1221 AZ1ZZ2AZl311 AZl312 AZl313 problems MOSB-E211 AZ1314MOSBmiddotE212

~

MOSB-E213M06E-E211 CC22HSD6 ~

_~ M06B-EZ12 Al2122 Extend the knowledge ofrational functions to remite in equivaleztformsltg M06B-E213

B ~ Al11S1 Al1152 Al1153 AZ1311 AZ1312AZ1313 AZ1314

e ~ M06B-EZ14 CC22HSD7middotcciz6iir------------ middotec2z7ii3------ -----shy middotcc-2z~S1ii middot----- ---middot---shy Create and graph equations or inequalitiesto describe numbers or relationships Represent and analyze Model and solve real- Analyze and solve linear Al1211 Al1212 Al1213 Al1Z21 Al1222 All311 Al1312 Al1313 s x

quantitative world and mathematical equations and pairs of Al1321 All322 AZl311 A21312 AZ1313 AZ13M AZ1321 AZ132Z~ problems by using andrelationships between Simultaneous linear A22211 AZ2212 AZZ213 AZ2214

dependent and connecting numerical equations CC22HS08independent variables algebraic andor Apply inverse operations to solve equations or formulas for a given variableMOSB-E311graphical Al1211 Al1Z12 Al1213 AZ1311 AZ1312 AZ1313 AZ1314M06B-E311 representations MOSB-E31Z AZl321 AZ1322M06B-E312 MOSB-E313

M07B-E211 CC22HS09MOSB-E314 Use reasooing to solve equations and justify the solution method M07B-EZZ1 MOBB-E31S

All141 Al1211 Al121Z Al1213 Al1221 Al1222 Al1311 Al13l2 M07B-EZ22 Al1211 M07B-EZ31 Al1313 AZ1311 AZ1312 AZ1313 AZ1314 AZ1321 AZ132ZAll221 A11141 CCZ2lSD10Al1222

Represent solve and interpret equationsinequalities and systems of equationsinequalities algebraically and graphically

AllZ11 Al1212 Al1213 Al1221 Al1222 Al1311 Al1312 All313 Al1321 Al1322 A21311 AZl312 A2l313 AZ13U

JPage13

January 2013

Pennsylvania Core Standards Mathematics

ZZ Algebraic Concepts

The Standards ofMathematical Practices Make sense ofproblems and persevere in solving them Reason abstractly and quantitatively Construct viable arguments and critique the reasoning of others Model with mathematics Use appropriate tools strategically Attend to precision Look for and make use ofstructure Look for and Pxnress repoundUlaritv in repeated reasoning

Z26 Grade 6 zz 7 Grade 7 Z2S Grade 8 ZZHS High School

Penm 1lvanias public schools shall teach challenae andsunnort ev~rv student to realize his orhermaximum Potential and to acm1ire the knowledae and skills needed to cc22sc1 CCZ2HSC1 Define evaluate and Use the conceptand notation offunttionsto interpretand appiythemin terrns oftheir context compare functions Al2111 Al2112 Al2113 Al2211 Al2212 AlZ213 Al2214 AZ21ll

AZ2112 AZ2113 A22114 G2221 G2222 G2223 G2224 GZ225 MOSBmiddotF111 MOSJH112 CC22HSC2 MOSBmiddotF113 Graph and analyze functions and use their properties to make connections between the different

representationsAl1211 Al2111 Al2112 Al2113 Al2121 Al2122 Al22l1 AZ1314 AZ1321

Al2121 Al2112

AZ1322 AZ2111 AZ2112 AZ2113 AZ2114 Al2122

CCZ2lSC3middotz2samiddotmiddotmiddotmiddotmiddotmiddotmiddotmiddotmiddotmiddotmiddotmiddotmiddotmiddot Write functions or sequences that model relationships between two quantitiesUse concepts offunctions

Al1Z11 AllZ12 Al1213 Al2111 Al2112 Al2113 Al2121 Al2l22 to model relationships Al2Z13 Al2214 A21311A21312 AZ1313 AZ1314 AZ1321AZ1322betvveen quantities AZ211l AZ2112 AZ2l13 AZZ114 A22211A22212A22Z13 AZ2214

MOSBmiddotF211 cc22HSC4MOSBmiddotF212 Interpret the effects transformations have on functions and find the inverses of functionsAl1213 =0 Al2121 Al2122 AZ1313 AZ1314 AZ1321 AZ2211 AZ2212 AZ2213g =

A12111 u AZ2Z14 AZ2221uAl2122Intentionally Blank Intentionally Blank= = Al2213 CC22HSC5Al2214 G G Construct and compare linear quadratic and exponential models to solve problems

~ ~

Al2211 Al2Z12 Al2213 Al2214 A213ll A2l312 AZ1313 AZ1314 AZ2111 AZ2112 AZ2113 AZ2114 AZ22ll AZZ21Z AZ2213 AZ2214 A2222l

CC22HSC6 Interpret functions in terms of the situations they modeL

Al2121 Al2212 Al2213 Al2221 AZ1313AZZ1l1 AZZ112 AZ2113 AZ2114 AZ2213 AZ2214 AZ2221

CC22HSC7 Apply radian measure ofan angle and the unit circle to analyze the trigonometric functions

CC22HSC8 Choose trigonometric functions to model periodic phenomena and describe the properties of the graphs

CC22HSC9 Prove the Pythagorean identity and 11Se it to calculate trigonometric ratios

G1321 G211l G2112

JPage14

January 2013

Pennsylvania Core Standards Mathematics

CC236A1 CC237A1 CC238A1 CC23lSA1 Apply appropriate tools Solve real-world and Apply the concepts of Use geometric figures and their properties to represent transformations in the plane to solve real~world and mathematical problems volume ofcylinders cones G1311 G131Z mathematical problems involving angle and spheres to solve realshy CC23HSA2 involving area surface measure area swface world and mathematical Apply rigid transformations to determine and explain congruence area and volume area circumference problems GU11 G1312

and volume CC23HSA3 M06C-Gll1 M08C-C3ll Verify and apply geometric theorems as they relate to geometric figures M06C-GllZ M07C-G2l1 G2312 G1211 G1212 G1213 G1214 G1215 G1321 G2211 G2212 G2221 G2222 M06C-Gll3 M07C-G212 G2223 G2224 G222S M06C-G1L4 M07C-G22l CC23HS-A4 M06C-Gli5 M07C-G222 Apply the concept ofcongruence to create geometric constructions

MQsectt_-_G~Jsect_ --- shy -- shy -- shy ---------------------middot-middot CC23HSA5

--------------------------middotCC237A2 CC238A2 Create justifications based on transformations to establish similarity ofplane figures VlSUalize and represent Understand and apply G1311 G1312 geometric figures and congruence similarity and CC23HSA6 descnbethe geometric transformations Verify and apply theorems involving similarity as they relate to plane figures relatiooships betWeen using various tools G1311 G1312 G1321 them

CC23HSA7_ _- Intentionally Blank MOSC-C111 - Apply trigonometric ratios to solve problems involving right triangles~ sect M07C-Glll M08C-Gll2 = G21ll G21120

M07C-Gll2 MOSC-G113 CC23HSA8 M07C-Gll3 M08C-Gll4 Apply geometric theorems to veruy properties ofcircless ~M07C-Gll4 GJ211 ~ G1111 G1112 G1113 G1114 G1321 G223l

G1214 CC23HS-A9

-----------------------shy ----------------------shyG2211 Extend the concept ofsimilarity to determine arc lengths and areas ofsectors ofcircles

CCi32A3--shy -shy G1111 G1112 G1l13 G1114 G2221 G2222 G2223 G2224 G2225 G2231 Understand and apply the CC23HSA10 Pythagorean Theoremto Translate beti-veen the geometric description and the equation for a conic section solve problems A221l4 AZ221l

CC23HSA11 MOSC-G211 Apply coordinate geometry to prove simple geometric theorems algebraically MOSC-G212 G2121 GZ122 G2123

Intentionally Blank Intentionally Blank MOSC-G213 CC23HSA12 G2111 Explain volume formulas and use them to solve problems G21Zl G2311 G231Z G2313

CC23llSA13 Analyze relationships between two-dimensional and three-dimensional objects

G1111 G111Z G1113 Gl114 G1211 G1212 G1213 G1214 G1215 G2321 CC23HSA14 Apply geometric concepts to model and solve real world problems

G2241 G231l G2312 GZ313

23 Geometrv The Standards ofMathematical Practices

Make sense of problems and persevere in solving them Reason abstractly and quantitatively ConstructViable arguments and critique the reasoning ofothers Model with mathematics Use appropriate tools strategically Attend to precision Look for and make use of structure Look for and evnress reUlaritv in reneated reasoniniz

Grade 6 Grade7 Grades High School Z36 237 23S Z3HS

Pennltvfvanias vublic schools shall teach challen e and sunnort evPrv student to realize his or her maximum votential and to acauire the knowledae and skills needed to

jPage15

)anuazy 2013

Pennsylvania Core Standards Mathematics

24 Measurement Data and Probabilitv The Standards ofMathematical Practices

Make sense ofproblems and persevere in solving them Reason abstractly and quantitatively Construct viable ar~ments and critique the reasoning ofothers Model with mathematics Use appropriate tools strategically Attend to precision Look for and make use ofstructure Look for and express regularity in repeated reasoning

Grade 6 246

Grade7 247

Grade3 243

High School 24HS

Pennsylvanias public schools shall teach challenge and support every student to realize his or her mt1Ximum potential and to acquire the mowedge andskills needed to

~ E 0 0

d ilc c g ~ e

CCZ46B1 Demonstrate an understanding of statistical vaiability by displaying analyzing and summarizing distributions

M06DmiddotSlll M06DmiddotSll2 M06D-Sll3 M06D-Sll4

------------------------shy

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------------------------shy

CCZ47B1 Draw inferences about populatioos based on rardom sampling concepts

M07D-S1l1 M07D-S1l2

middotcczyen7-szmiddot----middot----- shy -Draw informal comparative inferences about two populations

M07D-S211

middotcci47S3----- --- --- -shy[mrestigate cbaoce processes and develop use and evaluate probability models

CCZ48B1 Analyze andor interpret bivariate data displayed in multiple representations

MOSD-S11l MOSDmiddotS112 MOSDmiddotS113 AlZ22l

iCi4862 ----------shyUnderstand thatpatterns ofassociation can be seen in bivariate data utilizing frequencies

MOSDmiddotS121

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c a 0 0

d ltgt middotc ~ middotc g

sect

CCZ4HSB1 Summarize represent and interpret data on a single count or measurement variable

A12212 Al2311 A12321 Al2322 Al2323

CCZ4HSB2 Summarize represent and interpret data on two categorical and quantitative variables

Al21ll Al2112 A12113 Al2121 Al2122 Al2221 A2211l AZ2311 AZ2312

CCZ4HSB3 Analyze linear models to make interpretations based on the data

Al222l A1231l Al2321 Al2322 Al2323 A22311 AZ2312

CCZ4HSB4 Recognize and evaluate random processes underlying statistical experiments

Al2331 A223Z1 A2232Z A22323

CC24HSBS Make inferences and justify conclusions based on sample surveys experiments and observational studies

Al2321 Al2322 Al2323 A22321 A22322 A22323

CCZ4J5B6 Use the concepts ofindependence and conditional probability to interpret data

AZ2321 A22322 A22323

Intentionally Blunk M07D-S31l M07D-S32l M07D-S322 M07D-S323 Al2331

lntentionany Blank CCZ4HSB7 Apply the rules of probability to compute probabilities ofcompound events in a uniform probability model

Al2331 A223Z1 A223ZZ A22323

[Page16

January 2013

Pennsylvania Core Standards Mathematics

Key Terms for this Document

Standards for Mathematical Content-These standards define what students should know and be able to do in their study of mathematics

Standards for Mathematical Practice-These standards describe the processes and proficiencies in which all students grades K-12 should engage Educators

must instill these standards of practice in their students so that they become habitual The standards for mathematical practice should be used as the vehicle to

deliver the standards of mathematical content

Standard Algorithm-A locally agreed upon method of computation which is conventionally taught for solving mathematical problems

Decimal Fraction-A fraction whose denominator is a power of ten (examples 2100 810) These fractions are commonly expressed as decimals

Unit Fraction-A rational number written as a fraction where the numerator is one and the denominator is a positive integer (example 120)

Bivariate Data-The data involves two variables and is usually represented as a scatter plot

Rule-A single operation (examples add 5 multiply by 2)

IP age 17

January 2013

Page 4: Academic Standards for Mathematics...The Co=on Core Standards in Mathematics in grades PreK-5 lay a solid foundation in whole numbers, addition, subtraction, multiplication, division,

Pennsylvania Core Standards Mathematics

The PA Core Standards for Mathematics detail four standard areas Numbers and Operations Algebraic Concepts Geometry and Measurement Data and Probability These standard areas are reflective ofthe reporting categories in the PA Core Assessment Anchors and Eligible Content The middot intent of this document is to provide a useful tool for designing curriculum instruction and assessment The grade level curriculum and instructional shifts in mathematics cannot occur without the integrated emphasis on content and practice The chart below illustrates the four standard areas and the development and progression of the strands with an understanding that all is framed around the Standards for Mathematical Practice

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1lj[middot 1 middot ljI $eRi911na ~ oo I I 1111 I II11 flmiddot]f lt1bull 1middot llmiddoti I 1middot 1 1middot 1 middotmiddot bulliJi1 middot]llttenJ tomiddotprews1on I 1 11middot11 r-1iililiiir1i[iitiii[1middot1fii 1middot 11middot 1middot1middot ll middot ~1 bulll11~k1i-bull1_af~1f-rJiiLli=lh1Jl1b~~Jl1(l~ll1 11middot1I1J 111 11 111111 Ii 1bull1il~11 111 I 1lt11 middot middot ~ I imiddot1bullli middot lI 1+1 rl~ ~ l11 1~r1~1 1~r 1j1~111i11 j1fi-jl1 1bull1bull1 1middot1fi iJ11r1i1~~1t 11111i11 ~]11J111U ] piril 11[[ lj111111 r bullIbull-Diill L_ i ~I ii lli 111 middot_middot middot1 1 middot==1-1 1~1 =1 bull o oran -m~~iusev111 4iw1e1111bulll111-11i11 1 middot11middot 111111 middot i Imiddot I=~ - 1-middot11 middot1 middot_ 111 r1bullh _ middotl11-1middot middot11 1middotL1middot -1iJOOlmiddotitOr1~Ui-$Pressrezwan SO_middot gc11- ~~r

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1Page4

January 2013

--- ------ ---

------------------------ ------------------------ -------------------------

__________ -------------------------

Pennsylvania Core Standards Mathematics

21 Numbers and Operations The Standards ofMathematical Practices

Make sense ofproblems and persevere in solving them Reason abstractly and quantitatively Construct viable arguments and critique the reasoning ofothers Model with mathematics Use appropriate tools strategically Attend to precision Look for and make use ofstructure

GradePreK GradeK Z1PreK Z1K

Gradel Z11

GradeZ Z1Z

Look for and exnress re~laritv in repeated reasonin1

Grade3 Grade4 Z13 Z14

Grades Z15

Pennsylvanias public schools shall teach challenge andsupporteverystudent to realize his orhermaximum potential and to acquire the Jmowledge andskills needed to CCZ1PreKA1 ccz1KA1 Know number names Know number names and and the =Cunt sequence write and recite the count olt eshy

ao= middotccZipKAtbull --------~t~i=~middot--- s ccz1KAZ Count to tell the number=sect ofobjects 83

~ -----------------------middot CCZ1PreKA3 ~ Compare numbers

Apply one-to-one correspondence to count

_JflJtXlll2~t95~bj~middot- --shyccz1KA3 Apply the concept of magnitude to compare numbers and ouantities CCZ1KB1 Use place value to compose and decompose numbers within 19

= ~ s ~ = 0c Intentionally Blank 0 oil il = Intentionally Blanki s ~

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CC211B1 Extend the counting sequence to read and write numerals to represent objects

middotcc zi~isimiddot-- ----middotmiddot --- shyUse place-V3lue concepts to represent amounts of tens and ones and to compare two digit numbers

cC2Tia3middot----------middot Use place-value concepts and properties of operations to add and subtrattwithin 100

ccz1zs1 Use place-value concepts to represent amoWltS of tens and ones and to compare three digit numbers

CC21ZBZ Use place-value concepts to read write and skip count to 1000

CCZ13B1 Apply place-value understanding and properties ofoperations to perform multi-digit arithmetic

M03A-Tl1l M03A-T1lZ M03AmiddotTll3 M03A-Tll4

Intentionally Blank

middotccziiJij ---- --- ---- ------------------------shyUse place-value understanding and Intentionally Blankproperties ofoperations to add and subtract within 1000

CC214B1 Apply place-value concepts to show an understanding ofmulti-digit whole numbers

M04A-T1l1 M04A-Tl12 M04A-TLl3 M04A-Tll4

middotc-cziiiii---- --- --- shyUse place-value understanding and properties ofoperations to perform multi-digit arithmetic

M04A-T2ll M04A-T212 M04A-T213 191~r1

Intentionally Blank

CCZ15B1 Apply placemiddotvalue concepts to show an understanding of operations and rounding as they pertain to whole numbers and decimals

MOSA-Tlll MOSAmiddotT112 MOSA-T113 MOSA-T114 MOSAmiddotT115

middotcczis-B2middotmiddotmiddot---------shyExtend an understandiIg ofoperations with whole numbers to perform operations including decimals

MOSAmiddotTZ11 MOSA-TZlZ MOSA-TZ13

ntentional(y Blank

JPageS

)anuary2013

-------------------------------------------------------------------

Pennsylvania Core Standards Mathematics

CCZ13C1 CCZ14C1 ccz1sc1 Explore and develop an Extend the Use the understanding of unde=ndingof unde=ndingof equivalency to add and fractions as numbers fractions to show snbtract fractions

equivalence and M03A-F1ll ordering MOSA-Flll M03AmiddotF1l2 M03A-Fll3 M04A-Fltl M03A-F1l4 M04A-Fll2

~ M9amp~~1~b2 bullbullbull -- shy -- shy __ middotecii4cimiddot------middotmiddotmiddotmiddotshy middoteoisomiddot-----------shy= 0 Build fractions from Apply and extend ~ unit fractions by previomicros understandings applying and extending ofmultiplication and I previous division to multiply and ~ understandings of divide fractions = 0 operations on whole

- numbers MOSA-F211f lntentionany Blank Intentionally Blank Intentionally Blank Intentionally Blank Intentionally Blank MOSA-F2lZ

M04A-FZ11 MOSA-F2130 ~ M04AmiddotFZl2 MOSA-F214

~ M04A-FZ13

M04A-F214 M04A-FZ15 z M04AmiddotF216

G -----------------------shyM04AmiddotFZ17

------------------------shy~

middotcczi4c3middot-----middot--middot-shyConnect decimal notation to fractions and compare decimal fractions (base 10

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M04AmiddotF311 M04A-F3l2 M04AmiddotF313

21 Numbers and Operations

The Standards ofMathematical Practices Make sense ofproblems and persevere in solving them Reason abstractly and quantitatively Construct viable arguments and critique the reasoning ofothers Model with mathematics Use appropriate tools strategically Attend to precision Look for and make use ofstructure Look for and bull=ress reltgtuJaritv in ren eated reasonin

GradePreK GradeK Gradel GradeZ Grade3 Grade4 Z1PreK 21K 211 Z12 Z13 214

Grades Z15

Pennsylvanias public schools shall teach challenge and support every student to realize his orher maximum potentialand to acquire the knowledge and skills needed to

1Page6

January 2013

Pennsylvania Core Standards Mathematics

CCZ2lreKA1 CC22KA1 CC221A1 CCZ22A1 CC223A1 CC2Z4A1 CC22SA1 Understand addition as Extend the concepts of Representand solve Represent and solve Represent and solve Represent and solve Interpretand evaluate putting together and putting together and problems involviDg problems involving problems involving problems involving tbt numerical expressions adding to and taking apart to add and addition and subtraction addition and multiplication and four operations using order ofoperations understand subtraction subtract Within 10 Within20 subtraction Within 100 division astakingapartand M04ll-011l MOSJl011l taking from M03ll-Oll1 M04ll-0l12 MOSllmiddotOl12

M03B-OllZ M04B-Oll3 M03B-Ol2l M04B-Ol14

bO -----------------------shy ------------------------shyM03Bmiddot0122

-----------------------shy -------------------------shy= middotccz~z1umiddot-middotmiddot----shy middotcci-ZzA2middotmiddotmiddotmiddotmiddotmiddotmiddotmiddot middot middotshy middotcc2z1iA2middotmiddotmiddotmiddotmiddotmiddotmiddot--middotmiddot-middot CCZ24A2ii Understand and apply Use mental strategies to Understand properties of Develop andor apply 5 properties of operations add and subtract Within multiplication and the number tbeozy concepts= E-lt and the relationship 20 relationship between to find factors and

betvveen addition and multiplication and multiplesmiddot Intentionally Blank Intentionally Blank Intentionally Blank

subtraction division

M04Bmiddot0211 ~ M03B-OZ11 M03B-0212

MQ~JQ~J middot-middot--middotmiddot bullbullbullbull= -----------------------shy ------------------------shy -----------------------shy ~----------------------- ----------------------shy ------------------------shy CCZ22A3 CCZ23A3

WorkWitb equal groups Demonstrate= s Intentionally Blank Intentionally Blank Intentionally Blank ofobjects to gain multiplication and Intentionally Blank Intentionally Blank ~ foundations for division fluency a

-----------------------shy ------------------------shy ------------------------shy PP112iPltCl~~l__ ___ ----shy ------------------------shy -----------------------shy ------------------------shy CCZ23A4 CC224A4 CC225A4 0 Solve problems involving Generate and analyze Analyze patterns and ~ s the four operations and patterns using one rule relationships using tlNo

identify and explain rules patterns in arithmetic M04B-0311

M04B-0312 MOSB-0211 Intentionally Blank Intentionally Blank Intentionally Blank Intentionally Blank M03Bmiddot0311 M04llmiddot0313 MOSB-0212

M03Bmiddot0312 M03B-03l3 M03B-0314 M03B-031S M03B-0316 M03B-0317

22 Algebraic Concepts

The Standards ofMathematical Practices Make sense ofproblems and persevere in solVingthem Reason abstractly and quantitatively Construct viable arguments and critique the reasoning of others Model with mathematics Use appropriate tools strategically Attend to precision Look for and make use ofstructure Look for and Pvnress rerulari -v in reoeated reasonini

GradePreK GradeK Gradel Grade2 Grade3 Grade4 Grades 22PreK 22K 221 Z22 223 224 225

Pennsylvanias public schools shall teach challenge andsupport every student to realize his orher maximum potentialand to acquire the knowledge andskiIfs needed to

IPage7

January 2013

23 Geometry

Pennsylvania Core Standards Mathematics

The Standards of Mathematical Practices Make sense ofproblems and persevere in solving them Reason abstractly and quantitatively Construct viable arguments and critique the reasoning ofothers Model with mathematics Use appropriate tools strategically Attend to precision Look for and make use ofstructure Look for and exuress regularitv in reueated reasonin

GradePreK 23PreK

GradeK 23l(

Grade 1 Z31

GradeZ Z3Z

Grade3 233

Grade4 Z34

Grades 235

Pennsylvanias public schools shall teach challenge andsupport everystudent to realize his orhermaximum potential and to acquire the lmowledge andskills needed to

f s 0

~ sect

CCZ3PreKA1 Identify and describe shapes

middotcczerKAz-shy------Attalyze compare create and compose shapes

----------------------shy

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CC23KA1 Identify and descnbe two- and three-dimensional shapes

-CciTKApound-----------shyAnalyze compare create and compose twomiddot and three-dimensional shapes

------------------------shy

lntentionally Blank

CCZ31A1 Compose and distinguish between ruro- and three-shydimensional shapes based on their attrihutes

(C23ii2shy--shy------shy -shyUse the understanding of fractions to partition shapes into halves and quarters

------------------------shy

Intentionally Blank

CC232A1 Analyze and draw two-and threeffimensional shapes having specified attnOutes

middotce2s2A2 middot----shy --shy -shyUse the understanding offractions to partition shapes into halves quarters and thirds

-----------------------shy

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CC233A1 Identifycolllpareand classifyshapes and their attributes

M03C-G111 M03C-G112

------------------------shyCC233AZ Use the understanding of fractionstopartition shapes into parts with equal areas and express the area ofeach microwt as a unit fraction ofthe whole

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CC234A1 Draw lines and angles and identify these in tvvo-dimensional figures

M04C-G111

-ci3-4Ai___ --shy --shy --shy-Classifytwo-dimensional figures by properties oftheir llnes and angles

M04C-G112

middotccii4-Ar----------shyRecognize symmetric shapes and draw lines of symmetry

CC235A1 Graph points in the first quadranton the coordinate plane and interpret these points when solving real world and mathematical problems

MOSC-G111 _1P_~f~1~--shy -------shy -shyCC23SAZ Glassey twoditnensional figures into categories based on an understanding oftheir properties

MOSC-G211

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M04C-G113

[Pages

January2013

------------------------- ------------------------ --------------------------

Pennsylvania Core Standards Mathematics

24 Measurement Data and Probability The Standards ofMathematical Practices

Make sense of problems and persevere in solving them Reason abstractly and quantitatively Construct Viable arguments and critique the reasoning of others Model with mathematics Use appropriate tools strategically Attend to precision Look for and make use of strUcture Look for and vnress reunl~ri in reoeated reasonine-

GradePreK GradeK Gradel Grade2 Grade3 Grade4 Grades 24PreK 24K 241 242 243 Z44 24S

CC24PreKA1 Describe and compare measurable attributes oflength and weight of evecyday objects

CC24KA1 Descnbe and compare attributes oflength area weight and capacity of everyday objects

CC241A1 Order Iengtbs and measure them both indirelttly and by repeating length units

CC242A1 Measure and estimate lengths in standard units using appropriate tools

CCZ43A1 Solve problems involving measurement and estimation of temperature liqUid volume mass and length

CCZ44A1 Solve problems involving measurement and conversioos from a larger unit to a smaller unit

CCZ4SA1 Solve problems using conversions within a given measurement system

MOSD-M111

-A O = =

----------------------shy ------------------------shy -ec21A2_______ --shy --shyTell and write time to the

-----------------------shyCC24ZAZ Tell and write time to

M03D-M121 M03D-M122 M03D-M123

middotccZyen3u-middot----------shyTell and write time to the

M04D-M11l M04D-M112 M04D-M113 M04D-M114middotccz4u-shy --shy --shy --shyTranslate information

middotcci4s-AZ______________

Represent and interpret

s Intentionally Blank Intentionally Blank

nearest half hour using both analog and digital clocks

the nearest five minutes using both analog and digital clocks

nearest minute and solve problems by calculating time intervals

from one type of data display to another

data using appropriate scale

~ s -----------------------middot ------------------------shy ------------------------shy

-cci42A3____________

Solve problems and

M03DmiddotMll1 M9-3olMmiddotJJ _____ ----__ CCZ43A3 Solve problems and make

M04D-MZ13

-----------------------shy

MOSD-MZ1Z

-------------------------shy

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make change using coins and paper currency with appropriate symbols

chaDge involving money using a combination of coins and bills

MD3D-M13l M03D-Ml3Z

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P uJvanias public schools shaJJ teach chalenqe and surwort ev student to realize his or her maximum Dotential and to acauire the knowledae and skills needed to

-------------------------------------------------middot _119301-L~bullbullbullbullbullbullbullbullbullbullbullbullbullbullbullbullbullbullbullbullbullbullbullbullbullbullbullbull bullbullbullbullbullbullbull_

[Page9

January 2013

Pennsylvania Core Standards Mathematics

24 Measurement Data and Probabilitv The Standards ofMathematical Practices

Make sense ofproblems and persevere in solving them Reason abstractly and quantitatively Construct viable arguments and crltique the reasoning of others Model with mathematics Use appropriate tools strategically Attend to precision Look for and make use of structure Look for and exnress regularitv in repeated reasoning

GradePreK Z4K Grade K Gradel Z4Z Grade 2 243 Grade 3 244middot Grade 4 Z45 Grade 5 24PreK 241

PenTI vJvanias uublic schools shall teach challenae and sunnort evp~rstudent to realize his or her maximum Dotential and to acauire the knowledae andskills needed to CCZ4PreKA4 CCZ4KA4 CCZ41A4 CCZ4ZA4 CCZ43A4 CCZ44A4 CCZ4SA4 Classify objects and Classify objects and count Representand interpret Represent and interpret Representand interpret Representand interpret Solve problems involving count the number of objects iii each category

the number ofobjects in each category

data using tablescharts data using line plots pictUre graphs and bar

data using tally charts tables pictographs line

data irivolviog fractions using informationmiddot

computation offractions using information

graphs plots and bar graphs provided in a line plot provided in a line plot

M03DmiddotMZ11 MD4IJMZ11 MOSDmiddotMZ11 M03D-M212 M04IJM212 M03DmiddotM213

S ----------------------shy ------------------------shy ------------------------shy -----------------------shy

1D_3JlMJ~4t-bullbull_ __ bull__ CCZ43A5 -----------------------shy middotca4sAs----- --middot--middot -- shy

ilt

s

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Determine the area of a rectangle and apply the concept to multiplicati~n and to addition

M03D-M311

Intentionally Blank

Apply concepts ofvolume to solve problems and relate volume to multiplication and to addition

s

Intentionally Blank Jntentionally Blank Intentionally Blank M03DmiddotM312

laquociyeniA6-------bull -bull -- laquoci43A6middot--shy --shy --shy --shy -cc244A6____________ MOSDmiddotM31l

_Qsectl31~middot~___ -----middot-shy bull s Extend the concepts of Solve problems involTng Measure angles and use ~ addition and subtraction perimeters ofpolygons properties of adjacent ~ to problems involving

length-and distinguish between linear and area measures

angles to solve problems lntentionalb Blank

M03D-M411 M04DmiddotM311 M04DmiddotM312

IP age 10

Januazy2013

Pennsylvania Core Standards Mathematics

21 Numbers and Operations The Standards ofMathematical Practices

Make sense ofproblems and persevere in solving them Reason abstractly and quantitatively Construct viable arguments and critique the reasoning of others Model with mathematics Use appropriate tools strategically Attend to precision Look for and make use of structure Look for and eXPress regularitv in repeated reasoning

216Grade6 I 217Grade7 I 21SGradeS I I 21HSHighSchool

Pennsylvanias public schools shall teach challenge and support every student to realize his orher maximum potentialand to acquire the lmowledge andskills needed to

- CCZ16D1 CCZ17D1 I I I CCZ1lSF1 ~ Understand ratio Analyze proportional Apply and extend the properties ofexponents to solve problems with rational exponents sect concepts and use ratio relationships and use Al1111 Al1112 A1l131 A21211 A21212 A21213 A2lZ14 t vi reasoning to solve them to modcl and solve8 sect problems real-world and CCZ1HSFZ E lt mathematicalproblems Apply properties of rational and irrational numberS to solve real world or mathematical problems0 Intentionally Blartk Al1111 Al1112 All131 Al112l o1l il M06AmiddotR1l1 M07AmiddotR1l1 ~~ M06AmiddotR112 M07AmiddotR1l2 CCZllSF3= isect M06A-Rl13 M07A-R1l3 Apply quantitative reasoning to choose and interpret units and scales in formulas graphs and data ~ M06AmiddotR114 M07AmiddotR114 displayse M06A-Rl15 M07A-R11S Al1211 Al1212 Al1Z13 A12121 A12122 A2ZZ11 A22Z12 A223l1

M07A-R116 A2Z312 CC216E1 CCZ17E1 CC21SE1 Apply and extend Apply and extend 0 CCZlHSF4Distioguisb between

Use units as avray to understand problems and to guide the solution -0fmulti-step problemsprevious understandings previous understandings rational and irrational g Al1211 Al1212 Al1Z13 Al2121 A12122 A22211 A22212 of multiplication and of-Operations with numbers usiDg their sectdivision to diVide fractions to operations properties fractions by fractions with rational nUIIlbers CCZlHSFS] Choose a level of accuracy appropriate to limitations on measurement when reporting quantitiesMOSA-Nl1l a Al1211 A11Z12 Al1Z13 Al1221 Al12Z2 Al13l1 Al1312 Al1313 M06A-N111 M07A-N111 lMOSA-Nl12

Al13 21 All3 22 A2Z311 A22312 = Ei -~~~~~t~~~----------- -~t~t~t____________ _poundg ------------------------shy CCZ1HSF6 CC216E2 sect Extend the lmowiedge of arithmetic operations and apply to complex numbers sect appropriate processes to ~ Identify and choose

A2l111 A21112 A211Z1 A2l122 S compute fluently with

CC21HSF7~ multi-digit numbers Apply concepts ofcomplex numbers in polynomial identities and quadratic equations to solve problemssect J-~~~t~i1L_________ _ A2Zl11 A22112 A22l13 A22114

Intentionally Blank Intentionally Blank Develop mdor apply nUlDbertheoryconcepts to find common factors and multiples

M06A-N22l M06A-N222

----~-1h~~L-------------------------------------------------------middot-middot------~-~--------------------------------~

IP age 11

January 2013

Pennsylvania Core Standards Mathematics

21 Numbers and Operations The Standards ofMathematical Practices

Make sense ofproblems and persevere in solving them Reason abstractly and quantitatively Construct viable arguments and critique the reasoning of others Model with mathematics Use appropriate tools strategically Attend to precision Look for and make use ofstructure Look for and bullvnress reltnlaritv in reoeated reasoning

216 Grade 6 217 Grade 7 21HS High School 218 Grade 8

Pennsylvanias public schools shall teach challenge and support every studentw realize his orher maximum potential and to acquire the knowledge andskills needed W CC216E4 Apply and extend previous understandings ofnumbers to the system ofrational numbers

M06A-N311 M06A-N312 M06AmiddotN313 M06AmiddotN321 M06A-ll322 M06A-N323

Intentionally Blank

CC218E4 Estimate irrational numbers by compaing them to rational numbers

MOSAmiddotN113 MOSAmiddotN114 MOSA-N11S Al1111

[Page12

January 2013

Pennsylvania Core Standards Mathematics

22 Algebraic Concepts

The Standards ofMathematical Practices Make sense ofproblems and persevere in solvilg them Reason abstractly and quantitatively Construct viable arguments and critique the reasoning of others Model with mathematics Use appropriate tools strategically Attend to precision Look for and make use ofstructure Look for and exnress regularitvin repeated reasoning

226 Grade 6 22 7 Grade 7 228 Grade 8 22HS High School

Penn rvlvartias uublic schools shall teach challem1e and sunnort everv student to realize his orher maximum uotential and to acmrire the mowledae and skills needed to CC2Z681 CC22781 CC2ZHSD1 Apply and extend

CC2Z8B1 Apply properties of Apply concepts of radicals Interpret the structure of expressions to represent a quantity in terms of its context

Al1151 Al1152Al11S3 AZ1221 AZ1222previous understandings operations to generate and integer exponents to of arithmetic to algebraic equivalent expressions generate equivalent CC22HSD2 expressions expressions Write expressions in equivalent forms to solve problems

M07B-E111 Al11S1 Al1152 Al1153 AZ1211 AZ1Z12AZ1213 AZ1214 AZ1221 M06B-E111 MOSBmiddotE111 AZ1ZZ2 M06B-E112 MOSB-E112

CC22HSD3M06B-E113 MOSB-E113 Extend the knowledge of arithmetic operations and apply to polynomialsM06B-E114 MOSB-E114

_]1Qsect~~l ___________ Al11S1 Al1152 Al1153 AZl221 AZ1222 -~~J~_1__ ___ ---- --- --- -shy--~---------------------- CC22HSD4CCZ2682 CCZ28BZ

Understand the relationship between zeros and fac-ors of polynomials to make generalizations about Understand the process Understand the functions and their graphs of solving a one-variable connections between

AZ1ZZ1 AZ1222equation or inequality proportional relationshlps and apply it to real-worldg

~

CC22HSOSlines1 and linear equations Use polynomial identities to solve problemsand mathematical~ Intentionally Blank Al1151 Al1152 Al1153 AZ1221 AZ1ZZ2AZl311 AZl312 AZl313 problems MOSB-E211 AZ1314MOSBmiddotE212

~

MOSB-E213M06E-E211 CC22HSD6 ~

_~ M06B-EZ12 Al2122 Extend the knowledge ofrational functions to remite in equivaleztformsltg M06B-E213

B ~ Al11S1 Al1152 Al1153 AZ1311 AZ1312AZ1313 AZ1314

e ~ M06B-EZ14 CC22HSD7middotcciz6iir------------ middotec2z7ii3------ -----shy middotcc-2z~S1ii middot----- ---middot---shy Create and graph equations or inequalitiesto describe numbers or relationships Represent and analyze Model and solve real- Analyze and solve linear Al1211 Al1212 Al1213 Al1Z21 Al1222 All311 Al1312 Al1313 s x

quantitative world and mathematical equations and pairs of Al1321 All322 AZl311 A21312 AZ1313 AZ13M AZ1321 AZ132Z~ problems by using andrelationships between Simultaneous linear A22211 AZ2212 AZZ213 AZ2214

dependent and connecting numerical equations CC22HS08independent variables algebraic andor Apply inverse operations to solve equations or formulas for a given variableMOSB-E311graphical Al1211 Al1Z12 Al1213 AZ1311 AZ1312 AZ1313 AZ1314M06B-E311 representations MOSB-E31Z AZl321 AZ1322M06B-E312 MOSB-E313

M07B-E211 CC22HS09MOSB-E314 Use reasooing to solve equations and justify the solution method M07B-EZZ1 MOBB-E31S

All141 Al1211 Al121Z Al1213 Al1221 Al1222 Al1311 Al13l2 M07B-EZ22 Al1211 M07B-EZ31 Al1313 AZ1311 AZ1312 AZ1313 AZ1314 AZ1321 AZ132ZAll221 A11141 CCZ2lSD10Al1222

Represent solve and interpret equationsinequalities and systems of equationsinequalities algebraically and graphically

AllZ11 Al1212 Al1213 Al1221 Al1222 Al1311 Al1312 All313 Al1321 Al1322 A21311 AZl312 A2l313 AZ13U

JPage13

January 2013

Pennsylvania Core Standards Mathematics

ZZ Algebraic Concepts

The Standards ofMathematical Practices Make sense ofproblems and persevere in solving them Reason abstractly and quantitatively Construct viable arguments and critique the reasoning of others Model with mathematics Use appropriate tools strategically Attend to precision Look for and make use ofstructure Look for and Pxnress repoundUlaritv in repeated reasoning

Z26 Grade 6 zz 7 Grade 7 Z2S Grade 8 ZZHS High School

Penm 1lvanias public schools shall teach challenae andsunnort ev~rv student to realize his orhermaximum Potential and to acm1ire the knowledae and skills needed to cc22sc1 CCZ2HSC1 Define evaluate and Use the conceptand notation offunttionsto interpretand appiythemin terrns oftheir context compare functions Al2111 Al2112 Al2113 Al2211 Al2212 AlZ213 Al2214 AZ21ll

AZ2112 AZ2113 A22114 G2221 G2222 G2223 G2224 GZ225 MOSBmiddotF111 MOSJH112 CC22HSC2 MOSBmiddotF113 Graph and analyze functions and use their properties to make connections between the different

representationsAl1211 Al2111 Al2112 Al2113 Al2121 Al2122 Al22l1 AZ1314 AZ1321

Al2121 Al2112

AZ1322 AZ2111 AZ2112 AZ2113 AZ2114 Al2122

CCZ2lSC3middotz2samiddotmiddotmiddotmiddotmiddotmiddotmiddotmiddotmiddotmiddotmiddotmiddotmiddotmiddot Write functions or sequences that model relationships between two quantitiesUse concepts offunctions

Al1Z11 AllZ12 Al1213 Al2111 Al2112 Al2113 Al2121 Al2l22 to model relationships Al2Z13 Al2214 A21311A21312 AZ1313 AZ1314 AZ1321AZ1322betvveen quantities AZ211l AZ2112 AZ2l13 AZZ114 A22211A22212A22Z13 AZ2214

MOSBmiddotF211 cc22HSC4MOSBmiddotF212 Interpret the effects transformations have on functions and find the inverses of functionsAl1213 =0 Al2121 Al2122 AZ1313 AZ1314 AZ1321 AZ2211 AZ2212 AZ2213g =

A12111 u AZ2Z14 AZ2221uAl2122Intentionally Blank Intentionally Blank= = Al2213 CC22HSC5Al2214 G G Construct and compare linear quadratic and exponential models to solve problems

~ ~

Al2211 Al2Z12 Al2213 Al2214 A213ll A2l312 AZ1313 AZ1314 AZ2111 AZ2112 AZ2113 AZ2114 AZ22ll AZZ21Z AZ2213 AZ2214 A2222l

CC22HSC6 Interpret functions in terms of the situations they modeL

Al2121 Al2212 Al2213 Al2221 AZ1313AZZ1l1 AZZ112 AZ2113 AZ2114 AZ2213 AZ2214 AZ2221

CC22HSC7 Apply radian measure ofan angle and the unit circle to analyze the trigonometric functions

CC22HSC8 Choose trigonometric functions to model periodic phenomena and describe the properties of the graphs

CC22HSC9 Prove the Pythagorean identity and 11Se it to calculate trigonometric ratios

G1321 G211l G2112

JPage14

January 2013

Pennsylvania Core Standards Mathematics

CC236A1 CC237A1 CC238A1 CC23lSA1 Apply appropriate tools Solve real-world and Apply the concepts of Use geometric figures and their properties to represent transformations in the plane to solve real~world and mathematical problems volume ofcylinders cones G1311 G131Z mathematical problems involving angle and spheres to solve realshy CC23HSA2 involving area surface measure area swface world and mathematical Apply rigid transformations to determine and explain congruence area and volume area circumference problems GU11 G1312

and volume CC23HSA3 M06C-Gll1 M08C-C3ll Verify and apply geometric theorems as they relate to geometric figures M06C-GllZ M07C-G2l1 G2312 G1211 G1212 G1213 G1214 G1215 G1321 G2211 G2212 G2221 G2222 M06C-Gll3 M07C-G212 G2223 G2224 G222S M06C-G1L4 M07C-G22l CC23HS-A4 M06C-Gli5 M07C-G222 Apply the concept ofcongruence to create geometric constructions

MQsectt_-_G~Jsect_ --- shy -- shy -- shy ---------------------middot-middot CC23HSA5

--------------------------middotCC237A2 CC238A2 Create justifications based on transformations to establish similarity ofplane figures VlSUalize and represent Understand and apply G1311 G1312 geometric figures and congruence similarity and CC23HSA6 descnbethe geometric transformations Verify and apply theorems involving similarity as they relate to plane figures relatiooships betWeen using various tools G1311 G1312 G1321 them

CC23HSA7_ _- Intentionally Blank MOSC-C111 - Apply trigonometric ratios to solve problems involving right triangles~ sect M07C-Glll M08C-Gll2 = G21ll G21120

M07C-Gll2 MOSC-G113 CC23HSA8 M07C-Gll3 M08C-Gll4 Apply geometric theorems to veruy properties ofcircless ~M07C-Gll4 GJ211 ~ G1111 G1112 G1113 G1114 G1321 G223l

G1214 CC23HS-A9

-----------------------shy ----------------------shyG2211 Extend the concept ofsimilarity to determine arc lengths and areas ofsectors ofcircles

CCi32A3--shy -shy G1111 G1112 G1l13 G1114 G2221 G2222 G2223 G2224 G2225 G2231 Understand and apply the CC23HSA10 Pythagorean Theoremto Translate beti-veen the geometric description and the equation for a conic section solve problems A221l4 AZ221l

CC23HSA11 MOSC-G211 Apply coordinate geometry to prove simple geometric theorems algebraically MOSC-G212 G2121 GZ122 G2123

Intentionally Blank Intentionally Blank MOSC-G213 CC23HSA12 G2111 Explain volume formulas and use them to solve problems G21Zl G2311 G231Z G2313

CC23llSA13 Analyze relationships between two-dimensional and three-dimensional objects

G1111 G111Z G1113 Gl114 G1211 G1212 G1213 G1214 G1215 G2321 CC23HSA14 Apply geometric concepts to model and solve real world problems

G2241 G231l G2312 GZ313

23 Geometrv The Standards ofMathematical Practices

Make sense of problems and persevere in solving them Reason abstractly and quantitatively ConstructViable arguments and critique the reasoning ofothers Model with mathematics Use appropriate tools strategically Attend to precision Look for and make use of structure Look for and evnress reUlaritv in reneated reasoniniz

Grade 6 Grade7 Grades High School Z36 237 23S Z3HS

Pennltvfvanias vublic schools shall teach challen e and sunnort evPrv student to realize his or her maximum votential and to acauire the knowledae and skills needed to

jPage15

)anuazy 2013

Pennsylvania Core Standards Mathematics

24 Measurement Data and Probabilitv The Standards ofMathematical Practices

Make sense ofproblems and persevere in solving them Reason abstractly and quantitatively Construct viable ar~ments and critique the reasoning ofothers Model with mathematics Use appropriate tools strategically Attend to precision Look for and make use ofstructure Look for and express regularity in repeated reasoning

Grade 6 246

Grade7 247

Grade3 243

High School 24HS

Pennsylvanias public schools shall teach challenge and support every student to realize his or her mt1Ximum potential and to acquire the mowedge andskills needed to

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CCZ46B1 Demonstrate an understanding of statistical vaiability by displaying analyzing and summarizing distributions

M06DmiddotSlll M06DmiddotSll2 M06D-Sll3 M06D-Sll4

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CCZ47B1 Draw inferences about populatioos based on rardom sampling concepts

M07D-S1l1 M07D-S1l2

middotcczyen7-szmiddot----middot----- shy -Draw informal comparative inferences about two populations

M07D-S211

middotcci47S3----- --- --- -shy[mrestigate cbaoce processes and develop use and evaluate probability models

CCZ48B1 Analyze andor interpret bivariate data displayed in multiple representations

MOSD-S11l MOSDmiddotS112 MOSDmiddotS113 AlZ22l

iCi4862 ----------shyUnderstand thatpatterns ofassociation can be seen in bivariate data utilizing frequencies

MOSDmiddotS121

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sect

CCZ4HSB1 Summarize represent and interpret data on a single count or measurement variable

A12212 Al2311 A12321 Al2322 Al2323

CCZ4HSB2 Summarize represent and interpret data on two categorical and quantitative variables

Al21ll Al2112 A12113 Al2121 Al2122 Al2221 A2211l AZ2311 AZ2312

CCZ4HSB3 Analyze linear models to make interpretations based on the data

Al222l A1231l Al2321 Al2322 Al2323 A22311 AZ2312

CCZ4HSB4 Recognize and evaluate random processes underlying statistical experiments

Al2331 A223Z1 A2232Z A22323

CC24HSBS Make inferences and justify conclusions based on sample surveys experiments and observational studies

Al2321 Al2322 Al2323 A22321 A22322 A22323

CCZ4J5B6 Use the concepts ofindependence and conditional probability to interpret data

AZ2321 A22322 A22323

Intentionally Blunk M07D-S31l M07D-S32l M07D-S322 M07D-S323 Al2331

lntentionany Blank CCZ4HSB7 Apply the rules of probability to compute probabilities ofcompound events in a uniform probability model

Al2331 A223Z1 A223ZZ A22323

[Page16

January 2013

Pennsylvania Core Standards Mathematics

Key Terms for this Document

Standards for Mathematical Content-These standards define what students should know and be able to do in their study of mathematics

Standards for Mathematical Practice-These standards describe the processes and proficiencies in which all students grades K-12 should engage Educators

must instill these standards of practice in their students so that they become habitual The standards for mathematical practice should be used as the vehicle to

deliver the standards of mathematical content

Standard Algorithm-A locally agreed upon method of computation which is conventionally taught for solving mathematical problems

Decimal Fraction-A fraction whose denominator is a power of ten (examples 2100 810) These fractions are commonly expressed as decimals

Unit Fraction-A rational number written as a fraction where the numerator is one and the denominator is a positive integer (example 120)

Bivariate Data-The data involves two variables and is usually represented as a scatter plot

Rule-A single operation (examples add 5 multiply by 2)

IP age 17

January 2013

Page 5: Academic Standards for Mathematics...The Co=on Core Standards in Mathematics in grades PreK-5 lay a solid foundation in whole numbers, addition, subtraction, multiplication, division,

--- ------ ---

------------------------ ------------------------ -------------------------

__________ -------------------------

Pennsylvania Core Standards Mathematics

21 Numbers and Operations The Standards ofMathematical Practices

Make sense ofproblems and persevere in solving them Reason abstractly and quantitatively Construct viable arguments and critique the reasoning ofothers Model with mathematics Use appropriate tools strategically Attend to precision Look for and make use ofstructure

GradePreK GradeK Z1PreK Z1K

Gradel Z11

GradeZ Z1Z

Look for and exnress re~laritv in repeated reasonin1

Grade3 Grade4 Z13 Z14

Grades Z15

Pennsylvanias public schools shall teach challenge andsupporteverystudent to realize his orhermaximum potential and to acquire the Jmowledge andskills needed to CCZ1PreKA1 ccz1KA1 Know number names Know number names and and the =Cunt sequence write and recite the count olt eshy

ao= middotccZipKAtbull --------~t~i=~middot--- s ccz1KAZ Count to tell the number=sect ofobjects 83

~ -----------------------middot CCZ1PreKA3 ~ Compare numbers

Apply one-to-one correspondence to count

_JflJtXlll2~t95~bj~middot- --shyccz1KA3 Apply the concept of magnitude to compare numbers and ouantities CCZ1KB1 Use place value to compose and decompose numbers within 19

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CC211B1 Extend the counting sequence to read and write numerals to represent objects

middotcc zi~isimiddot-- ----middotmiddot --- shyUse place-V3lue concepts to represent amounts of tens and ones and to compare two digit numbers

cC2Tia3middot----------middot Use place-value concepts and properties of operations to add and subtrattwithin 100

ccz1zs1 Use place-value concepts to represent amoWltS of tens and ones and to compare three digit numbers

CC21ZBZ Use place-value concepts to read write and skip count to 1000

CCZ13B1 Apply place-value understanding and properties ofoperations to perform multi-digit arithmetic

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middotccziiJij ---- --- ---- ------------------------shyUse place-value understanding and Intentionally Blankproperties ofoperations to add and subtract within 1000

CC214B1 Apply place-value concepts to show an understanding ofmulti-digit whole numbers

M04A-T1l1 M04A-Tl12 M04A-TLl3 M04A-Tll4

middotc-cziiiii---- --- --- shyUse place-value understanding and properties ofoperations to perform multi-digit arithmetic

M04A-T2ll M04A-T212 M04A-T213 191~r1

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CCZ15B1 Apply placemiddotvalue concepts to show an understanding of operations and rounding as they pertain to whole numbers and decimals

MOSA-Tlll MOSAmiddotT112 MOSA-T113 MOSA-T114 MOSAmiddotT115

middotcczis-B2middotmiddotmiddot---------shyExtend an understandiIg ofoperations with whole numbers to perform operations including decimals

MOSAmiddotTZ11 MOSA-TZlZ MOSA-TZ13

ntentional(y Blank

JPageS

)anuary2013

-------------------------------------------------------------------

Pennsylvania Core Standards Mathematics

CCZ13C1 CCZ14C1 ccz1sc1 Explore and develop an Extend the Use the understanding of unde=ndingof unde=ndingof equivalency to add and fractions as numbers fractions to show snbtract fractions

equivalence and M03A-F1ll ordering MOSA-Flll M03AmiddotF1l2 M03A-Fll3 M04A-Fltl M03A-F1l4 M04A-Fll2

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M04AmiddotF311 M04A-F3l2 M04AmiddotF313

21 Numbers and Operations

The Standards ofMathematical Practices Make sense ofproblems and persevere in solving them Reason abstractly and quantitatively Construct viable arguments and critique the reasoning ofothers Model with mathematics Use appropriate tools strategically Attend to precision Look for and make use ofstructure Look for and bull=ress reltgtuJaritv in ren eated reasonin

GradePreK GradeK Gradel GradeZ Grade3 Grade4 Z1PreK 21K 211 Z12 Z13 214

Grades Z15

Pennsylvanias public schools shall teach challenge and support every student to realize his orher maximum potentialand to acquire the knowledge and skills needed to

1Page6

January 2013

Pennsylvania Core Standards Mathematics

CCZ2lreKA1 CC22KA1 CC221A1 CCZ22A1 CC223A1 CC2Z4A1 CC22SA1 Understand addition as Extend the concepts of Representand solve Represent and solve Represent and solve Represent and solve Interpretand evaluate putting together and putting together and problems involviDg problems involving problems involving problems involving tbt numerical expressions adding to and taking apart to add and addition and subtraction addition and multiplication and four operations using order ofoperations understand subtraction subtract Within 10 Within20 subtraction Within 100 division astakingapartand M04ll-011l MOSJl011l taking from M03ll-Oll1 M04ll-0l12 MOSllmiddotOl12

M03B-OllZ M04B-Oll3 M03B-Ol2l M04B-Ol14

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subtraction division

M04Bmiddot0211 ~ M03B-OZ11 M03B-0212

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M03Bmiddot0312 M03B-03l3 M03B-0314 M03B-031S M03B-0316 M03B-0317

22 Algebraic Concepts

The Standards ofMathematical Practices Make sense ofproblems and persevere in solVingthem Reason abstractly and quantitatively Construct viable arguments and critique the reasoning of others Model with mathematics Use appropriate tools strategically Attend to precision Look for and make use ofstructure Look for and Pvnress rerulari -v in reoeated reasonini

GradePreK GradeK Gradel Grade2 Grade3 Grade4 Grades 22PreK 22K 221 Z22 223 224 225

Pennsylvanias public schools shall teach challenge andsupport every student to realize his orher maximum potentialand to acquire the knowledge andskiIfs needed to

IPage7

January 2013

23 Geometry

Pennsylvania Core Standards Mathematics

The Standards of Mathematical Practices Make sense ofproblems and persevere in solving them Reason abstractly and quantitatively Construct viable arguments and critique the reasoning ofothers Model with mathematics Use appropriate tools strategically Attend to precision Look for and make use ofstructure Look for and exuress regularitv in reueated reasonin

GradePreK 23PreK

GradeK 23l(

Grade 1 Z31

GradeZ Z3Z

Grade3 233

Grade4 Z34

Grades 235

Pennsylvanias public schools shall teach challenge andsupport everystudent to realize his orhermaximum potential and to acquire the lmowledge andskills needed to

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CCZ3PreKA1 Identify and describe shapes

middotcczerKAz-shy------Attalyze compare create and compose shapes

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CC23KA1 Identify and descnbe two- and three-dimensional shapes

-CciTKApound-----------shyAnalyze compare create and compose twomiddot and three-dimensional shapes

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CCZ31A1 Compose and distinguish between ruro- and three-shydimensional shapes based on their attrihutes

(C23ii2shy--shy------shy -shyUse the understanding of fractions to partition shapes into halves and quarters

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CC232A1 Analyze and draw two-and threeffimensional shapes having specified attnOutes

middotce2s2A2 middot----shy --shy -shyUse the understanding offractions to partition shapes into halves quarters and thirds

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CC233A1 Identifycolllpareand classifyshapes and their attributes

M03C-G111 M03C-G112

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CC234A1 Draw lines and angles and identify these in tvvo-dimensional figures

M04C-G111

-ci3-4Ai___ --shy --shy --shy-Classifytwo-dimensional figures by properties oftheir llnes and angles

M04C-G112

middotccii4-Ar----------shyRecognize symmetric shapes and draw lines of symmetry

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M04C-G113

[Pages

January2013

------------------------- ------------------------ --------------------------

Pennsylvania Core Standards Mathematics

24 Measurement Data and Probability The Standards ofMathematical Practices

Make sense of problems and persevere in solving them Reason abstractly and quantitatively Construct Viable arguments and critique the reasoning of others Model with mathematics Use appropriate tools strategically Attend to precision Look for and make use of strUcture Look for and vnress reunl~ri in reoeated reasonine-

GradePreK GradeK Gradel Grade2 Grade3 Grade4 Grades 24PreK 24K 241 242 243 Z44 24S

CC24PreKA1 Describe and compare measurable attributes oflength and weight of evecyday objects

CC24KA1 Descnbe and compare attributes oflength area weight and capacity of everyday objects

CC241A1 Order Iengtbs and measure them both indirelttly and by repeating length units

CC242A1 Measure and estimate lengths in standard units using appropriate tools

CCZ43A1 Solve problems involving measurement and estimation of temperature liqUid volume mass and length

CCZ44A1 Solve problems involving measurement and conversioos from a larger unit to a smaller unit

CCZ4SA1 Solve problems using conversions within a given measurement system

MOSD-M111

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M03D-M121 M03D-M122 M03D-M123

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middotcci4s-AZ______________

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nearest half hour using both analog and digital clocks

the nearest five minutes using both analog and digital clocks

nearest minute and solve problems by calculating time intervals

from one type of data display to another

data using appropriate scale

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make change using coins and paper currency with appropriate symbols

chaDge involving money using a combination of coins and bills

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P uJvanias public schools shaJJ teach chalenqe and surwort ev student to realize his or her maximum Dotential and to acauire the knowledae and skills needed to

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[Page9

January 2013

Pennsylvania Core Standards Mathematics

24 Measurement Data and Probabilitv The Standards ofMathematical Practices

Make sense ofproblems and persevere in solving them Reason abstractly and quantitatively Construct viable arguments and crltique the reasoning of others Model with mathematics Use appropriate tools strategically Attend to precision Look for and make use of structure Look for and exnress regularitv in repeated reasoning

GradePreK Z4K Grade K Gradel Z4Z Grade 2 243 Grade 3 244middot Grade 4 Z45 Grade 5 24PreK 241

PenTI vJvanias uublic schools shall teach challenae and sunnort evp~rstudent to realize his or her maximum Dotential and to acauire the knowledae andskills needed to CCZ4PreKA4 CCZ4KA4 CCZ41A4 CCZ4ZA4 CCZ43A4 CCZ44A4 CCZ4SA4 Classify objects and Classify objects and count Representand interpret Represent and interpret Representand interpret Representand interpret Solve problems involving count the number of objects iii each category

the number ofobjects in each category

data using tablescharts data using line plots pictUre graphs and bar

data using tally charts tables pictographs line

data irivolviog fractions using informationmiddot

computation offractions using information

graphs plots and bar graphs provided in a line plot provided in a line plot

M03DmiddotMZ11 MD4IJMZ11 MOSDmiddotMZ11 M03D-M212 M04IJM212 M03DmiddotM213

S ----------------------shy ------------------------shy ------------------------shy -----------------------shy

1D_3JlMJ~4t-bullbull_ __ bull__ CCZ43A5 -----------------------shy middotca4sAs----- --middot--middot -- shy

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Determine the area of a rectangle and apply the concept to multiplicati~n and to addition

M03D-M311

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Apply concepts ofvolume to solve problems and relate volume to multiplication and to addition

s

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laquociyeniA6-------bull -bull -- laquoci43A6middot--shy --shy --shy --shy -cc244A6____________ MOSDmiddotM31l

_Qsectl31~middot~___ -----middot-shy bull s Extend the concepts of Solve problems involTng Measure angles and use ~ addition and subtraction perimeters ofpolygons properties of adjacent ~ to problems involving

length-and distinguish between linear and area measures

angles to solve problems lntentionalb Blank

M03D-M411 M04DmiddotM311 M04DmiddotM312

IP age 10

Januazy2013

Pennsylvania Core Standards Mathematics

21 Numbers and Operations The Standards ofMathematical Practices

Make sense ofproblems and persevere in solving them Reason abstractly and quantitatively Construct viable arguments and critique the reasoning of others Model with mathematics Use appropriate tools strategically Attend to precision Look for and make use of structure Look for and eXPress regularitv in repeated reasoning

216Grade6 I 217Grade7 I 21SGradeS I I 21HSHighSchool

Pennsylvanias public schools shall teach challenge and support every student to realize his orher maximum potentialand to acquire the lmowledge andskills needed to

- CCZ16D1 CCZ17D1 I I I CCZ1lSF1 ~ Understand ratio Analyze proportional Apply and extend the properties ofexponents to solve problems with rational exponents sect concepts and use ratio relationships and use Al1111 Al1112 A1l131 A21211 A21212 A21213 A2lZ14 t vi reasoning to solve them to modcl and solve8 sect problems real-world and CCZ1HSFZ E lt mathematicalproblems Apply properties of rational and irrational numberS to solve real world or mathematical problems0 Intentionally Blartk Al1111 Al1112 All131 Al112l o1l il M06AmiddotR1l1 M07AmiddotR1l1 ~~ M06AmiddotR112 M07AmiddotR1l2 CCZllSF3= isect M06A-Rl13 M07A-R1l3 Apply quantitative reasoning to choose and interpret units and scales in formulas graphs and data ~ M06AmiddotR114 M07AmiddotR114 displayse M06A-Rl15 M07A-R11S Al1211 Al1212 Al1Z13 A12121 A12122 A2ZZ11 A22Z12 A223l1

M07A-R116 A2Z312 CC216E1 CCZ17E1 CC21SE1 Apply and extend Apply and extend 0 CCZlHSF4Distioguisb between

Use units as avray to understand problems and to guide the solution -0fmulti-step problemsprevious understandings previous understandings rational and irrational g Al1211 Al1212 Al1Z13 Al2121 A12122 A22211 A22212 of multiplication and of-Operations with numbers usiDg their sectdivision to diVide fractions to operations properties fractions by fractions with rational nUIIlbers CCZlHSFS] Choose a level of accuracy appropriate to limitations on measurement when reporting quantitiesMOSA-Nl1l a Al1211 A11Z12 Al1Z13 Al1221 Al12Z2 Al13l1 Al1312 Al1313 M06A-N111 M07A-N111 lMOSA-Nl12

Al13 21 All3 22 A2Z311 A22312 = Ei -~~~~~t~~~----------- -~t~t~t____________ _poundg ------------------------shy CCZ1HSF6 CC216E2 sect Extend the lmowiedge of arithmetic operations and apply to complex numbers sect appropriate processes to ~ Identify and choose

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M06A-N22l M06A-N222

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IP age 11

January 2013

Pennsylvania Core Standards Mathematics

21 Numbers and Operations The Standards ofMathematical Practices

Make sense ofproblems and persevere in solving them Reason abstractly and quantitatively Construct viable arguments and critique the reasoning of others Model with mathematics Use appropriate tools strategically Attend to precision Look for and make use ofstructure Look for and bullvnress reltnlaritv in reoeated reasoning

216 Grade 6 217 Grade 7 21HS High School 218 Grade 8

Pennsylvanias public schools shall teach challenge and support every studentw realize his orher maximum potential and to acquire the knowledge andskills needed W CC216E4 Apply and extend previous understandings ofnumbers to the system ofrational numbers

M06A-N311 M06A-N312 M06AmiddotN313 M06AmiddotN321 M06A-ll322 M06A-N323

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CC218E4 Estimate irrational numbers by compaing them to rational numbers

MOSAmiddotN113 MOSAmiddotN114 MOSA-N11S Al1111

[Page12

January 2013

Pennsylvania Core Standards Mathematics

22 Algebraic Concepts

The Standards ofMathematical Practices Make sense ofproblems and persevere in solvilg them Reason abstractly and quantitatively Construct viable arguments and critique the reasoning of others Model with mathematics Use appropriate tools strategically Attend to precision Look for and make use ofstructure Look for and exnress regularitvin repeated reasoning

226 Grade 6 22 7 Grade 7 228 Grade 8 22HS High School

Penn rvlvartias uublic schools shall teach challem1e and sunnort everv student to realize his orher maximum uotential and to acmrire the mowledae and skills needed to CC2Z681 CC22781 CC2ZHSD1 Apply and extend

CC2Z8B1 Apply properties of Apply concepts of radicals Interpret the structure of expressions to represent a quantity in terms of its context

Al1151 Al1152Al11S3 AZ1221 AZ1222previous understandings operations to generate and integer exponents to of arithmetic to algebraic equivalent expressions generate equivalent CC22HSD2 expressions expressions Write expressions in equivalent forms to solve problems

M07B-E111 Al11S1 Al1152 Al1153 AZ1211 AZ1Z12AZ1213 AZ1214 AZ1221 M06B-E111 MOSBmiddotE111 AZ1ZZ2 M06B-E112 MOSB-E112

CC22HSD3M06B-E113 MOSB-E113 Extend the knowledge of arithmetic operations and apply to polynomialsM06B-E114 MOSB-E114

_]1Qsect~~l ___________ Al11S1 Al1152 Al1153 AZl221 AZ1222 -~~J~_1__ ___ ---- --- --- -shy--~---------------------- CC22HSD4CCZ2682 CCZ28BZ

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~

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e ~ M06B-EZ14 CC22HSD7middotcciz6iir------------ middotec2z7ii3------ -----shy middotcc-2z~S1ii middot----- ---middot---shy Create and graph equations or inequalitiesto describe numbers or relationships Represent and analyze Model and solve real- Analyze and solve linear Al1211 Al1212 Al1213 Al1Z21 Al1222 All311 Al1312 Al1313 s x

quantitative world and mathematical equations and pairs of Al1321 All322 AZl311 A21312 AZ1313 AZ13M AZ1321 AZ132Z~ problems by using andrelationships between Simultaneous linear A22211 AZ2212 AZZ213 AZ2214

dependent and connecting numerical equations CC22HS08independent variables algebraic andor Apply inverse operations to solve equations or formulas for a given variableMOSB-E311graphical Al1211 Al1Z12 Al1213 AZ1311 AZ1312 AZ1313 AZ1314M06B-E311 representations MOSB-E31Z AZl321 AZ1322M06B-E312 MOSB-E313

M07B-E211 CC22HS09MOSB-E314 Use reasooing to solve equations and justify the solution method M07B-EZZ1 MOBB-E31S

All141 Al1211 Al121Z Al1213 Al1221 Al1222 Al1311 Al13l2 M07B-EZ22 Al1211 M07B-EZ31 Al1313 AZ1311 AZ1312 AZ1313 AZ1314 AZ1321 AZ132ZAll221 A11141 CCZ2lSD10Al1222

Represent solve and interpret equationsinequalities and systems of equationsinequalities algebraically and graphically

AllZ11 Al1212 Al1213 Al1221 Al1222 Al1311 Al1312 All313 Al1321 Al1322 A21311 AZl312 A2l313 AZ13U

JPage13

January 2013

Pennsylvania Core Standards Mathematics

ZZ Algebraic Concepts

The Standards ofMathematical Practices Make sense ofproblems and persevere in solving them Reason abstractly and quantitatively Construct viable arguments and critique the reasoning of others Model with mathematics Use appropriate tools strategically Attend to precision Look for and make use ofstructure Look for and Pxnress repoundUlaritv in repeated reasoning

Z26 Grade 6 zz 7 Grade 7 Z2S Grade 8 ZZHS High School

Penm 1lvanias public schools shall teach challenae andsunnort ev~rv student to realize his orhermaximum Potential and to acm1ire the knowledae and skills needed to cc22sc1 CCZ2HSC1 Define evaluate and Use the conceptand notation offunttionsto interpretand appiythemin terrns oftheir context compare functions Al2111 Al2112 Al2113 Al2211 Al2212 AlZ213 Al2214 AZ21ll

AZ2112 AZ2113 A22114 G2221 G2222 G2223 G2224 GZ225 MOSBmiddotF111 MOSJH112 CC22HSC2 MOSBmiddotF113 Graph and analyze functions and use their properties to make connections between the different

representationsAl1211 Al2111 Al2112 Al2113 Al2121 Al2122 Al22l1 AZ1314 AZ1321

Al2121 Al2112

AZ1322 AZ2111 AZ2112 AZ2113 AZ2114 Al2122

CCZ2lSC3middotz2samiddotmiddotmiddotmiddotmiddotmiddotmiddotmiddotmiddotmiddotmiddotmiddotmiddotmiddot Write functions or sequences that model relationships between two quantitiesUse concepts offunctions

Al1Z11 AllZ12 Al1213 Al2111 Al2112 Al2113 Al2121 Al2l22 to model relationships Al2Z13 Al2214 A21311A21312 AZ1313 AZ1314 AZ1321AZ1322betvveen quantities AZ211l AZ2112 AZ2l13 AZZ114 A22211A22212A22Z13 AZ2214

MOSBmiddotF211 cc22HSC4MOSBmiddotF212 Interpret the effects transformations have on functions and find the inverses of functionsAl1213 =0 Al2121 Al2122 AZ1313 AZ1314 AZ1321 AZ2211 AZ2212 AZ2213g =

A12111 u AZ2Z14 AZ2221uAl2122Intentionally Blank Intentionally Blank= = Al2213 CC22HSC5Al2214 G G Construct and compare linear quadratic and exponential models to solve problems

~ ~

Al2211 Al2Z12 Al2213 Al2214 A213ll A2l312 AZ1313 AZ1314 AZ2111 AZ2112 AZ2113 AZ2114 AZ22ll AZZ21Z AZ2213 AZ2214 A2222l

CC22HSC6 Interpret functions in terms of the situations they modeL

Al2121 Al2212 Al2213 Al2221 AZ1313AZZ1l1 AZZ112 AZ2113 AZ2114 AZ2213 AZ2214 AZ2221

CC22HSC7 Apply radian measure ofan angle and the unit circle to analyze the trigonometric functions

CC22HSC8 Choose trigonometric functions to model periodic phenomena and describe the properties of the graphs

CC22HSC9 Prove the Pythagorean identity and 11Se it to calculate trigonometric ratios

G1321 G211l G2112

JPage14

January 2013

Pennsylvania Core Standards Mathematics

CC236A1 CC237A1 CC238A1 CC23lSA1 Apply appropriate tools Solve real-world and Apply the concepts of Use geometric figures and their properties to represent transformations in the plane to solve real~world and mathematical problems volume ofcylinders cones G1311 G131Z mathematical problems involving angle and spheres to solve realshy CC23HSA2 involving area surface measure area swface world and mathematical Apply rigid transformations to determine and explain congruence area and volume area circumference problems GU11 G1312

and volume CC23HSA3 M06C-Gll1 M08C-C3ll Verify and apply geometric theorems as they relate to geometric figures M06C-GllZ M07C-G2l1 G2312 G1211 G1212 G1213 G1214 G1215 G1321 G2211 G2212 G2221 G2222 M06C-Gll3 M07C-G212 G2223 G2224 G222S M06C-G1L4 M07C-G22l CC23HS-A4 M06C-Gli5 M07C-G222 Apply the concept ofcongruence to create geometric constructions

MQsectt_-_G~Jsect_ --- shy -- shy -- shy ---------------------middot-middot CC23HSA5

--------------------------middotCC237A2 CC238A2 Create justifications based on transformations to establish similarity ofplane figures VlSUalize and represent Understand and apply G1311 G1312 geometric figures and congruence similarity and CC23HSA6 descnbethe geometric transformations Verify and apply theorems involving similarity as they relate to plane figures relatiooships betWeen using various tools G1311 G1312 G1321 them

CC23HSA7_ _- Intentionally Blank MOSC-C111 - Apply trigonometric ratios to solve problems involving right triangles~ sect M07C-Glll M08C-Gll2 = G21ll G21120

M07C-Gll2 MOSC-G113 CC23HSA8 M07C-Gll3 M08C-Gll4 Apply geometric theorems to veruy properties ofcircless ~M07C-Gll4 GJ211 ~ G1111 G1112 G1113 G1114 G1321 G223l

G1214 CC23HS-A9

-----------------------shy ----------------------shyG2211 Extend the concept ofsimilarity to determine arc lengths and areas ofsectors ofcircles

CCi32A3--shy -shy G1111 G1112 G1l13 G1114 G2221 G2222 G2223 G2224 G2225 G2231 Understand and apply the CC23HSA10 Pythagorean Theoremto Translate beti-veen the geometric description and the equation for a conic section solve problems A221l4 AZ221l

CC23HSA11 MOSC-G211 Apply coordinate geometry to prove simple geometric theorems algebraically MOSC-G212 G2121 GZ122 G2123

Intentionally Blank Intentionally Blank MOSC-G213 CC23HSA12 G2111 Explain volume formulas and use them to solve problems G21Zl G2311 G231Z G2313

CC23llSA13 Analyze relationships between two-dimensional and three-dimensional objects

G1111 G111Z G1113 Gl114 G1211 G1212 G1213 G1214 G1215 G2321 CC23HSA14 Apply geometric concepts to model and solve real world problems

G2241 G231l G2312 GZ313

23 Geometrv The Standards ofMathematical Practices

Make sense of problems and persevere in solving them Reason abstractly and quantitatively ConstructViable arguments and critique the reasoning ofothers Model with mathematics Use appropriate tools strategically Attend to precision Look for and make use of structure Look for and evnress reUlaritv in reneated reasoniniz

Grade 6 Grade7 Grades High School Z36 237 23S Z3HS

Pennltvfvanias vublic schools shall teach challen e and sunnort evPrv student to realize his or her maximum votential and to acauire the knowledae and skills needed to

jPage15

)anuazy 2013

Pennsylvania Core Standards Mathematics

24 Measurement Data and Probabilitv The Standards ofMathematical Practices

Make sense ofproblems and persevere in solving them Reason abstractly and quantitatively Construct viable ar~ments and critique the reasoning ofothers Model with mathematics Use appropriate tools strategically Attend to precision Look for and make use ofstructure Look for and express regularity in repeated reasoning

Grade 6 246

Grade7 247

Grade3 243

High School 24HS

Pennsylvanias public schools shall teach challenge and support every student to realize his or her mt1Ximum potential and to acquire the mowedge andskills needed to

~ E 0 0

d ilc c g ~ e

CCZ46B1 Demonstrate an understanding of statistical vaiability by displaying analyzing and summarizing distributions

M06DmiddotSlll M06DmiddotSll2 M06D-Sll3 M06D-Sll4

------------------------shy

Intentionally Blank

------------------------shy

CCZ47B1 Draw inferences about populatioos based on rardom sampling concepts

M07D-S1l1 M07D-S1l2

middotcczyen7-szmiddot----middot----- shy -Draw informal comparative inferences about two populations

M07D-S211

middotcci47S3----- --- --- -shy[mrestigate cbaoce processes and develop use and evaluate probability models

CCZ48B1 Analyze andor interpret bivariate data displayed in multiple representations

MOSD-S11l MOSDmiddotS112 MOSDmiddotS113 AlZ22l

iCi4862 ----------shyUnderstand thatpatterns ofassociation can be seen in bivariate data utilizing frequencies

MOSDmiddotS121

-------------------------shy

c a 0 0

d ltgt middotc ~ middotc g

sect

CCZ4HSB1 Summarize represent and interpret data on a single count or measurement variable

A12212 Al2311 A12321 Al2322 Al2323

CCZ4HSB2 Summarize represent and interpret data on two categorical and quantitative variables

Al21ll Al2112 A12113 Al2121 Al2122 Al2221 A2211l AZ2311 AZ2312

CCZ4HSB3 Analyze linear models to make interpretations based on the data

Al222l A1231l Al2321 Al2322 Al2323 A22311 AZ2312

CCZ4HSB4 Recognize and evaluate random processes underlying statistical experiments

Al2331 A223Z1 A2232Z A22323

CC24HSBS Make inferences and justify conclusions based on sample surveys experiments and observational studies

Al2321 Al2322 Al2323 A22321 A22322 A22323

CCZ4J5B6 Use the concepts ofindependence and conditional probability to interpret data

AZ2321 A22322 A22323

Intentionally Blunk M07D-S31l M07D-S32l M07D-S322 M07D-S323 Al2331

lntentionany Blank CCZ4HSB7 Apply the rules of probability to compute probabilities ofcompound events in a uniform probability model

Al2331 A223Z1 A223ZZ A22323

[Page16

January 2013

Pennsylvania Core Standards Mathematics

Key Terms for this Document

Standards for Mathematical Content-These standards define what students should know and be able to do in their study of mathematics

Standards for Mathematical Practice-These standards describe the processes and proficiencies in which all students grades K-12 should engage Educators

must instill these standards of practice in their students so that they become habitual The standards for mathematical practice should be used as the vehicle to

deliver the standards of mathematical content

Standard Algorithm-A locally agreed upon method of computation which is conventionally taught for solving mathematical problems

Decimal Fraction-A fraction whose denominator is a power of ten (examples 2100 810) These fractions are commonly expressed as decimals

Unit Fraction-A rational number written as a fraction where the numerator is one and the denominator is a positive integer (example 120)

Bivariate Data-The data involves two variables and is usually represented as a scatter plot

Rule-A single operation (examples add 5 multiply by 2)

IP age 17

January 2013

Page 6: Academic Standards for Mathematics...The Co=on Core Standards in Mathematics in grades PreK-5 lay a solid foundation in whole numbers, addition, subtraction, multiplication, division,

-------------------------------------------------------------------

Pennsylvania Core Standards Mathematics

CCZ13C1 CCZ14C1 ccz1sc1 Explore and develop an Extend the Use the understanding of unde=ndingof unde=ndingof equivalency to add and fractions as numbers fractions to show snbtract fractions

equivalence and M03A-F1ll ordering MOSA-Flll M03AmiddotF1l2 M03A-Fll3 M04A-Fltl M03A-F1l4 M04A-Fll2

~ M9amp~~1~b2 bullbullbull -- shy -- shy __ middotecii4cimiddot------middotmiddotmiddotmiddotshy middoteoisomiddot-----------shy= 0 Build fractions from Apply and extend ~ unit fractions by previomicros understandings applying and extending ofmultiplication and I previous division to multiply and ~ understandings of divide fractions = 0 operations on whole

- numbers MOSA-F211f lntentionany Blank Intentionally Blank Intentionally Blank Intentionally Blank Intentionally Blank MOSA-F2lZ

M04A-FZ11 MOSA-F2130 ~ M04AmiddotFZl2 MOSA-F214

~ M04A-FZ13

M04A-F214 M04A-FZ15 z M04AmiddotF216

G -----------------------shyM04AmiddotFZ17

------------------------shy~

middotcczi4c3middot-----middot--middot-shyConnect decimal notation to fractions and compare decimal fractions (base 10

Intentionally Blank denominator eg bttentionally Blank 19100)

M04AmiddotF311 M04A-F3l2 M04AmiddotF313

21 Numbers and Operations

The Standards ofMathematical Practices Make sense ofproblems and persevere in solving them Reason abstractly and quantitatively Construct viable arguments and critique the reasoning ofothers Model with mathematics Use appropriate tools strategically Attend to precision Look for and make use ofstructure Look for and bull=ress reltgtuJaritv in ren eated reasonin

GradePreK GradeK Gradel GradeZ Grade3 Grade4 Z1PreK 21K 211 Z12 Z13 214

Grades Z15

Pennsylvanias public schools shall teach challenge and support every student to realize his orher maximum potentialand to acquire the knowledge and skills needed to

1Page6

January 2013

Pennsylvania Core Standards Mathematics

CCZ2lreKA1 CC22KA1 CC221A1 CCZ22A1 CC223A1 CC2Z4A1 CC22SA1 Understand addition as Extend the concepts of Representand solve Represent and solve Represent and solve Represent and solve Interpretand evaluate putting together and putting together and problems involviDg problems involving problems involving problems involving tbt numerical expressions adding to and taking apart to add and addition and subtraction addition and multiplication and four operations using order ofoperations understand subtraction subtract Within 10 Within20 subtraction Within 100 division astakingapartand M04ll-011l MOSJl011l taking from M03ll-Oll1 M04ll-0l12 MOSllmiddotOl12

M03B-OllZ M04B-Oll3 M03B-Ol2l M04B-Ol14

bO -----------------------shy ------------------------shyM03Bmiddot0122

-----------------------shy -------------------------shy= middotccz~z1umiddot-middotmiddot----shy middotcci-ZzA2middotmiddotmiddotmiddotmiddotmiddotmiddotmiddot middot middotshy middotcc2z1iA2middotmiddotmiddotmiddotmiddotmiddotmiddot--middotmiddot-middot CCZ24A2ii Understand and apply Use mental strategies to Understand properties of Develop andor apply 5 properties of operations add and subtract Within multiplication and the number tbeozy concepts= E-lt and the relationship 20 relationship between to find factors and

betvveen addition and multiplication and multiplesmiddot Intentionally Blank Intentionally Blank Intentionally Blank

subtraction division

M04Bmiddot0211 ~ M03B-OZ11 M03B-0212

MQ~JQ~J middot-middot--middotmiddot bullbullbullbull= -----------------------shy ------------------------shy -----------------------shy ~----------------------- ----------------------shy ------------------------shy CCZ22A3 CCZ23A3

WorkWitb equal groups Demonstrate= s Intentionally Blank Intentionally Blank Intentionally Blank ofobjects to gain multiplication and Intentionally Blank Intentionally Blank ~ foundations for division fluency a

-----------------------shy ------------------------shy ------------------------shy PP112iPltCl~~l__ ___ ----shy ------------------------shy -----------------------shy ------------------------shy CCZ23A4 CC224A4 CC225A4 0 Solve problems involving Generate and analyze Analyze patterns and ~ s the four operations and patterns using one rule relationships using tlNo

identify and explain rules patterns in arithmetic M04B-0311

M04B-0312 MOSB-0211 Intentionally Blank Intentionally Blank Intentionally Blank Intentionally Blank M03Bmiddot0311 M04llmiddot0313 MOSB-0212

M03Bmiddot0312 M03B-03l3 M03B-0314 M03B-031S M03B-0316 M03B-0317

22 Algebraic Concepts

The Standards ofMathematical Practices Make sense ofproblems and persevere in solVingthem Reason abstractly and quantitatively Construct viable arguments and critique the reasoning of others Model with mathematics Use appropriate tools strategically Attend to precision Look for and make use ofstructure Look for and Pvnress rerulari -v in reoeated reasonini

GradePreK GradeK Gradel Grade2 Grade3 Grade4 Grades 22PreK 22K 221 Z22 223 224 225

Pennsylvanias public schools shall teach challenge andsupport every student to realize his orher maximum potentialand to acquire the knowledge andskiIfs needed to

IPage7

January 2013

23 Geometry

Pennsylvania Core Standards Mathematics

The Standards of Mathematical Practices Make sense ofproblems and persevere in solving them Reason abstractly and quantitatively Construct viable arguments and critique the reasoning ofothers Model with mathematics Use appropriate tools strategically Attend to precision Look for and make use ofstructure Look for and exuress regularitv in reueated reasonin

GradePreK 23PreK

GradeK 23l(

Grade 1 Z31

GradeZ Z3Z

Grade3 233

Grade4 Z34

Grades 235

Pennsylvanias public schools shall teach challenge andsupport everystudent to realize his orhermaximum potential and to acquire the lmowledge andskills needed to

f s 0

~ sect

CCZ3PreKA1 Identify and describe shapes

middotcczerKAz-shy------Attalyze compare create and compose shapes

----------------------shy

Intentionally Blank

CC23KA1 Identify and descnbe two- and three-dimensional shapes

-CciTKApound-----------shyAnalyze compare create and compose twomiddot and three-dimensional shapes

------------------------shy

lntentionally Blank

CCZ31A1 Compose and distinguish between ruro- and three-shydimensional shapes based on their attrihutes

(C23ii2shy--shy------shy -shyUse the understanding of fractions to partition shapes into halves and quarters

------------------------shy

Intentionally Blank

CC232A1 Analyze and draw two-and threeffimensional shapes having specified attnOutes

middotce2s2A2 middot----shy --shy -shyUse the understanding offractions to partition shapes into halves quarters and thirds

-----------------------shy

Intentionally Blank

CC233A1 Identifycolllpareand classifyshapes and their attributes

M03C-G111 M03C-G112

------------------------shyCC233AZ Use the understanding of fractionstopartition shapes into parts with equal areas and express the area ofeach microwt as a unit fraction ofthe whole

_J1Qg~j1~ailc___________

Intentionally Blank

CC234A1 Draw lines and angles and identify these in tvvo-dimensional figures

M04C-G111

-ci3-4Ai___ --shy --shy --shy-Classifytwo-dimensional figures by properties oftheir llnes and angles

M04C-G112

middotccii4-Ar----------shyRecognize symmetric shapes and draw lines of symmetry

CC235A1 Graph points in the first quadranton the coordinate plane and interpret these points when solving real world and mathematical problems

MOSC-G111 _1P_~f~1~--shy -------shy -shyCC23SAZ Glassey twoditnensional figures into categories based on an understanding oftheir properties

MOSC-G211

-------------------------middot

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M04C-G113

[Pages

January2013

------------------------- ------------------------ --------------------------

Pennsylvania Core Standards Mathematics

24 Measurement Data and Probability The Standards ofMathematical Practices

Make sense of problems and persevere in solving them Reason abstractly and quantitatively Construct Viable arguments and critique the reasoning of others Model with mathematics Use appropriate tools strategically Attend to precision Look for and make use of strUcture Look for and vnress reunl~ri in reoeated reasonine-

GradePreK GradeK Gradel Grade2 Grade3 Grade4 Grades 24PreK 24K 241 242 243 Z44 24S

CC24PreKA1 Describe and compare measurable attributes oflength and weight of evecyday objects

CC24KA1 Descnbe and compare attributes oflength area weight and capacity of everyday objects

CC241A1 Order Iengtbs and measure them both indirelttly and by repeating length units

CC242A1 Measure and estimate lengths in standard units using appropriate tools

CCZ43A1 Solve problems involving measurement and estimation of temperature liqUid volume mass and length

CCZ44A1 Solve problems involving measurement and conversioos from a larger unit to a smaller unit

CCZ4SA1 Solve problems using conversions within a given measurement system

MOSD-M111

-A O = =

----------------------shy ------------------------shy -ec21A2_______ --shy --shyTell and write time to the

-----------------------shyCC24ZAZ Tell and write time to

M03D-M121 M03D-M122 M03D-M123

middotccZyen3u-middot----------shyTell and write time to the

M04D-M11l M04D-M112 M04D-M113 M04D-M114middotccz4u-shy --shy --shy --shyTranslate information

middotcci4s-AZ______________

Represent and interpret

s Intentionally Blank Intentionally Blank

nearest half hour using both analog and digital clocks

the nearest five minutes using both analog and digital clocks

nearest minute and solve problems by calculating time intervals

from one type of data display to another

data using appropriate scale

~ s -----------------------middot ------------------------shy ------------------------shy

-cci42A3____________

Solve problems and

M03DmiddotMll1 M9-3olMmiddotJJ _____ ----__ CCZ43A3 Solve problems and make

M04D-MZ13

-----------------------shy

MOSD-MZ1Z

-------------------------shy

IntentJdegonally Blank Intentionally Blank Intentionally Blank

make change using coins and paper currency with appropriate symbols

chaDge involving money using a combination of coins and bills

MD3D-M13l M03D-Ml3Z

Intentionally Blank Intentionally Blank

P uJvanias public schools shaJJ teach chalenqe and surwort ev student to realize his or her maximum Dotential and to acauire the knowledae and skills needed to

-------------------------------------------------middot _119301-L~bullbullbullbullbullbullbullbullbullbullbullbullbullbullbullbullbullbullbullbullbullbullbullbullbullbullbullbull bullbullbullbullbullbullbull_

[Page9

January 2013

Pennsylvania Core Standards Mathematics

24 Measurement Data and Probabilitv The Standards ofMathematical Practices

Make sense ofproblems and persevere in solving them Reason abstractly and quantitatively Construct viable arguments and crltique the reasoning of others Model with mathematics Use appropriate tools strategically Attend to precision Look for and make use of structure Look for and exnress regularitv in repeated reasoning

GradePreK Z4K Grade K Gradel Z4Z Grade 2 243 Grade 3 244middot Grade 4 Z45 Grade 5 24PreK 241

PenTI vJvanias uublic schools shall teach challenae and sunnort evp~rstudent to realize his or her maximum Dotential and to acauire the knowledae andskills needed to CCZ4PreKA4 CCZ4KA4 CCZ41A4 CCZ4ZA4 CCZ43A4 CCZ44A4 CCZ4SA4 Classify objects and Classify objects and count Representand interpret Represent and interpret Representand interpret Representand interpret Solve problems involving count the number of objects iii each category

the number ofobjects in each category

data using tablescharts data using line plots pictUre graphs and bar

data using tally charts tables pictographs line

data irivolviog fractions using informationmiddot

computation offractions using information

graphs plots and bar graphs provided in a line plot provided in a line plot

M03DmiddotMZ11 MD4IJMZ11 MOSDmiddotMZ11 M03D-M212 M04IJM212 M03DmiddotM213

S ----------------------shy ------------------------shy ------------------------shy -----------------------shy

1D_3JlMJ~4t-bullbull_ __ bull__ CCZ43A5 -----------------------shy middotca4sAs----- --middot--middot -- shy

ilt

s

Intentionally Blank

Determine the area of a rectangle and apply the concept to multiplicati~n and to addition

M03D-M311

Intentionally Blank

Apply concepts ofvolume to solve problems and relate volume to multiplication and to addition

s

Intentionally Blank Jntentionally Blank Intentionally Blank M03DmiddotM312

laquociyeniA6-------bull -bull -- laquoci43A6middot--shy --shy --shy --shy -cc244A6____________ MOSDmiddotM31l

_Qsectl31~middot~___ -----middot-shy bull s Extend the concepts of Solve problems involTng Measure angles and use ~ addition and subtraction perimeters ofpolygons properties of adjacent ~ to problems involving

length-and distinguish between linear and area measures

angles to solve problems lntentionalb Blank

M03D-M411 M04DmiddotM311 M04DmiddotM312

IP age 10

Januazy2013

Pennsylvania Core Standards Mathematics

21 Numbers and Operations The Standards ofMathematical Practices

Make sense ofproblems and persevere in solving them Reason abstractly and quantitatively Construct viable arguments and critique the reasoning of others Model with mathematics Use appropriate tools strategically Attend to precision Look for and make use of structure Look for and eXPress regularitv in repeated reasoning

216Grade6 I 217Grade7 I 21SGradeS I I 21HSHighSchool

Pennsylvanias public schools shall teach challenge and support every student to realize his orher maximum potentialand to acquire the lmowledge andskills needed to

- CCZ16D1 CCZ17D1 I I I CCZ1lSF1 ~ Understand ratio Analyze proportional Apply and extend the properties ofexponents to solve problems with rational exponents sect concepts and use ratio relationships and use Al1111 Al1112 A1l131 A21211 A21212 A21213 A2lZ14 t vi reasoning to solve them to modcl and solve8 sect problems real-world and CCZ1HSFZ E lt mathematicalproblems Apply properties of rational and irrational numberS to solve real world or mathematical problems0 Intentionally Blartk Al1111 Al1112 All131 Al112l o1l il M06AmiddotR1l1 M07AmiddotR1l1 ~~ M06AmiddotR112 M07AmiddotR1l2 CCZllSF3= isect M06A-Rl13 M07A-R1l3 Apply quantitative reasoning to choose and interpret units and scales in formulas graphs and data ~ M06AmiddotR114 M07AmiddotR114 displayse M06A-Rl15 M07A-R11S Al1211 Al1212 Al1Z13 A12121 A12122 A2ZZ11 A22Z12 A223l1

M07A-R116 A2Z312 CC216E1 CCZ17E1 CC21SE1 Apply and extend Apply and extend 0 CCZlHSF4Distioguisb between

Use units as avray to understand problems and to guide the solution -0fmulti-step problemsprevious understandings previous understandings rational and irrational g Al1211 Al1212 Al1Z13 Al2121 A12122 A22211 A22212 of multiplication and of-Operations with numbers usiDg their sectdivision to diVide fractions to operations properties fractions by fractions with rational nUIIlbers CCZlHSFS] Choose a level of accuracy appropriate to limitations on measurement when reporting quantitiesMOSA-Nl1l a Al1211 A11Z12 Al1Z13 Al1221 Al12Z2 Al13l1 Al1312 Al1313 M06A-N111 M07A-N111 lMOSA-Nl12

Al13 21 All3 22 A2Z311 A22312 = Ei -~~~~~t~~~----------- -~t~t~t____________ _poundg ------------------------shy CCZ1HSF6 CC216E2 sect Extend the lmowiedge of arithmetic operations and apply to complex numbers sect appropriate processes to ~ Identify and choose

A2l111 A21112 A211Z1 A2l122 S compute fluently with

CC21HSF7~ multi-digit numbers Apply concepts ofcomplex numbers in polynomial identities and quadratic equations to solve problemssect J-~~~t~i1L_________ _ A2Zl11 A22112 A22l13 A22114

Intentionally Blank Intentionally Blank Develop mdor apply nUlDbertheoryconcepts to find common factors and multiples

M06A-N22l M06A-N222

----~-1h~~L-------------------------------------------------------middot-middot------~-~--------------------------------~

IP age 11

January 2013

Pennsylvania Core Standards Mathematics

21 Numbers and Operations The Standards ofMathematical Practices

Make sense ofproblems and persevere in solving them Reason abstractly and quantitatively Construct viable arguments and critique the reasoning of others Model with mathematics Use appropriate tools strategically Attend to precision Look for and make use ofstructure Look for and bullvnress reltnlaritv in reoeated reasoning

216 Grade 6 217 Grade 7 21HS High School 218 Grade 8

Pennsylvanias public schools shall teach challenge and support every studentw realize his orher maximum potential and to acquire the knowledge andskills needed W CC216E4 Apply and extend previous understandings ofnumbers to the system ofrational numbers

M06A-N311 M06A-N312 M06AmiddotN313 M06AmiddotN321 M06A-ll322 M06A-N323

Intentionally Blank

CC218E4 Estimate irrational numbers by compaing them to rational numbers

MOSAmiddotN113 MOSAmiddotN114 MOSA-N11S Al1111

[Page12

January 2013

Pennsylvania Core Standards Mathematics

22 Algebraic Concepts

The Standards ofMathematical Practices Make sense ofproblems and persevere in solvilg them Reason abstractly and quantitatively Construct viable arguments and critique the reasoning of others Model with mathematics Use appropriate tools strategically Attend to precision Look for and make use ofstructure Look for and exnress regularitvin repeated reasoning

226 Grade 6 22 7 Grade 7 228 Grade 8 22HS High School

Penn rvlvartias uublic schools shall teach challem1e and sunnort everv student to realize his orher maximum uotential and to acmrire the mowledae and skills needed to CC2Z681 CC22781 CC2ZHSD1 Apply and extend

CC2Z8B1 Apply properties of Apply concepts of radicals Interpret the structure of expressions to represent a quantity in terms of its context

Al1151 Al1152Al11S3 AZ1221 AZ1222previous understandings operations to generate and integer exponents to of arithmetic to algebraic equivalent expressions generate equivalent CC22HSD2 expressions expressions Write expressions in equivalent forms to solve problems

M07B-E111 Al11S1 Al1152 Al1153 AZ1211 AZ1Z12AZ1213 AZ1214 AZ1221 M06B-E111 MOSBmiddotE111 AZ1ZZ2 M06B-E112 MOSB-E112

CC22HSD3M06B-E113 MOSB-E113 Extend the knowledge of arithmetic operations and apply to polynomialsM06B-E114 MOSB-E114

_]1Qsect~~l ___________ Al11S1 Al1152 Al1153 AZl221 AZ1222 -~~J~_1__ ___ ---- --- --- -shy--~---------------------- CC22HSD4CCZ2682 CCZ28BZ

Understand the relationship between zeros and fac-ors of polynomials to make generalizations about Understand the process Understand the functions and their graphs of solving a one-variable connections between

AZ1ZZ1 AZ1222equation or inequality proportional relationshlps and apply it to real-worldg

~

CC22HSOSlines1 and linear equations Use polynomial identities to solve problemsand mathematical~ Intentionally Blank Al1151 Al1152 Al1153 AZ1221 AZ1ZZ2AZl311 AZl312 AZl313 problems MOSB-E211 AZ1314MOSBmiddotE212

~

MOSB-E213M06E-E211 CC22HSD6 ~

_~ M06B-EZ12 Al2122 Extend the knowledge ofrational functions to remite in equivaleztformsltg M06B-E213

B ~ Al11S1 Al1152 Al1153 AZ1311 AZ1312AZ1313 AZ1314

e ~ M06B-EZ14 CC22HSD7middotcciz6iir------------ middotec2z7ii3------ -----shy middotcc-2z~S1ii middot----- ---middot---shy Create and graph equations or inequalitiesto describe numbers or relationships Represent and analyze Model and solve real- Analyze and solve linear Al1211 Al1212 Al1213 Al1Z21 Al1222 All311 Al1312 Al1313 s x

quantitative world and mathematical equations and pairs of Al1321 All322 AZl311 A21312 AZ1313 AZ13M AZ1321 AZ132Z~ problems by using andrelationships between Simultaneous linear A22211 AZ2212 AZZ213 AZ2214

dependent and connecting numerical equations CC22HS08independent variables algebraic andor Apply inverse operations to solve equations or formulas for a given variableMOSB-E311graphical Al1211 Al1Z12 Al1213 AZ1311 AZ1312 AZ1313 AZ1314M06B-E311 representations MOSB-E31Z AZl321 AZ1322M06B-E312 MOSB-E313

M07B-E211 CC22HS09MOSB-E314 Use reasooing to solve equations and justify the solution method M07B-EZZ1 MOBB-E31S

All141 Al1211 Al121Z Al1213 Al1221 Al1222 Al1311 Al13l2 M07B-EZ22 Al1211 M07B-EZ31 Al1313 AZ1311 AZ1312 AZ1313 AZ1314 AZ1321 AZ132ZAll221 A11141 CCZ2lSD10Al1222

Represent solve and interpret equationsinequalities and systems of equationsinequalities algebraically and graphically

AllZ11 Al1212 Al1213 Al1221 Al1222 Al1311 Al1312 All313 Al1321 Al1322 A21311 AZl312 A2l313 AZ13U

JPage13

January 2013

Pennsylvania Core Standards Mathematics

ZZ Algebraic Concepts

The Standards ofMathematical Practices Make sense ofproblems and persevere in solving them Reason abstractly and quantitatively Construct viable arguments and critique the reasoning of others Model with mathematics Use appropriate tools strategically Attend to precision Look for and make use ofstructure Look for and Pxnress repoundUlaritv in repeated reasoning

Z26 Grade 6 zz 7 Grade 7 Z2S Grade 8 ZZHS High School

Penm 1lvanias public schools shall teach challenae andsunnort ev~rv student to realize his orhermaximum Potential and to acm1ire the knowledae and skills needed to cc22sc1 CCZ2HSC1 Define evaluate and Use the conceptand notation offunttionsto interpretand appiythemin terrns oftheir context compare functions Al2111 Al2112 Al2113 Al2211 Al2212 AlZ213 Al2214 AZ21ll

AZ2112 AZ2113 A22114 G2221 G2222 G2223 G2224 GZ225 MOSBmiddotF111 MOSJH112 CC22HSC2 MOSBmiddotF113 Graph and analyze functions and use their properties to make connections between the different

representationsAl1211 Al2111 Al2112 Al2113 Al2121 Al2122 Al22l1 AZ1314 AZ1321

Al2121 Al2112

AZ1322 AZ2111 AZ2112 AZ2113 AZ2114 Al2122

CCZ2lSC3middotz2samiddotmiddotmiddotmiddotmiddotmiddotmiddotmiddotmiddotmiddotmiddotmiddotmiddotmiddot Write functions or sequences that model relationships between two quantitiesUse concepts offunctions

Al1Z11 AllZ12 Al1213 Al2111 Al2112 Al2113 Al2121 Al2l22 to model relationships Al2Z13 Al2214 A21311A21312 AZ1313 AZ1314 AZ1321AZ1322betvveen quantities AZ211l AZ2112 AZ2l13 AZZ114 A22211A22212A22Z13 AZ2214

MOSBmiddotF211 cc22HSC4MOSBmiddotF212 Interpret the effects transformations have on functions and find the inverses of functionsAl1213 =0 Al2121 Al2122 AZ1313 AZ1314 AZ1321 AZ2211 AZ2212 AZ2213g =

A12111 u AZ2Z14 AZ2221uAl2122Intentionally Blank Intentionally Blank= = Al2213 CC22HSC5Al2214 G G Construct and compare linear quadratic and exponential models to solve problems

~ ~

Al2211 Al2Z12 Al2213 Al2214 A213ll A2l312 AZ1313 AZ1314 AZ2111 AZ2112 AZ2113 AZ2114 AZ22ll AZZ21Z AZ2213 AZ2214 A2222l

CC22HSC6 Interpret functions in terms of the situations they modeL

Al2121 Al2212 Al2213 Al2221 AZ1313AZZ1l1 AZZ112 AZ2113 AZ2114 AZ2213 AZ2214 AZ2221

CC22HSC7 Apply radian measure ofan angle and the unit circle to analyze the trigonometric functions

CC22HSC8 Choose trigonometric functions to model periodic phenomena and describe the properties of the graphs

CC22HSC9 Prove the Pythagorean identity and 11Se it to calculate trigonometric ratios

G1321 G211l G2112

JPage14

January 2013

Pennsylvania Core Standards Mathematics

CC236A1 CC237A1 CC238A1 CC23lSA1 Apply appropriate tools Solve real-world and Apply the concepts of Use geometric figures and their properties to represent transformations in the plane to solve real~world and mathematical problems volume ofcylinders cones G1311 G131Z mathematical problems involving angle and spheres to solve realshy CC23HSA2 involving area surface measure area swface world and mathematical Apply rigid transformations to determine and explain congruence area and volume area circumference problems GU11 G1312

and volume CC23HSA3 M06C-Gll1 M08C-C3ll Verify and apply geometric theorems as they relate to geometric figures M06C-GllZ M07C-G2l1 G2312 G1211 G1212 G1213 G1214 G1215 G1321 G2211 G2212 G2221 G2222 M06C-Gll3 M07C-G212 G2223 G2224 G222S M06C-G1L4 M07C-G22l CC23HS-A4 M06C-Gli5 M07C-G222 Apply the concept ofcongruence to create geometric constructions

MQsectt_-_G~Jsect_ --- shy -- shy -- shy ---------------------middot-middot CC23HSA5

--------------------------middotCC237A2 CC238A2 Create justifications based on transformations to establish similarity ofplane figures VlSUalize and represent Understand and apply G1311 G1312 geometric figures and congruence similarity and CC23HSA6 descnbethe geometric transformations Verify and apply theorems involving similarity as they relate to plane figures relatiooships betWeen using various tools G1311 G1312 G1321 them

CC23HSA7_ _- Intentionally Blank MOSC-C111 - Apply trigonometric ratios to solve problems involving right triangles~ sect M07C-Glll M08C-Gll2 = G21ll G21120

M07C-Gll2 MOSC-G113 CC23HSA8 M07C-Gll3 M08C-Gll4 Apply geometric theorems to veruy properties ofcircless ~M07C-Gll4 GJ211 ~ G1111 G1112 G1113 G1114 G1321 G223l

G1214 CC23HS-A9

-----------------------shy ----------------------shyG2211 Extend the concept ofsimilarity to determine arc lengths and areas ofsectors ofcircles

CCi32A3--shy -shy G1111 G1112 G1l13 G1114 G2221 G2222 G2223 G2224 G2225 G2231 Understand and apply the CC23HSA10 Pythagorean Theoremto Translate beti-veen the geometric description and the equation for a conic section solve problems A221l4 AZ221l

CC23HSA11 MOSC-G211 Apply coordinate geometry to prove simple geometric theorems algebraically MOSC-G212 G2121 GZ122 G2123

Intentionally Blank Intentionally Blank MOSC-G213 CC23HSA12 G2111 Explain volume formulas and use them to solve problems G21Zl G2311 G231Z G2313

CC23llSA13 Analyze relationships between two-dimensional and three-dimensional objects

G1111 G111Z G1113 Gl114 G1211 G1212 G1213 G1214 G1215 G2321 CC23HSA14 Apply geometric concepts to model and solve real world problems

G2241 G231l G2312 GZ313

23 Geometrv The Standards ofMathematical Practices

Make sense of problems and persevere in solving them Reason abstractly and quantitatively ConstructViable arguments and critique the reasoning ofothers Model with mathematics Use appropriate tools strategically Attend to precision Look for and make use of structure Look for and evnress reUlaritv in reneated reasoniniz

Grade 6 Grade7 Grades High School Z36 237 23S Z3HS

Pennltvfvanias vublic schools shall teach challen e and sunnort evPrv student to realize his or her maximum votential and to acauire the knowledae and skills needed to

jPage15

)anuazy 2013

Pennsylvania Core Standards Mathematics

24 Measurement Data and Probabilitv The Standards ofMathematical Practices

Make sense ofproblems and persevere in solving them Reason abstractly and quantitatively Construct viable ar~ments and critique the reasoning ofothers Model with mathematics Use appropriate tools strategically Attend to precision Look for and make use ofstructure Look for and express regularity in repeated reasoning

Grade 6 246

Grade7 247

Grade3 243

High School 24HS

Pennsylvanias public schools shall teach challenge and support every student to realize his or her mt1Ximum potential and to acquire the mowedge andskills needed to

~ E 0 0

d ilc c g ~ e

CCZ46B1 Demonstrate an understanding of statistical vaiability by displaying analyzing and summarizing distributions

M06DmiddotSlll M06DmiddotSll2 M06D-Sll3 M06D-Sll4

------------------------shy

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------------------------shy

CCZ47B1 Draw inferences about populatioos based on rardom sampling concepts

M07D-S1l1 M07D-S1l2

middotcczyen7-szmiddot----middot----- shy -Draw informal comparative inferences about two populations

M07D-S211

middotcci47S3----- --- --- -shy[mrestigate cbaoce processes and develop use and evaluate probability models

CCZ48B1 Analyze andor interpret bivariate data displayed in multiple representations

MOSD-S11l MOSDmiddotS112 MOSDmiddotS113 AlZ22l

iCi4862 ----------shyUnderstand thatpatterns ofassociation can be seen in bivariate data utilizing frequencies

MOSDmiddotS121

-------------------------shy

c a 0 0

d ltgt middotc ~ middotc g

sect

CCZ4HSB1 Summarize represent and interpret data on a single count or measurement variable

A12212 Al2311 A12321 Al2322 Al2323

CCZ4HSB2 Summarize represent and interpret data on two categorical and quantitative variables

Al21ll Al2112 A12113 Al2121 Al2122 Al2221 A2211l AZ2311 AZ2312

CCZ4HSB3 Analyze linear models to make interpretations based on the data

Al222l A1231l Al2321 Al2322 Al2323 A22311 AZ2312

CCZ4HSB4 Recognize and evaluate random processes underlying statistical experiments

Al2331 A223Z1 A2232Z A22323

CC24HSBS Make inferences and justify conclusions based on sample surveys experiments and observational studies

Al2321 Al2322 Al2323 A22321 A22322 A22323

CCZ4J5B6 Use the concepts ofindependence and conditional probability to interpret data

AZ2321 A22322 A22323

Intentionally Blunk M07D-S31l M07D-S32l M07D-S322 M07D-S323 Al2331

lntentionany Blank CCZ4HSB7 Apply the rules of probability to compute probabilities ofcompound events in a uniform probability model

Al2331 A223Z1 A223ZZ A22323

[Page16

January 2013

Pennsylvania Core Standards Mathematics

Key Terms for this Document

Standards for Mathematical Content-These standards define what students should know and be able to do in their study of mathematics

Standards for Mathematical Practice-These standards describe the processes and proficiencies in which all students grades K-12 should engage Educators

must instill these standards of practice in their students so that they become habitual The standards for mathematical practice should be used as the vehicle to

deliver the standards of mathematical content

Standard Algorithm-A locally agreed upon method of computation which is conventionally taught for solving mathematical problems

Decimal Fraction-A fraction whose denominator is a power of ten (examples 2100 810) These fractions are commonly expressed as decimals

Unit Fraction-A rational number written as a fraction where the numerator is one and the denominator is a positive integer (example 120)

Bivariate Data-The data involves two variables and is usually represented as a scatter plot

Rule-A single operation (examples add 5 multiply by 2)

IP age 17

January 2013

Page 7: Academic Standards for Mathematics...The Co=on Core Standards in Mathematics in grades PreK-5 lay a solid foundation in whole numbers, addition, subtraction, multiplication, division,

Pennsylvania Core Standards Mathematics

CCZ2lreKA1 CC22KA1 CC221A1 CCZ22A1 CC223A1 CC2Z4A1 CC22SA1 Understand addition as Extend the concepts of Representand solve Represent and solve Represent and solve Represent and solve Interpretand evaluate putting together and putting together and problems involviDg problems involving problems involving problems involving tbt numerical expressions adding to and taking apart to add and addition and subtraction addition and multiplication and four operations using order ofoperations understand subtraction subtract Within 10 Within20 subtraction Within 100 division astakingapartand M04ll-011l MOSJl011l taking from M03ll-Oll1 M04ll-0l12 MOSllmiddotOl12

M03B-OllZ M04B-Oll3 M03B-Ol2l M04B-Ol14

bO -----------------------shy ------------------------shyM03Bmiddot0122

-----------------------shy -------------------------shy= middotccz~z1umiddot-middotmiddot----shy middotcci-ZzA2middotmiddotmiddotmiddotmiddotmiddotmiddotmiddot middot middotshy middotcc2z1iA2middotmiddotmiddotmiddotmiddotmiddotmiddot--middotmiddot-middot CCZ24A2ii Understand and apply Use mental strategies to Understand properties of Develop andor apply 5 properties of operations add and subtract Within multiplication and the number tbeozy concepts= E-lt and the relationship 20 relationship between to find factors and

betvveen addition and multiplication and multiplesmiddot Intentionally Blank Intentionally Blank Intentionally Blank

subtraction division

M04Bmiddot0211 ~ M03B-OZ11 M03B-0212

MQ~JQ~J middot-middot--middotmiddot bullbullbullbull= -----------------------shy ------------------------shy -----------------------shy ~----------------------- ----------------------shy ------------------------shy CCZ22A3 CCZ23A3

WorkWitb equal groups Demonstrate= s Intentionally Blank Intentionally Blank Intentionally Blank ofobjects to gain multiplication and Intentionally Blank Intentionally Blank ~ foundations for division fluency a

-----------------------shy ------------------------shy ------------------------shy PP112iPltCl~~l__ ___ ----shy ------------------------shy -----------------------shy ------------------------shy CCZ23A4 CC224A4 CC225A4 0 Solve problems involving Generate and analyze Analyze patterns and ~ s the four operations and patterns using one rule relationships using tlNo

identify and explain rules patterns in arithmetic M04B-0311

M04B-0312 MOSB-0211 Intentionally Blank Intentionally Blank Intentionally Blank Intentionally Blank M03Bmiddot0311 M04llmiddot0313 MOSB-0212

M03Bmiddot0312 M03B-03l3 M03B-0314 M03B-031S M03B-0316 M03B-0317

22 Algebraic Concepts

The Standards ofMathematical Practices Make sense ofproblems and persevere in solVingthem Reason abstractly and quantitatively Construct viable arguments and critique the reasoning of others Model with mathematics Use appropriate tools strategically Attend to precision Look for and make use ofstructure Look for and Pvnress rerulari -v in reoeated reasonini

GradePreK GradeK Gradel Grade2 Grade3 Grade4 Grades 22PreK 22K 221 Z22 223 224 225

Pennsylvanias public schools shall teach challenge andsupport every student to realize his orher maximum potentialand to acquire the knowledge andskiIfs needed to

IPage7

January 2013

23 Geometry

Pennsylvania Core Standards Mathematics

The Standards of Mathematical Practices Make sense ofproblems and persevere in solving them Reason abstractly and quantitatively Construct viable arguments and critique the reasoning ofothers Model with mathematics Use appropriate tools strategically Attend to precision Look for and make use ofstructure Look for and exuress regularitv in reueated reasonin

GradePreK 23PreK

GradeK 23l(

Grade 1 Z31

GradeZ Z3Z

Grade3 233

Grade4 Z34

Grades 235

Pennsylvanias public schools shall teach challenge andsupport everystudent to realize his orhermaximum potential and to acquire the lmowledge andskills needed to

f s 0

~ sect

CCZ3PreKA1 Identify and describe shapes

middotcczerKAz-shy------Attalyze compare create and compose shapes

----------------------shy

Intentionally Blank

CC23KA1 Identify and descnbe two- and three-dimensional shapes

-CciTKApound-----------shyAnalyze compare create and compose twomiddot and three-dimensional shapes

------------------------shy

lntentionally Blank

CCZ31A1 Compose and distinguish between ruro- and three-shydimensional shapes based on their attrihutes

(C23ii2shy--shy------shy -shyUse the understanding of fractions to partition shapes into halves and quarters

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Intentionally Blank

CC232A1 Analyze and draw two-and threeffimensional shapes having specified attnOutes

middotce2s2A2 middot----shy --shy -shyUse the understanding offractions to partition shapes into halves quarters and thirds

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CC233A1 Identifycolllpareand classifyshapes and their attributes

M03C-G111 M03C-G112

------------------------shyCC233AZ Use the understanding of fractionstopartition shapes into parts with equal areas and express the area ofeach microwt as a unit fraction ofthe whole

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CC234A1 Draw lines and angles and identify these in tvvo-dimensional figures

M04C-G111

-ci3-4Ai___ --shy --shy --shy-Classifytwo-dimensional figures by properties oftheir llnes and angles

M04C-G112

middotccii4-Ar----------shyRecognize symmetric shapes and draw lines of symmetry

CC235A1 Graph points in the first quadranton the coordinate plane and interpret these points when solving real world and mathematical problems

MOSC-G111 _1P_~f~1~--shy -------shy -shyCC23SAZ Glassey twoditnensional figures into categories based on an understanding oftheir properties

MOSC-G211

-------------------------middot

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M04C-G113

[Pages

January2013

------------------------- ------------------------ --------------------------

Pennsylvania Core Standards Mathematics

24 Measurement Data and Probability The Standards ofMathematical Practices

Make sense of problems and persevere in solving them Reason abstractly and quantitatively Construct Viable arguments and critique the reasoning of others Model with mathematics Use appropriate tools strategically Attend to precision Look for and make use of strUcture Look for and vnress reunl~ri in reoeated reasonine-

GradePreK GradeK Gradel Grade2 Grade3 Grade4 Grades 24PreK 24K 241 242 243 Z44 24S

CC24PreKA1 Describe and compare measurable attributes oflength and weight of evecyday objects

CC24KA1 Descnbe and compare attributes oflength area weight and capacity of everyday objects

CC241A1 Order Iengtbs and measure them both indirelttly and by repeating length units

CC242A1 Measure and estimate lengths in standard units using appropriate tools

CCZ43A1 Solve problems involving measurement and estimation of temperature liqUid volume mass and length

CCZ44A1 Solve problems involving measurement and conversioos from a larger unit to a smaller unit

CCZ4SA1 Solve problems using conversions within a given measurement system

MOSD-M111

-A O = =

----------------------shy ------------------------shy -ec21A2_______ --shy --shyTell and write time to the

-----------------------shyCC24ZAZ Tell and write time to

M03D-M121 M03D-M122 M03D-M123

middotccZyen3u-middot----------shyTell and write time to the

M04D-M11l M04D-M112 M04D-M113 M04D-M114middotccz4u-shy --shy --shy --shyTranslate information

middotcci4s-AZ______________

Represent and interpret

s Intentionally Blank Intentionally Blank

nearest half hour using both analog and digital clocks

the nearest five minutes using both analog and digital clocks

nearest minute and solve problems by calculating time intervals

from one type of data display to another

data using appropriate scale

~ s -----------------------middot ------------------------shy ------------------------shy

-cci42A3____________

Solve problems and

M03DmiddotMll1 M9-3olMmiddotJJ _____ ----__ CCZ43A3 Solve problems and make

M04D-MZ13

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make change using coins and paper currency with appropriate symbols

chaDge involving money using a combination of coins and bills

MD3D-M13l M03D-Ml3Z

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P uJvanias public schools shaJJ teach chalenqe and surwort ev student to realize his or her maximum Dotential and to acauire the knowledae and skills needed to

-------------------------------------------------middot _119301-L~bullbullbullbullbullbullbullbullbullbullbullbullbullbullbullbullbullbullbullbullbullbullbullbullbullbullbullbull bullbullbullbullbullbullbull_

[Page9

January 2013

Pennsylvania Core Standards Mathematics

24 Measurement Data and Probabilitv The Standards ofMathematical Practices

Make sense ofproblems and persevere in solving them Reason abstractly and quantitatively Construct viable arguments and crltique the reasoning of others Model with mathematics Use appropriate tools strategically Attend to precision Look for and make use of structure Look for and exnress regularitv in repeated reasoning

GradePreK Z4K Grade K Gradel Z4Z Grade 2 243 Grade 3 244middot Grade 4 Z45 Grade 5 24PreK 241

PenTI vJvanias uublic schools shall teach challenae and sunnort evp~rstudent to realize his or her maximum Dotential and to acauire the knowledae andskills needed to CCZ4PreKA4 CCZ4KA4 CCZ41A4 CCZ4ZA4 CCZ43A4 CCZ44A4 CCZ4SA4 Classify objects and Classify objects and count Representand interpret Represent and interpret Representand interpret Representand interpret Solve problems involving count the number of objects iii each category

the number ofobjects in each category

data using tablescharts data using line plots pictUre graphs and bar

data using tally charts tables pictographs line

data irivolviog fractions using informationmiddot

computation offractions using information

graphs plots and bar graphs provided in a line plot provided in a line plot

M03DmiddotMZ11 MD4IJMZ11 MOSDmiddotMZ11 M03D-M212 M04IJM212 M03DmiddotM213

S ----------------------shy ------------------------shy ------------------------shy -----------------------shy

1D_3JlMJ~4t-bullbull_ __ bull__ CCZ43A5 -----------------------shy middotca4sAs----- --middot--middot -- shy

ilt

s

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Determine the area of a rectangle and apply the concept to multiplicati~n and to addition

M03D-M311

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Apply concepts ofvolume to solve problems and relate volume to multiplication and to addition

s

Intentionally Blank Jntentionally Blank Intentionally Blank M03DmiddotM312

laquociyeniA6-------bull -bull -- laquoci43A6middot--shy --shy --shy --shy -cc244A6____________ MOSDmiddotM31l

_Qsectl31~middot~___ -----middot-shy bull s Extend the concepts of Solve problems involTng Measure angles and use ~ addition and subtraction perimeters ofpolygons properties of adjacent ~ to problems involving

length-and distinguish between linear and area measures

angles to solve problems lntentionalb Blank

M03D-M411 M04DmiddotM311 M04DmiddotM312

IP age 10

Januazy2013

Pennsylvania Core Standards Mathematics

21 Numbers and Operations The Standards ofMathematical Practices

Make sense ofproblems and persevere in solving them Reason abstractly and quantitatively Construct viable arguments and critique the reasoning of others Model with mathematics Use appropriate tools strategically Attend to precision Look for and make use of structure Look for and eXPress regularitv in repeated reasoning

216Grade6 I 217Grade7 I 21SGradeS I I 21HSHighSchool

Pennsylvanias public schools shall teach challenge and support every student to realize his orher maximum potentialand to acquire the lmowledge andskills needed to

- CCZ16D1 CCZ17D1 I I I CCZ1lSF1 ~ Understand ratio Analyze proportional Apply and extend the properties ofexponents to solve problems with rational exponents sect concepts and use ratio relationships and use Al1111 Al1112 A1l131 A21211 A21212 A21213 A2lZ14 t vi reasoning to solve them to modcl and solve8 sect problems real-world and CCZ1HSFZ E lt mathematicalproblems Apply properties of rational and irrational numberS to solve real world or mathematical problems0 Intentionally Blartk Al1111 Al1112 All131 Al112l o1l il M06AmiddotR1l1 M07AmiddotR1l1 ~~ M06AmiddotR112 M07AmiddotR1l2 CCZllSF3= isect M06A-Rl13 M07A-R1l3 Apply quantitative reasoning to choose and interpret units and scales in formulas graphs and data ~ M06AmiddotR114 M07AmiddotR114 displayse M06A-Rl15 M07A-R11S Al1211 Al1212 Al1Z13 A12121 A12122 A2ZZ11 A22Z12 A223l1

M07A-R116 A2Z312 CC216E1 CCZ17E1 CC21SE1 Apply and extend Apply and extend 0 CCZlHSF4Distioguisb between

Use units as avray to understand problems and to guide the solution -0fmulti-step problemsprevious understandings previous understandings rational and irrational g Al1211 Al1212 Al1Z13 Al2121 A12122 A22211 A22212 of multiplication and of-Operations with numbers usiDg their sectdivision to diVide fractions to operations properties fractions by fractions with rational nUIIlbers CCZlHSFS] Choose a level of accuracy appropriate to limitations on measurement when reporting quantitiesMOSA-Nl1l a Al1211 A11Z12 Al1Z13 Al1221 Al12Z2 Al13l1 Al1312 Al1313 M06A-N111 M07A-N111 lMOSA-Nl12

Al13 21 All3 22 A2Z311 A22312 = Ei -~~~~~t~~~----------- -~t~t~t____________ _poundg ------------------------shy CCZ1HSF6 CC216E2 sect Extend the lmowiedge of arithmetic operations and apply to complex numbers sect appropriate processes to ~ Identify and choose

A2l111 A21112 A211Z1 A2l122 S compute fluently with

CC21HSF7~ multi-digit numbers Apply concepts ofcomplex numbers in polynomial identities and quadratic equations to solve problemssect J-~~~t~i1L_________ _ A2Zl11 A22112 A22l13 A22114

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M06A-N22l M06A-N222

----~-1h~~L-------------------------------------------------------middot-middot------~-~--------------------------------~

IP age 11

January 2013

Pennsylvania Core Standards Mathematics

21 Numbers and Operations The Standards ofMathematical Practices

Make sense ofproblems and persevere in solving them Reason abstractly and quantitatively Construct viable arguments and critique the reasoning of others Model with mathematics Use appropriate tools strategically Attend to precision Look for and make use ofstructure Look for and bullvnress reltnlaritv in reoeated reasoning

216 Grade 6 217 Grade 7 21HS High School 218 Grade 8

Pennsylvanias public schools shall teach challenge and support every studentw realize his orher maximum potential and to acquire the knowledge andskills needed W CC216E4 Apply and extend previous understandings ofnumbers to the system ofrational numbers

M06A-N311 M06A-N312 M06AmiddotN313 M06AmiddotN321 M06A-ll322 M06A-N323

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CC218E4 Estimate irrational numbers by compaing them to rational numbers

MOSAmiddotN113 MOSAmiddotN114 MOSA-N11S Al1111

[Page12

January 2013

Pennsylvania Core Standards Mathematics

22 Algebraic Concepts

The Standards ofMathematical Practices Make sense ofproblems and persevere in solvilg them Reason abstractly and quantitatively Construct viable arguments and critique the reasoning of others Model with mathematics Use appropriate tools strategically Attend to precision Look for and make use ofstructure Look for and exnress regularitvin repeated reasoning

226 Grade 6 22 7 Grade 7 228 Grade 8 22HS High School

Penn rvlvartias uublic schools shall teach challem1e and sunnort everv student to realize his orher maximum uotential and to acmrire the mowledae and skills needed to CC2Z681 CC22781 CC2ZHSD1 Apply and extend

CC2Z8B1 Apply properties of Apply concepts of radicals Interpret the structure of expressions to represent a quantity in terms of its context

Al1151 Al1152Al11S3 AZ1221 AZ1222previous understandings operations to generate and integer exponents to of arithmetic to algebraic equivalent expressions generate equivalent CC22HSD2 expressions expressions Write expressions in equivalent forms to solve problems

M07B-E111 Al11S1 Al1152 Al1153 AZ1211 AZ1Z12AZ1213 AZ1214 AZ1221 M06B-E111 MOSBmiddotE111 AZ1ZZ2 M06B-E112 MOSB-E112

CC22HSD3M06B-E113 MOSB-E113 Extend the knowledge of arithmetic operations and apply to polynomialsM06B-E114 MOSB-E114

_]1Qsect~~l ___________ Al11S1 Al1152 Al1153 AZl221 AZ1222 -~~J~_1__ ___ ---- --- --- -shy--~---------------------- CC22HSD4CCZ2682 CCZ28BZ

Understand the relationship between zeros and fac-ors of polynomials to make generalizations about Understand the process Understand the functions and their graphs of solving a one-variable connections between

AZ1ZZ1 AZ1222equation or inequality proportional relationshlps and apply it to real-worldg

~

CC22HSOSlines1 and linear equations Use polynomial identities to solve problemsand mathematical~ Intentionally Blank Al1151 Al1152 Al1153 AZ1221 AZ1ZZ2AZl311 AZl312 AZl313 problems MOSB-E211 AZ1314MOSBmiddotE212

~

MOSB-E213M06E-E211 CC22HSD6 ~

_~ M06B-EZ12 Al2122 Extend the knowledge ofrational functions to remite in equivaleztformsltg M06B-E213

B ~ Al11S1 Al1152 Al1153 AZ1311 AZ1312AZ1313 AZ1314

e ~ M06B-EZ14 CC22HSD7middotcciz6iir------------ middotec2z7ii3------ -----shy middotcc-2z~S1ii middot----- ---middot---shy Create and graph equations or inequalitiesto describe numbers or relationships Represent and analyze Model and solve real- Analyze and solve linear Al1211 Al1212 Al1213 Al1Z21 Al1222 All311 Al1312 Al1313 s x

quantitative world and mathematical equations and pairs of Al1321 All322 AZl311 A21312 AZ1313 AZ13M AZ1321 AZ132Z~ problems by using andrelationships between Simultaneous linear A22211 AZ2212 AZZ213 AZ2214

dependent and connecting numerical equations CC22HS08independent variables algebraic andor Apply inverse operations to solve equations or formulas for a given variableMOSB-E311graphical Al1211 Al1Z12 Al1213 AZ1311 AZ1312 AZ1313 AZ1314M06B-E311 representations MOSB-E31Z AZl321 AZ1322M06B-E312 MOSB-E313

M07B-E211 CC22HS09MOSB-E314 Use reasooing to solve equations and justify the solution method M07B-EZZ1 MOBB-E31S

All141 Al1211 Al121Z Al1213 Al1221 Al1222 Al1311 Al13l2 M07B-EZ22 Al1211 M07B-EZ31 Al1313 AZ1311 AZ1312 AZ1313 AZ1314 AZ1321 AZ132ZAll221 A11141 CCZ2lSD10Al1222

Represent solve and interpret equationsinequalities and systems of equationsinequalities algebraically and graphically

AllZ11 Al1212 Al1213 Al1221 Al1222 Al1311 Al1312 All313 Al1321 Al1322 A21311 AZl312 A2l313 AZ13U

JPage13

January 2013

Pennsylvania Core Standards Mathematics

ZZ Algebraic Concepts

The Standards ofMathematical Practices Make sense ofproblems and persevere in solving them Reason abstractly and quantitatively Construct viable arguments and critique the reasoning of others Model with mathematics Use appropriate tools strategically Attend to precision Look for and make use ofstructure Look for and Pxnress repoundUlaritv in repeated reasoning

Z26 Grade 6 zz 7 Grade 7 Z2S Grade 8 ZZHS High School

Penm 1lvanias public schools shall teach challenae andsunnort ev~rv student to realize his orhermaximum Potential and to acm1ire the knowledae and skills needed to cc22sc1 CCZ2HSC1 Define evaluate and Use the conceptand notation offunttionsto interpretand appiythemin terrns oftheir context compare functions Al2111 Al2112 Al2113 Al2211 Al2212 AlZ213 Al2214 AZ21ll

AZ2112 AZ2113 A22114 G2221 G2222 G2223 G2224 GZ225 MOSBmiddotF111 MOSJH112 CC22HSC2 MOSBmiddotF113 Graph and analyze functions and use their properties to make connections between the different

representationsAl1211 Al2111 Al2112 Al2113 Al2121 Al2122 Al22l1 AZ1314 AZ1321

Al2121 Al2112

AZ1322 AZ2111 AZ2112 AZ2113 AZ2114 Al2122

CCZ2lSC3middotz2samiddotmiddotmiddotmiddotmiddotmiddotmiddotmiddotmiddotmiddotmiddotmiddotmiddotmiddot Write functions or sequences that model relationships between two quantitiesUse concepts offunctions

Al1Z11 AllZ12 Al1213 Al2111 Al2112 Al2113 Al2121 Al2l22 to model relationships Al2Z13 Al2214 A21311A21312 AZ1313 AZ1314 AZ1321AZ1322betvveen quantities AZ211l AZ2112 AZ2l13 AZZ114 A22211A22212A22Z13 AZ2214

MOSBmiddotF211 cc22HSC4MOSBmiddotF212 Interpret the effects transformations have on functions and find the inverses of functionsAl1213 =0 Al2121 Al2122 AZ1313 AZ1314 AZ1321 AZ2211 AZ2212 AZ2213g =

A12111 u AZ2Z14 AZ2221uAl2122Intentionally Blank Intentionally Blank= = Al2213 CC22HSC5Al2214 G G Construct and compare linear quadratic and exponential models to solve problems

~ ~

Al2211 Al2Z12 Al2213 Al2214 A213ll A2l312 AZ1313 AZ1314 AZ2111 AZ2112 AZ2113 AZ2114 AZ22ll AZZ21Z AZ2213 AZ2214 A2222l

CC22HSC6 Interpret functions in terms of the situations they modeL

Al2121 Al2212 Al2213 Al2221 AZ1313AZZ1l1 AZZ112 AZ2113 AZ2114 AZ2213 AZ2214 AZ2221

CC22HSC7 Apply radian measure ofan angle and the unit circle to analyze the trigonometric functions

CC22HSC8 Choose trigonometric functions to model periodic phenomena and describe the properties of the graphs

CC22HSC9 Prove the Pythagorean identity and 11Se it to calculate trigonometric ratios

G1321 G211l G2112

JPage14

January 2013

Pennsylvania Core Standards Mathematics

CC236A1 CC237A1 CC238A1 CC23lSA1 Apply appropriate tools Solve real-world and Apply the concepts of Use geometric figures and their properties to represent transformations in the plane to solve real~world and mathematical problems volume ofcylinders cones G1311 G131Z mathematical problems involving angle and spheres to solve realshy CC23HSA2 involving area surface measure area swface world and mathematical Apply rigid transformations to determine and explain congruence area and volume area circumference problems GU11 G1312

and volume CC23HSA3 M06C-Gll1 M08C-C3ll Verify and apply geometric theorems as they relate to geometric figures M06C-GllZ M07C-G2l1 G2312 G1211 G1212 G1213 G1214 G1215 G1321 G2211 G2212 G2221 G2222 M06C-Gll3 M07C-G212 G2223 G2224 G222S M06C-G1L4 M07C-G22l CC23HS-A4 M06C-Gli5 M07C-G222 Apply the concept ofcongruence to create geometric constructions

MQsectt_-_G~Jsect_ --- shy -- shy -- shy ---------------------middot-middot CC23HSA5

--------------------------middotCC237A2 CC238A2 Create justifications based on transformations to establish similarity ofplane figures VlSUalize and represent Understand and apply G1311 G1312 geometric figures and congruence similarity and CC23HSA6 descnbethe geometric transformations Verify and apply theorems involving similarity as they relate to plane figures relatiooships betWeen using various tools G1311 G1312 G1321 them

CC23HSA7_ _- Intentionally Blank MOSC-C111 - Apply trigonometric ratios to solve problems involving right triangles~ sect M07C-Glll M08C-Gll2 = G21ll G21120

M07C-Gll2 MOSC-G113 CC23HSA8 M07C-Gll3 M08C-Gll4 Apply geometric theorems to veruy properties ofcircless ~M07C-Gll4 GJ211 ~ G1111 G1112 G1113 G1114 G1321 G223l

G1214 CC23HS-A9

-----------------------shy ----------------------shyG2211 Extend the concept ofsimilarity to determine arc lengths and areas ofsectors ofcircles

CCi32A3--shy -shy G1111 G1112 G1l13 G1114 G2221 G2222 G2223 G2224 G2225 G2231 Understand and apply the CC23HSA10 Pythagorean Theoremto Translate beti-veen the geometric description and the equation for a conic section solve problems A221l4 AZ221l

CC23HSA11 MOSC-G211 Apply coordinate geometry to prove simple geometric theorems algebraically MOSC-G212 G2121 GZ122 G2123

Intentionally Blank Intentionally Blank MOSC-G213 CC23HSA12 G2111 Explain volume formulas and use them to solve problems G21Zl G2311 G231Z G2313

CC23llSA13 Analyze relationships between two-dimensional and three-dimensional objects

G1111 G111Z G1113 Gl114 G1211 G1212 G1213 G1214 G1215 G2321 CC23HSA14 Apply geometric concepts to model and solve real world problems

G2241 G231l G2312 GZ313

23 Geometrv The Standards ofMathematical Practices

Make sense of problems and persevere in solving them Reason abstractly and quantitatively ConstructViable arguments and critique the reasoning ofothers Model with mathematics Use appropriate tools strategically Attend to precision Look for and make use of structure Look for and evnress reUlaritv in reneated reasoniniz

Grade 6 Grade7 Grades High School Z36 237 23S Z3HS

Pennltvfvanias vublic schools shall teach challen e and sunnort evPrv student to realize his or her maximum votential and to acauire the knowledae and skills needed to

jPage15

)anuazy 2013

Pennsylvania Core Standards Mathematics

24 Measurement Data and Probabilitv The Standards ofMathematical Practices

Make sense ofproblems and persevere in solving them Reason abstractly and quantitatively Construct viable ar~ments and critique the reasoning ofothers Model with mathematics Use appropriate tools strategically Attend to precision Look for and make use ofstructure Look for and express regularity in repeated reasoning

Grade 6 246

Grade7 247

Grade3 243

High School 24HS

Pennsylvanias public schools shall teach challenge and support every student to realize his or her mt1Ximum potential and to acquire the mowedge andskills needed to

~ E 0 0

d ilc c g ~ e

CCZ46B1 Demonstrate an understanding of statistical vaiability by displaying analyzing and summarizing distributions

M06DmiddotSlll M06DmiddotSll2 M06D-Sll3 M06D-Sll4

------------------------shy

Intentionally Blank

------------------------shy

CCZ47B1 Draw inferences about populatioos based on rardom sampling concepts

M07D-S1l1 M07D-S1l2

middotcczyen7-szmiddot----middot----- shy -Draw informal comparative inferences about two populations

M07D-S211

middotcci47S3----- --- --- -shy[mrestigate cbaoce processes and develop use and evaluate probability models

CCZ48B1 Analyze andor interpret bivariate data displayed in multiple representations

MOSD-S11l MOSDmiddotS112 MOSDmiddotS113 AlZ22l

iCi4862 ----------shyUnderstand thatpatterns ofassociation can be seen in bivariate data utilizing frequencies

MOSDmiddotS121

-------------------------shy

c a 0 0

d ltgt middotc ~ middotc g

sect

CCZ4HSB1 Summarize represent and interpret data on a single count or measurement variable

A12212 Al2311 A12321 Al2322 Al2323

CCZ4HSB2 Summarize represent and interpret data on two categorical and quantitative variables

Al21ll Al2112 A12113 Al2121 Al2122 Al2221 A2211l AZ2311 AZ2312

CCZ4HSB3 Analyze linear models to make interpretations based on the data

Al222l A1231l Al2321 Al2322 Al2323 A22311 AZ2312

CCZ4HSB4 Recognize and evaluate random processes underlying statistical experiments

Al2331 A223Z1 A2232Z A22323

CC24HSBS Make inferences and justify conclusions based on sample surveys experiments and observational studies

Al2321 Al2322 Al2323 A22321 A22322 A22323

CCZ4J5B6 Use the concepts ofindependence and conditional probability to interpret data

AZ2321 A22322 A22323

Intentionally Blunk M07D-S31l M07D-S32l M07D-S322 M07D-S323 Al2331

lntentionany Blank CCZ4HSB7 Apply the rules of probability to compute probabilities ofcompound events in a uniform probability model

Al2331 A223Z1 A223ZZ A22323

[Page16

January 2013

Pennsylvania Core Standards Mathematics

Key Terms for this Document

Standards for Mathematical Content-These standards define what students should know and be able to do in their study of mathematics

Standards for Mathematical Practice-These standards describe the processes and proficiencies in which all students grades K-12 should engage Educators

must instill these standards of practice in their students so that they become habitual The standards for mathematical practice should be used as the vehicle to

deliver the standards of mathematical content

Standard Algorithm-A locally agreed upon method of computation which is conventionally taught for solving mathematical problems

Decimal Fraction-A fraction whose denominator is a power of ten (examples 2100 810) These fractions are commonly expressed as decimals

Unit Fraction-A rational number written as a fraction where the numerator is one and the denominator is a positive integer (example 120)

Bivariate Data-The data involves two variables and is usually represented as a scatter plot

Rule-A single operation (examples add 5 multiply by 2)

IP age 17

January 2013

Page 8: Academic Standards for Mathematics...The Co=on Core Standards in Mathematics in grades PreK-5 lay a solid foundation in whole numbers, addition, subtraction, multiplication, division,

23 Geometry

Pennsylvania Core Standards Mathematics

The Standards of Mathematical Practices Make sense ofproblems and persevere in solving them Reason abstractly and quantitatively Construct viable arguments and critique the reasoning ofothers Model with mathematics Use appropriate tools strategically Attend to precision Look for and make use ofstructure Look for and exuress regularitv in reueated reasonin

GradePreK 23PreK

GradeK 23l(

Grade 1 Z31

GradeZ Z3Z

Grade3 233

Grade4 Z34

Grades 235

Pennsylvanias public schools shall teach challenge andsupport everystudent to realize his orhermaximum potential and to acquire the lmowledge andskills needed to

f s 0

~ sect

CCZ3PreKA1 Identify and describe shapes

middotcczerKAz-shy------Attalyze compare create and compose shapes

----------------------shy

Intentionally Blank

CC23KA1 Identify and descnbe two- and three-dimensional shapes

-CciTKApound-----------shyAnalyze compare create and compose twomiddot and three-dimensional shapes

------------------------shy

lntentionally Blank

CCZ31A1 Compose and distinguish between ruro- and three-shydimensional shapes based on their attrihutes

(C23ii2shy--shy------shy -shyUse the understanding of fractions to partition shapes into halves and quarters

------------------------shy

Intentionally Blank

CC232A1 Analyze and draw two-and threeffimensional shapes having specified attnOutes

middotce2s2A2 middot----shy --shy -shyUse the understanding offractions to partition shapes into halves quarters and thirds

-----------------------shy

Intentionally Blank

CC233A1 Identifycolllpareand classifyshapes and their attributes

M03C-G111 M03C-G112

------------------------shyCC233AZ Use the understanding of fractionstopartition shapes into parts with equal areas and express the area ofeach microwt as a unit fraction ofthe whole

_J1Qg~j1~ailc___________

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CC234A1 Draw lines and angles and identify these in tvvo-dimensional figures

M04C-G111

-ci3-4Ai___ --shy --shy --shy-Classifytwo-dimensional figures by properties oftheir llnes and angles

M04C-G112

middotccii4-Ar----------shyRecognize symmetric shapes and draw lines of symmetry

CC235A1 Graph points in the first quadranton the coordinate plane and interpret these points when solving real world and mathematical problems

MOSC-G111 _1P_~f~1~--shy -------shy -shyCC23SAZ Glassey twoditnensional figures into categories based on an understanding oftheir properties

MOSC-G211

-------------------------middot

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M04C-G113

[Pages

January2013

------------------------- ------------------------ --------------------------

Pennsylvania Core Standards Mathematics

24 Measurement Data and Probability The Standards ofMathematical Practices

Make sense of problems and persevere in solving them Reason abstractly and quantitatively Construct Viable arguments and critique the reasoning of others Model with mathematics Use appropriate tools strategically Attend to precision Look for and make use of strUcture Look for and vnress reunl~ri in reoeated reasonine-

GradePreK GradeK Gradel Grade2 Grade3 Grade4 Grades 24PreK 24K 241 242 243 Z44 24S

CC24PreKA1 Describe and compare measurable attributes oflength and weight of evecyday objects

CC24KA1 Descnbe and compare attributes oflength area weight and capacity of everyday objects

CC241A1 Order Iengtbs and measure them both indirelttly and by repeating length units

CC242A1 Measure and estimate lengths in standard units using appropriate tools

CCZ43A1 Solve problems involving measurement and estimation of temperature liqUid volume mass and length

CCZ44A1 Solve problems involving measurement and conversioos from a larger unit to a smaller unit

CCZ4SA1 Solve problems using conversions within a given measurement system

MOSD-M111

-A O = =

----------------------shy ------------------------shy -ec21A2_______ --shy --shyTell and write time to the

-----------------------shyCC24ZAZ Tell and write time to

M03D-M121 M03D-M122 M03D-M123

middotccZyen3u-middot----------shyTell and write time to the

M04D-M11l M04D-M112 M04D-M113 M04D-M114middotccz4u-shy --shy --shy --shyTranslate information

middotcci4s-AZ______________

Represent and interpret

s Intentionally Blank Intentionally Blank

nearest half hour using both analog and digital clocks

the nearest five minutes using both analog and digital clocks

nearest minute and solve problems by calculating time intervals

from one type of data display to another

data using appropriate scale

~ s -----------------------middot ------------------------shy ------------------------shy

-cci42A3____________

Solve problems and

M03DmiddotMll1 M9-3olMmiddotJJ _____ ----__ CCZ43A3 Solve problems and make

M04D-MZ13

-----------------------shy

MOSD-MZ1Z

-------------------------shy

IntentJdegonally Blank Intentionally Blank Intentionally Blank

make change using coins and paper currency with appropriate symbols

chaDge involving money using a combination of coins and bills

MD3D-M13l M03D-Ml3Z

Intentionally Blank Intentionally Blank

P uJvanias public schools shaJJ teach chalenqe and surwort ev student to realize his or her maximum Dotential and to acauire the knowledae and skills needed to

-------------------------------------------------middot _119301-L~bullbullbullbullbullbullbullbullbullbullbullbullbullbullbullbullbullbullbullbullbullbullbullbullbullbullbullbull bullbullbullbullbullbullbull_

[Page9

January 2013

Pennsylvania Core Standards Mathematics

24 Measurement Data and Probabilitv The Standards ofMathematical Practices

Make sense ofproblems and persevere in solving them Reason abstractly and quantitatively Construct viable arguments and crltique the reasoning of others Model with mathematics Use appropriate tools strategically Attend to precision Look for and make use of structure Look for and exnress regularitv in repeated reasoning

GradePreK Z4K Grade K Gradel Z4Z Grade 2 243 Grade 3 244middot Grade 4 Z45 Grade 5 24PreK 241

PenTI vJvanias uublic schools shall teach challenae and sunnort evp~rstudent to realize his or her maximum Dotential and to acauire the knowledae andskills needed to CCZ4PreKA4 CCZ4KA4 CCZ41A4 CCZ4ZA4 CCZ43A4 CCZ44A4 CCZ4SA4 Classify objects and Classify objects and count Representand interpret Represent and interpret Representand interpret Representand interpret Solve problems involving count the number of objects iii each category

the number ofobjects in each category

data using tablescharts data using line plots pictUre graphs and bar

data using tally charts tables pictographs line

data irivolviog fractions using informationmiddot

computation offractions using information

graphs plots and bar graphs provided in a line plot provided in a line plot

M03DmiddotMZ11 MD4IJMZ11 MOSDmiddotMZ11 M03D-M212 M04IJM212 M03DmiddotM213

S ----------------------shy ------------------------shy ------------------------shy -----------------------shy

1D_3JlMJ~4t-bullbull_ __ bull__ CCZ43A5 -----------------------shy middotca4sAs----- --middot--middot -- shy

ilt

s

Intentionally Blank

Determine the area of a rectangle and apply the concept to multiplicati~n and to addition

M03D-M311

Intentionally Blank

Apply concepts ofvolume to solve problems and relate volume to multiplication and to addition

s

Intentionally Blank Jntentionally Blank Intentionally Blank M03DmiddotM312

laquociyeniA6-------bull -bull -- laquoci43A6middot--shy --shy --shy --shy -cc244A6____________ MOSDmiddotM31l

_Qsectl31~middot~___ -----middot-shy bull s Extend the concepts of Solve problems involTng Measure angles and use ~ addition and subtraction perimeters ofpolygons properties of adjacent ~ to problems involving

length-and distinguish between linear and area measures

angles to solve problems lntentionalb Blank

M03D-M411 M04DmiddotM311 M04DmiddotM312

IP age 10

Januazy2013

Pennsylvania Core Standards Mathematics

21 Numbers and Operations The Standards ofMathematical Practices

Make sense ofproblems and persevere in solving them Reason abstractly and quantitatively Construct viable arguments and critique the reasoning of others Model with mathematics Use appropriate tools strategically Attend to precision Look for and make use of structure Look for and eXPress regularitv in repeated reasoning

216Grade6 I 217Grade7 I 21SGradeS I I 21HSHighSchool

Pennsylvanias public schools shall teach challenge and support every student to realize his orher maximum potentialand to acquire the lmowledge andskills needed to

- CCZ16D1 CCZ17D1 I I I CCZ1lSF1 ~ Understand ratio Analyze proportional Apply and extend the properties ofexponents to solve problems with rational exponents sect concepts and use ratio relationships and use Al1111 Al1112 A1l131 A21211 A21212 A21213 A2lZ14 t vi reasoning to solve them to modcl and solve8 sect problems real-world and CCZ1HSFZ E lt mathematicalproblems Apply properties of rational and irrational numberS to solve real world or mathematical problems0 Intentionally Blartk Al1111 Al1112 All131 Al112l o1l il M06AmiddotR1l1 M07AmiddotR1l1 ~~ M06AmiddotR112 M07AmiddotR1l2 CCZllSF3= isect M06A-Rl13 M07A-R1l3 Apply quantitative reasoning to choose and interpret units and scales in formulas graphs and data ~ M06AmiddotR114 M07AmiddotR114 displayse M06A-Rl15 M07A-R11S Al1211 Al1212 Al1Z13 A12121 A12122 A2ZZ11 A22Z12 A223l1

M07A-R116 A2Z312 CC216E1 CCZ17E1 CC21SE1 Apply and extend Apply and extend 0 CCZlHSF4Distioguisb between

Use units as avray to understand problems and to guide the solution -0fmulti-step problemsprevious understandings previous understandings rational and irrational g Al1211 Al1212 Al1Z13 Al2121 A12122 A22211 A22212 of multiplication and of-Operations with numbers usiDg their sectdivision to diVide fractions to operations properties fractions by fractions with rational nUIIlbers CCZlHSFS] Choose a level of accuracy appropriate to limitations on measurement when reporting quantitiesMOSA-Nl1l a Al1211 A11Z12 Al1Z13 Al1221 Al12Z2 Al13l1 Al1312 Al1313 M06A-N111 M07A-N111 lMOSA-Nl12

Al13 21 All3 22 A2Z311 A22312 = Ei -~~~~~t~~~----------- -~t~t~t____________ _poundg ------------------------shy CCZ1HSF6 CC216E2 sect Extend the lmowiedge of arithmetic operations and apply to complex numbers sect appropriate processes to ~ Identify and choose

A2l111 A21112 A211Z1 A2l122 S compute fluently with

CC21HSF7~ multi-digit numbers Apply concepts ofcomplex numbers in polynomial identities and quadratic equations to solve problemssect J-~~~t~i1L_________ _ A2Zl11 A22112 A22l13 A22114

Intentionally Blank Intentionally Blank Develop mdor apply nUlDbertheoryconcepts to find common factors and multiples

M06A-N22l M06A-N222

----~-1h~~L-------------------------------------------------------middot-middot------~-~--------------------------------~

IP age 11

January 2013

Pennsylvania Core Standards Mathematics

21 Numbers and Operations The Standards ofMathematical Practices

Make sense ofproblems and persevere in solving them Reason abstractly and quantitatively Construct viable arguments and critique the reasoning of others Model with mathematics Use appropriate tools strategically Attend to precision Look for and make use ofstructure Look for and bullvnress reltnlaritv in reoeated reasoning

216 Grade 6 217 Grade 7 21HS High School 218 Grade 8

Pennsylvanias public schools shall teach challenge and support every studentw realize his orher maximum potential and to acquire the knowledge andskills needed W CC216E4 Apply and extend previous understandings ofnumbers to the system ofrational numbers

M06A-N311 M06A-N312 M06AmiddotN313 M06AmiddotN321 M06A-ll322 M06A-N323

Intentionally Blank

CC218E4 Estimate irrational numbers by compaing them to rational numbers

MOSAmiddotN113 MOSAmiddotN114 MOSA-N11S Al1111

[Page12

January 2013

Pennsylvania Core Standards Mathematics

22 Algebraic Concepts

The Standards ofMathematical Practices Make sense ofproblems and persevere in solvilg them Reason abstractly and quantitatively Construct viable arguments and critique the reasoning of others Model with mathematics Use appropriate tools strategically Attend to precision Look for and make use ofstructure Look for and exnress regularitvin repeated reasoning

226 Grade 6 22 7 Grade 7 228 Grade 8 22HS High School

Penn rvlvartias uublic schools shall teach challem1e and sunnort everv student to realize his orher maximum uotential and to acmrire the mowledae and skills needed to CC2Z681 CC22781 CC2ZHSD1 Apply and extend

CC2Z8B1 Apply properties of Apply concepts of radicals Interpret the structure of expressions to represent a quantity in terms of its context

Al1151 Al1152Al11S3 AZ1221 AZ1222previous understandings operations to generate and integer exponents to of arithmetic to algebraic equivalent expressions generate equivalent CC22HSD2 expressions expressions Write expressions in equivalent forms to solve problems

M07B-E111 Al11S1 Al1152 Al1153 AZ1211 AZ1Z12AZ1213 AZ1214 AZ1221 M06B-E111 MOSBmiddotE111 AZ1ZZ2 M06B-E112 MOSB-E112

CC22HSD3M06B-E113 MOSB-E113 Extend the knowledge of arithmetic operations and apply to polynomialsM06B-E114 MOSB-E114

_]1Qsect~~l ___________ Al11S1 Al1152 Al1153 AZl221 AZ1222 -~~J~_1__ ___ ---- --- --- -shy--~---------------------- CC22HSD4CCZ2682 CCZ28BZ

Understand the relationship between zeros and fac-ors of polynomials to make generalizations about Understand the process Understand the functions and their graphs of solving a one-variable connections between

AZ1ZZ1 AZ1222equation or inequality proportional relationshlps and apply it to real-worldg

~

CC22HSOSlines1 and linear equations Use polynomial identities to solve problemsand mathematical~ Intentionally Blank Al1151 Al1152 Al1153 AZ1221 AZ1ZZ2AZl311 AZl312 AZl313 problems MOSB-E211 AZ1314MOSBmiddotE212

~

MOSB-E213M06E-E211 CC22HSD6 ~

_~ M06B-EZ12 Al2122 Extend the knowledge ofrational functions to remite in equivaleztformsltg M06B-E213

B ~ Al11S1 Al1152 Al1153 AZ1311 AZ1312AZ1313 AZ1314

e ~ M06B-EZ14 CC22HSD7middotcciz6iir------------ middotec2z7ii3------ -----shy middotcc-2z~S1ii middot----- ---middot---shy Create and graph equations or inequalitiesto describe numbers or relationships Represent and analyze Model and solve real- Analyze and solve linear Al1211 Al1212 Al1213 Al1Z21 Al1222 All311 Al1312 Al1313 s x

quantitative world and mathematical equations and pairs of Al1321 All322 AZl311 A21312 AZ1313 AZ13M AZ1321 AZ132Z~ problems by using andrelationships between Simultaneous linear A22211 AZ2212 AZZ213 AZ2214

dependent and connecting numerical equations CC22HS08independent variables algebraic andor Apply inverse operations to solve equations or formulas for a given variableMOSB-E311graphical Al1211 Al1Z12 Al1213 AZ1311 AZ1312 AZ1313 AZ1314M06B-E311 representations MOSB-E31Z AZl321 AZ1322M06B-E312 MOSB-E313

M07B-E211 CC22HS09MOSB-E314 Use reasooing to solve equations and justify the solution method M07B-EZZ1 MOBB-E31S

All141 Al1211 Al121Z Al1213 Al1221 Al1222 Al1311 Al13l2 M07B-EZ22 Al1211 M07B-EZ31 Al1313 AZ1311 AZ1312 AZ1313 AZ1314 AZ1321 AZ132ZAll221 A11141 CCZ2lSD10Al1222

Represent solve and interpret equationsinequalities and systems of equationsinequalities algebraically and graphically

AllZ11 Al1212 Al1213 Al1221 Al1222 Al1311 Al1312 All313 Al1321 Al1322 A21311 AZl312 A2l313 AZ13U

JPage13

January 2013

Pennsylvania Core Standards Mathematics

ZZ Algebraic Concepts

The Standards ofMathematical Practices Make sense ofproblems and persevere in solving them Reason abstractly and quantitatively Construct viable arguments and critique the reasoning of others Model with mathematics Use appropriate tools strategically Attend to precision Look for and make use ofstructure Look for and Pxnress repoundUlaritv in repeated reasoning

Z26 Grade 6 zz 7 Grade 7 Z2S Grade 8 ZZHS High School

Penm 1lvanias public schools shall teach challenae andsunnort ev~rv student to realize his orhermaximum Potential and to acm1ire the knowledae and skills needed to cc22sc1 CCZ2HSC1 Define evaluate and Use the conceptand notation offunttionsto interpretand appiythemin terrns oftheir context compare functions Al2111 Al2112 Al2113 Al2211 Al2212 AlZ213 Al2214 AZ21ll

AZ2112 AZ2113 A22114 G2221 G2222 G2223 G2224 GZ225 MOSBmiddotF111 MOSJH112 CC22HSC2 MOSBmiddotF113 Graph and analyze functions and use their properties to make connections between the different

representationsAl1211 Al2111 Al2112 Al2113 Al2121 Al2122 Al22l1 AZ1314 AZ1321

Al2121 Al2112

AZ1322 AZ2111 AZ2112 AZ2113 AZ2114 Al2122

CCZ2lSC3middotz2samiddotmiddotmiddotmiddotmiddotmiddotmiddotmiddotmiddotmiddotmiddotmiddotmiddotmiddot Write functions or sequences that model relationships between two quantitiesUse concepts offunctions

Al1Z11 AllZ12 Al1213 Al2111 Al2112 Al2113 Al2121 Al2l22 to model relationships Al2Z13 Al2214 A21311A21312 AZ1313 AZ1314 AZ1321AZ1322betvveen quantities AZ211l AZ2112 AZ2l13 AZZ114 A22211A22212A22Z13 AZ2214

MOSBmiddotF211 cc22HSC4MOSBmiddotF212 Interpret the effects transformations have on functions and find the inverses of functionsAl1213 =0 Al2121 Al2122 AZ1313 AZ1314 AZ1321 AZ2211 AZ2212 AZ2213g =

A12111 u AZ2Z14 AZ2221uAl2122Intentionally Blank Intentionally Blank= = Al2213 CC22HSC5Al2214 G G Construct and compare linear quadratic and exponential models to solve problems

~ ~

Al2211 Al2Z12 Al2213 Al2214 A213ll A2l312 AZ1313 AZ1314 AZ2111 AZ2112 AZ2113 AZ2114 AZ22ll AZZ21Z AZ2213 AZ2214 A2222l

CC22HSC6 Interpret functions in terms of the situations they modeL

Al2121 Al2212 Al2213 Al2221 AZ1313AZZ1l1 AZZ112 AZ2113 AZ2114 AZ2213 AZ2214 AZ2221

CC22HSC7 Apply radian measure ofan angle and the unit circle to analyze the trigonometric functions

CC22HSC8 Choose trigonometric functions to model periodic phenomena and describe the properties of the graphs

CC22HSC9 Prove the Pythagorean identity and 11Se it to calculate trigonometric ratios

G1321 G211l G2112

JPage14

January 2013

Pennsylvania Core Standards Mathematics

CC236A1 CC237A1 CC238A1 CC23lSA1 Apply appropriate tools Solve real-world and Apply the concepts of Use geometric figures and their properties to represent transformations in the plane to solve real~world and mathematical problems volume ofcylinders cones G1311 G131Z mathematical problems involving angle and spheres to solve realshy CC23HSA2 involving area surface measure area swface world and mathematical Apply rigid transformations to determine and explain congruence area and volume area circumference problems GU11 G1312

and volume CC23HSA3 M06C-Gll1 M08C-C3ll Verify and apply geometric theorems as they relate to geometric figures M06C-GllZ M07C-G2l1 G2312 G1211 G1212 G1213 G1214 G1215 G1321 G2211 G2212 G2221 G2222 M06C-Gll3 M07C-G212 G2223 G2224 G222S M06C-G1L4 M07C-G22l CC23HS-A4 M06C-Gli5 M07C-G222 Apply the concept ofcongruence to create geometric constructions

MQsectt_-_G~Jsect_ --- shy -- shy -- shy ---------------------middot-middot CC23HSA5

--------------------------middotCC237A2 CC238A2 Create justifications based on transformations to establish similarity ofplane figures VlSUalize and represent Understand and apply G1311 G1312 geometric figures and congruence similarity and CC23HSA6 descnbethe geometric transformations Verify and apply theorems involving similarity as they relate to plane figures relatiooships betWeen using various tools G1311 G1312 G1321 them

CC23HSA7_ _- Intentionally Blank MOSC-C111 - Apply trigonometric ratios to solve problems involving right triangles~ sect M07C-Glll M08C-Gll2 = G21ll G21120

M07C-Gll2 MOSC-G113 CC23HSA8 M07C-Gll3 M08C-Gll4 Apply geometric theorems to veruy properties ofcircless ~M07C-Gll4 GJ211 ~ G1111 G1112 G1113 G1114 G1321 G223l

G1214 CC23HS-A9

-----------------------shy ----------------------shyG2211 Extend the concept ofsimilarity to determine arc lengths and areas ofsectors ofcircles

CCi32A3--shy -shy G1111 G1112 G1l13 G1114 G2221 G2222 G2223 G2224 G2225 G2231 Understand and apply the CC23HSA10 Pythagorean Theoremto Translate beti-veen the geometric description and the equation for a conic section solve problems A221l4 AZ221l

CC23HSA11 MOSC-G211 Apply coordinate geometry to prove simple geometric theorems algebraically MOSC-G212 G2121 GZ122 G2123

Intentionally Blank Intentionally Blank MOSC-G213 CC23HSA12 G2111 Explain volume formulas and use them to solve problems G21Zl G2311 G231Z G2313

CC23llSA13 Analyze relationships between two-dimensional and three-dimensional objects

G1111 G111Z G1113 Gl114 G1211 G1212 G1213 G1214 G1215 G2321 CC23HSA14 Apply geometric concepts to model and solve real world problems

G2241 G231l G2312 GZ313

23 Geometrv The Standards ofMathematical Practices

Make sense of problems and persevere in solving them Reason abstractly and quantitatively ConstructViable arguments and critique the reasoning ofothers Model with mathematics Use appropriate tools strategically Attend to precision Look for and make use of structure Look for and evnress reUlaritv in reneated reasoniniz

Grade 6 Grade7 Grades High School Z36 237 23S Z3HS

Pennltvfvanias vublic schools shall teach challen e and sunnort evPrv student to realize his or her maximum votential and to acauire the knowledae and skills needed to

jPage15

)anuazy 2013

Pennsylvania Core Standards Mathematics

24 Measurement Data and Probabilitv The Standards ofMathematical Practices

Make sense ofproblems and persevere in solving them Reason abstractly and quantitatively Construct viable ar~ments and critique the reasoning ofothers Model with mathematics Use appropriate tools strategically Attend to precision Look for and make use ofstructure Look for and express regularity in repeated reasoning

Grade 6 246

Grade7 247

Grade3 243

High School 24HS

Pennsylvanias public schools shall teach challenge and support every student to realize his or her mt1Ximum potential and to acquire the mowedge andskills needed to

~ E 0 0

d ilc c g ~ e

CCZ46B1 Demonstrate an understanding of statistical vaiability by displaying analyzing and summarizing distributions

M06DmiddotSlll M06DmiddotSll2 M06D-Sll3 M06D-Sll4

------------------------shy

Intentionally Blank

------------------------shy

CCZ47B1 Draw inferences about populatioos based on rardom sampling concepts

M07D-S1l1 M07D-S1l2

middotcczyen7-szmiddot----middot----- shy -Draw informal comparative inferences about two populations

M07D-S211

middotcci47S3----- --- --- -shy[mrestigate cbaoce processes and develop use and evaluate probability models

CCZ48B1 Analyze andor interpret bivariate data displayed in multiple representations

MOSD-S11l MOSDmiddotS112 MOSDmiddotS113 AlZ22l

iCi4862 ----------shyUnderstand thatpatterns ofassociation can be seen in bivariate data utilizing frequencies

MOSDmiddotS121

-------------------------shy

c a 0 0

d ltgt middotc ~ middotc g

sect

CCZ4HSB1 Summarize represent and interpret data on a single count or measurement variable

A12212 Al2311 A12321 Al2322 Al2323

CCZ4HSB2 Summarize represent and interpret data on two categorical and quantitative variables

Al21ll Al2112 A12113 Al2121 Al2122 Al2221 A2211l AZ2311 AZ2312

CCZ4HSB3 Analyze linear models to make interpretations based on the data

Al222l A1231l Al2321 Al2322 Al2323 A22311 AZ2312

CCZ4HSB4 Recognize and evaluate random processes underlying statistical experiments

Al2331 A223Z1 A2232Z A22323

CC24HSBS Make inferences and justify conclusions based on sample surveys experiments and observational studies

Al2321 Al2322 Al2323 A22321 A22322 A22323

CCZ4J5B6 Use the concepts ofindependence and conditional probability to interpret data

AZ2321 A22322 A22323

Intentionally Blunk M07D-S31l M07D-S32l M07D-S322 M07D-S323 Al2331

lntentionany Blank CCZ4HSB7 Apply the rules of probability to compute probabilities ofcompound events in a uniform probability model

Al2331 A223Z1 A223ZZ A22323

[Page16

January 2013

Pennsylvania Core Standards Mathematics

Key Terms for this Document

Standards for Mathematical Content-These standards define what students should know and be able to do in their study of mathematics

Standards for Mathematical Practice-These standards describe the processes and proficiencies in which all students grades K-12 should engage Educators

must instill these standards of practice in their students so that they become habitual The standards for mathematical practice should be used as the vehicle to

deliver the standards of mathematical content

Standard Algorithm-A locally agreed upon method of computation which is conventionally taught for solving mathematical problems

Decimal Fraction-A fraction whose denominator is a power of ten (examples 2100 810) These fractions are commonly expressed as decimals

Unit Fraction-A rational number written as a fraction where the numerator is one and the denominator is a positive integer (example 120)

Bivariate Data-The data involves two variables and is usually represented as a scatter plot

Rule-A single operation (examples add 5 multiply by 2)

IP age 17

January 2013

Page 9: Academic Standards for Mathematics...The Co=on Core Standards in Mathematics in grades PreK-5 lay a solid foundation in whole numbers, addition, subtraction, multiplication, division,

------------------------- ------------------------ --------------------------

Pennsylvania Core Standards Mathematics

24 Measurement Data and Probability The Standards ofMathematical Practices

Make sense of problems and persevere in solving them Reason abstractly and quantitatively Construct Viable arguments and critique the reasoning of others Model with mathematics Use appropriate tools strategically Attend to precision Look for and make use of strUcture Look for and vnress reunl~ri in reoeated reasonine-

GradePreK GradeK Gradel Grade2 Grade3 Grade4 Grades 24PreK 24K 241 242 243 Z44 24S

CC24PreKA1 Describe and compare measurable attributes oflength and weight of evecyday objects

CC24KA1 Descnbe and compare attributes oflength area weight and capacity of everyday objects

CC241A1 Order Iengtbs and measure them both indirelttly and by repeating length units

CC242A1 Measure and estimate lengths in standard units using appropriate tools

CCZ43A1 Solve problems involving measurement and estimation of temperature liqUid volume mass and length

CCZ44A1 Solve problems involving measurement and conversioos from a larger unit to a smaller unit

CCZ4SA1 Solve problems using conversions within a given measurement system

MOSD-M111

-A O = =

----------------------shy ------------------------shy -ec21A2_______ --shy --shyTell and write time to the

-----------------------shyCC24ZAZ Tell and write time to

M03D-M121 M03D-M122 M03D-M123

middotccZyen3u-middot----------shyTell and write time to the

M04D-M11l M04D-M112 M04D-M113 M04D-M114middotccz4u-shy --shy --shy --shyTranslate information

middotcci4s-AZ______________

Represent and interpret

s Intentionally Blank Intentionally Blank

nearest half hour using both analog and digital clocks

the nearest five minutes using both analog and digital clocks

nearest minute and solve problems by calculating time intervals

from one type of data display to another

data using appropriate scale

~ s -----------------------middot ------------------------shy ------------------------shy

-cci42A3____________

Solve problems and

M03DmiddotMll1 M9-3olMmiddotJJ _____ ----__ CCZ43A3 Solve problems and make

M04D-MZ13

-----------------------shy

MOSD-MZ1Z

-------------------------shy

IntentJdegonally Blank Intentionally Blank Intentionally Blank

make change using coins and paper currency with appropriate symbols

chaDge involving money using a combination of coins and bills

MD3D-M13l M03D-Ml3Z

Intentionally Blank Intentionally Blank

P uJvanias public schools shaJJ teach chalenqe and surwort ev student to realize his or her maximum Dotential and to acauire the knowledae and skills needed to

-------------------------------------------------middot _119301-L~bullbullbullbullbullbullbullbullbullbullbullbullbullbullbullbullbullbullbullbullbullbullbullbullbullbullbullbull bullbullbullbullbullbullbull_

[Page9

January 2013

Pennsylvania Core Standards Mathematics

24 Measurement Data and Probabilitv The Standards ofMathematical Practices

Make sense ofproblems and persevere in solving them Reason abstractly and quantitatively Construct viable arguments and crltique the reasoning of others Model with mathematics Use appropriate tools strategically Attend to precision Look for and make use of structure Look for and exnress regularitv in repeated reasoning

GradePreK Z4K Grade K Gradel Z4Z Grade 2 243 Grade 3 244middot Grade 4 Z45 Grade 5 24PreK 241

PenTI vJvanias uublic schools shall teach challenae and sunnort evp~rstudent to realize his or her maximum Dotential and to acauire the knowledae andskills needed to CCZ4PreKA4 CCZ4KA4 CCZ41A4 CCZ4ZA4 CCZ43A4 CCZ44A4 CCZ4SA4 Classify objects and Classify objects and count Representand interpret Represent and interpret Representand interpret Representand interpret Solve problems involving count the number of objects iii each category

the number ofobjects in each category

data using tablescharts data using line plots pictUre graphs and bar

data using tally charts tables pictographs line

data irivolviog fractions using informationmiddot

computation offractions using information

graphs plots and bar graphs provided in a line plot provided in a line plot

M03DmiddotMZ11 MD4IJMZ11 MOSDmiddotMZ11 M03D-M212 M04IJM212 M03DmiddotM213

S ----------------------shy ------------------------shy ------------------------shy -----------------------shy

1D_3JlMJ~4t-bullbull_ __ bull__ CCZ43A5 -----------------------shy middotca4sAs----- --middot--middot -- shy

ilt

s

Intentionally Blank

Determine the area of a rectangle and apply the concept to multiplicati~n and to addition

M03D-M311

Intentionally Blank

Apply concepts ofvolume to solve problems and relate volume to multiplication and to addition

s

Intentionally Blank Jntentionally Blank Intentionally Blank M03DmiddotM312

laquociyeniA6-------bull -bull -- laquoci43A6middot--shy --shy --shy --shy -cc244A6____________ MOSDmiddotM31l

_Qsectl31~middot~___ -----middot-shy bull s Extend the concepts of Solve problems involTng Measure angles and use ~ addition and subtraction perimeters ofpolygons properties of adjacent ~ to problems involving

length-and distinguish between linear and area measures

angles to solve problems lntentionalb Blank

M03D-M411 M04DmiddotM311 M04DmiddotM312

IP age 10

Januazy2013

Pennsylvania Core Standards Mathematics

21 Numbers and Operations The Standards ofMathematical Practices

Make sense ofproblems and persevere in solving them Reason abstractly and quantitatively Construct viable arguments and critique the reasoning of others Model with mathematics Use appropriate tools strategically Attend to precision Look for and make use of structure Look for and eXPress regularitv in repeated reasoning

216Grade6 I 217Grade7 I 21SGradeS I I 21HSHighSchool

Pennsylvanias public schools shall teach challenge and support every student to realize his orher maximum potentialand to acquire the lmowledge andskills needed to

- CCZ16D1 CCZ17D1 I I I CCZ1lSF1 ~ Understand ratio Analyze proportional Apply and extend the properties ofexponents to solve problems with rational exponents sect concepts and use ratio relationships and use Al1111 Al1112 A1l131 A21211 A21212 A21213 A2lZ14 t vi reasoning to solve them to modcl and solve8 sect problems real-world and CCZ1HSFZ E lt mathematicalproblems Apply properties of rational and irrational numberS to solve real world or mathematical problems0 Intentionally Blartk Al1111 Al1112 All131 Al112l o1l il M06AmiddotR1l1 M07AmiddotR1l1 ~~ M06AmiddotR112 M07AmiddotR1l2 CCZllSF3= isect M06A-Rl13 M07A-R1l3 Apply quantitative reasoning to choose and interpret units and scales in formulas graphs and data ~ M06AmiddotR114 M07AmiddotR114 displayse M06A-Rl15 M07A-R11S Al1211 Al1212 Al1Z13 A12121 A12122 A2ZZ11 A22Z12 A223l1

M07A-R116 A2Z312 CC216E1 CCZ17E1 CC21SE1 Apply and extend Apply and extend 0 CCZlHSF4Distioguisb between

Use units as avray to understand problems and to guide the solution -0fmulti-step problemsprevious understandings previous understandings rational and irrational g Al1211 Al1212 Al1Z13 Al2121 A12122 A22211 A22212 of multiplication and of-Operations with numbers usiDg their sectdivision to diVide fractions to operations properties fractions by fractions with rational nUIIlbers CCZlHSFS] Choose a level of accuracy appropriate to limitations on measurement when reporting quantitiesMOSA-Nl1l a Al1211 A11Z12 Al1Z13 Al1221 Al12Z2 Al13l1 Al1312 Al1313 M06A-N111 M07A-N111 lMOSA-Nl12

Al13 21 All3 22 A2Z311 A22312 = Ei -~~~~~t~~~----------- -~t~t~t____________ _poundg ------------------------shy CCZ1HSF6 CC216E2 sect Extend the lmowiedge of arithmetic operations and apply to complex numbers sect appropriate processes to ~ Identify and choose

A2l111 A21112 A211Z1 A2l122 S compute fluently with

CC21HSF7~ multi-digit numbers Apply concepts ofcomplex numbers in polynomial identities and quadratic equations to solve problemssect J-~~~t~i1L_________ _ A2Zl11 A22112 A22l13 A22114

Intentionally Blank Intentionally Blank Develop mdor apply nUlDbertheoryconcepts to find common factors and multiples

M06A-N22l M06A-N222

----~-1h~~L-------------------------------------------------------middot-middot------~-~--------------------------------~

IP age 11

January 2013

Pennsylvania Core Standards Mathematics

21 Numbers and Operations The Standards ofMathematical Practices

Make sense ofproblems and persevere in solving them Reason abstractly and quantitatively Construct viable arguments and critique the reasoning of others Model with mathematics Use appropriate tools strategically Attend to precision Look for and make use ofstructure Look for and bullvnress reltnlaritv in reoeated reasoning

216 Grade 6 217 Grade 7 21HS High School 218 Grade 8

Pennsylvanias public schools shall teach challenge and support every studentw realize his orher maximum potential and to acquire the knowledge andskills needed W CC216E4 Apply and extend previous understandings ofnumbers to the system ofrational numbers

M06A-N311 M06A-N312 M06AmiddotN313 M06AmiddotN321 M06A-ll322 M06A-N323

Intentionally Blank

CC218E4 Estimate irrational numbers by compaing them to rational numbers

MOSAmiddotN113 MOSAmiddotN114 MOSA-N11S Al1111

[Page12

January 2013

Pennsylvania Core Standards Mathematics

22 Algebraic Concepts

The Standards ofMathematical Practices Make sense ofproblems and persevere in solvilg them Reason abstractly and quantitatively Construct viable arguments and critique the reasoning of others Model with mathematics Use appropriate tools strategically Attend to precision Look for and make use ofstructure Look for and exnress regularitvin repeated reasoning

226 Grade 6 22 7 Grade 7 228 Grade 8 22HS High School

Penn rvlvartias uublic schools shall teach challem1e and sunnort everv student to realize his orher maximum uotential and to acmrire the mowledae and skills needed to CC2Z681 CC22781 CC2ZHSD1 Apply and extend

CC2Z8B1 Apply properties of Apply concepts of radicals Interpret the structure of expressions to represent a quantity in terms of its context

Al1151 Al1152Al11S3 AZ1221 AZ1222previous understandings operations to generate and integer exponents to of arithmetic to algebraic equivalent expressions generate equivalent CC22HSD2 expressions expressions Write expressions in equivalent forms to solve problems

M07B-E111 Al11S1 Al1152 Al1153 AZ1211 AZ1Z12AZ1213 AZ1214 AZ1221 M06B-E111 MOSBmiddotE111 AZ1ZZ2 M06B-E112 MOSB-E112

CC22HSD3M06B-E113 MOSB-E113 Extend the knowledge of arithmetic operations and apply to polynomialsM06B-E114 MOSB-E114

_]1Qsect~~l ___________ Al11S1 Al1152 Al1153 AZl221 AZ1222 -~~J~_1__ ___ ---- --- --- -shy--~---------------------- CC22HSD4CCZ2682 CCZ28BZ

Understand the relationship between zeros and fac-ors of polynomials to make generalizations about Understand the process Understand the functions and their graphs of solving a one-variable connections between

AZ1ZZ1 AZ1222equation or inequality proportional relationshlps and apply it to real-worldg

~

CC22HSOSlines1 and linear equations Use polynomial identities to solve problemsand mathematical~ Intentionally Blank Al1151 Al1152 Al1153 AZ1221 AZ1ZZ2AZl311 AZl312 AZl313 problems MOSB-E211 AZ1314MOSBmiddotE212

~

MOSB-E213M06E-E211 CC22HSD6 ~

_~ M06B-EZ12 Al2122 Extend the knowledge ofrational functions to remite in equivaleztformsltg M06B-E213

B ~ Al11S1 Al1152 Al1153 AZ1311 AZ1312AZ1313 AZ1314

e ~ M06B-EZ14 CC22HSD7middotcciz6iir------------ middotec2z7ii3------ -----shy middotcc-2z~S1ii middot----- ---middot---shy Create and graph equations or inequalitiesto describe numbers or relationships Represent and analyze Model and solve real- Analyze and solve linear Al1211 Al1212 Al1213 Al1Z21 Al1222 All311 Al1312 Al1313 s x

quantitative world and mathematical equations and pairs of Al1321 All322 AZl311 A21312 AZ1313 AZ13M AZ1321 AZ132Z~ problems by using andrelationships between Simultaneous linear A22211 AZ2212 AZZ213 AZ2214

dependent and connecting numerical equations CC22HS08independent variables algebraic andor Apply inverse operations to solve equations or formulas for a given variableMOSB-E311graphical Al1211 Al1Z12 Al1213 AZ1311 AZ1312 AZ1313 AZ1314M06B-E311 representations MOSB-E31Z AZl321 AZ1322M06B-E312 MOSB-E313

M07B-E211 CC22HS09MOSB-E314 Use reasooing to solve equations and justify the solution method M07B-EZZ1 MOBB-E31S

All141 Al1211 Al121Z Al1213 Al1221 Al1222 Al1311 Al13l2 M07B-EZ22 Al1211 M07B-EZ31 Al1313 AZ1311 AZ1312 AZ1313 AZ1314 AZ1321 AZ132ZAll221 A11141 CCZ2lSD10Al1222

Represent solve and interpret equationsinequalities and systems of equationsinequalities algebraically and graphically

AllZ11 Al1212 Al1213 Al1221 Al1222 Al1311 Al1312 All313 Al1321 Al1322 A21311 AZl312 A2l313 AZ13U

JPage13

January 2013

Pennsylvania Core Standards Mathematics

ZZ Algebraic Concepts

The Standards ofMathematical Practices Make sense ofproblems and persevere in solving them Reason abstractly and quantitatively Construct viable arguments and critique the reasoning of others Model with mathematics Use appropriate tools strategically Attend to precision Look for and make use ofstructure Look for and Pxnress repoundUlaritv in repeated reasoning

Z26 Grade 6 zz 7 Grade 7 Z2S Grade 8 ZZHS High School

Penm 1lvanias public schools shall teach challenae andsunnort ev~rv student to realize his orhermaximum Potential and to acm1ire the knowledae and skills needed to cc22sc1 CCZ2HSC1 Define evaluate and Use the conceptand notation offunttionsto interpretand appiythemin terrns oftheir context compare functions Al2111 Al2112 Al2113 Al2211 Al2212 AlZ213 Al2214 AZ21ll

AZ2112 AZ2113 A22114 G2221 G2222 G2223 G2224 GZ225 MOSBmiddotF111 MOSJH112 CC22HSC2 MOSBmiddotF113 Graph and analyze functions and use their properties to make connections between the different

representationsAl1211 Al2111 Al2112 Al2113 Al2121 Al2122 Al22l1 AZ1314 AZ1321

Al2121 Al2112

AZ1322 AZ2111 AZ2112 AZ2113 AZ2114 Al2122

CCZ2lSC3middotz2samiddotmiddotmiddotmiddotmiddotmiddotmiddotmiddotmiddotmiddotmiddotmiddotmiddotmiddot Write functions or sequences that model relationships between two quantitiesUse concepts offunctions

Al1Z11 AllZ12 Al1213 Al2111 Al2112 Al2113 Al2121 Al2l22 to model relationships Al2Z13 Al2214 A21311A21312 AZ1313 AZ1314 AZ1321AZ1322betvveen quantities AZ211l AZ2112 AZ2l13 AZZ114 A22211A22212A22Z13 AZ2214

MOSBmiddotF211 cc22HSC4MOSBmiddotF212 Interpret the effects transformations have on functions and find the inverses of functionsAl1213 =0 Al2121 Al2122 AZ1313 AZ1314 AZ1321 AZ2211 AZ2212 AZ2213g =

A12111 u AZ2Z14 AZ2221uAl2122Intentionally Blank Intentionally Blank= = Al2213 CC22HSC5Al2214 G G Construct and compare linear quadratic and exponential models to solve problems

~ ~

Al2211 Al2Z12 Al2213 Al2214 A213ll A2l312 AZ1313 AZ1314 AZ2111 AZ2112 AZ2113 AZ2114 AZ22ll AZZ21Z AZ2213 AZ2214 A2222l

CC22HSC6 Interpret functions in terms of the situations they modeL

Al2121 Al2212 Al2213 Al2221 AZ1313AZZ1l1 AZZ112 AZ2113 AZ2114 AZ2213 AZ2214 AZ2221

CC22HSC7 Apply radian measure ofan angle and the unit circle to analyze the trigonometric functions

CC22HSC8 Choose trigonometric functions to model periodic phenomena and describe the properties of the graphs

CC22HSC9 Prove the Pythagorean identity and 11Se it to calculate trigonometric ratios

G1321 G211l G2112

JPage14

January 2013

Pennsylvania Core Standards Mathematics

CC236A1 CC237A1 CC238A1 CC23lSA1 Apply appropriate tools Solve real-world and Apply the concepts of Use geometric figures and their properties to represent transformations in the plane to solve real~world and mathematical problems volume ofcylinders cones G1311 G131Z mathematical problems involving angle and spheres to solve realshy CC23HSA2 involving area surface measure area swface world and mathematical Apply rigid transformations to determine and explain congruence area and volume area circumference problems GU11 G1312

and volume CC23HSA3 M06C-Gll1 M08C-C3ll Verify and apply geometric theorems as they relate to geometric figures M06C-GllZ M07C-G2l1 G2312 G1211 G1212 G1213 G1214 G1215 G1321 G2211 G2212 G2221 G2222 M06C-Gll3 M07C-G212 G2223 G2224 G222S M06C-G1L4 M07C-G22l CC23HS-A4 M06C-Gli5 M07C-G222 Apply the concept ofcongruence to create geometric constructions

MQsectt_-_G~Jsect_ --- shy -- shy -- shy ---------------------middot-middot CC23HSA5

--------------------------middotCC237A2 CC238A2 Create justifications based on transformations to establish similarity ofplane figures VlSUalize and represent Understand and apply G1311 G1312 geometric figures and congruence similarity and CC23HSA6 descnbethe geometric transformations Verify and apply theorems involving similarity as they relate to plane figures relatiooships betWeen using various tools G1311 G1312 G1321 them

CC23HSA7_ _- Intentionally Blank MOSC-C111 - Apply trigonometric ratios to solve problems involving right triangles~ sect M07C-Glll M08C-Gll2 = G21ll G21120

M07C-Gll2 MOSC-G113 CC23HSA8 M07C-Gll3 M08C-Gll4 Apply geometric theorems to veruy properties ofcircless ~M07C-Gll4 GJ211 ~ G1111 G1112 G1113 G1114 G1321 G223l

G1214 CC23HS-A9

-----------------------shy ----------------------shyG2211 Extend the concept ofsimilarity to determine arc lengths and areas ofsectors ofcircles

CCi32A3--shy -shy G1111 G1112 G1l13 G1114 G2221 G2222 G2223 G2224 G2225 G2231 Understand and apply the CC23HSA10 Pythagorean Theoremto Translate beti-veen the geometric description and the equation for a conic section solve problems A221l4 AZ221l

CC23HSA11 MOSC-G211 Apply coordinate geometry to prove simple geometric theorems algebraically MOSC-G212 G2121 GZ122 G2123

Intentionally Blank Intentionally Blank MOSC-G213 CC23HSA12 G2111 Explain volume formulas and use them to solve problems G21Zl G2311 G231Z G2313

CC23llSA13 Analyze relationships between two-dimensional and three-dimensional objects

G1111 G111Z G1113 Gl114 G1211 G1212 G1213 G1214 G1215 G2321 CC23HSA14 Apply geometric concepts to model and solve real world problems

G2241 G231l G2312 GZ313

23 Geometrv The Standards ofMathematical Practices

Make sense of problems and persevere in solving them Reason abstractly and quantitatively ConstructViable arguments and critique the reasoning ofothers Model with mathematics Use appropriate tools strategically Attend to precision Look for and make use of structure Look for and evnress reUlaritv in reneated reasoniniz

Grade 6 Grade7 Grades High School Z36 237 23S Z3HS

Pennltvfvanias vublic schools shall teach challen e and sunnort evPrv student to realize his or her maximum votential and to acauire the knowledae and skills needed to

jPage15

)anuazy 2013

Pennsylvania Core Standards Mathematics

24 Measurement Data and Probabilitv The Standards ofMathematical Practices

Make sense ofproblems and persevere in solving them Reason abstractly and quantitatively Construct viable ar~ments and critique the reasoning ofothers Model with mathematics Use appropriate tools strategically Attend to precision Look for and make use ofstructure Look for and express regularity in repeated reasoning

Grade 6 246

Grade7 247

Grade3 243

High School 24HS

Pennsylvanias public schools shall teach challenge and support every student to realize his or her mt1Ximum potential and to acquire the mowedge andskills needed to

~ E 0 0

d ilc c g ~ e

CCZ46B1 Demonstrate an understanding of statistical vaiability by displaying analyzing and summarizing distributions

M06DmiddotSlll M06DmiddotSll2 M06D-Sll3 M06D-Sll4

------------------------shy

Intentionally Blank

------------------------shy

CCZ47B1 Draw inferences about populatioos based on rardom sampling concepts

M07D-S1l1 M07D-S1l2

middotcczyen7-szmiddot----middot----- shy -Draw informal comparative inferences about two populations

M07D-S211

middotcci47S3----- --- --- -shy[mrestigate cbaoce processes and develop use and evaluate probability models

CCZ48B1 Analyze andor interpret bivariate data displayed in multiple representations

MOSD-S11l MOSDmiddotS112 MOSDmiddotS113 AlZ22l

iCi4862 ----------shyUnderstand thatpatterns ofassociation can be seen in bivariate data utilizing frequencies

MOSDmiddotS121

-------------------------shy

c a 0 0

d ltgt middotc ~ middotc g

sect

CCZ4HSB1 Summarize represent and interpret data on a single count or measurement variable

A12212 Al2311 A12321 Al2322 Al2323

CCZ4HSB2 Summarize represent and interpret data on two categorical and quantitative variables

Al21ll Al2112 A12113 Al2121 Al2122 Al2221 A2211l AZ2311 AZ2312

CCZ4HSB3 Analyze linear models to make interpretations based on the data

Al222l A1231l Al2321 Al2322 Al2323 A22311 AZ2312

CCZ4HSB4 Recognize and evaluate random processes underlying statistical experiments

Al2331 A223Z1 A2232Z A22323

CC24HSBS Make inferences and justify conclusions based on sample surveys experiments and observational studies

Al2321 Al2322 Al2323 A22321 A22322 A22323

CCZ4J5B6 Use the concepts ofindependence and conditional probability to interpret data

AZ2321 A22322 A22323

Intentionally Blunk M07D-S31l M07D-S32l M07D-S322 M07D-S323 Al2331

lntentionany Blank CCZ4HSB7 Apply the rules of probability to compute probabilities ofcompound events in a uniform probability model

Al2331 A223Z1 A223ZZ A22323

[Page16

January 2013

Pennsylvania Core Standards Mathematics

Key Terms for this Document

Standards for Mathematical Content-These standards define what students should know and be able to do in their study of mathematics

Standards for Mathematical Practice-These standards describe the processes and proficiencies in which all students grades K-12 should engage Educators

must instill these standards of practice in their students so that they become habitual The standards for mathematical practice should be used as the vehicle to

deliver the standards of mathematical content

Standard Algorithm-A locally agreed upon method of computation which is conventionally taught for solving mathematical problems

Decimal Fraction-A fraction whose denominator is a power of ten (examples 2100 810) These fractions are commonly expressed as decimals

Unit Fraction-A rational number written as a fraction where the numerator is one and the denominator is a positive integer (example 120)

Bivariate Data-The data involves two variables and is usually represented as a scatter plot

Rule-A single operation (examples add 5 multiply by 2)

IP age 17

January 2013

Page 10: Academic Standards for Mathematics...The Co=on Core Standards in Mathematics in grades PreK-5 lay a solid foundation in whole numbers, addition, subtraction, multiplication, division,

Pennsylvania Core Standards Mathematics

24 Measurement Data and Probabilitv The Standards ofMathematical Practices

Make sense ofproblems and persevere in solving them Reason abstractly and quantitatively Construct viable arguments and crltique the reasoning of others Model with mathematics Use appropriate tools strategically Attend to precision Look for and make use of structure Look for and exnress regularitv in repeated reasoning

GradePreK Z4K Grade K Gradel Z4Z Grade 2 243 Grade 3 244middot Grade 4 Z45 Grade 5 24PreK 241

PenTI vJvanias uublic schools shall teach challenae and sunnort evp~rstudent to realize his or her maximum Dotential and to acauire the knowledae andskills needed to CCZ4PreKA4 CCZ4KA4 CCZ41A4 CCZ4ZA4 CCZ43A4 CCZ44A4 CCZ4SA4 Classify objects and Classify objects and count Representand interpret Represent and interpret Representand interpret Representand interpret Solve problems involving count the number of objects iii each category

the number ofobjects in each category

data using tablescharts data using line plots pictUre graphs and bar

data using tally charts tables pictographs line

data irivolviog fractions using informationmiddot

computation offractions using information

graphs plots and bar graphs provided in a line plot provided in a line plot

M03DmiddotMZ11 MD4IJMZ11 MOSDmiddotMZ11 M03D-M212 M04IJM212 M03DmiddotM213

S ----------------------shy ------------------------shy ------------------------shy -----------------------shy

1D_3JlMJ~4t-bullbull_ __ bull__ CCZ43A5 -----------------------shy middotca4sAs----- --middot--middot -- shy

ilt

s

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Determine the area of a rectangle and apply the concept to multiplicati~n and to addition

M03D-M311

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Apply concepts ofvolume to solve problems and relate volume to multiplication and to addition

s

Intentionally Blank Jntentionally Blank Intentionally Blank M03DmiddotM312

laquociyeniA6-------bull -bull -- laquoci43A6middot--shy --shy --shy --shy -cc244A6____________ MOSDmiddotM31l

_Qsectl31~middot~___ -----middot-shy bull s Extend the concepts of Solve problems involTng Measure angles and use ~ addition and subtraction perimeters ofpolygons properties of adjacent ~ to problems involving

length-and distinguish between linear and area measures

angles to solve problems lntentionalb Blank

M03D-M411 M04DmiddotM311 M04DmiddotM312

IP age 10

Januazy2013

Pennsylvania Core Standards Mathematics

21 Numbers and Operations The Standards ofMathematical Practices

Make sense ofproblems and persevere in solving them Reason abstractly and quantitatively Construct viable arguments and critique the reasoning of others Model with mathematics Use appropriate tools strategically Attend to precision Look for and make use of structure Look for and eXPress regularitv in repeated reasoning

216Grade6 I 217Grade7 I 21SGradeS I I 21HSHighSchool

Pennsylvanias public schools shall teach challenge and support every student to realize his orher maximum potentialand to acquire the lmowledge andskills needed to

- CCZ16D1 CCZ17D1 I I I CCZ1lSF1 ~ Understand ratio Analyze proportional Apply and extend the properties ofexponents to solve problems with rational exponents sect concepts and use ratio relationships and use Al1111 Al1112 A1l131 A21211 A21212 A21213 A2lZ14 t vi reasoning to solve them to modcl and solve8 sect problems real-world and CCZ1HSFZ E lt mathematicalproblems Apply properties of rational and irrational numberS to solve real world or mathematical problems0 Intentionally Blartk Al1111 Al1112 All131 Al112l o1l il M06AmiddotR1l1 M07AmiddotR1l1 ~~ M06AmiddotR112 M07AmiddotR1l2 CCZllSF3= isect M06A-Rl13 M07A-R1l3 Apply quantitative reasoning to choose and interpret units and scales in formulas graphs and data ~ M06AmiddotR114 M07AmiddotR114 displayse M06A-Rl15 M07A-R11S Al1211 Al1212 Al1Z13 A12121 A12122 A2ZZ11 A22Z12 A223l1

M07A-R116 A2Z312 CC216E1 CCZ17E1 CC21SE1 Apply and extend Apply and extend 0 CCZlHSF4Distioguisb between

Use units as avray to understand problems and to guide the solution -0fmulti-step problemsprevious understandings previous understandings rational and irrational g Al1211 Al1212 Al1Z13 Al2121 A12122 A22211 A22212 of multiplication and of-Operations with numbers usiDg their sectdivision to diVide fractions to operations properties fractions by fractions with rational nUIIlbers CCZlHSFS] Choose a level of accuracy appropriate to limitations on measurement when reporting quantitiesMOSA-Nl1l a Al1211 A11Z12 Al1Z13 Al1221 Al12Z2 Al13l1 Al1312 Al1313 M06A-N111 M07A-N111 lMOSA-Nl12

Al13 21 All3 22 A2Z311 A22312 = Ei -~~~~~t~~~----------- -~t~t~t____________ _poundg ------------------------shy CCZ1HSF6 CC216E2 sect Extend the lmowiedge of arithmetic operations and apply to complex numbers sect appropriate processes to ~ Identify and choose

A2l111 A21112 A211Z1 A2l122 S compute fluently with

CC21HSF7~ multi-digit numbers Apply concepts ofcomplex numbers in polynomial identities and quadratic equations to solve problemssect J-~~~t~i1L_________ _ A2Zl11 A22112 A22l13 A22114

Intentionally Blank Intentionally Blank Develop mdor apply nUlDbertheoryconcepts to find common factors and multiples

M06A-N22l M06A-N222

----~-1h~~L-------------------------------------------------------middot-middot------~-~--------------------------------~

IP age 11

January 2013

Pennsylvania Core Standards Mathematics

21 Numbers and Operations The Standards ofMathematical Practices

Make sense ofproblems and persevere in solving them Reason abstractly and quantitatively Construct viable arguments and critique the reasoning of others Model with mathematics Use appropriate tools strategically Attend to precision Look for and make use ofstructure Look for and bullvnress reltnlaritv in reoeated reasoning

216 Grade 6 217 Grade 7 21HS High School 218 Grade 8

Pennsylvanias public schools shall teach challenge and support every studentw realize his orher maximum potential and to acquire the knowledge andskills needed W CC216E4 Apply and extend previous understandings ofnumbers to the system ofrational numbers

M06A-N311 M06A-N312 M06AmiddotN313 M06AmiddotN321 M06A-ll322 M06A-N323

Intentionally Blank

CC218E4 Estimate irrational numbers by compaing them to rational numbers

MOSAmiddotN113 MOSAmiddotN114 MOSA-N11S Al1111

[Page12

January 2013

Pennsylvania Core Standards Mathematics

22 Algebraic Concepts

The Standards ofMathematical Practices Make sense ofproblems and persevere in solvilg them Reason abstractly and quantitatively Construct viable arguments and critique the reasoning of others Model with mathematics Use appropriate tools strategically Attend to precision Look for and make use ofstructure Look for and exnress regularitvin repeated reasoning

226 Grade 6 22 7 Grade 7 228 Grade 8 22HS High School

Penn rvlvartias uublic schools shall teach challem1e and sunnort everv student to realize his orher maximum uotential and to acmrire the mowledae and skills needed to CC2Z681 CC22781 CC2ZHSD1 Apply and extend

CC2Z8B1 Apply properties of Apply concepts of radicals Interpret the structure of expressions to represent a quantity in terms of its context

Al1151 Al1152Al11S3 AZ1221 AZ1222previous understandings operations to generate and integer exponents to of arithmetic to algebraic equivalent expressions generate equivalent CC22HSD2 expressions expressions Write expressions in equivalent forms to solve problems

M07B-E111 Al11S1 Al1152 Al1153 AZ1211 AZ1Z12AZ1213 AZ1214 AZ1221 M06B-E111 MOSBmiddotE111 AZ1ZZ2 M06B-E112 MOSB-E112

CC22HSD3M06B-E113 MOSB-E113 Extend the knowledge of arithmetic operations and apply to polynomialsM06B-E114 MOSB-E114

_]1Qsect~~l ___________ Al11S1 Al1152 Al1153 AZl221 AZ1222 -~~J~_1__ ___ ---- --- --- -shy--~---------------------- CC22HSD4CCZ2682 CCZ28BZ

Understand the relationship between zeros and fac-ors of polynomials to make generalizations about Understand the process Understand the functions and their graphs of solving a one-variable connections between

AZ1ZZ1 AZ1222equation or inequality proportional relationshlps and apply it to real-worldg

~

CC22HSOSlines1 and linear equations Use polynomial identities to solve problemsand mathematical~ Intentionally Blank Al1151 Al1152 Al1153 AZ1221 AZ1ZZ2AZl311 AZl312 AZl313 problems MOSB-E211 AZ1314MOSBmiddotE212

~

MOSB-E213M06E-E211 CC22HSD6 ~

_~ M06B-EZ12 Al2122 Extend the knowledge ofrational functions to remite in equivaleztformsltg M06B-E213

B ~ Al11S1 Al1152 Al1153 AZ1311 AZ1312AZ1313 AZ1314

e ~ M06B-EZ14 CC22HSD7middotcciz6iir------------ middotec2z7ii3------ -----shy middotcc-2z~S1ii middot----- ---middot---shy Create and graph equations or inequalitiesto describe numbers or relationships Represent and analyze Model and solve real- Analyze and solve linear Al1211 Al1212 Al1213 Al1Z21 Al1222 All311 Al1312 Al1313 s x

quantitative world and mathematical equations and pairs of Al1321 All322 AZl311 A21312 AZ1313 AZ13M AZ1321 AZ132Z~ problems by using andrelationships between Simultaneous linear A22211 AZ2212 AZZ213 AZ2214

dependent and connecting numerical equations CC22HS08independent variables algebraic andor Apply inverse operations to solve equations or formulas for a given variableMOSB-E311graphical Al1211 Al1Z12 Al1213 AZ1311 AZ1312 AZ1313 AZ1314M06B-E311 representations MOSB-E31Z AZl321 AZ1322M06B-E312 MOSB-E313

M07B-E211 CC22HS09MOSB-E314 Use reasooing to solve equations and justify the solution method M07B-EZZ1 MOBB-E31S

All141 Al1211 Al121Z Al1213 Al1221 Al1222 Al1311 Al13l2 M07B-EZ22 Al1211 M07B-EZ31 Al1313 AZ1311 AZ1312 AZ1313 AZ1314 AZ1321 AZ132ZAll221 A11141 CCZ2lSD10Al1222

Represent solve and interpret equationsinequalities and systems of equationsinequalities algebraically and graphically

AllZ11 Al1212 Al1213 Al1221 Al1222 Al1311 Al1312 All313 Al1321 Al1322 A21311 AZl312 A2l313 AZ13U

JPage13

January 2013

Pennsylvania Core Standards Mathematics

ZZ Algebraic Concepts

The Standards ofMathematical Practices Make sense ofproblems and persevere in solving them Reason abstractly and quantitatively Construct viable arguments and critique the reasoning of others Model with mathematics Use appropriate tools strategically Attend to precision Look for and make use ofstructure Look for and Pxnress repoundUlaritv in repeated reasoning

Z26 Grade 6 zz 7 Grade 7 Z2S Grade 8 ZZHS High School

Penm 1lvanias public schools shall teach challenae andsunnort ev~rv student to realize his orhermaximum Potential and to acm1ire the knowledae and skills needed to cc22sc1 CCZ2HSC1 Define evaluate and Use the conceptand notation offunttionsto interpretand appiythemin terrns oftheir context compare functions Al2111 Al2112 Al2113 Al2211 Al2212 AlZ213 Al2214 AZ21ll

AZ2112 AZ2113 A22114 G2221 G2222 G2223 G2224 GZ225 MOSBmiddotF111 MOSJH112 CC22HSC2 MOSBmiddotF113 Graph and analyze functions and use their properties to make connections between the different

representationsAl1211 Al2111 Al2112 Al2113 Al2121 Al2122 Al22l1 AZ1314 AZ1321

Al2121 Al2112

AZ1322 AZ2111 AZ2112 AZ2113 AZ2114 Al2122

CCZ2lSC3middotz2samiddotmiddotmiddotmiddotmiddotmiddotmiddotmiddotmiddotmiddotmiddotmiddotmiddotmiddot Write functions or sequences that model relationships between two quantitiesUse concepts offunctions

Al1Z11 AllZ12 Al1213 Al2111 Al2112 Al2113 Al2121 Al2l22 to model relationships Al2Z13 Al2214 A21311A21312 AZ1313 AZ1314 AZ1321AZ1322betvveen quantities AZ211l AZ2112 AZ2l13 AZZ114 A22211A22212A22Z13 AZ2214

MOSBmiddotF211 cc22HSC4MOSBmiddotF212 Interpret the effects transformations have on functions and find the inverses of functionsAl1213 =0 Al2121 Al2122 AZ1313 AZ1314 AZ1321 AZ2211 AZ2212 AZ2213g =

A12111 u AZ2Z14 AZ2221uAl2122Intentionally Blank Intentionally Blank= = Al2213 CC22HSC5Al2214 G G Construct and compare linear quadratic and exponential models to solve problems

~ ~

Al2211 Al2Z12 Al2213 Al2214 A213ll A2l312 AZ1313 AZ1314 AZ2111 AZ2112 AZ2113 AZ2114 AZ22ll AZZ21Z AZ2213 AZ2214 A2222l

CC22HSC6 Interpret functions in terms of the situations they modeL

Al2121 Al2212 Al2213 Al2221 AZ1313AZZ1l1 AZZ112 AZ2113 AZ2114 AZ2213 AZ2214 AZ2221

CC22HSC7 Apply radian measure ofan angle and the unit circle to analyze the trigonometric functions

CC22HSC8 Choose trigonometric functions to model periodic phenomena and describe the properties of the graphs

CC22HSC9 Prove the Pythagorean identity and 11Se it to calculate trigonometric ratios

G1321 G211l G2112

JPage14

January 2013

Pennsylvania Core Standards Mathematics

CC236A1 CC237A1 CC238A1 CC23lSA1 Apply appropriate tools Solve real-world and Apply the concepts of Use geometric figures and their properties to represent transformations in the plane to solve real~world and mathematical problems volume ofcylinders cones G1311 G131Z mathematical problems involving angle and spheres to solve realshy CC23HSA2 involving area surface measure area swface world and mathematical Apply rigid transformations to determine and explain congruence area and volume area circumference problems GU11 G1312

and volume CC23HSA3 M06C-Gll1 M08C-C3ll Verify and apply geometric theorems as they relate to geometric figures M06C-GllZ M07C-G2l1 G2312 G1211 G1212 G1213 G1214 G1215 G1321 G2211 G2212 G2221 G2222 M06C-Gll3 M07C-G212 G2223 G2224 G222S M06C-G1L4 M07C-G22l CC23HS-A4 M06C-Gli5 M07C-G222 Apply the concept ofcongruence to create geometric constructions

MQsectt_-_G~Jsect_ --- shy -- shy -- shy ---------------------middot-middot CC23HSA5

--------------------------middotCC237A2 CC238A2 Create justifications based on transformations to establish similarity ofplane figures VlSUalize and represent Understand and apply G1311 G1312 geometric figures and congruence similarity and CC23HSA6 descnbethe geometric transformations Verify and apply theorems involving similarity as they relate to plane figures relatiooships betWeen using various tools G1311 G1312 G1321 them

CC23HSA7_ _- Intentionally Blank MOSC-C111 - Apply trigonometric ratios to solve problems involving right triangles~ sect M07C-Glll M08C-Gll2 = G21ll G21120

M07C-Gll2 MOSC-G113 CC23HSA8 M07C-Gll3 M08C-Gll4 Apply geometric theorems to veruy properties ofcircless ~M07C-Gll4 GJ211 ~ G1111 G1112 G1113 G1114 G1321 G223l

G1214 CC23HS-A9

-----------------------shy ----------------------shyG2211 Extend the concept ofsimilarity to determine arc lengths and areas ofsectors ofcircles

CCi32A3--shy -shy G1111 G1112 G1l13 G1114 G2221 G2222 G2223 G2224 G2225 G2231 Understand and apply the CC23HSA10 Pythagorean Theoremto Translate beti-veen the geometric description and the equation for a conic section solve problems A221l4 AZ221l

CC23HSA11 MOSC-G211 Apply coordinate geometry to prove simple geometric theorems algebraically MOSC-G212 G2121 GZ122 G2123

Intentionally Blank Intentionally Blank MOSC-G213 CC23HSA12 G2111 Explain volume formulas and use them to solve problems G21Zl G2311 G231Z G2313

CC23llSA13 Analyze relationships between two-dimensional and three-dimensional objects

G1111 G111Z G1113 Gl114 G1211 G1212 G1213 G1214 G1215 G2321 CC23HSA14 Apply geometric concepts to model and solve real world problems

G2241 G231l G2312 GZ313

23 Geometrv The Standards ofMathematical Practices

Make sense of problems and persevere in solving them Reason abstractly and quantitatively ConstructViable arguments and critique the reasoning ofothers Model with mathematics Use appropriate tools strategically Attend to precision Look for and make use of structure Look for and evnress reUlaritv in reneated reasoniniz

Grade 6 Grade7 Grades High School Z36 237 23S Z3HS

Pennltvfvanias vublic schools shall teach challen e and sunnort evPrv student to realize his or her maximum votential and to acauire the knowledae and skills needed to

jPage15

)anuazy 2013

Pennsylvania Core Standards Mathematics

24 Measurement Data and Probabilitv The Standards ofMathematical Practices

Make sense ofproblems and persevere in solving them Reason abstractly and quantitatively Construct viable ar~ments and critique the reasoning ofothers Model with mathematics Use appropriate tools strategically Attend to precision Look for and make use ofstructure Look for and express regularity in repeated reasoning

Grade 6 246

Grade7 247

Grade3 243

High School 24HS

Pennsylvanias public schools shall teach challenge and support every student to realize his or her mt1Ximum potential and to acquire the mowedge andskills needed to

~ E 0 0

d ilc c g ~ e

CCZ46B1 Demonstrate an understanding of statistical vaiability by displaying analyzing and summarizing distributions

M06DmiddotSlll M06DmiddotSll2 M06D-Sll3 M06D-Sll4

------------------------shy

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------------------------shy

CCZ47B1 Draw inferences about populatioos based on rardom sampling concepts

M07D-S1l1 M07D-S1l2

middotcczyen7-szmiddot----middot----- shy -Draw informal comparative inferences about two populations

M07D-S211

middotcci47S3----- --- --- -shy[mrestigate cbaoce processes and develop use and evaluate probability models

CCZ48B1 Analyze andor interpret bivariate data displayed in multiple representations

MOSD-S11l MOSDmiddotS112 MOSDmiddotS113 AlZ22l

iCi4862 ----------shyUnderstand thatpatterns ofassociation can be seen in bivariate data utilizing frequencies

MOSDmiddotS121

-------------------------shy

c a 0 0

d ltgt middotc ~ middotc g

sect

CCZ4HSB1 Summarize represent and interpret data on a single count or measurement variable

A12212 Al2311 A12321 Al2322 Al2323

CCZ4HSB2 Summarize represent and interpret data on two categorical and quantitative variables

Al21ll Al2112 A12113 Al2121 Al2122 Al2221 A2211l AZ2311 AZ2312

CCZ4HSB3 Analyze linear models to make interpretations based on the data

Al222l A1231l Al2321 Al2322 Al2323 A22311 AZ2312

CCZ4HSB4 Recognize and evaluate random processes underlying statistical experiments

Al2331 A223Z1 A2232Z A22323

CC24HSBS Make inferences and justify conclusions based on sample surveys experiments and observational studies

Al2321 Al2322 Al2323 A22321 A22322 A22323

CCZ4J5B6 Use the concepts ofindependence and conditional probability to interpret data

AZ2321 A22322 A22323

Intentionally Blunk M07D-S31l M07D-S32l M07D-S322 M07D-S323 Al2331

lntentionany Blank CCZ4HSB7 Apply the rules of probability to compute probabilities ofcompound events in a uniform probability model

Al2331 A223Z1 A223ZZ A22323

[Page16

January 2013

Pennsylvania Core Standards Mathematics

Key Terms for this Document

Standards for Mathematical Content-These standards define what students should know and be able to do in their study of mathematics

Standards for Mathematical Practice-These standards describe the processes and proficiencies in which all students grades K-12 should engage Educators

must instill these standards of practice in their students so that they become habitual The standards for mathematical practice should be used as the vehicle to

deliver the standards of mathematical content

Standard Algorithm-A locally agreed upon method of computation which is conventionally taught for solving mathematical problems

Decimal Fraction-A fraction whose denominator is a power of ten (examples 2100 810) These fractions are commonly expressed as decimals

Unit Fraction-A rational number written as a fraction where the numerator is one and the denominator is a positive integer (example 120)

Bivariate Data-The data involves two variables and is usually represented as a scatter plot

Rule-A single operation (examples add 5 multiply by 2)

IP age 17

January 2013

Page 11: Academic Standards for Mathematics...The Co=on Core Standards in Mathematics in grades PreK-5 lay a solid foundation in whole numbers, addition, subtraction, multiplication, division,

Pennsylvania Core Standards Mathematics

21 Numbers and Operations The Standards ofMathematical Practices

Make sense ofproblems and persevere in solving them Reason abstractly and quantitatively Construct viable arguments and critique the reasoning of others Model with mathematics Use appropriate tools strategically Attend to precision Look for and make use of structure Look for and eXPress regularitv in repeated reasoning

216Grade6 I 217Grade7 I 21SGradeS I I 21HSHighSchool

Pennsylvanias public schools shall teach challenge and support every student to realize his orher maximum potentialand to acquire the lmowledge andskills needed to

- CCZ16D1 CCZ17D1 I I I CCZ1lSF1 ~ Understand ratio Analyze proportional Apply and extend the properties ofexponents to solve problems with rational exponents sect concepts and use ratio relationships and use Al1111 Al1112 A1l131 A21211 A21212 A21213 A2lZ14 t vi reasoning to solve them to modcl and solve8 sect problems real-world and CCZ1HSFZ E lt mathematicalproblems Apply properties of rational and irrational numberS to solve real world or mathematical problems0 Intentionally Blartk Al1111 Al1112 All131 Al112l o1l il M06AmiddotR1l1 M07AmiddotR1l1 ~~ M06AmiddotR112 M07AmiddotR1l2 CCZllSF3= isect M06A-Rl13 M07A-R1l3 Apply quantitative reasoning to choose and interpret units and scales in formulas graphs and data ~ M06AmiddotR114 M07AmiddotR114 displayse M06A-Rl15 M07A-R11S Al1211 Al1212 Al1Z13 A12121 A12122 A2ZZ11 A22Z12 A223l1

M07A-R116 A2Z312 CC216E1 CCZ17E1 CC21SE1 Apply and extend Apply and extend 0 CCZlHSF4Distioguisb between

Use units as avray to understand problems and to guide the solution -0fmulti-step problemsprevious understandings previous understandings rational and irrational g Al1211 Al1212 Al1Z13 Al2121 A12122 A22211 A22212 of multiplication and of-Operations with numbers usiDg their sectdivision to diVide fractions to operations properties fractions by fractions with rational nUIIlbers CCZlHSFS] Choose a level of accuracy appropriate to limitations on measurement when reporting quantitiesMOSA-Nl1l a Al1211 A11Z12 Al1Z13 Al1221 Al12Z2 Al13l1 Al1312 Al1313 M06A-N111 M07A-N111 lMOSA-Nl12

Al13 21 All3 22 A2Z311 A22312 = Ei -~~~~~t~~~----------- -~t~t~t____________ _poundg ------------------------shy CCZ1HSF6 CC216E2 sect Extend the lmowiedge of arithmetic operations and apply to complex numbers sect appropriate processes to ~ Identify and choose

A2l111 A21112 A211Z1 A2l122 S compute fluently with

CC21HSF7~ multi-digit numbers Apply concepts ofcomplex numbers in polynomial identities and quadratic equations to solve problemssect J-~~~t~i1L_________ _ A2Zl11 A22112 A22l13 A22114

Intentionally Blank Intentionally Blank Develop mdor apply nUlDbertheoryconcepts to find common factors and multiples

M06A-N22l M06A-N222

----~-1h~~L-------------------------------------------------------middot-middot------~-~--------------------------------~

IP age 11

January 2013

Pennsylvania Core Standards Mathematics

21 Numbers and Operations The Standards ofMathematical Practices

Make sense ofproblems and persevere in solving them Reason abstractly and quantitatively Construct viable arguments and critique the reasoning of others Model with mathematics Use appropriate tools strategically Attend to precision Look for and make use ofstructure Look for and bullvnress reltnlaritv in reoeated reasoning

216 Grade 6 217 Grade 7 21HS High School 218 Grade 8

Pennsylvanias public schools shall teach challenge and support every studentw realize his orher maximum potential and to acquire the knowledge andskills needed W CC216E4 Apply and extend previous understandings ofnumbers to the system ofrational numbers

M06A-N311 M06A-N312 M06AmiddotN313 M06AmiddotN321 M06A-ll322 M06A-N323

Intentionally Blank

CC218E4 Estimate irrational numbers by compaing them to rational numbers

MOSAmiddotN113 MOSAmiddotN114 MOSA-N11S Al1111

[Page12

January 2013

Pennsylvania Core Standards Mathematics

22 Algebraic Concepts

The Standards ofMathematical Practices Make sense ofproblems and persevere in solvilg them Reason abstractly and quantitatively Construct viable arguments and critique the reasoning of others Model with mathematics Use appropriate tools strategically Attend to precision Look for and make use ofstructure Look for and exnress regularitvin repeated reasoning

226 Grade 6 22 7 Grade 7 228 Grade 8 22HS High School

Penn rvlvartias uublic schools shall teach challem1e and sunnort everv student to realize his orher maximum uotential and to acmrire the mowledae and skills needed to CC2Z681 CC22781 CC2ZHSD1 Apply and extend

CC2Z8B1 Apply properties of Apply concepts of radicals Interpret the structure of expressions to represent a quantity in terms of its context

Al1151 Al1152Al11S3 AZ1221 AZ1222previous understandings operations to generate and integer exponents to of arithmetic to algebraic equivalent expressions generate equivalent CC22HSD2 expressions expressions Write expressions in equivalent forms to solve problems

M07B-E111 Al11S1 Al1152 Al1153 AZ1211 AZ1Z12AZ1213 AZ1214 AZ1221 M06B-E111 MOSBmiddotE111 AZ1ZZ2 M06B-E112 MOSB-E112

CC22HSD3M06B-E113 MOSB-E113 Extend the knowledge of arithmetic operations and apply to polynomialsM06B-E114 MOSB-E114

_]1Qsect~~l ___________ Al11S1 Al1152 Al1153 AZl221 AZ1222 -~~J~_1__ ___ ---- --- --- -shy--~---------------------- CC22HSD4CCZ2682 CCZ28BZ

Understand the relationship between zeros and fac-ors of polynomials to make generalizations about Understand the process Understand the functions and their graphs of solving a one-variable connections between

AZ1ZZ1 AZ1222equation or inequality proportional relationshlps and apply it to real-worldg

~

CC22HSOSlines1 and linear equations Use polynomial identities to solve problemsand mathematical~ Intentionally Blank Al1151 Al1152 Al1153 AZ1221 AZ1ZZ2AZl311 AZl312 AZl313 problems MOSB-E211 AZ1314MOSBmiddotE212

~

MOSB-E213M06E-E211 CC22HSD6 ~

_~ M06B-EZ12 Al2122 Extend the knowledge ofrational functions to remite in equivaleztformsltg M06B-E213

B ~ Al11S1 Al1152 Al1153 AZ1311 AZ1312AZ1313 AZ1314

e ~ M06B-EZ14 CC22HSD7middotcciz6iir------------ middotec2z7ii3------ -----shy middotcc-2z~S1ii middot----- ---middot---shy Create and graph equations or inequalitiesto describe numbers or relationships Represent and analyze Model and solve real- Analyze and solve linear Al1211 Al1212 Al1213 Al1Z21 Al1222 All311 Al1312 Al1313 s x

quantitative world and mathematical equations and pairs of Al1321 All322 AZl311 A21312 AZ1313 AZ13M AZ1321 AZ132Z~ problems by using andrelationships between Simultaneous linear A22211 AZ2212 AZZ213 AZ2214

dependent and connecting numerical equations CC22HS08independent variables algebraic andor Apply inverse operations to solve equations or formulas for a given variableMOSB-E311graphical Al1211 Al1Z12 Al1213 AZ1311 AZ1312 AZ1313 AZ1314M06B-E311 representations MOSB-E31Z AZl321 AZ1322M06B-E312 MOSB-E313

M07B-E211 CC22HS09MOSB-E314 Use reasooing to solve equations and justify the solution method M07B-EZZ1 MOBB-E31S

All141 Al1211 Al121Z Al1213 Al1221 Al1222 Al1311 Al13l2 M07B-EZ22 Al1211 M07B-EZ31 Al1313 AZ1311 AZ1312 AZ1313 AZ1314 AZ1321 AZ132ZAll221 A11141 CCZ2lSD10Al1222

Represent solve and interpret equationsinequalities and systems of equationsinequalities algebraically and graphically

AllZ11 Al1212 Al1213 Al1221 Al1222 Al1311 Al1312 All313 Al1321 Al1322 A21311 AZl312 A2l313 AZ13U

JPage13

January 2013

Pennsylvania Core Standards Mathematics

ZZ Algebraic Concepts

The Standards ofMathematical Practices Make sense ofproblems and persevere in solving them Reason abstractly and quantitatively Construct viable arguments and critique the reasoning of others Model with mathematics Use appropriate tools strategically Attend to precision Look for and make use ofstructure Look for and Pxnress repoundUlaritv in repeated reasoning

Z26 Grade 6 zz 7 Grade 7 Z2S Grade 8 ZZHS High School

Penm 1lvanias public schools shall teach challenae andsunnort ev~rv student to realize his orhermaximum Potential and to acm1ire the knowledae and skills needed to cc22sc1 CCZ2HSC1 Define evaluate and Use the conceptand notation offunttionsto interpretand appiythemin terrns oftheir context compare functions Al2111 Al2112 Al2113 Al2211 Al2212 AlZ213 Al2214 AZ21ll

AZ2112 AZ2113 A22114 G2221 G2222 G2223 G2224 GZ225 MOSBmiddotF111 MOSJH112 CC22HSC2 MOSBmiddotF113 Graph and analyze functions and use their properties to make connections between the different

representationsAl1211 Al2111 Al2112 Al2113 Al2121 Al2122 Al22l1 AZ1314 AZ1321

Al2121 Al2112

AZ1322 AZ2111 AZ2112 AZ2113 AZ2114 Al2122

CCZ2lSC3middotz2samiddotmiddotmiddotmiddotmiddotmiddotmiddotmiddotmiddotmiddotmiddotmiddotmiddotmiddot Write functions or sequences that model relationships between two quantitiesUse concepts offunctions

Al1Z11 AllZ12 Al1213 Al2111 Al2112 Al2113 Al2121 Al2l22 to model relationships Al2Z13 Al2214 A21311A21312 AZ1313 AZ1314 AZ1321AZ1322betvveen quantities AZ211l AZ2112 AZ2l13 AZZ114 A22211A22212A22Z13 AZ2214

MOSBmiddotF211 cc22HSC4MOSBmiddotF212 Interpret the effects transformations have on functions and find the inverses of functionsAl1213 =0 Al2121 Al2122 AZ1313 AZ1314 AZ1321 AZ2211 AZ2212 AZ2213g =

A12111 u AZ2Z14 AZ2221uAl2122Intentionally Blank Intentionally Blank= = Al2213 CC22HSC5Al2214 G G Construct and compare linear quadratic and exponential models to solve problems

~ ~

Al2211 Al2Z12 Al2213 Al2214 A213ll A2l312 AZ1313 AZ1314 AZ2111 AZ2112 AZ2113 AZ2114 AZ22ll AZZ21Z AZ2213 AZ2214 A2222l

CC22HSC6 Interpret functions in terms of the situations they modeL

Al2121 Al2212 Al2213 Al2221 AZ1313AZZ1l1 AZZ112 AZ2113 AZ2114 AZ2213 AZ2214 AZ2221

CC22HSC7 Apply radian measure ofan angle and the unit circle to analyze the trigonometric functions

CC22HSC8 Choose trigonometric functions to model periodic phenomena and describe the properties of the graphs

CC22HSC9 Prove the Pythagorean identity and 11Se it to calculate trigonometric ratios

G1321 G211l G2112

JPage14

January 2013

Pennsylvania Core Standards Mathematics

CC236A1 CC237A1 CC238A1 CC23lSA1 Apply appropriate tools Solve real-world and Apply the concepts of Use geometric figures and their properties to represent transformations in the plane to solve real~world and mathematical problems volume ofcylinders cones G1311 G131Z mathematical problems involving angle and spheres to solve realshy CC23HSA2 involving area surface measure area swface world and mathematical Apply rigid transformations to determine and explain congruence area and volume area circumference problems GU11 G1312

and volume CC23HSA3 M06C-Gll1 M08C-C3ll Verify and apply geometric theorems as they relate to geometric figures M06C-GllZ M07C-G2l1 G2312 G1211 G1212 G1213 G1214 G1215 G1321 G2211 G2212 G2221 G2222 M06C-Gll3 M07C-G212 G2223 G2224 G222S M06C-G1L4 M07C-G22l CC23HS-A4 M06C-Gli5 M07C-G222 Apply the concept ofcongruence to create geometric constructions

MQsectt_-_G~Jsect_ --- shy -- shy -- shy ---------------------middot-middot CC23HSA5

--------------------------middotCC237A2 CC238A2 Create justifications based on transformations to establish similarity ofplane figures VlSUalize and represent Understand and apply G1311 G1312 geometric figures and congruence similarity and CC23HSA6 descnbethe geometric transformations Verify and apply theorems involving similarity as they relate to plane figures relatiooships betWeen using various tools G1311 G1312 G1321 them

CC23HSA7_ _- Intentionally Blank MOSC-C111 - Apply trigonometric ratios to solve problems involving right triangles~ sect M07C-Glll M08C-Gll2 = G21ll G21120

M07C-Gll2 MOSC-G113 CC23HSA8 M07C-Gll3 M08C-Gll4 Apply geometric theorems to veruy properties ofcircless ~M07C-Gll4 GJ211 ~ G1111 G1112 G1113 G1114 G1321 G223l

G1214 CC23HS-A9

-----------------------shy ----------------------shyG2211 Extend the concept ofsimilarity to determine arc lengths and areas ofsectors ofcircles

CCi32A3--shy -shy G1111 G1112 G1l13 G1114 G2221 G2222 G2223 G2224 G2225 G2231 Understand and apply the CC23HSA10 Pythagorean Theoremto Translate beti-veen the geometric description and the equation for a conic section solve problems A221l4 AZ221l

CC23HSA11 MOSC-G211 Apply coordinate geometry to prove simple geometric theorems algebraically MOSC-G212 G2121 GZ122 G2123

Intentionally Blank Intentionally Blank MOSC-G213 CC23HSA12 G2111 Explain volume formulas and use them to solve problems G21Zl G2311 G231Z G2313

CC23llSA13 Analyze relationships between two-dimensional and three-dimensional objects

G1111 G111Z G1113 Gl114 G1211 G1212 G1213 G1214 G1215 G2321 CC23HSA14 Apply geometric concepts to model and solve real world problems

G2241 G231l G2312 GZ313

23 Geometrv The Standards ofMathematical Practices

Make sense of problems and persevere in solving them Reason abstractly and quantitatively ConstructViable arguments and critique the reasoning ofothers Model with mathematics Use appropriate tools strategically Attend to precision Look for and make use of structure Look for and evnress reUlaritv in reneated reasoniniz

Grade 6 Grade7 Grades High School Z36 237 23S Z3HS

Pennltvfvanias vublic schools shall teach challen e and sunnort evPrv student to realize his or her maximum votential and to acauire the knowledae and skills needed to

jPage15

)anuazy 2013

Pennsylvania Core Standards Mathematics

24 Measurement Data and Probabilitv The Standards ofMathematical Practices

Make sense ofproblems and persevere in solving them Reason abstractly and quantitatively Construct viable ar~ments and critique the reasoning ofothers Model with mathematics Use appropriate tools strategically Attend to precision Look for and make use ofstructure Look for and express regularity in repeated reasoning

Grade 6 246

Grade7 247

Grade3 243

High School 24HS

Pennsylvanias public schools shall teach challenge and support every student to realize his or her mt1Ximum potential and to acquire the mowedge andskills needed to

~ E 0 0

d ilc c g ~ e

CCZ46B1 Demonstrate an understanding of statistical vaiability by displaying analyzing and summarizing distributions

M06DmiddotSlll M06DmiddotSll2 M06D-Sll3 M06D-Sll4

------------------------shy

Intentionally Blank

------------------------shy

CCZ47B1 Draw inferences about populatioos based on rardom sampling concepts

M07D-S1l1 M07D-S1l2

middotcczyen7-szmiddot----middot----- shy -Draw informal comparative inferences about two populations

M07D-S211

middotcci47S3----- --- --- -shy[mrestigate cbaoce processes and develop use and evaluate probability models

CCZ48B1 Analyze andor interpret bivariate data displayed in multiple representations

MOSD-S11l MOSDmiddotS112 MOSDmiddotS113 AlZ22l

iCi4862 ----------shyUnderstand thatpatterns ofassociation can be seen in bivariate data utilizing frequencies

MOSDmiddotS121

-------------------------shy

c a 0 0

d ltgt middotc ~ middotc g

sect

CCZ4HSB1 Summarize represent and interpret data on a single count or measurement variable

A12212 Al2311 A12321 Al2322 Al2323

CCZ4HSB2 Summarize represent and interpret data on two categorical and quantitative variables

Al21ll Al2112 A12113 Al2121 Al2122 Al2221 A2211l AZ2311 AZ2312

CCZ4HSB3 Analyze linear models to make interpretations based on the data

Al222l A1231l Al2321 Al2322 Al2323 A22311 AZ2312

CCZ4HSB4 Recognize and evaluate random processes underlying statistical experiments

Al2331 A223Z1 A2232Z A22323

CC24HSBS Make inferences and justify conclusions based on sample surveys experiments and observational studies

Al2321 Al2322 Al2323 A22321 A22322 A22323

CCZ4J5B6 Use the concepts ofindependence and conditional probability to interpret data

AZ2321 A22322 A22323

Intentionally Blunk M07D-S31l M07D-S32l M07D-S322 M07D-S323 Al2331

lntentionany Blank CCZ4HSB7 Apply the rules of probability to compute probabilities ofcompound events in a uniform probability model

Al2331 A223Z1 A223ZZ A22323

[Page16

January 2013

Pennsylvania Core Standards Mathematics

Key Terms for this Document

Standards for Mathematical Content-These standards define what students should know and be able to do in their study of mathematics

Standards for Mathematical Practice-These standards describe the processes and proficiencies in which all students grades K-12 should engage Educators

must instill these standards of practice in their students so that they become habitual The standards for mathematical practice should be used as the vehicle to

deliver the standards of mathematical content

Standard Algorithm-A locally agreed upon method of computation which is conventionally taught for solving mathematical problems

Decimal Fraction-A fraction whose denominator is a power of ten (examples 2100 810) These fractions are commonly expressed as decimals

Unit Fraction-A rational number written as a fraction where the numerator is one and the denominator is a positive integer (example 120)

Bivariate Data-The data involves two variables and is usually represented as a scatter plot

Rule-A single operation (examples add 5 multiply by 2)

IP age 17

January 2013

Page 12: Academic Standards for Mathematics...The Co=on Core Standards in Mathematics in grades PreK-5 lay a solid foundation in whole numbers, addition, subtraction, multiplication, division,

Pennsylvania Core Standards Mathematics

21 Numbers and Operations The Standards ofMathematical Practices

Make sense ofproblems and persevere in solving them Reason abstractly and quantitatively Construct viable arguments and critique the reasoning of others Model with mathematics Use appropriate tools strategically Attend to precision Look for and make use ofstructure Look for and bullvnress reltnlaritv in reoeated reasoning

216 Grade 6 217 Grade 7 21HS High School 218 Grade 8

Pennsylvanias public schools shall teach challenge and support every studentw realize his orher maximum potential and to acquire the knowledge andskills needed W CC216E4 Apply and extend previous understandings ofnumbers to the system ofrational numbers

M06A-N311 M06A-N312 M06AmiddotN313 M06AmiddotN321 M06A-ll322 M06A-N323

Intentionally Blank

CC218E4 Estimate irrational numbers by compaing them to rational numbers

MOSAmiddotN113 MOSAmiddotN114 MOSA-N11S Al1111

[Page12

January 2013

Pennsylvania Core Standards Mathematics

22 Algebraic Concepts

The Standards ofMathematical Practices Make sense ofproblems and persevere in solvilg them Reason abstractly and quantitatively Construct viable arguments and critique the reasoning of others Model with mathematics Use appropriate tools strategically Attend to precision Look for and make use ofstructure Look for and exnress regularitvin repeated reasoning

226 Grade 6 22 7 Grade 7 228 Grade 8 22HS High School

Penn rvlvartias uublic schools shall teach challem1e and sunnort everv student to realize his orher maximum uotential and to acmrire the mowledae and skills needed to CC2Z681 CC22781 CC2ZHSD1 Apply and extend

CC2Z8B1 Apply properties of Apply concepts of radicals Interpret the structure of expressions to represent a quantity in terms of its context

Al1151 Al1152Al11S3 AZ1221 AZ1222previous understandings operations to generate and integer exponents to of arithmetic to algebraic equivalent expressions generate equivalent CC22HSD2 expressions expressions Write expressions in equivalent forms to solve problems

M07B-E111 Al11S1 Al1152 Al1153 AZ1211 AZ1Z12AZ1213 AZ1214 AZ1221 M06B-E111 MOSBmiddotE111 AZ1ZZ2 M06B-E112 MOSB-E112

CC22HSD3M06B-E113 MOSB-E113 Extend the knowledge of arithmetic operations and apply to polynomialsM06B-E114 MOSB-E114

_]1Qsect~~l ___________ Al11S1 Al1152 Al1153 AZl221 AZ1222 -~~J~_1__ ___ ---- --- --- -shy--~---------------------- CC22HSD4CCZ2682 CCZ28BZ

Understand the relationship between zeros and fac-ors of polynomials to make generalizations about Understand the process Understand the functions and their graphs of solving a one-variable connections between

AZ1ZZ1 AZ1222equation or inequality proportional relationshlps and apply it to real-worldg

~

CC22HSOSlines1 and linear equations Use polynomial identities to solve problemsand mathematical~ Intentionally Blank Al1151 Al1152 Al1153 AZ1221 AZ1ZZ2AZl311 AZl312 AZl313 problems MOSB-E211 AZ1314MOSBmiddotE212

~

MOSB-E213M06E-E211 CC22HSD6 ~

_~ M06B-EZ12 Al2122 Extend the knowledge ofrational functions to remite in equivaleztformsltg M06B-E213

B ~ Al11S1 Al1152 Al1153 AZ1311 AZ1312AZ1313 AZ1314

e ~ M06B-EZ14 CC22HSD7middotcciz6iir------------ middotec2z7ii3------ -----shy middotcc-2z~S1ii middot----- ---middot---shy Create and graph equations or inequalitiesto describe numbers or relationships Represent and analyze Model and solve real- Analyze and solve linear Al1211 Al1212 Al1213 Al1Z21 Al1222 All311 Al1312 Al1313 s x

quantitative world and mathematical equations and pairs of Al1321 All322 AZl311 A21312 AZ1313 AZ13M AZ1321 AZ132Z~ problems by using andrelationships between Simultaneous linear A22211 AZ2212 AZZ213 AZ2214

dependent and connecting numerical equations CC22HS08independent variables algebraic andor Apply inverse operations to solve equations or formulas for a given variableMOSB-E311graphical Al1211 Al1Z12 Al1213 AZ1311 AZ1312 AZ1313 AZ1314M06B-E311 representations MOSB-E31Z AZl321 AZ1322M06B-E312 MOSB-E313

M07B-E211 CC22HS09MOSB-E314 Use reasooing to solve equations and justify the solution method M07B-EZZ1 MOBB-E31S

All141 Al1211 Al121Z Al1213 Al1221 Al1222 Al1311 Al13l2 M07B-EZ22 Al1211 M07B-EZ31 Al1313 AZ1311 AZ1312 AZ1313 AZ1314 AZ1321 AZ132ZAll221 A11141 CCZ2lSD10Al1222

Represent solve and interpret equationsinequalities and systems of equationsinequalities algebraically and graphically

AllZ11 Al1212 Al1213 Al1221 Al1222 Al1311 Al1312 All313 Al1321 Al1322 A21311 AZl312 A2l313 AZ13U

JPage13

January 2013

Pennsylvania Core Standards Mathematics

ZZ Algebraic Concepts

The Standards ofMathematical Practices Make sense ofproblems and persevere in solving them Reason abstractly and quantitatively Construct viable arguments and critique the reasoning of others Model with mathematics Use appropriate tools strategically Attend to precision Look for and make use ofstructure Look for and Pxnress repoundUlaritv in repeated reasoning

Z26 Grade 6 zz 7 Grade 7 Z2S Grade 8 ZZHS High School

Penm 1lvanias public schools shall teach challenae andsunnort ev~rv student to realize his orhermaximum Potential and to acm1ire the knowledae and skills needed to cc22sc1 CCZ2HSC1 Define evaluate and Use the conceptand notation offunttionsto interpretand appiythemin terrns oftheir context compare functions Al2111 Al2112 Al2113 Al2211 Al2212 AlZ213 Al2214 AZ21ll

AZ2112 AZ2113 A22114 G2221 G2222 G2223 G2224 GZ225 MOSBmiddotF111 MOSJH112 CC22HSC2 MOSBmiddotF113 Graph and analyze functions and use their properties to make connections between the different

representationsAl1211 Al2111 Al2112 Al2113 Al2121 Al2122 Al22l1 AZ1314 AZ1321

Al2121 Al2112

AZ1322 AZ2111 AZ2112 AZ2113 AZ2114 Al2122

CCZ2lSC3middotz2samiddotmiddotmiddotmiddotmiddotmiddotmiddotmiddotmiddotmiddotmiddotmiddotmiddotmiddot Write functions or sequences that model relationships between two quantitiesUse concepts offunctions

Al1Z11 AllZ12 Al1213 Al2111 Al2112 Al2113 Al2121 Al2l22 to model relationships Al2Z13 Al2214 A21311A21312 AZ1313 AZ1314 AZ1321AZ1322betvveen quantities AZ211l AZ2112 AZ2l13 AZZ114 A22211A22212A22Z13 AZ2214

MOSBmiddotF211 cc22HSC4MOSBmiddotF212 Interpret the effects transformations have on functions and find the inverses of functionsAl1213 =0 Al2121 Al2122 AZ1313 AZ1314 AZ1321 AZ2211 AZ2212 AZ2213g =

A12111 u AZ2Z14 AZ2221uAl2122Intentionally Blank Intentionally Blank= = Al2213 CC22HSC5Al2214 G G Construct and compare linear quadratic and exponential models to solve problems

~ ~

Al2211 Al2Z12 Al2213 Al2214 A213ll A2l312 AZ1313 AZ1314 AZ2111 AZ2112 AZ2113 AZ2114 AZ22ll AZZ21Z AZ2213 AZ2214 A2222l

CC22HSC6 Interpret functions in terms of the situations they modeL

Al2121 Al2212 Al2213 Al2221 AZ1313AZZ1l1 AZZ112 AZ2113 AZ2114 AZ2213 AZ2214 AZ2221

CC22HSC7 Apply radian measure ofan angle and the unit circle to analyze the trigonometric functions

CC22HSC8 Choose trigonometric functions to model periodic phenomena and describe the properties of the graphs

CC22HSC9 Prove the Pythagorean identity and 11Se it to calculate trigonometric ratios

G1321 G211l G2112

JPage14

January 2013

Pennsylvania Core Standards Mathematics

CC236A1 CC237A1 CC238A1 CC23lSA1 Apply appropriate tools Solve real-world and Apply the concepts of Use geometric figures and their properties to represent transformations in the plane to solve real~world and mathematical problems volume ofcylinders cones G1311 G131Z mathematical problems involving angle and spheres to solve realshy CC23HSA2 involving area surface measure area swface world and mathematical Apply rigid transformations to determine and explain congruence area and volume area circumference problems GU11 G1312

and volume CC23HSA3 M06C-Gll1 M08C-C3ll Verify and apply geometric theorems as they relate to geometric figures M06C-GllZ M07C-G2l1 G2312 G1211 G1212 G1213 G1214 G1215 G1321 G2211 G2212 G2221 G2222 M06C-Gll3 M07C-G212 G2223 G2224 G222S M06C-G1L4 M07C-G22l CC23HS-A4 M06C-Gli5 M07C-G222 Apply the concept ofcongruence to create geometric constructions

MQsectt_-_G~Jsect_ --- shy -- shy -- shy ---------------------middot-middot CC23HSA5

--------------------------middotCC237A2 CC238A2 Create justifications based on transformations to establish similarity ofplane figures VlSUalize and represent Understand and apply G1311 G1312 geometric figures and congruence similarity and CC23HSA6 descnbethe geometric transformations Verify and apply theorems involving similarity as they relate to plane figures relatiooships betWeen using various tools G1311 G1312 G1321 them

CC23HSA7_ _- Intentionally Blank MOSC-C111 - Apply trigonometric ratios to solve problems involving right triangles~ sect M07C-Glll M08C-Gll2 = G21ll G21120

M07C-Gll2 MOSC-G113 CC23HSA8 M07C-Gll3 M08C-Gll4 Apply geometric theorems to veruy properties ofcircless ~M07C-Gll4 GJ211 ~ G1111 G1112 G1113 G1114 G1321 G223l

G1214 CC23HS-A9

-----------------------shy ----------------------shyG2211 Extend the concept ofsimilarity to determine arc lengths and areas ofsectors ofcircles

CCi32A3--shy -shy G1111 G1112 G1l13 G1114 G2221 G2222 G2223 G2224 G2225 G2231 Understand and apply the CC23HSA10 Pythagorean Theoremto Translate beti-veen the geometric description and the equation for a conic section solve problems A221l4 AZ221l

CC23HSA11 MOSC-G211 Apply coordinate geometry to prove simple geometric theorems algebraically MOSC-G212 G2121 GZ122 G2123

Intentionally Blank Intentionally Blank MOSC-G213 CC23HSA12 G2111 Explain volume formulas and use them to solve problems G21Zl G2311 G231Z G2313

CC23llSA13 Analyze relationships between two-dimensional and three-dimensional objects

G1111 G111Z G1113 Gl114 G1211 G1212 G1213 G1214 G1215 G2321 CC23HSA14 Apply geometric concepts to model and solve real world problems

G2241 G231l G2312 GZ313

23 Geometrv The Standards ofMathematical Practices

Make sense of problems and persevere in solving them Reason abstractly and quantitatively ConstructViable arguments and critique the reasoning ofothers Model with mathematics Use appropriate tools strategically Attend to precision Look for and make use of structure Look for and evnress reUlaritv in reneated reasoniniz

Grade 6 Grade7 Grades High School Z36 237 23S Z3HS

Pennltvfvanias vublic schools shall teach challen e and sunnort evPrv student to realize his or her maximum votential and to acauire the knowledae and skills needed to

jPage15

)anuazy 2013

Pennsylvania Core Standards Mathematics

24 Measurement Data and Probabilitv The Standards ofMathematical Practices

Make sense ofproblems and persevere in solving them Reason abstractly and quantitatively Construct viable ar~ments and critique the reasoning ofothers Model with mathematics Use appropriate tools strategically Attend to precision Look for and make use ofstructure Look for and express regularity in repeated reasoning

Grade 6 246

Grade7 247

Grade3 243

High School 24HS

Pennsylvanias public schools shall teach challenge and support every student to realize his or her mt1Ximum potential and to acquire the mowedge andskills needed to

~ E 0 0

d ilc c g ~ e

CCZ46B1 Demonstrate an understanding of statistical vaiability by displaying analyzing and summarizing distributions

M06DmiddotSlll M06DmiddotSll2 M06D-Sll3 M06D-Sll4

------------------------shy

Intentionally Blank

------------------------shy

CCZ47B1 Draw inferences about populatioos based on rardom sampling concepts

M07D-S1l1 M07D-S1l2

middotcczyen7-szmiddot----middot----- shy -Draw informal comparative inferences about two populations

M07D-S211

middotcci47S3----- --- --- -shy[mrestigate cbaoce processes and develop use and evaluate probability models

CCZ48B1 Analyze andor interpret bivariate data displayed in multiple representations

MOSD-S11l MOSDmiddotS112 MOSDmiddotS113 AlZ22l

iCi4862 ----------shyUnderstand thatpatterns ofassociation can be seen in bivariate data utilizing frequencies

MOSDmiddotS121

-------------------------shy

c a 0 0

d ltgt middotc ~ middotc g

sect

CCZ4HSB1 Summarize represent and interpret data on a single count or measurement variable

A12212 Al2311 A12321 Al2322 Al2323

CCZ4HSB2 Summarize represent and interpret data on two categorical and quantitative variables

Al21ll Al2112 A12113 Al2121 Al2122 Al2221 A2211l AZ2311 AZ2312

CCZ4HSB3 Analyze linear models to make interpretations based on the data

Al222l A1231l Al2321 Al2322 Al2323 A22311 AZ2312

CCZ4HSB4 Recognize and evaluate random processes underlying statistical experiments

Al2331 A223Z1 A2232Z A22323

CC24HSBS Make inferences and justify conclusions based on sample surveys experiments and observational studies

Al2321 Al2322 Al2323 A22321 A22322 A22323

CCZ4J5B6 Use the concepts ofindependence and conditional probability to interpret data

AZ2321 A22322 A22323

Intentionally Blunk M07D-S31l M07D-S32l M07D-S322 M07D-S323 Al2331

lntentionany Blank CCZ4HSB7 Apply the rules of probability to compute probabilities ofcompound events in a uniform probability model

Al2331 A223Z1 A223ZZ A22323

[Page16

January 2013

Pennsylvania Core Standards Mathematics

Key Terms for this Document

Standards for Mathematical Content-These standards define what students should know and be able to do in their study of mathematics

Standards for Mathematical Practice-These standards describe the processes and proficiencies in which all students grades K-12 should engage Educators

must instill these standards of practice in their students so that they become habitual The standards for mathematical practice should be used as the vehicle to

deliver the standards of mathematical content

Standard Algorithm-A locally agreed upon method of computation which is conventionally taught for solving mathematical problems

Decimal Fraction-A fraction whose denominator is a power of ten (examples 2100 810) These fractions are commonly expressed as decimals

Unit Fraction-A rational number written as a fraction where the numerator is one and the denominator is a positive integer (example 120)

Bivariate Data-The data involves two variables and is usually represented as a scatter plot

Rule-A single operation (examples add 5 multiply by 2)

IP age 17

January 2013

Page 13: Academic Standards for Mathematics...The Co=on Core Standards in Mathematics in grades PreK-5 lay a solid foundation in whole numbers, addition, subtraction, multiplication, division,

Pennsylvania Core Standards Mathematics

22 Algebraic Concepts

The Standards ofMathematical Practices Make sense ofproblems and persevere in solvilg them Reason abstractly and quantitatively Construct viable arguments and critique the reasoning of others Model with mathematics Use appropriate tools strategically Attend to precision Look for and make use ofstructure Look for and exnress regularitvin repeated reasoning

226 Grade 6 22 7 Grade 7 228 Grade 8 22HS High School

Penn rvlvartias uublic schools shall teach challem1e and sunnort everv student to realize his orher maximum uotential and to acmrire the mowledae and skills needed to CC2Z681 CC22781 CC2ZHSD1 Apply and extend

CC2Z8B1 Apply properties of Apply concepts of radicals Interpret the structure of expressions to represent a quantity in terms of its context

Al1151 Al1152Al11S3 AZ1221 AZ1222previous understandings operations to generate and integer exponents to of arithmetic to algebraic equivalent expressions generate equivalent CC22HSD2 expressions expressions Write expressions in equivalent forms to solve problems

M07B-E111 Al11S1 Al1152 Al1153 AZ1211 AZ1Z12AZ1213 AZ1214 AZ1221 M06B-E111 MOSBmiddotE111 AZ1ZZ2 M06B-E112 MOSB-E112

CC22HSD3M06B-E113 MOSB-E113 Extend the knowledge of arithmetic operations and apply to polynomialsM06B-E114 MOSB-E114

_]1Qsect~~l ___________ Al11S1 Al1152 Al1153 AZl221 AZ1222 -~~J~_1__ ___ ---- --- --- -shy--~---------------------- CC22HSD4CCZ2682 CCZ28BZ

Understand the relationship between zeros and fac-ors of polynomials to make generalizations about Understand the process Understand the functions and their graphs of solving a one-variable connections between

AZ1ZZ1 AZ1222equation or inequality proportional relationshlps and apply it to real-worldg

~

CC22HSOSlines1 and linear equations Use polynomial identities to solve problemsand mathematical~ Intentionally Blank Al1151 Al1152 Al1153 AZ1221 AZ1ZZ2AZl311 AZl312 AZl313 problems MOSB-E211 AZ1314MOSBmiddotE212

~

MOSB-E213M06E-E211 CC22HSD6 ~

_~ M06B-EZ12 Al2122 Extend the knowledge ofrational functions to remite in equivaleztformsltg M06B-E213

B ~ Al11S1 Al1152 Al1153 AZ1311 AZ1312AZ1313 AZ1314

e ~ M06B-EZ14 CC22HSD7middotcciz6iir------------ middotec2z7ii3------ -----shy middotcc-2z~S1ii middot----- ---middot---shy Create and graph equations or inequalitiesto describe numbers or relationships Represent and analyze Model and solve real- Analyze and solve linear Al1211 Al1212 Al1213 Al1Z21 Al1222 All311 Al1312 Al1313 s x

quantitative world and mathematical equations and pairs of Al1321 All322 AZl311 A21312 AZ1313 AZ13M AZ1321 AZ132Z~ problems by using andrelationships between Simultaneous linear A22211 AZ2212 AZZ213 AZ2214

dependent and connecting numerical equations CC22HS08independent variables algebraic andor Apply inverse operations to solve equations or formulas for a given variableMOSB-E311graphical Al1211 Al1Z12 Al1213 AZ1311 AZ1312 AZ1313 AZ1314M06B-E311 representations MOSB-E31Z AZl321 AZ1322M06B-E312 MOSB-E313

M07B-E211 CC22HS09MOSB-E314 Use reasooing to solve equations and justify the solution method M07B-EZZ1 MOBB-E31S

All141 Al1211 Al121Z Al1213 Al1221 Al1222 Al1311 Al13l2 M07B-EZ22 Al1211 M07B-EZ31 Al1313 AZ1311 AZ1312 AZ1313 AZ1314 AZ1321 AZ132ZAll221 A11141 CCZ2lSD10Al1222

Represent solve and interpret equationsinequalities and systems of equationsinequalities algebraically and graphically

AllZ11 Al1212 Al1213 Al1221 Al1222 Al1311 Al1312 All313 Al1321 Al1322 A21311 AZl312 A2l313 AZ13U

JPage13

January 2013

Pennsylvania Core Standards Mathematics

ZZ Algebraic Concepts

The Standards ofMathematical Practices Make sense ofproblems and persevere in solving them Reason abstractly and quantitatively Construct viable arguments and critique the reasoning of others Model with mathematics Use appropriate tools strategically Attend to precision Look for and make use ofstructure Look for and Pxnress repoundUlaritv in repeated reasoning

Z26 Grade 6 zz 7 Grade 7 Z2S Grade 8 ZZHS High School

Penm 1lvanias public schools shall teach challenae andsunnort ev~rv student to realize his orhermaximum Potential and to acm1ire the knowledae and skills needed to cc22sc1 CCZ2HSC1 Define evaluate and Use the conceptand notation offunttionsto interpretand appiythemin terrns oftheir context compare functions Al2111 Al2112 Al2113 Al2211 Al2212 AlZ213 Al2214 AZ21ll

AZ2112 AZ2113 A22114 G2221 G2222 G2223 G2224 GZ225 MOSBmiddotF111 MOSJH112 CC22HSC2 MOSBmiddotF113 Graph and analyze functions and use their properties to make connections between the different

representationsAl1211 Al2111 Al2112 Al2113 Al2121 Al2122 Al22l1 AZ1314 AZ1321

Al2121 Al2112

AZ1322 AZ2111 AZ2112 AZ2113 AZ2114 Al2122

CCZ2lSC3middotz2samiddotmiddotmiddotmiddotmiddotmiddotmiddotmiddotmiddotmiddotmiddotmiddotmiddotmiddot Write functions or sequences that model relationships between two quantitiesUse concepts offunctions

Al1Z11 AllZ12 Al1213 Al2111 Al2112 Al2113 Al2121 Al2l22 to model relationships Al2Z13 Al2214 A21311A21312 AZ1313 AZ1314 AZ1321AZ1322betvveen quantities AZ211l AZ2112 AZ2l13 AZZ114 A22211A22212A22Z13 AZ2214

MOSBmiddotF211 cc22HSC4MOSBmiddotF212 Interpret the effects transformations have on functions and find the inverses of functionsAl1213 =0 Al2121 Al2122 AZ1313 AZ1314 AZ1321 AZ2211 AZ2212 AZ2213g =

A12111 u AZ2Z14 AZ2221uAl2122Intentionally Blank Intentionally Blank= = Al2213 CC22HSC5Al2214 G G Construct and compare linear quadratic and exponential models to solve problems

~ ~

Al2211 Al2Z12 Al2213 Al2214 A213ll A2l312 AZ1313 AZ1314 AZ2111 AZ2112 AZ2113 AZ2114 AZ22ll AZZ21Z AZ2213 AZ2214 A2222l

CC22HSC6 Interpret functions in terms of the situations they modeL

Al2121 Al2212 Al2213 Al2221 AZ1313AZZ1l1 AZZ112 AZ2113 AZ2114 AZ2213 AZ2214 AZ2221

CC22HSC7 Apply radian measure ofan angle and the unit circle to analyze the trigonometric functions

CC22HSC8 Choose trigonometric functions to model periodic phenomena and describe the properties of the graphs

CC22HSC9 Prove the Pythagorean identity and 11Se it to calculate trigonometric ratios

G1321 G211l G2112

JPage14

January 2013

Pennsylvania Core Standards Mathematics

CC236A1 CC237A1 CC238A1 CC23lSA1 Apply appropriate tools Solve real-world and Apply the concepts of Use geometric figures and their properties to represent transformations in the plane to solve real~world and mathematical problems volume ofcylinders cones G1311 G131Z mathematical problems involving angle and spheres to solve realshy CC23HSA2 involving area surface measure area swface world and mathematical Apply rigid transformations to determine and explain congruence area and volume area circumference problems GU11 G1312

and volume CC23HSA3 M06C-Gll1 M08C-C3ll Verify and apply geometric theorems as they relate to geometric figures M06C-GllZ M07C-G2l1 G2312 G1211 G1212 G1213 G1214 G1215 G1321 G2211 G2212 G2221 G2222 M06C-Gll3 M07C-G212 G2223 G2224 G222S M06C-G1L4 M07C-G22l CC23HS-A4 M06C-Gli5 M07C-G222 Apply the concept ofcongruence to create geometric constructions

MQsectt_-_G~Jsect_ --- shy -- shy -- shy ---------------------middot-middot CC23HSA5

--------------------------middotCC237A2 CC238A2 Create justifications based on transformations to establish similarity ofplane figures VlSUalize and represent Understand and apply G1311 G1312 geometric figures and congruence similarity and CC23HSA6 descnbethe geometric transformations Verify and apply theorems involving similarity as they relate to plane figures relatiooships betWeen using various tools G1311 G1312 G1321 them

CC23HSA7_ _- Intentionally Blank MOSC-C111 - Apply trigonometric ratios to solve problems involving right triangles~ sect M07C-Glll M08C-Gll2 = G21ll G21120

M07C-Gll2 MOSC-G113 CC23HSA8 M07C-Gll3 M08C-Gll4 Apply geometric theorems to veruy properties ofcircless ~M07C-Gll4 GJ211 ~ G1111 G1112 G1113 G1114 G1321 G223l

G1214 CC23HS-A9

-----------------------shy ----------------------shyG2211 Extend the concept ofsimilarity to determine arc lengths and areas ofsectors ofcircles

CCi32A3--shy -shy G1111 G1112 G1l13 G1114 G2221 G2222 G2223 G2224 G2225 G2231 Understand and apply the CC23HSA10 Pythagorean Theoremto Translate beti-veen the geometric description and the equation for a conic section solve problems A221l4 AZ221l

CC23HSA11 MOSC-G211 Apply coordinate geometry to prove simple geometric theorems algebraically MOSC-G212 G2121 GZ122 G2123

Intentionally Blank Intentionally Blank MOSC-G213 CC23HSA12 G2111 Explain volume formulas and use them to solve problems G21Zl G2311 G231Z G2313

CC23llSA13 Analyze relationships between two-dimensional and three-dimensional objects

G1111 G111Z G1113 Gl114 G1211 G1212 G1213 G1214 G1215 G2321 CC23HSA14 Apply geometric concepts to model and solve real world problems

G2241 G231l G2312 GZ313

23 Geometrv The Standards ofMathematical Practices

Make sense of problems and persevere in solving them Reason abstractly and quantitatively ConstructViable arguments and critique the reasoning ofothers Model with mathematics Use appropriate tools strategically Attend to precision Look for and make use of structure Look for and evnress reUlaritv in reneated reasoniniz

Grade 6 Grade7 Grades High School Z36 237 23S Z3HS

Pennltvfvanias vublic schools shall teach challen e and sunnort evPrv student to realize his or her maximum votential and to acauire the knowledae and skills needed to

jPage15

)anuazy 2013

Pennsylvania Core Standards Mathematics

24 Measurement Data and Probabilitv The Standards ofMathematical Practices

Make sense ofproblems and persevere in solving them Reason abstractly and quantitatively Construct viable ar~ments and critique the reasoning ofothers Model with mathematics Use appropriate tools strategically Attend to precision Look for and make use ofstructure Look for and express regularity in repeated reasoning

Grade 6 246

Grade7 247

Grade3 243

High School 24HS

Pennsylvanias public schools shall teach challenge and support every student to realize his or her mt1Ximum potential and to acquire the mowedge andskills needed to

~ E 0 0

d ilc c g ~ e

CCZ46B1 Demonstrate an understanding of statistical vaiability by displaying analyzing and summarizing distributions

M06DmiddotSlll M06DmiddotSll2 M06D-Sll3 M06D-Sll4

------------------------shy

Intentionally Blank

------------------------shy

CCZ47B1 Draw inferences about populatioos based on rardom sampling concepts

M07D-S1l1 M07D-S1l2

middotcczyen7-szmiddot----middot----- shy -Draw informal comparative inferences about two populations

M07D-S211

middotcci47S3----- --- --- -shy[mrestigate cbaoce processes and develop use and evaluate probability models

CCZ48B1 Analyze andor interpret bivariate data displayed in multiple representations

MOSD-S11l MOSDmiddotS112 MOSDmiddotS113 AlZ22l

iCi4862 ----------shyUnderstand thatpatterns ofassociation can be seen in bivariate data utilizing frequencies

MOSDmiddotS121

-------------------------shy

c a 0 0

d ltgt middotc ~ middotc g

sect

CCZ4HSB1 Summarize represent and interpret data on a single count or measurement variable

A12212 Al2311 A12321 Al2322 Al2323

CCZ4HSB2 Summarize represent and interpret data on two categorical and quantitative variables

Al21ll Al2112 A12113 Al2121 Al2122 Al2221 A2211l AZ2311 AZ2312

CCZ4HSB3 Analyze linear models to make interpretations based on the data

Al222l A1231l Al2321 Al2322 Al2323 A22311 AZ2312

CCZ4HSB4 Recognize and evaluate random processes underlying statistical experiments

Al2331 A223Z1 A2232Z A22323

CC24HSBS Make inferences and justify conclusions based on sample surveys experiments and observational studies

Al2321 Al2322 Al2323 A22321 A22322 A22323

CCZ4J5B6 Use the concepts ofindependence and conditional probability to interpret data

AZ2321 A22322 A22323

Intentionally Blunk M07D-S31l M07D-S32l M07D-S322 M07D-S323 Al2331

lntentionany Blank CCZ4HSB7 Apply the rules of probability to compute probabilities ofcompound events in a uniform probability model

Al2331 A223Z1 A223ZZ A22323

[Page16

January 2013

Pennsylvania Core Standards Mathematics

Key Terms for this Document

Standards for Mathematical Content-These standards define what students should know and be able to do in their study of mathematics

Standards for Mathematical Practice-These standards describe the processes and proficiencies in which all students grades K-12 should engage Educators

must instill these standards of practice in their students so that they become habitual The standards for mathematical practice should be used as the vehicle to

deliver the standards of mathematical content

Standard Algorithm-A locally agreed upon method of computation which is conventionally taught for solving mathematical problems

Decimal Fraction-A fraction whose denominator is a power of ten (examples 2100 810) These fractions are commonly expressed as decimals

Unit Fraction-A rational number written as a fraction where the numerator is one and the denominator is a positive integer (example 120)

Bivariate Data-The data involves two variables and is usually represented as a scatter plot

Rule-A single operation (examples add 5 multiply by 2)

IP age 17

January 2013

Page 14: Academic Standards for Mathematics...The Co=on Core Standards in Mathematics in grades PreK-5 lay a solid foundation in whole numbers, addition, subtraction, multiplication, division,

Pennsylvania Core Standards Mathematics

ZZ Algebraic Concepts

The Standards ofMathematical Practices Make sense ofproblems and persevere in solving them Reason abstractly and quantitatively Construct viable arguments and critique the reasoning of others Model with mathematics Use appropriate tools strategically Attend to precision Look for and make use ofstructure Look for and Pxnress repoundUlaritv in repeated reasoning

Z26 Grade 6 zz 7 Grade 7 Z2S Grade 8 ZZHS High School

Penm 1lvanias public schools shall teach challenae andsunnort ev~rv student to realize his orhermaximum Potential and to acm1ire the knowledae and skills needed to cc22sc1 CCZ2HSC1 Define evaluate and Use the conceptand notation offunttionsto interpretand appiythemin terrns oftheir context compare functions Al2111 Al2112 Al2113 Al2211 Al2212 AlZ213 Al2214 AZ21ll

AZ2112 AZ2113 A22114 G2221 G2222 G2223 G2224 GZ225 MOSBmiddotF111 MOSJH112 CC22HSC2 MOSBmiddotF113 Graph and analyze functions and use their properties to make connections between the different

representationsAl1211 Al2111 Al2112 Al2113 Al2121 Al2122 Al22l1 AZ1314 AZ1321

Al2121 Al2112

AZ1322 AZ2111 AZ2112 AZ2113 AZ2114 Al2122

CCZ2lSC3middotz2samiddotmiddotmiddotmiddotmiddotmiddotmiddotmiddotmiddotmiddotmiddotmiddotmiddotmiddot Write functions or sequences that model relationships between two quantitiesUse concepts offunctions

Al1Z11 AllZ12 Al1213 Al2111 Al2112 Al2113 Al2121 Al2l22 to model relationships Al2Z13 Al2214 A21311A21312 AZ1313 AZ1314 AZ1321AZ1322betvveen quantities AZ211l AZ2112 AZ2l13 AZZ114 A22211A22212A22Z13 AZ2214

MOSBmiddotF211 cc22HSC4MOSBmiddotF212 Interpret the effects transformations have on functions and find the inverses of functionsAl1213 =0 Al2121 Al2122 AZ1313 AZ1314 AZ1321 AZ2211 AZ2212 AZ2213g =

A12111 u AZ2Z14 AZ2221uAl2122Intentionally Blank Intentionally Blank= = Al2213 CC22HSC5Al2214 G G Construct and compare linear quadratic and exponential models to solve problems

~ ~

Al2211 Al2Z12 Al2213 Al2214 A213ll A2l312 AZ1313 AZ1314 AZ2111 AZ2112 AZ2113 AZ2114 AZ22ll AZZ21Z AZ2213 AZ2214 A2222l

CC22HSC6 Interpret functions in terms of the situations they modeL

Al2121 Al2212 Al2213 Al2221 AZ1313AZZ1l1 AZZ112 AZ2113 AZ2114 AZ2213 AZ2214 AZ2221

CC22HSC7 Apply radian measure ofan angle and the unit circle to analyze the trigonometric functions

CC22HSC8 Choose trigonometric functions to model periodic phenomena and describe the properties of the graphs

CC22HSC9 Prove the Pythagorean identity and 11Se it to calculate trigonometric ratios

G1321 G211l G2112

JPage14

January 2013

Pennsylvania Core Standards Mathematics

CC236A1 CC237A1 CC238A1 CC23lSA1 Apply appropriate tools Solve real-world and Apply the concepts of Use geometric figures and their properties to represent transformations in the plane to solve real~world and mathematical problems volume ofcylinders cones G1311 G131Z mathematical problems involving angle and spheres to solve realshy CC23HSA2 involving area surface measure area swface world and mathematical Apply rigid transformations to determine and explain congruence area and volume area circumference problems GU11 G1312

and volume CC23HSA3 M06C-Gll1 M08C-C3ll Verify and apply geometric theorems as they relate to geometric figures M06C-GllZ M07C-G2l1 G2312 G1211 G1212 G1213 G1214 G1215 G1321 G2211 G2212 G2221 G2222 M06C-Gll3 M07C-G212 G2223 G2224 G222S M06C-G1L4 M07C-G22l CC23HS-A4 M06C-Gli5 M07C-G222 Apply the concept ofcongruence to create geometric constructions

MQsectt_-_G~Jsect_ --- shy -- shy -- shy ---------------------middot-middot CC23HSA5

--------------------------middotCC237A2 CC238A2 Create justifications based on transformations to establish similarity ofplane figures VlSUalize and represent Understand and apply G1311 G1312 geometric figures and congruence similarity and CC23HSA6 descnbethe geometric transformations Verify and apply theorems involving similarity as they relate to plane figures relatiooships betWeen using various tools G1311 G1312 G1321 them

CC23HSA7_ _- Intentionally Blank MOSC-C111 - Apply trigonometric ratios to solve problems involving right triangles~ sect M07C-Glll M08C-Gll2 = G21ll G21120

M07C-Gll2 MOSC-G113 CC23HSA8 M07C-Gll3 M08C-Gll4 Apply geometric theorems to veruy properties ofcircless ~M07C-Gll4 GJ211 ~ G1111 G1112 G1113 G1114 G1321 G223l

G1214 CC23HS-A9

-----------------------shy ----------------------shyG2211 Extend the concept ofsimilarity to determine arc lengths and areas ofsectors ofcircles

CCi32A3--shy -shy G1111 G1112 G1l13 G1114 G2221 G2222 G2223 G2224 G2225 G2231 Understand and apply the CC23HSA10 Pythagorean Theoremto Translate beti-veen the geometric description and the equation for a conic section solve problems A221l4 AZ221l

CC23HSA11 MOSC-G211 Apply coordinate geometry to prove simple geometric theorems algebraically MOSC-G212 G2121 GZ122 G2123

Intentionally Blank Intentionally Blank MOSC-G213 CC23HSA12 G2111 Explain volume formulas and use them to solve problems G21Zl G2311 G231Z G2313

CC23llSA13 Analyze relationships between two-dimensional and three-dimensional objects

G1111 G111Z G1113 Gl114 G1211 G1212 G1213 G1214 G1215 G2321 CC23HSA14 Apply geometric concepts to model and solve real world problems

G2241 G231l G2312 GZ313

23 Geometrv The Standards ofMathematical Practices

Make sense of problems and persevere in solving them Reason abstractly and quantitatively ConstructViable arguments and critique the reasoning ofothers Model with mathematics Use appropriate tools strategically Attend to precision Look for and make use of structure Look for and evnress reUlaritv in reneated reasoniniz

Grade 6 Grade7 Grades High School Z36 237 23S Z3HS

Pennltvfvanias vublic schools shall teach challen e and sunnort evPrv student to realize his or her maximum votential and to acauire the knowledae and skills needed to

jPage15

)anuazy 2013

Pennsylvania Core Standards Mathematics

24 Measurement Data and Probabilitv The Standards ofMathematical Practices

Make sense ofproblems and persevere in solving them Reason abstractly and quantitatively Construct viable ar~ments and critique the reasoning ofothers Model with mathematics Use appropriate tools strategically Attend to precision Look for and make use ofstructure Look for and express regularity in repeated reasoning

Grade 6 246

Grade7 247

Grade3 243

High School 24HS

Pennsylvanias public schools shall teach challenge and support every student to realize his or her mt1Ximum potential and to acquire the mowedge andskills needed to

~ E 0 0

d ilc c g ~ e

CCZ46B1 Demonstrate an understanding of statistical vaiability by displaying analyzing and summarizing distributions

M06DmiddotSlll M06DmiddotSll2 M06D-Sll3 M06D-Sll4

------------------------shy

Intentionally Blank

------------------------shy

CCZ47B1 Draw inferences about populatioos based on rardom sampling concepts

M07D-S1l1 M07D-S1l2

middotcczyen7-szmiddot----middot----- shy -Draw informal comparative inferences about two populations

M07D-S211

middotcci47S3----- --- --- -shy[mrestigate cbaoce processes and develop use and evaluate probability models

CCZ48B1 Analyze andor interpret bivariate data displayed in multiple representations

MOSD-S11l MOSDmiddotS112 MOSDmiddotS113 AlZ22l

iCi4862 ----------shyUnderstand thatpatterns ofassociation can be seen in bivariate data utilizing frequencies

MOSDmiddotS121

-------------------------shy

c a 0 0

d ltgt middotc ~ middotc g

sect

CCZ4HSB1 Summarize represent and interpret data on a single count or measurement variable

A12212 Al2311 A12321 Al2322 Al2323

CCZ4HSB2 Summarize represent and interpret data on two categorical and quantitative variables

Al21ll Al2112 A12113 Al2121 Al2122 Al2221 A2211l AZ2311 AZ2312

CCZ4HSB3 Analyze linear models to make interpretations based on the data

Al222l A1231l Al2321 Al2322 Al2323 A22311 AZ2312

CCZ4HSB4 Recognize and evaluate random processes underlying statistical experiments

Al2331 A223Z1 A2232Z A22323

CC24HSBS Make inferences and justify conclusions based on sample surveys experiments and observational studies

Al2321 Al2322 Al2323 A22321 A22322 A22323

CCZ4J5B6 Use the concepts ofindependence and conditional probability to interpret data

AZ2321 A22322 A22323

Intentionally Blunk M07D-S31l M07D-S32l M07D-S322 M07D-S323 Al2331

lntentionany Blank CCZ4HSB7 Apply the rules of probability to compute probabilities ofcompound events in a uniform probability model

Al2331 A223Z1 A223ZZ A22323

[Page16

January 2013

Pennsylvania Core Standards Mathematics

Key Terms for this Document

Standards for Mathematical Content-These standards define what students should know and be able to do in their study of mathematics

Standards for Mathematical Practice-These standards describe the processes and proficiencies in which all students grades K-12 should engage Educators

must instill these standards of practice in their students so that they become habitual The standards for mathematical practice should be used as the vehicle to

deliver the standards of mathematical content

Standard Algorithm-A locally agreed upon method of computation which is conventionally taught for solving mathematical problems

Decimal Fraction-A fraction whose denominator is a power of ten (examples 2100 810) These fractions are commonly expressed as decimals

Unit Fraction-A rational number written as a fraction where the numerator is one and the denominator is a positive integer (example 120)

Bivariate Data-The data involves two variables and is usually represented as a scatter plot

Rule-A single operation (examples add 5 multiply by 2)

IP age 17

January 2013

Page 15: Academic Standards for Mathematics...The Co=on Core Standards in Mathematics in grades PreK-5 lay a solid foundation in whole numbers, addition, subtraction, multiplication, division,

Pennsylvania Core Standards Mathematics

CC236A1 CC237A1 CC238A1 CC23lSA1 Apply appropriate tools Solve real-world and Apply the concepts of Use geometric figures and their properties to represent transformations in the plane to solve real~world and mathematical problems volume ofcylinders cones G1311 G131Z mathematical problems involving angle and spheres to solve realshy CC23HSA2 involving area surface measure area swface world and mathematical Apply rigid transformations to determine and explain congruence area and volume area circumference problems GU11 G1312

and volume CC23HSA3 M06C-Gll1 M08C-C3ll Verify and apply geometric theorems as they relate to geometric figures M06C-GllZ M07C-G2l1 G2312 G1211 G1212 G1213 G1214 G1215 G1321 G2211 G2212 G2221 G2222 M06C-Gll3 M07C-G212 G2223 G2224 G222S M06C-G1L4 M07C-G22l CC23HS-A4 M06C-Gli5 M07C-G222 Apply the concept ofcongruence to create geometric constructions

MQsectt_-_G~Jsect_ --- shy -- shy -- shy ---------------------middot-middot CC23HSA5

--------------------------middotCC237A2 CC238A2 Create justifications based on transformations to establish similarity ofplane figures VlSUalize and represent Understand and apply G1311 G1312 geometric figures and congruence similarity and CC23HSA6 descnbethe geometric transformations Verify and apply theorems involving similarity as they relate to plane figures relatiooships betWeen using various tools G1311 G1312 G1321 them

CC23HSA7_ _- Intentionally Blank MOSC-C111 - Apply trigonometric ratios to solve problems involving right triangles~ sect M07C-Glll M08C-Gll2 = G21ll G21120

M07C-Gll2 MOSC-G113 CC23HSA8 M07C-Gll3 M08C-Gll4 Apply geometric theorems to veruy properties ofcircless ~M07C-Gll4 GJ211 ~ G1111 G1112 G1113 G1114 G1321 G223l

G1214 CC23HS-A9

-----------------------shy ----------------------shyG2211 Extend the concept ofsimilarity to determine arc lengths and areas ofsectors ofcircles

CCi32A3--shy -shy G1111 G1112 G1l13 G1114 G2221 G2222 G2223 G2224 G2225 G2231 Understand and apply the CC23HSA10 Pythagorean Theoremto Translate beti-veen the geometric description and the equation for a conic section solve problems A221l4 AZ221l

CC23HSA11 MOSC-G211 Apply coordinate geometry to prove simple geometric theorems algebraically MOSC-G212 G2121 GZ122 G2123

Intentionally Blank Intentionally Blank MOSC-G213 CC23HSA12 G2111 Explain volume formulas and use them to solve problems G21Zl G2311 G231Z G2313

CC23llSA13 Analyze relationships between two-dimensional and three-dimensional objects

G1111 G111Z G1113 Gl114 G1211 G1212 G1213 G1214 G1215 G2321 CC23HSA14 Apply geometric concepts to model and solve real world problems

G2241 G231l G2312 GZ313

23 Geometrv The Standards ofMathematical Practices

Make sense of problems and persevere in solving them Reason abstractly and quantitatively ConstructViable arguments and critique the reasoning ofothers Model with mathematics Use appropriate tools strategically Attend to precision Look for and make use of structure Look for and evnress reUlaritv in reneated reasoniniz

Grade 6 Grade7 Grades High School Z36 237 23S Z3HS

Pennltvfvanias vublic schools shall teach challen e and sunnort evPrv student to realize his or her maximum votential and to acauire the knowledae and skills needed to

jPage15

)anuazy 2013

Pennsylvania Core Standards Mathematics

24 Measurement Data and Probabilitv The Standards ofMathematical Practices

Make sense ofproblems and persevere in solving them Reason abstractly and quantitatively Construct viable ar~ments and critique the reasoning ofothers Model with mathematics Use appropriate tools strategically Attend to precision Look for and make use ofstructure Look for and express regularity in repeated reasoning

Grade 6 246

Grade7 247

Grade3 243

High School 24HS

Pennsylvanias public schools shall teach challenge and support every student to realize his or her mt1Ximum potential and to acquire the mowedge andskills needed to

~ E 0 0

d ilc c g ~ e

CCZ46B1 Demonstrate an understanding of statistical vaiability by displaying analyzing and summarizing distributions

M06DmiddotSlll M06DmiddotSll2 M06D-Sll3 M06D-Sll4

------------------------shy

Intentionally Blank

------------------------shy

CCZ47B1 Draw inferences about populatioos based on rardom sampling concepts

M07D-S1l1 M07D-S1l2

middotcczyen7-szmiddot----middot----- shy -Draw informal comparative inferences about two populations

M07D-S211

middotcci47S3----- --- --- -shy[mrestigate cbaoce processes and develop use and evaluate probability models

CCZ48B1 Analyze andor interpret bivariate data displayed in multiple representations

MOSD-S11l MOSDmiddotS112 MOSDmiddotS113 AlZ22l

iCi4862 ----------shyUnderstand thatpatterns ofassociation can be seen in bivariate data utilizing frequencies

MOSDmiddotS121

-------------------------shy

c a 0 0

d ltgt middotc ~ middotc g

sect

CCZ4HSB1 Summarize represent and interpret data on a single count or measurement variable

A12212 Al2311 A12321 Al2322 Al2323

CCZ4HSB2 Summarize represent and interpret data on two categorical and quantitative variables

Al21ll Al2112 A12113 Al2121 Al2122 Al2221 A2211l AZ2311 AZ2312

CCZ4HSB3 Analyze linear models to make interpretations based on the data

Al222l A1231l Al2321 Al2322 Al2323 A22311 AZ2312

CCZ4HSB4 Recognize and evaluate random processes underlying statistical experiments

Al2331 A223Z1 A2232Z A22323

CC24HSBS Make inferences and justify conclusions based on sample surveys experiments and observational studies

Al2321 Al2322 Al2323 A22321 A22322 A22323

CCZ4J5B6 Use the concepts ofindependence and conditional probability to interpret data

AZ2321 A22322 A22323

Intentionally Blunk M07D-S31l M07D-S32l M07D-S322 M07D-S323 Al2331

lntentionany Blank CCZ4HSB7 Apply the rules of probability to compute probabilities ofcompound events in a uniform probability model

Al2331 A223Z1 A223ZZ A22323

[Page16

January 2013

Pennsylvania Core Standards Mathematics

Key Terms for this Document

Standards for Mathematical Content-These standards define what students should know and be able to do in their study of mathematics

Standards for Mathematical Practice-These standards describe the processes and proficiencies in which all students grades K-12 should engage Educators

must instill these standards of practice in their students so that they become habitual The standards for mathematical practice should be used as the vehicle to

deliver the standards of mathematical content

Standard Algorithm-A locally agreed upon method of computation which is conventionally taught for solving mathematical problems

Decimal Fraction-A fraction whose denominator is a power of ten (examples 2100 810) These fractions are commonly expressed as decimals

Unit Fraction-A rational number written as a fraction where the numerator is one and the denominator is a positive integer (example 120)

Bivariate Data-The data involves two variables and is usually represented as a scatter plot

Rule-A single operation (examples add 5 multiply by 2)

IP age 17

January 2013

Page 16: Academic Standards for Mathematics...The Co=on Core Standards in Mathematics in grades PreK-5 lay a solid foundation in whole numbers, addition, subtraction, multiplication, division,

Pennsylvania Core Standards Mathematics

24 Measurement Data and Probabilitv The Standards ofMathematical Practices

Make sense ofproblems and persevere in solving them Reason abstractly and quantitatively Construct viable ar~ments and critique the reasoning ofothers Model with mathematics Use appropriate tools strategically Attend to precision Look for and make use ofstructure Look for and express regularity in repeated reasoning

Grade 6 246

Grade7 247

Grade3 243

High School 24HS

Pennsylvanias public schools shall teach challenge and support every student to realize his or her mt1Ximum potential and to acquire the mowedge andskills needed to

~ E 0 0

d ilc c g ~ e

CCZ46B1 Demonstrate an understanding of statistical vaiability by displaying analyzing and summarizing distributions

M06DmiddotSlll M06DmiddotSll2 M06D-Sll3 M06D-Sll4

------------------------shy

Intentionally Blank

------------------------shy

CCZ47B1 Draw inferences about populatioos based on rardom sampling concepts

M07D-S1l1 M07D-S1l2

middotcczyen7-szmiddot----middot----- shy -Draw informal comparative inferences about two populations

M07D-S211

middotcci47S3----- --- --- -shy[mrestigate cbaoce processes and develop use and evaluate probability models

CCZ48B1 Analyze andor interpret bivariate data displayed in multiple representations

MOSD-S11l MOSDmiddotS112 MOSDmiddotS113 AlZ22l

iCi4862 ----------shyUnderstand thatpatterns ofassociation can be seen in bivariate data utilizing frequencies

MOSDmiddotS121

-------------------------shy

c a 0 0

d ltgt middotc ~ middotc g

sect

CCZ4HSB1 Summarize represent and interpret data on a single count or measurement variable

A12212 Al2311 A12321 Al2322 Al2323

CCZ4HSB2 Summarize represent and interpret data on two categorical and quantitative variables

Al21ll Al2112 A12113 Al2121 Al2122 Al2221 A2211l AZ2311 AZ2312

CCZ4HSB3 Analyze linear models to make interpretations based on the data

Al222l A1231l Al2321 Al2322 Al2323 A22311 AZ2312

CCZ4HSB4 Recognize and evaluate random processes underlying statistical experiments

Al2331 A223Z1 A2232Z A22323

CC24HSBS Make inferences and justify conclusions based on sample surveys experiments and observational studies

Al2321 Al2322 Al2323 A22321 A22322 A22323

CCZ4J5B6 Use the concepts ofindependence and conditional probability to interpret data

AZ2321 A22322 A22323

Intentionally Blunk M07D-S31l M07D-S32l M07D-S322 M07D-S323 Al2331

lntentionany Blank CCZ4HSB7 Apply the rules of probability to compute probabilities ofcompound events in a uniform probability model

Al2331 A223Z1 A223ZZ A22323

[Page16

January 2013

Pennsylvania Core Standards Mathematics

Key Terms for this Document

Standards for Mathematical Content-These standards define what students should know and be able to do in their study of mathematics

Standards for Mathematical Practice-These standards describe the processes and proficiencies in which all students grades K-12 should engage Educators

must instill these standards of practice in their students so that they become habitual The standards for mathematical practice should be used as the vehicle to

deliver the standards of mathematical content

Standard Algorithm-A locally agreed upon method of computation which is conventionally taught for solving mathematical problems

Decimal Fraction-A fraction whose denominator is a power of ten (examples 2100 810) These fractions are commonly expressed as decimals

Unit Fraction-A rational number written as a fraction where the numerator is one and the denominator is a positive integer (example 120)

Bivariate Data-The data involves two variables and is usually represented as a scatter plot

Rule-A single operation (examples add 5 multiply by 2)

IP age 17

January 2013

Page 17: Academic Standards for Mathematics...The Co=on Core Standards in Mathematics in grades PreK-5 lay a solid foundation in whole numbers, addition, subtraction, multiplication, division,

Pennsylvania Core Standards Mathematics

Key Terms for this Document

Standards for Mathematical Content-These standards define what students should know and be able to do in their study of mathematics

Standards for Mathematical Practice-These standards describe the processes and proficiencies in which all students grades K-12 should engage Educators

must instill these standards of practice in their students so that they become habitual The standards for mathematical practice should be used as the vehicle to

deliver the standards of mathematical content

Standard Algorithm-A locally agreed upon method of computation which is conventionally taught for solving mathematical problems

Decimal Fraction-A fraction whose denominator is a power of ten (examples 2100 810) These fractions are commonly expressed as decimals

Unit Fraction-A rational number written as a fraction where the numerator is one and the denominator is a positive integer (example 120)

Bivariate Data-The data involves two variables and is usually represented as a scatter plot

Rule-A single operation (examples add 5 multiply by 2)

IP age 17

January 2013

Page 18: Academic Standards for Mathematics...The Co=on Core Standards in Mathematics in grades PreK-5 lay a solid foundation in whole numbers, addition, subtraction, multiplication, division,