Lining Up: The Relationship
between the Common Core State Standards
and Five Sets of Comparison Standards
David T. Conley
Kathryn V. Drummond
Alicia de Gonzalez
Mary Seburn
Odile Stout
Jennifer Rooseboom
Acknowledgements
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the project and data collection.
Additional EPIC staff made contributions beyond those listed as authors of the
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The Authors
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of the Bill & Melinda Gates Foundation.
Prepared and published by the Educational Policy Improvement Center.
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Alignment Study •
Executive Summary
In June , the National Governors Association
Center for Best Practices (NGA Center) and the Council
of Chief State School Officers (CCSSO) released the
Common Core State Standards. The stated aim of the
Common Core standards is to define the knowledge
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$$440 SFMFBTFEUIF$PNNPO$PSF4UBUF4UBOEBSET1 The stated aim
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adopted the standards. This widespread potential implementation of
the Common Core standards has led to interest by states and national
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topic areas with the same emphases?
Alig n m e nt
To help answer these questions, the Educational Policy
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Core standards cover similar content, how broadly they cover
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mathematics:
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Executive Summary •
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Study Overview
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mathematics, and cross-disciplinary standards
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and mathematics,2 EFWFMPQFE BT DPMMFHF
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mathematics standards, developed by EPIC,
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Comparison Standards
Methodology
The comparison standards selected for the study come
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quality educational standards: California and Massachusetts
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1.
comparison standards the same as or different from what
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2.
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3.
How broadly do the matched comparison standards cover
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Massachusetts: The Massachusetts Curriculum
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1.
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between the comparison standards and the Common
Core standards.
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and mathematics sections.
3
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additional required components, which each IB school selects. The number of
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standards.
2
Executive Summary •
2.
3.
Depth of Knowledge Consistency: a comparison of
contained in the Common Core standards. For ELA and
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sets of comparison standards and the Common Core
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standards.
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Breadth of Coverage: how broadly matched comparison
standards cover content elements of the Common Core
standards.
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every standard in the Common Core standards may not have
a match with each and every set of comparison standards,
the topics around which the Common Core standards are
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Conclusion
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each comparison standard matched content in the Common
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up to three Common Core standards that corresponded with
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a standard in a comparison set. The limit of three standards
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should concentrate only on content central to the statements.
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Findings
to enable all students to pursue successful futures beyond
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concurrence between the Common Core standards and the
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mathematics than in ELA and literacy. For ELA and literacy,
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Concurrence criterion. For mathematics, all 25 analyses at the
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criterion.
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strand-level analyses indicate that the comparison standard
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sets are at or above the level of the Common Core standards.
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indicate that the comparison standard sets are at or above the
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from the comparison sets tend to cover the breadth of topics
Executive Summary •
Table of Contents
Executive Summary ....................................................................&4
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'JOEJOHT .........................................................................................................&4
Conclusion.....................................................................................................&4
Chapter 1: Introduction .................................................................... 1
Chapter 2: Methodology ..................................................................
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3BUFST ...........................................................................................................
3BUFS0SJFOUBUJPO .......................................................................................... 5
3BUFS1SPDFTT ............................................................................................... 5
3BUJOHPG$PNNPO$PSF4UBOEBSET ................................................................... 5
&OHMJTI-BOHVBHF"SUTBOE-JUFSBDZ ............................................................ 5
Mathematics ................................................................................................. 7
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3BUFS3FMJBCJMJUZ ............................................................................................
%BUB"OBMZTJT.................................................................................................... 10
$BUFHPSJDBM$PODVSSFODF ........................................................................... 10
%FQUIPG,OPXMFEHF$POTJTUFODZ.............................................................. 10
#SFBEUIPG$PWFSBHF .................................................................................. 11
Chapter 3: Results for English Language Arts
and Literacy ............................................................................................ 12
Match................................................................................................................ 12
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$PSF4UBOEBSET .......................................................................................... 12
.BUDIGPS&BDI$PNQBSJTPO4FUUPUIF$PNNPO$PSF
4UBOEBSET$BUFHPSJDBM$PODVSSFODF4UBUJTUJD ............................................ 13
%FQUIPG,OPXMFEHF......................................................................................... 15
3BUJOHGPS$PNNPO$PSF4UBOEBSET .......................................................... 15
%0,$POTJTUFODZPG&BDI$PNQBSJTPO4FUUPUIF
$PNNPO$PSF4UBOEBSET........................................................................... 15
#SFBEUIPG$PWFSBHF ........................................................................................ 17
Chapter 4: Results for Mathematics ..................................................
Match................................................................................................................
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$PSF4UBOEBSET ..........................................................................................
.BUDIGPS&BDI$PNQBSJTPO4FUUPUIF$PNNPO$PSF4UBOEBSET ............ 21
$BUFHPSJDBM$PODVSSFODF4UBUJTUJD ............................................................. 21
%FQUIPG,OPXMFEHF......................................................................................... 21
3BUJOHTGPS$PNNPO$PSF4UBOEBSET ........................................................ 22
%0,$POTJTUFODZPG&BDI$PNQBSJTPO4FUUPUIF$PNNPO
$PSF4UBOEBSET .......................................................................................... 23
#SFBEUIPG$PWFSBHF ........................................................................................
Table of Contents • i
Table of Contents
Chapter 5: Summary and Discussion ............................................... 25
$MPTJOH/PUFGSPNUIF"VUIPST ......................................................................... 27
References ..............................................................................................
Appendix A: Description of the Depth of Knowledge
Calculation .............................................................................................. 32
Appendix B: Common Core Standards ............................................ 33
Appendix C: Results by Individual Comparison
Standards ................................................................................................ 52
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Match ......................................................................................................... 52
#SFBEUIPG$PWFSBHF .................................................................................. 53
%FQUIPG,OPXMFEHF .................................................................................. 53
.BUIFNBUJDT'JOEJOHTGPSUIF$BMJGPSOJB4UBOEBSET .........................................
Match .........................................................................................................
#SFBEUIPG$PWFSBHF .................................................................................. 55
%FQUIPG,OPXMFEHF .................................................................................. 55
.BTTBDIVTFUUT4UBOEBSET ................................................................................
&OHMJTI-BOHVBHF"SUTBOE-JUFSBDZ'JOEJOHTGPSUIF
.BTTBDIVTFUUT4UBOEBSET ................................................................................
Match .........................................................................................................
#SFBEUIPG$PWFSBHF .................................................................................. 57
%FQUIPG,OPXMFEHF .................................................................................. 57
.BUIFNBUJDT'JOEJOHTGPSUIF.BTTBDIVTFUUT4UBOEBSET ................................
Match .........................................................................................................
#SFBEUIPG$PWFSBHF ..................................................................................
%FQUIPG,OPXMFEHF ..................................................................................
5FYBT$PMMFHFBOE$BSFFS3FBEJOFTT4UBOEBSET ............................................
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5FYBT$PMMFHFBOE$BSFFS3FBEJOFTT4UBOEBSET ............................................
Match .........................................................................................................
#SFBEUIPG$PWFSBHF ..................................................................................
%FQUIPG,OPXMFEHF ..................................................................................
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Match .........................................................................................................
#SFBEUIPG$PWFSBHF ..................................................................................
%FQUIPG,OPXMFEHF ..................................................................................
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,OPXMFEHFBOE4LJMMTGPS6OJWFSTJUZ4VDDFTT4UBOEBSET .................................
Match .........................................................................................................
Table of Contents • ii
Table of Contents
#SFBEUIPG$PWFSBHF ..................................................................................
%FQUIPG,OPXMFEHF ..................................................................................
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Match .........................................................................................................
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%FQUIPG,OPXMFEHF ..................................................................................
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Match .........................................................................................................
#SFBEUIPG$PWFSBHF ..................................................................................
%FQUIPG,OPXMFEHF ..................................................................................
.BUIFNBUJDT'JOEJOHTGPSUIF*OUFSOBUJPOBM#BDDBMBVSFBUF4UBOEBSET ............ 70
Match ......................................................................................................... 70
#SFBEUIPG$PWFSBHF .................................................................................. 71
%FQUIPG,OPXMFEHF .................................................................................. 71
Appendix D: Alignment Matches for Common
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"SUTBOE-JUFSBDZ5PQJDT CZ$PNQBSJTPO4UBOEBSE4FU .................................. 72
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$PNQBSJTPO4UBOEBSE4FUGPS.BUIFNBUJDT ..................................................... 75
Table of Contents • iii
Chapter
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sets of standards were selected because they were either
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DPWFSFETJNJMBSDPOUFOUJGTP IPXCSPBEMZUIFZDPWFSFEUIF
DPNQBSJTPOTUBOEBSETBOEXIFUIFSUIFDPHOJUJWFDIBMMFOHF
MFWFMPGBMJHOFEDPOUFOUXBTDPNQBSBCMF
The study addressed three research questions for each
PG UIF UXP TVCKFDU BSFBT GPS XIJDI $PNNPO $PSF 4UBUF
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arts and literacy, and mathematics. These three questions
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| Introduction
The research questions are as follows:
1.
5PXIBUFYUFOUBSFUIFLOPXMFEHFBOETLJMMTGPVOEJO
the comparison standards the same as or different
from what is described in the Common Core
TUBOEBSET NBUDI
2.
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$PNNPO$PSFTUBOEBSETBOEUPXIBUFYUFOUBSFUIF
NBUDIFEDPNQBSJTPOTUBOEBSETBUBIJHIFSPSMPXFS
MFWFMPGDPHOJUJWFDPNQMFYJUZ EFQUI
3.
How broadly do the matched comparison standards
cover the content of the Common Core standards?
CSFBEUI
The comparison standards included sets of standards from
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standards: California and Massachusetts (Achieve, Inc.,
5IF 'PSEIBN 'PVOEBUJPO BXBSEFE UIF $BMJGPSOJB
TUBOEBSET B SBSF " HSBEF GPS CPUI &OHMJTI MBOHVBHF BSUT
and mathematics in its 2005 and 2010 analyses (Carmichael
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HBWF UIF &OHMJTI MBOHVBHF BSUT TUBUF TUBOEBSET " HSBEFT
JO JUT BOE BOBMZTFT BOE HBWF UIF NBUIFNBUJDT
standards a B+ in 2005 and an A in 2010 (Carmichael et
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-FF (SJHH%POBIVF /BUJPOBM$FOUFSGPS&EVDBUJPO
4UBUJTUJDT B C
8FBMTPDPNQBSFEUIF$PNNPO$PSFTUBOEBSETUPUXPTFUT
PGDPMMFHFBOEDBSFFSSFBEJOFTTTUBOEBSETPOFGSPNBTUBUF
5FYBT BOE BOPUIFS UIBU IBT CFFO VTFE CSPBEMZ EVSJOH UIF
QBTU FJHIU ZFBST o UIF ,OPXMFEHF BOE 4LJMMT GPS 6OJWFSTJUZ
4VDDFTT5IF5FYBT$PMMFHFBOE$BSFFS3FBEJOFTT4UBOEBSET
BSF B DPMMFDUJPO PG DPNQFUFODJFT BOE TLJMMT UIBU TFDPOEBSZ
students must possess to succeed in postsecondary
FEVDBUJPO 5IFZ BSF JOUFOEFE UP DPNQMFNFOU FYJTUJOH TUBUF
IJHITDIPPMTUBOEBSET BOEDSFBUFBDVMUVSFPGDPMMFHFBOE
DBSFFSSFBEJOFTT 5FYBT&EVDBUJPO"HFODZ 1VCMJTIFE
JO UIF ,OPXMFEHF BOE 4LJMMT GPS 6OJWFSTJUZ 4VDDFTT
,464 TUBOEBSETSFnFDUUIFDPOUSJCVUJPOTPGNPSFUIBO
GBDVMUZ BOE TUBGG GSPN MFBEJOH SFTFBSDI VOJWFSTJUJFT 5IF
GBDVMUZJEFOUJmFELOPXMFEHFBOETLJMMTUIBUTUVEFOUTOFFEUP
succeed in entry-level courses at their institutions. Multiple
peer reviews were used to hone the standards and ensure
Chapter One •
Chapter | Introduction
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at the institutions for students in entry-level courses (Conley
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as a reference in the development of its assessments and
TUBOEBSET #SPXO$POMFZ
Finally, we included a set of international standards from
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PWFS UIF mOBM UXP ZFBST PG IJHI TDIPPM *O JUT BOBMZTJT PG UIF
*# UIF'PSEIBN'PVOEBUJPOHBWFUIF*#-BOHVBHF"&OHMJTI
4UBOEBSE-FWFM 4- DPVSTFBHSBEFPG# CBTFEPODPOUFOU
SJHPS BOEDMBSJUZ #ZSE &MMJOHUPO (SPTT +BHP 4UFSO
3FWJFXFST EFFNFE UIBU UIF DPVSTF SFRVJSFT TUVEFOUT UP CF
iXFMM HSPVOEFE JO MJUFSBSZ HFOSFTw Q 5IFZ HBWF UIF
.BUI 4UBOEBSE -FWFM DPVSTF B # QSBJTJOH JO QBSUJDVMBS UIF
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OPSNBM IJHI TDIPPM GBSFw Q 5IF DPVSTFT BSF LOPXO UP
FNQIBTJ[FUIFBQQMJDBUJPOPGTUVEFOUMFBSOJOHTPUIBUTUVEFOUT
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8POH )JTUPSJDBMMZ UIF *# %JQMPNB 1SPHSBNNF IBT
SFMJFEPOUIFBJNTBOEHPBMTTQFDJmFEJODPVSTFEPDVNFOUTUP
DPOWFZSFRVJSFEDPOUFOU3FMBUJWFMZSFDFOUMZ GPSNBMTUBOEBSET
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serve as the reference point for this analysis.
In this study, the Common Core standards are the reference
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Common Core standards, particularly as a companion piece
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$PNNPO$PSFTUBOEBSETBSFSFBTPOBCMFDPMMFHFBOEDBSFFS
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3PPTFCPPN 4UPVU XXXFQJDPOMJOFPSH 8FVTFEUIF
$PNNPO$PSFTUBOEBSETBTUIFSFGFSFODFQPJOUGPSNBUDIJOH
UP FYJTUJOH TUBOEBSET JO PSEFS UP JEFOUJGZ DPOTJTUFOU QBUUFSOT
PGBMJHONFOUPSNJTBMJHONFOUBDSPTTTUBOEBSETFUT 'JOEJOHT
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JO UIF BQQFOEJDFT IPXFWFS UIF $PNNPO $PSF TUBOEBSET
XFSFDPOTJTUFOUMZUIFSFGFSFODFQPJOU 8FEJEOPUDPOEVDUUIF
SFWFSTF BOBMZTJT VTJOH FBDI TFU PG FYUFSOBM TUBOEBSET BT B
SFGFSFODFGPSNBUDIJOHUPUIF$PNNPO$PSF5IFJOUFOUXBT
OPU UP QSPWJEF JOEJWJEVBM BMJHONFOU QSPmMFT GPS B OVNCFS PG
TUBOEBSET TFUT UP UIF $PNNPO $PSF 8F VOEFSTUBOE NBOZ
TUBUFT BSF FOHBHJOH JO UIJT UZQF PG BOBMZTJT BOE XF EJE OPU
want to duplicate such efforts.
M et h od
We used Cook and
W
() conception
ilmes’s
of standardsto-standards alignm
ent – a
combination of lin
king (match
between standard
s) and
correspondence (d
epth and
breadth).
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TUBOEBSET NFUIPEPMPHZ B 8F VTFE UIF
8FC "MJHONFOU 5PPM 8"5 DSFBUFE CZ 8FCC GPS BOBMZTJT
&YQFSUTSBUFEBMMUIFTUBOEBSETTFUTJOUFSNTPGUIFJSDPHOJUJWF
DPNQMFYJUZ BOE UIFO GPMMPXJOH 8FCCT NFUIPEPMPHZ 8FCC
C 3PBDI &MMJPU 8FCC $PPL NBUDIFE
up to three standards from Common Core standards to each
standard in the comparison standard sets.
This method differs from other standards-to-standards
methods in two important ways. First, the method we used
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PUIFS NFUIPET BMMPX BO VOMJNJUFE OVNCFS PG NBUDIFT FH
3PMGVT %FDLFS #SJUF (SFHPSZ 5JNNT 4DIOFJEFS
-FF 3PMGVT 8FCC PSJHJOBMMZ DSFBUFE UIJT MJNJUBUJPO
so that reviewers would concentrate on only the central
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4FDPOE UIF 8FCC NFUIPEPMPHZ BOE 8"5 UPPM BTTJHOT
FRVBM JNQPSUBODF UP FWFSZ TFU PG NBUDIFT 5IFSFGPSF 8FCC
FNQIBTJ[FTUIBUXIFONBLJOHBNBUDI SBUFSTTIPVMEFOTVSF
UIBU UIF DPNQBSJTPO TUBUFNFOU UBSHFUT JO GVMM UIF SFGFSFODF
TUBUFNFOU 8FCC "MU &MZ 7FTQFSNBO *OTIPSU UIF
Chapter One 2
Chapter | Introduction
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UIBUPUIFSBMJHONFOUTUVEJFTEP FH 3PMGIVT $PPL #SJUF
)BSUNBO "T3PMGIVT $PPL #SJUF BOE)BSUNBO
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JOEJDBUJPOPGQBSUJBMNBUDIJOHDBONFBOUIBUUIFDPNQBSJTPO
standard matches just one element of a multidimensional
reference standard or that it matches all but one of the many
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DPOTFSWBUJWFEFmOJUJPOPGNBUDIJOH
8FVTFUISFFNFUSJDTNBUDI EFQUI BOECSFBEUI UPBOTXFS
UIF UISFF SFTFBSDI RVFTUJPOT 5P BOTXFS UIF mSTU SFTFBSDI
RVFTUJPO XF MPPL BU UIF NFBTVSF PG NBUDI $BUFHPSJDBM
$PODVSSFODF UP EFUFSNJOF UIF FYUFOU UP XIJDI DPOUFOU JT
consistent across the Common Core standards and each set
of comparison standards. To answer the second research
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Common Core standards and the comparison standards by
NFBOTPGUIF%FQUIPG,OPXMFEHFSBUJOH5IFO XFDPNQBSF
DPHOJUJWF EFNBOE UP HBVHF XIFSF DPHOJUJWF DIBMMFOHF JT
IJHIFS MPXFS PS UIF TBNF VTJOH UIF %FQUI PG ,OPXMFEHF
Consistency statistic for content areas that match with the
$PNNPO $PSF TUBOEBSET 8F BEESFTT UIF UIJSE SFTFBSDI
RVFTUJPOVTJOHUIF#SFBEUIPG$PWFSBHFNFUSJDUIBUBTDFSUBJOT
UIF FYUFOU UP XIJDI UIF DPNQBSJTPO TUBOEBSET UIBU NBUDI
Common Core standards cover a similar scope of content.
M et rics
Three metrics: match
, depth,
and breadth were used
to
answer the three rese
arch
questions.
*O$IBQUFS XFEFTDSJCFUIFNFUIPEPMPHZBOEQSPWJEFBO
overview of the standards that were used in the study. Chapter
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TUBOEBSETGPS&OHMJTIMBOHVBHFBSUTBOEMJUFSBDZ BOE$IBQUFS
QSFTFOUT SFTVMUT GPS NBUIFNBUJDT $IBQUFS EJTDVTTFT
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JOGPSNBUJPOBCPVUUIFNFUIPEPMPHZUIBUXBTVTFE"QQFOEJY
B lists the Common Core standards and summary information
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EFUBJMFEJOGPSNBUJPOPOUIFmOEJOHTGPSFBDITFUPGDPNQBSJTPO
TUBOEBSET -FOHUIJFS BOE NPSF EFUBJMFE JOGPSNBUJPO BCPVU
each set of comparison standards and precise matches with
the Common Core standards is provided under separate
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PSHmMFTQEG-JOJOH6Q5FDIOJDBM4VQQMFNFOUQEG
Chapter One 3
Chapter
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8FCC BMJHONFOU QSPUPDPM 5IF 8FCC NFUIPEPMPHZ
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of assessments to standards. The approach relies on
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processes in assessments and standards and then, based
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These statistics demonstrate how closely the assessment
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0WFSUJNF SFTFBSDIFSTIBWFVTFENPEJmFEWFSTJPOTPGUIF
8FCC NFUIPE XJUI EJGGFSFOU WBSJBUJPOT PG BMJHONFOU JOEJDFT
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5IF BQQSPBDI IBT BMTP CFFO NPEJmFE UP EFUFSNJOF
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CFUXFFOEJGGFSFOUTFUTPGTUBOEBSETJOUFSNTPGLOPXMFEHF
TLJMMT BOE DPOUFOU "MJHONFOU NFUIPEPMPHZ BMTP BMMPXT GPS
DPNQBSJTPO CFUXFFO TUBOEBSET JO UFSNT PG UIF DPHOJUJWF
demand of content and in terms of the breadth of overlap. In
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1.
Categorical Concurrence:UIFFYUFOUPGPWFSMBQPS
match between the comparison standards and the
Common Core standards.
2.
Depth of Knowledge Consistency: a comparison
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the sets of comparison standards and the Common
Core standards.
3.
Breadth of Coverage: how broadly matched
comparison standards cover content elements of
the Common Core standards.
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and data analysis.
Data Collection
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PVUCZ8FCCFUBM
Raters
3BUFST XFSF SFDSVJUFE GSPN B QPPM PG FYQFSUT XIP IBE
FYQFSJFODF XJUI TUBOEBSET BMJHONFOU 3FQSFTFOUBUJPO GSPN
OBUJPOBMFEVDBUJPOBMPSHBOJ[BUJPOTXBTBMTPTPVHIUJOWJUBUJPOT
| Methodology
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UIF/BUJPOBM$PVODJMPG5FBDIFSTPG.BUIFNBUJDT
" UPUBM PG SBUFST QBSUJDJQBUFE JODMVEJOH OJOF &OHMJTI
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FYQFSUT5IFSBUFSTDPNQSJTFEBNJYPGTFDPOEBSZBOEQPTU
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5IJT JOEJWJEVBM IBE NPSF TUBOEBSET BMJHONFOU FYQFSJFODF
than other raters in the subject area and helped facilitate the
HSPVQ
Rater Orientation
&BDI HSPVQ MFBEFS QBSUJDJQBUFE JO B XFC DPOGFSFODF
PSJFOUBUJPO TFTTJPO QSJPS UP UIF GVMM HSPVQ TFTTJPOT &1*$
SFTFBSDIFST FYQMBJOFE UIF PWFSBMM BMJHONFOU QSPDFTT BOE
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UIF MFBEFST FYQMBJOFE UIF %FQUI PG ,OPXMFEHF %0,
SBUJOHTBOEDPEJOHQSPDFTTBOEHVJEFEPUIFSSBUFSTUISPVHI
BMJHONFOU FYBNQMFT VOEFS UIF PWFSBMM TVQFSWJTJPO PG &1*$
researchers.
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DPOGFSFODFT %VSJOH UIF mSTU TFTTJPO &1*$ SFTFBSDIFST
FYQMBJOFE UIF TUBOEBSETUPTUBOEBSET BMJHONFOU QSPDFTT
BOE EFmOFE UFSNJOPMPHZ 6OEFS HVJEBODF GSPN UIF HSPVQ
MFBEFS UIF SBUFST EFWFMPQFE BO JOJUJBM VOEFSTUBOEJOH PG
%0,DBUFHPSJFT FYQMBJOFECFMPX BOEFOHBHFEJOQSBDUJDF
SBUJOHT"UUIFFOEPGUIFmSTUUSBJOJOH FBDIHSPVQXBTHJWFO
UIF UBTL PG BTTJHOJOH B %0, SBUJOH UP FBDI $PNNPO $PSF
IJHI TDIPPM NBUIFNBUJDT TUBOEBSE PS FBDI $PNNPO $PSF
TUBOEBSEGPS&-"BOEMJUFSBDZGPSHSBEFTo
%VSJOH UIF TFDPOE TFTTJPO SBUFST BHSFFE VQPO B TJOHMF
%0, SBUJOH GPS FBDI $PNNPO $PSF TUBOEBSE 5IJT XBT
BDDPNQMJTIFE CZ QSFTFOUJOH BMM SBUFST %0, MFWFMT GPS
FBDI$PNNPO$PSFTUBOEBSEUPUIFFOUJSFHSPVQPGSBUFST
4UBOEBSET XJUIPVU B DMFBS NBKPSJUZ SBUJOH XFSF EJTDVTTFE
until consensus was reached. In the second part of the call,
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to determine whether to match comparison standards and
Common Core standards. They developed decision rules
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PS DPOGVTJPO DPVME BSJTF JO UIF SBUJOHT QSPDFTT "T 8FCC
C QPJOUT PVU BMUIPVHI UIF USBJOJOH QSPDFTT JOWPMWFT
DBMJCSBUJPO JU JT OPU EFTJHOFE GPS SBUFST UP SFBDI FYBDU
BHSFFNFOU3FWJFXFSTSFTQPOTFTBSFBWFSBHFE XIJDIIFMQT
BDDPVOUGPSEJGGFSFODFTJODPEJOH 8FCC "EEJUJPOBMMZ
Chapter Two •
Chapter | Methodology
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SFTVMUJOH GSPN MBDL PG DMBSJUZ JO TUBOEBSET TUBUFNFOUT 8FCC
C
standards refer to this level as a cluster 3BUJOH EBUB XFSF
FOUFSFEJOUPUIF8FC"MJHONFOU5PPM 8"5 GPSBOBMZTJT/FYU
XF QSFTFOU NPSF TQFDJmD JOGPSNBUJPO BCPVU UIF OVNCFS PG
statements that were rated for each set of standards.
Rating Process
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JOEFQFOEFOUMZ DPNQMFUFE UXP UBTLT 5IFZ SBUFE UIF %0, PG
FBDI DPNQBSJTPO TUBOEBSE BOE UIFO EFUFSNJOFE UIF EFHSFF
to which each comparison standard matched content in
UIF $PNNPO $PSF TUBOEBSET 8IFO EFUFSNJOJOH NBUDI
UIFZ JEFOUJmFE VQ UP UISFF $PNNPO $PSF TUBOEBSET UIBU
corresponded with a standard in a comparison set. The limit
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UIBU BMJHONFOU TIPVME DPODFOUSBUF POMZ PO DPOUFOU DFOUSBM UP
the statements. If raters found more than three statements that
DPVME NBUDI UIFZ VTFE QSPGFTTJPOBM KVEHNFOU UP TFMFDU UIF
UISFF CFTU NBUDIFT 3BUFST XFSF OPU BMMPXFE UP NBLF QBSUJBM
NBUDIFTUIBUJT UIFDPNQBSJTPOTUBOEBSEIBEUPNBUDIUIFGVMM
Common Core standard. This meant that a broader comparison
standard could be matched to a more narrow Common Core
standard, but the reverse could not occur because the content
in the Common Core standard would not be fully addressed.
If raters found that every standard within a particular Common
Core subarea corresponded with comparison standards, then
they rated at the superordinate level. This was the only time
that more than three standards could be matched. For ease
of reference, we call this level a topic for the Common Core
ELA and literacy standards. The Common Core mathematics
Rating of Common Core Standards
English Language Arts and Literacy
5IF $PNNPO $PSF &OHMJTI MBOHVBHF BSUT &-" BOE MJUFSBDZ
TUBOEBSET GPS HSBEFT o BSF PSHBOJ[FE JOUP strands,
anchor standards, and standards8FVTFUIFUFSNstrand to
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BOE $BSFFS 3FBEJOFTT $$3 "ODIPS 4UBOEBSET 5IF $$3
"ODIPS 4UBOEBSET BJN UP EFTDSJCF DSPTTEJTDJQMJOBSZ MJUFSBDZ
FYQFDUBUJPOT UIBU TIPVME CF NFU JO PSEFS GPS TUVEFOUT UP
CF QSFQBSFE GPS TVDDFTT JO DPMMFHF BOE XPSLGPSDF USBJOJOH
QSPHSBNT $PNNPO $PSF 4UBUF 4UBOEBSET *OJUJBUJWF C
'PSFBDITUSBOE UIF$$3TUBOEBSETQSFTFOUCSPBEDPODFQUT
UIBU BSF BQQMJFE UP BMM HSBEF MFWFMT 4QFDJmD TUBOEBSET UIFO
TQFMMPVUIPXUIF$$3"ODIPS4UBOEBSETBSFBQQSPBDIFEGPS
EJGGFSFOUHSBEFCBOET1 For this study, we used the Common
$PSF&-"BOEMJUFSBDZTUBOEBSETGPSUIFIJHIFTUHSBEFCBOE
HSBEFT o 5BCMF TVNNBSJ[FT UIF PSHBOJ[BUJPO PG UIF
$PNNPO$PSF&-"BOEMJUFSBDZTUBOEBSETGPSIJHITDIPPM
&BDIPGUIFTUSBOETDPOUBJOTUXPUPGPVSPSHBOJ[JOHDBUFHPSJFT
*OTPNFDBTFTUIFIJHITDIPPMHSBEFTQFDJmDTUBOEBSEJTJEFOUJDBMUPUIF
$PMMFHFBOE$BSFFS3FBEJOFTTBODIPSTUBOEBSE
1
Table . Organization of the Common Core English Language Arts and Literacy Standards
Standards for English Language Arts
a
CCR Anchor Standards for Reading
Standards for Literacy
CCR Anchor Standards for Readinga
. Reading in History/Social Studies
. Reading for Literature
. Reading in Science and Technical Subjects
. Reading for Informational Texts
b
CCR Anchor Standards for Writing
. Writing
CCR Anchor Standards for Writingb
. Writing in History/Social Studies, Science, and
Technical Subjects
CCR Anchor Standards for Speaking and Listening
. Speaking and Listening
CCR Anchor Standards for Language
. Language
a
The reading CCR anchor standards are the same for the English language arts and literacy strands.
The writing CCR anchor standards are the same for English language arts and literacy strands.
b
Chapter Two 5
Chapter | Methodology
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both labeled as objectives.
2
Figure . Common Core English Language Arts and Literacy Standards for Grades and : Number of Rated Statements
Common Core
standard statements
rated for ELA and
literacy (113)
Reading for Literature (9)
4 topics
=
9
standards
Reading for Informational Texts (10)
4 topics
=
10
standards
Writing (28)
4 topics
=
10
standards
+
18 substandards
Speaking and Listening (10)
2 topics
=
6
standards
+
4 substandards
Language (17)
3 topics
=
6
standards
+
11 substandards
Reading for Literacy in History/Social
Studies (10)
4 topics
=
10
standards
Reading for Literacy in Science and
Technical Subjects (10)
4 topics
=
10
standards
Writing for Literacy in History/Social
Studies, Science and Technical Subjects (19)
4 topics
=
9
standards
+
10 substandards
Chapter Two 6
Chapter | Methodology
Mathematics
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indicated in the Common Core document with a star symbol (+
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3
Figure . Common Core Mathematics Standards for High School: Number of Rated Statements
Common Core
standard statements
rated for mathematics
(192)
Number and Quantity (32)
9 clusters
=
27
standards
+
5 substandards
Algebra (34)
11 clusters
=
27
standards
+
7 substandards
Functions (45)
10 clusters
=
28
standards
+
17 substandards
Geometry (45)
15 clusters
=
43
standards
+
2 substandards
Statistics and Probability (36)
9 clusters
=
31
standards
+
5 substandards
Chapter Two 7
Chapter | Methodology
Table . Descriptive Information About the Five Comparison
Standards Sets for English Language Arts (ELA) and Literacy
ELA comparison standards sets
California ELA standards for grades –
Massachusetts ELA standards for grades –
Texas ELA and cross-disciplinary college and career
readiness standards
Number of comparison
standards
( are cross-disciplinary)
Knowledge and Skills for University Success ELA
college and career readiness standards
International Baccalaureate ELA standards for
grades –
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document.
Table . Descriptive Information About the Five Comparison
Standards Sets for Mathematics
Mathematics comparison standards sets
Number of comparison
standards
California mathematics standards for grades –
Massachusetts mathematics standards
for grades –
Texas mathematics and cross-disciplinary college
and career readiness standards
Rating of Comparison Standards
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for the 11thothHSBEF CBOE JO &OHMJTI
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mathematics, and cross-disciplinary standards
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mathematics standards, developed by EPIC,
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standards but rather the level that had consistent
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each of the comparison standards sets for ELA and
literacy and mathematics.
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These are additional required components, which each IB school
selects. The number of options varies by course and by subject.
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5
( are cross-disciplinary)
Knowledge and Skills for University Success
mathematics college and career readiness
standards
International Baccalaureate mathematics standards
for grades –
Chapter Two 8
Chapter | Methodology
Rater Reliability
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,OPXMFEHFSBUJOHT'PSFBDITFUPGDPNQBSJTPOTXFFYBNJOFE
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ELA and literacy, the intraclass correlation was close to .70 for
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For mathematics, the intraclass correlations were close to or
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and therefore warranted removal from the analysis data.
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retained.
Table . Consistency of Depth of Knowledge Ratings Across Nine
Raters for English Language Arts and Literacy
Number of
standards
Intraclass
correlation
California
.
Massachusetts
.
Texas and College and Career Readiness
.
Knowledge and Skills for University Success
.
International Baccalaureate
.
Comparison standard set
Table . Consistency of Depth of Knowledge Ratings Across Seven
Raters for Mathematics
Number of
standards
Intraclass
correlation
California
.
Massachusetts
.
Texas and College and Career Readiness
.
Knowledge and Skills for University Success
.
International Baccalaureate
.
Comparison standard set
Chapter Two 9
Chapter | Methodology
Figure . Illustration of Categorical Concurrence Statistic
IF
Total number
of matches
THEN
1.0
Categorical
Concurrence
criterion met
Number of raters
Data Analysis
Categorical Concurrence
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a standard in the comparison standard set, the criterion for
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Depth of Knowledge Consistency
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Level 2:4LJMMTBOEDPODFQUT
Level 3:4USBUFHJDUIJOLJOH
Level 4:&YUFOEFEUIJOLJOH
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BM
Chapter Two 10
Chapter | Methodology
Figure . Illustration of Depth of Knowledge Consistency Statistic
At
Above
THEN
IF
>
Depth of
Knowledge
Consistency
criterion met
75%
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the fact that a substantial number of test items are supposed
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standards comparisons, since the match requirement is less,
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has typically been adopted for standards-to-standards
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"QQFOEJY"
Breadth of Coverage
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scope of content as that found in the reference standards.
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Core standards that are covered by matched standards in the
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subareas as topics. For mathematics, the subareas are referred
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area that have standards matched with comparison standards.
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area match with the comparison standard set. Moderate
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$PNNPO$PSFTUBOEBSET'JHVSFJMMVTUSBUFTUIJTDSJUFSJPO
Figure . Illustration of Coverage Statistic
Strong (all or majority)
Number of subareas with matches
Under
0
1
2
3
4
0
1
2
3
4
Moderate (less than majority, more
than 1)
0
1
2
3
4
Limited (0 or 1)
0
1
2
3
4
0
1
2
3
4
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XFVTFUFSNTTQFDJmDBMMZSFMBUFEUPUIFPSHBOJ[BUJPOPGUIF$PNNPO$PSF
standards.
Chapter Two 11
Chapter
| Results for English Language
Arts and Literacy
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presented at the strand level.
Match
Overall Match of Comparison Standards to the Common Core Standards
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UPQJD
Figure . Average Number of Matches per Standard Across All Comparison Standards, by Topic
0
10
20
30
40
50
60
70
Speaking and
Listening
Reading for Literature
Integration of Knowledge and Ideas (2)
Range of Reading and Level of Text Complexity (1)
Craft and Structure (3)
Key Ideas and Details (3)
Presentation of Knowledge and Ideas (3)
Comprehension and Collaboration (7)
Production and Distribution of Writing (3)
Writing
Research to Build and Present Knowledge (5)
Range of Writing (1)
Reading for Informational
Texts
Text Types and Purposes (19)
Craft and Structure (3)
Key Ideas and Details (3)
Integration of Knowledge and Ideas (3)
Range of Reading and Level of Text Complexity (1)
Note/VNCFSTJOQBSFOUIFTFTJOEJDBUFIPXNBOZTUBOEBSETTUBUFNFOUTBQQFBSXJUIJOUIFUPQJD
Chapter Three •
Chapter | Results for English Language
Arts and Literacy
Figure . Average Number of Matches per Standard Across All Comparison Standards, by Topic
0
10
20
30
40
50
60
70
Reading in Science and
Technical Subjects
Reading in History/Social
Studies
Writing in History/Social
Studies, Science, and
Technical Subjects
Language
Conventions of Standard English (6)
Vocabulary Acquisition and Use (9)
Knowledge of Language (2)
Research to Build and Present Knowledge (3)
Production and Distribution of Writing (3)
Range of Writing (1)
Text Types and Purposes (12)
Integration of Knowledge and Ideas (3)
Key Ideas and Details (3)
Craft and Structure (3)
Range of Reading and Level of Text Complexity (1)
Craft and Structure (3)
Integration of Knowledge and Ideas (3)
Key Ideas and Details (3)
Range of Reading and Level of Text Complexity (1)
Note/VNCFSTJOQBSFOUIFTFTJOEJDBUFIPXNBOZTUBOEBSETTUBUFNFOUTBQQFBSXJUIJOUIFUPQJD
Match for Each Comparison Set to the Common Core Standards
5BCMFQSFTFOUTUIFBWFSBHFOVNCFSPGNBUDIFTQFSTUSBOECFUXFFOUIF$PNNPO$PSFTUBOEBSETGPSFBDITFUPGDPNQBSJTPO
TUBOEBSET5IFEBUBJMMVTUSBUFUIBUUIFSFJTBXJEFSBOHFJOUIFOVNCFSPGBWFSBHFNBUDIFTBOEUIBUTPNFTUSBOETIBWFIJHI
TUBOEBSEEFWJBUJPOT JOEJDBUJOHUIBUSBUFSTWBSJFEXJEFMZJOUIFOVNCFSPGNBUDIFTUIFZJEFOUJmFE
Chapter Three 13
Chapter | Results for English Language
Arts and Literacy
Table . Average Number of Matches for English Language Arts (ELA) and Literacy Common Core
Strands Across All Comparison Standards
Average number of matches
Common Core ELA and
literacy strands
CA
MA
TCCRS
KSUS
IB
M
SD
M
SD
M
SD
M
SD
M
SD
Reading for Literature
.
.
.
.
.
.
.
.
.
.
Reading for Informational
Texts
.
.
.
.
.
.
.
.
.
.
Writing
.
.
.
.
.
.
.
.
.
.
Speaking and Listening
.
.
.
.
.
.
.
.
.
.
Language
.
.
.
.
.
.
.
.
.
.
Reading in History/Social
Studies
.
.
.
.
.
.
.
.
.
.
Reading in Science and
Technical Subjects
.
.
.
.
.
.
.
.
.
.
Writing in History/Social
Studies, Science, and
Technical Subjects
.
.
.
.
.
.
.
.
.
.
Total
.
.
.
.
.
.
.
.
.
.
CA = California; MA = Massachusetts; TCCRS = Texas College and Career Readiness Standards; KSUS = Knowledge and Skills for University Success; IB = International
Baccalaureate.
Categorical Concurrence Statistic
3FDBMMUIBUBTJOHMFDPSSFTQPOEFODFJOBDPOUFOUBSFBCFUXFFO
UXP TFUT PG TUBOEBSET JT DPOTJEFSFE TVGmDJFOU UP NFFU UIF
TUBOEBSETUPTUBOEBSETBMJHONFOUDSJUFSJPO $PPL 5IVT
PWFSBMMUIFDSJUFSJPOGPS$BUFHPSJDBM$PODVSSFODFCFUXFFOUIF
$PNNPO $PSF BOE UIF mWF TFUT PG DPNQBSJTPO TUBOEBSET JT
NFUGSFRVFOUMZ0OBWFSBHFBDSPTTSBUFST BUMFBTUPOFTUBOEBSE
GSPNFWFSZTFUPGUIFmWFDPNQBSJTPOTUBOEBSETJTNBUDIFEUP
BTUBOEBSEJOBMM$PNNPO$PSFTUSBOET XJUIGFXFYDFQUJPOT
5IJT JOEJDBUFT PWFSMBQ CFUXFFO UIF LOPXMFEHF BOE TLJMMT
TQFDJmFE JO UIF $PNNPO $PSF TUBOEBSET BOE UIF DPOUFOU PG
the comparison standards. Table 7 shows the Common Core
TUSBOETGPSXIJDIUIF$BUFHPSJDBM$PODVSSFODFDSJUFSJPOJTNFU
BDSPTTUIFmWFTFUTPGDPNQBSJTPOTUBOEBSET
Table . Categorical Concurrence for English Language Arts (ELA) and Literacy
Common Core
ELA and literacy strands
CA
MA
TCCRS
KSUS
IB
Reading for Literature
Reading for Informational Texts
Writing
Speaking and Listening
Language
−
Reading in History/Social Studies
−
Reading in Science and Technical Subjects
−
−
Writing in History/Social Studies, Science, and
Technical Subjects
CA = California; MA = Massachusetts; TCCRS = Texas College and Career Readiness Standards; KSUS = Knowledge and Skills for University Success; IB =
International Baccalaureate.
Meets the criterion for Categorical Concurrence (averaged across raters, a single correspondence exists between the two sets of standards);
Does not meet the criterion for Categorical Concurrence.
Chapter Three 14
Chapter | Results for English Language
Arts and Literacy
5IFDSJUFSJPOJTNFUGPSBMM FJHIUPGFJHIU $PNNPO$PSF&-"
BOEMJUFSBDZTUSBOETGPSUIF$BMJGPSOJBTUBOEBSET 5FYBT$PMMFHF
BOE $BSFFS 3FBEJOFTT 4UBOEBSET BOE UIF ,OPXMFEHF BOE
4LJMMTGPS6OJWFSTJUZ4VDDFTT5IFDSJUFSJPOJTNFUGPSTJYPGFJHIU
Common Core ELA and literacy strands for the Massachusetts
and International Baccalaureate standards.
TFF 5BCMF "T BO FYBNQMF GPS UIF $BMJGPSOJB TUBOEBSET
SBUFST JEFOUJmFE BO BWFSBHF PG TUBOEBSE SD UIBU
NBUDIFTXJUIUIF$PNNPO$PSF3FBEJOH4UBOEBSETJO4DJFODF
BOE5FDIOJDBM4VCKFDUTBOEBOBWFSBHFPGTUBOEBSET SD
UIBUNBUDIXJUIUIF8SJUJOH4UBOEBSET#PUIPGUIFTF
meet the criterion.
For the Massachusetts standards, the criterion is not met for
UIF$PNNPO$PSF3FBEJOH4UBOEBSETJO)JTUPSZ4PDJBM4UVEJFT
BOEUIF3FBEJOH4UBOEBSETJO4DJFODFBOE5FDIOJDBM4VCKFDUT
5BCMFTIPXTXIZUIFDSJUFSJPOJTOPUNFUGPSFBDIPGUIFTFUXP
BSFBT'PSUIF.BTTBDIVTFUUTTUBOEBSET UIFSFJTBOBWFSBHF
PG TUBOEBSET SD UIBU NBUDI XJUI UIF 3FBEJOH
4UBOEBSETJO)JTUPSZ4PDJBM4UVEJFT5IFSFJTBOBWFSBHFPG
standards (SD UIBUNBUDIXJUIUIF3FBEJOH4UBOEBSETJO
4DJFODFBOE5FDIOJDBM4VCKFDUT
*O"QQFOEJY$ UIFSFJTNPSFEFUBJMFEEJTDVTTJPOBCPVUFBDI
TFUPGDPNQBSJTPOTUBOEBSETBOEIPXJUBMJHOTUPUIF$PNNPO
Core. The precise correspondence of matches between the
Common Core standards and individual comparison sets of
TUBOEBSETJTQSPWJEFEJOUIF5FDIOJDBM4VQQMFNFOU
For the International Baccalaureate standards, the criterion
JT OPU NFU GPS UIF $PNNPO $PSF -BOHVBHF 4UBOEBSET BOE
3FBEJOH4UBOEBSETJO4DJFODFBOE5FDIOJDBM4VCKFDUT5IFSF
JTBOBWFSBHFPGTUBOEBSET SD UIBUNBUDIXJUIUIF
$PNNPO $PSF -BOHVBHF 4UBOEBSET BOE BO BWFSBHF PG
standards (SD UIBUNBUDIXJUI3FBEJOH4UBOEBSETJO
4DJFODFBOE5FDIOJDBM4VCKFDUT
5BCMFTIPXTUIFNPEBM%FQUIPG,OPXMFEHF %0, SBUJOHGPS
FBDI PG UIF $PNNPO $PSF &OHMJTI MBOHVBHF BSUT &-" BOE
MJUFSBDZTUSBOET.PTUSFQSFTFOUUIFTUSBUFHJDUIJOLJOHMFWFMPG
DPHOJUJWFEFNBOE MFWFM "TUIFUBCMFTIPXT UIF-BOHVBHF
4UBOEBSETIBWFMPXFSSBUJOHTUIBOUIFPUIFSTUSBOET NPEFPG
MFWFM 5IJTNJHIUCFCFDBVTFUIFTUSBOEDPOUBJOTFMFNFOUT
PG HSBNNBS DPOWFOUJPOT BOE VTBHF XIJDI EP OPU UFOE UP
JOWPMWFBCTUSBDUBOEDPNQMFYUIJOLJOH
"NPOHUIFTFUTPGDPNQBSJTPOTUBOEBSETGPSXIJDIBMMDSJUFSJB
BSFNFU UIFSFJTBXJEFSBOHFJOUIFOVNCFSPGBWFSBHFNBUDIFT
Depth of Knowledge
Ratings for Common Core Standards
Table . Depth of Knowledge (DOK) Modal Ratings for English
Language Arts and Literacy Common Core Strands
Common Core ELA and literacy strand
DOK mode
Reading for Literature
Reading for Informational Texts
Writing
Speaking and Listening
Language
Reading in History/Social Studies
Reading in Science and Technical Subjects
Writing in History/Social Studies, Science, and Technical Subjects
Chapter Three 15
Chapter | Results for English Language
Arts and Literacy
"UUIFTUBOEBSEMFWFM UIF$PNNPO$PSFTUBOEBSETGBMMBDSPTTUIFGVMMSBOHFPGUIF%0,TDBMF CVUMFTTGSFRVFOUMZBUUIFMPXFS
MFWFMTPGUIFTDBMF0WFSBMM POMZPGUIFTUBOEBSETBSFBUBMFWFM SFDBMMBOESFQSPEVDUJPO BSFBUBMFWFM TLJMMTBOE
DPODFQUT BSFBUBMFWFM TUSBUFHJDUIJOLJOH BOEBSFBUMFWFM FYUFOEFEUIJOLJOH 5IJTTVNNBSZJOGPSNBUJPOJT
QSFTFOUFEHSBQIJDBMMZJO'JHVSF%0,SBUJOHTGPSBMMTUBOEBSETBSFQSPWJEFEJO"QQFOEJY#
Figure . Percent of Common Core ELA and Literacy Standards at each
Depth of Knowledge Level
Level 1
Recall and
Reproduction
7%
Level 4
Extended Thinking
26%
Level 2
Skills and Concepts
12%
Level 3
Strategic Thinking
55%
DOK Consistency of Each Comparison Set to the Common
Core Standards
%0, $POTJTUFODZ EFTDSJCFT UIF FYUFOU UP XIJDI UIF &-"
BOE MJUFSBDZ TUBOEBSET UIBU FYQFSUT NBUDIFE CFUXFFO UIF
comparison sets and the Common Core are consistent in level
PGDPHOJUJWFEFNBOE.FFUJOHUIJTDSJUFSJPOSFRVJSFTNPSFUIBO
PGUIFDPNQBSJTPOTUBOEBSETNBUDIJOHGPSUIFDPOUFOUBSFB
UPCFBUPSBCPWFUIFMFWFMPGDPHOJUJWFEFNBOEPGUIF$PNNPO
Core standards. Consistency is only computed for those
DPOUFOUTQFDJmDBSFBTGPSXIJDIUIF$BUFHPSJDBM$PODVSSFODF
criterion is met.
'JHVSF TIPXT GPS FBDI DPNQBSJTPO TFU UIF QFSDFOU PG
TUBOEBSET BWFSBHFE BDSPTT SBUFST TFF "QQFOEJY " UIBU
GFMM BCPWF BU BOE VOEFS UIF DPHOJUJWF EFNBOE MFWFM PG UIF
$PNNPO$PSFTUBOEBSET*OUIFmHVSF BMJOFJTESBXOBU
XIJDIJTUIFDSJUFSJPOGPSUIFQFSDFOUPGTUBOEBSETGBMMJOHBCPWF
PSBUUIFDPHOJUJWFEFNBOEMFWFMPGUIF$PNNPO$PSFJOPSEFS
UP NFFU UIF %0, $POTJTUFODZ TUBUJTUJD 'JOEJOHT GPS UIF %0,
Consistency statistic are inconsistent across the different
DPNQBSJTPO TFUT BOE EJGGFSFOU TUSBOET 0WFSBMM UIF $PNNPO
$PSF TUSBOE GPS XIJDI UIF %0, DSJUFSJPO JT NPTU PGUFO NFU JT
UIF -BOHVBHF 4UBOEBSET TUSBOE JOEJDBUJOH UIBU UIF NBUDIFE
DPNQBSJTPOTUBOEBSETBSFBUPSBCPWFUIF%0,PGUIF$PNNPO
$PSF-BOHVBHF4UBOEBSET5IFTUSBOETGPSXIJDIUIFDSJUFSJPO
is met for less than half of the comparison standards sets are
UIF 3FBEJOH 4UBOEBSET GPS *OGPSNBUJPOBM 5FYUT UIF 8SJUJOH
4UBOEBSET UIF4QFBLJOHBOE-JTUFOJOH4UBOEBSET UIF3FBEJOH
4UBOEBSETJO)JTUPSZ4PDJBM4UVEJFT UIF3FBEJOH4UBOEBSETJO
4DJFODF BOE 5FDIOJDBM 4VCKFDUT BOE UIF 8SJUJOH 4UBOEBSET
JO )JTUPSZ4PDJBM 4UVEJFT 4DJFODF BOE 5FDIOJDBM 4VCKFDUT
For these strands, there are more comparisons for which the
$PNNPO $PSF TUBOEBSET BSF SBUFE BU B IJHIFS MFWFM JO UFSNT
PGDPHOJUJWFEFNBOE"T'JHVSFTIPXT TPNFTUBOEBSETTFUT
GBMMKVTUBCPWFPSKVTUCFMPXGPSTPNFTUSBOETBOESFTVMUT
would be different if an alternative criterion had been selected.
-PPLJOH BU %0, $POTJTUFODZ BDSPTT UIF DPNQBSJTPO TFUT PG
standards, the criterion is met most often for the Massachusetts
TUBOEBSET GPSmWFPVUPGTJYTUSBOETUIBUGVMmMMUIF$BUFHPSJDBM
$PODVSSFODFDSJUFSJPO 5IJTTVHHFTUTUIBUGPS&-"BOEMJUFSBDZ
UIF DPHOJUJWF EFNBOE PG UIF .BTTBDIVTFUUT TUBOEBSET JT
TJNJMBSUPPSNPSFDPHOJUJWFMZDPNQMFYUIBOUIF$PNNPO$PSF
standards. The International Baccalaureate standards meet
UIFDSJUFSJPOGPSGPVSPVUPGTJYTUSBOETUIBUGVMmMMUIF$BUFHPSJDBM
$PODVSSFODFDSJUFSJPO'PSUIFPUIFSUISFFTFUT $BMJGPSOJB 5FYBT
$PMMFHFBOE$BSFFS3FBEJOFTT BOE,OPXMFEHFBOE4LJMMTGPS
6OJWFSTJUZ4VDDFTT UIFDSJUFSJPOJTNFUGPSUXPPSUISFFPGFJHIU
TUSBOETUIBUGVMmMMUIF$BUFHPSJDBM$PODVSSFODFDSJUFSJPO
Chapter Three 16
Chapter | Results for English Language
Arts and Literacy
Figure . Depth of Knowledge Level Comparisons of the Five Sets of Comparison
Standards to Common Core ELA and Literacy Standards
Reading for
Literature
CA
MA
TCCRS
KSUS
IB
25
50
75
CA
MA
TCCRS
KSUS
IB
CA
MA
TCCRS
KSUS
IB
Reading in
Science and
Technical
Subjects
CA
MA
TCCRS
KSUS
IB
CA
MA
TCCRS
KSUS
IB
CA
MA
TCCRS
KSUS
IB
100
Average
Percent
Above
At
Under
CA
MA
TCCRS
KSUS
IB
Writing in
History/Social
Studies,
Science, and
Technical
Subjects
Reading in
History/Social
Studies
Language
Speaking and
Listening
Writing
Reading for
Informational
Texts
0
CA
MA
TCCRS
KSUS
IB
NA
NA
NA
NA
Note5PUBMQFSDFOUNBZFRVBMTMJHIUMZBCPWFPSCFMPXEVFUPSPVOEJOH
Breadth of Coverage
#SFBEUI PG $PWFSBHF HJWFT JOGPSNBUJPO PO UIF CSFBEUI PS
EJTQFSTJPOPGDPSSFTQPOEJOHTUBOEBSETBDSPTTTUBOEBSETTFUT
" DPNQBSJTPO TFU PG TUBOEBSET DPVME IBWF B IJHI EFHSFF PG
concurrence with reference standards but still not cover the
entire scope or breadth of content of the reference standards.
In this study, the criterion is related to the number of Common
Core topics within a strand for which a set of comparison
standards has matches to the Common Core standards.
4USPOHDPWFSBHFNFBOTUIBUBNBKPSJUZPGUPQJDTJOUIFTUSBOE
IBWFNBUDIFT.PEFSBUFDPWFSBHFNFBOTUIBUNPSFUIBOPOF
UPQJD JO UIF TUSBOE IBT NBUDIFT -JNJUFE DPWFSBHF NFBOT
that one or fewer than one topic in the strand has matches.
*G DPWFSBHF JT MJNJUFE UIJT JOEJDBUFT UIBU DPNQBSJTPO DPOUFOU
tends to concentrate in particular topics of the Common Core
TUSBOE BDDPSEJOH UP UIF XBZ UIF $PNNPO $PSF TUBOEBSET
BSF PSHBOJ[FE 5IFSFGPSF PUIFS DBUFHPSJFT PG DPOUFOU BSF OPU
covered by the comparison standards.
'PS UIF NPTU QBSU DPWFSBHF CFUXFFO UIF $PNNPO $PSF
standards and the comparison standards was consistently
TUSPOHPSCSPBE TFF5BCMF .PTUTFUTPGDPNQBSJTPOTUBOEBSET
cover a majority of Common Core topics for each strand. There
Chapter Three 17
Chapter | Results for English Language
Arts and Literacy
XFSFBGFXFYDFQUJPOT'PSUIF.BTTBDIVTFUUTTUBOEBSET UIF
3FBEJOH4UBOEBSETJO4DJFODFBOE5FDIOJDBM4VCKFDUTTUSBOE
IBT NPEFSBUF DPWFSBHF 'PS UIF *OUFSOBUJPOBM #BDDBMBVSFBUF
TUBOEBSET UIF3FBEJOH4UBOEBSETGPS*OGPSNBUJPOBM5FYUTTUSBOE
BMTP IBT NPEFSBUF DPWFSBHF BOE UIF -BOHVBHF 4UBOEBSET
TUSBOEIBTMJNJUFEDPWFSBHF5XPPGUIFTF UIF.BTTBDIVTFUUT
SFBEJOHTUSBOEBOEUIF*OUFSOBUJPOBM#BDDBMBVSFBUFMBOHVBHF
TUSBOE BMTPEPOPUNFFUUIF$BUFHPSJDBM$PODVSSFODFDSJUFSJPO
XIJDITVHHFTUTUIBUUIFMPXFSOVNCFSPGBWFSBHFNBUDIFTGPS
UIFTFTUSBOETNBZIBWFMJNJUFEDPWFSBHF)PXFWFS UIJTJTOPU
a necessary relationship because there are also two strands for
XIJDIUIF$BUFHPSJDBM$PODVSSFODFDSJUFSJPOJTOPUNFUCVUUIBU
TUJMMIBWFTUSPOHDPWFSBHF 3FBEJOH4UBOEBSETJO)JTUPSZ4PDJBM
4UVEJFTGPS.BTTBDIVTFUUTBOE3FBEJOH4UBOEBSETJO4DJFODF
BOE5FDIOJDBM4VCKFDUTGPS*OUFSOBUJPOBM#BDDBMBVSFBUF
"QQFOEJY % QSFTFOUT NPSF JOGPSNBUJPO BCPVU UIF EJTUSJCVUJPO
PGTUBOEBSENBUDIFTXJUIJOFBDIPGUIFFJHIU&-"BOEMJUFSBDZ
strands.
Table . Breadth of Coverage Criterion for English Language Arts and Literacy
Common Core ELA and literacy strand
CA
MA
TCCRS
KSUS
IB
Reading for Literature
Reading for Informational Texts
Writing
Speaking and Listening
Language Standards
Reading in History/Social Studies
Reading in Science and Technical Subjects
Writing in History/Social Studies, Science, and Technical
Subjects
CA = California; MA = Massachusetts; TCCRS = Texas College and Career Readiness Standards; KSUS = Knowledge and Skills for University Success; IB =
International Baccalaureate.
means that a majority of topics in the Common Core strand have at least one matched comparison standard;
means that one topic in the Common Core strand have at least one matched comparison standard;
means that one or fewer than one topic in the Common Core strand have at least one matched comparison standard.
Chapter Three 18
Chapter
| Results for Mathematics
3FTVMUT CFMPX EFTDSJCF UIF NBUDI CFUXFFO UIF $PNNPO $PSF NBUIFNBUJDT TUBOEBSET BOE UIF mWF TFUT PG DPNQBSJTPO
TUBOEBSET3FTVMUTBSFHFOFSBMMZQSFTFOUFEBUUIFDPODFQUVBMDBUFHPSZMFWFM
Match
Overall Match of Comparison Standards to the Common Core Standards
'JHVSFTBOETIPXUIFBWFSBHFOVNCFSPGNBUDIFTQFS$PNNPO$PSFTUBOEBSEJOFBDIDMVTUFSBDSPTTBMMDPNQBSJTPO
TUBOEBSET #PUI UIF DPODFQUVBM DBUFHPSJFT BOE DMVTUFST XJUIJO B DBUFHPSZ BSF TPSUFE JO EFTDFOEJOH PSEFS BDDPSEJOH UP
GSFRVFODZ'JHVSFQSPWJEFTUIFJOGPSNBUJPOGPS4UBUJTUJDTBOE1SPCBCJMJUZ BOE(FPNFUSZ'JHVSFQSPWJEFTUIFJOGPSNBUJPO
GPS'VODUJPOT "MHFCSB BOE/VNCFSBOE2VBOUJUZ5IFHSBQITTIPXUFOEFODJFTCFUXFFOBOEXJUIJODPODFQUVBMDBUFHPSJFT
Figure . Average Number of Matches per Standard Across All Comparison Standards, by Cluster
0
10
20
30
40
50
Summarize, represent, and interpret data on a single count or
measurement variable (4)
Summarize, represent, and interpret data on two categorical and
quantitative variables (5)
Statistics and Probability
Understand and evaluate random processes underlying
statistical experiments (2)
Understand independence and conditional probability and use
them to interpret data (5)
Make inferences and justify conclusions from sample surveys,
experiments, and observational studies (4)
Use the rules of probability to compute probabilities of
compound events in a uniform probability model (4)
Interpret linear models (3)
Calculate expected values and use them to solve problems (4)
Use probability to evaluate outcomes of decisions (5)
4'-+" ('(&-+"+-"(,',(%/)+(%&,"'/(%/"' +" !-
triangles (3)
Use coordinates to prove simple geometric theorems
algebraically (4)
Prove theorems involving similarity (2)
Explain volume formulas and use them to solve problems (3)
Translate between the geometric description and the equation for
a conic section (3)
Geometry
Visualize relationships between two-dimensional and threedimensional objects (1)
Apply trigonometry to general triangles (3)
Prove geometric theorems (3)
Make geometric constructions (2)
Apply geometric concepts in modeling situations (3)
Understand and apply theorems about circles (4)
Understand congruence in terms of rigid motions (3)
Experiment with transformations in the plane (5)
Find arc lengths and areas of sectors of circles (1)
Understand similarity in terms of similarity transformations (5)
Note/VNCFSTJOQBSFOUIFTFTJOEJDBUFIPXNBOZTUBOEBSETTUBUFNFOUTBQQFBSXJUIJOUIFDMVTUFS
Chapter Four •
Figure . Average Number of Matches per Standard Across All Comparison Standards, by Cluster
0
10
20
30
40
50
Understand the concept of a function and use function notation
(3)
Interpret functions that arise in applications in terms of the
context (3)
Prove and apply trigonometric identities (2)
Functions
Build a function that models a relationship between two
quantities (5)
Analyze functions using different representations (10)
Model periodic phenomena with trigonometric functions (3)
Extend the domain of trigonometric functions using the unit circle
(4)
Construct and compare linear and exponential models and solve
problems (7)
Build new functions from existing functions (7)
Interpret expressions for functions in terms of the situation they
model (1)
Solve equations and inequalities in one variable (4)
Perform arithmetic operations on polynomials(1)
Represent and solve equations and inequalities graphically (3)
Write expressions in equivalent forms to solve problems (5)
Algebra
Understand solving equations as a process of reasoning and
explain the reasoning (2)
Solve systems of equations (5)
Rewrite rational expressions (2)
Create equations that describe numbers or relationships (4)
Understand the relationship between zeros and factors of
polynomials (2)
Interpret the structure of expressions (4)
Use polynomial identities to solve problems (2)
Extend the properties of exponents to rational exponents (2)
Reason quantitatively and use units to solve problems (3)
Number and Quanitiy
Perform arithmetic operations with complex numbers (3)
Represent complex numbers and their operations on the
complex plane (3)
Use properties of rational and irrational numbers (1)
Represent and model with vector quantities (3)
Perform operations on matrices and use matrices in applications
(7)
Perform operations on vectors (7)
Use complex numbers in polynomial identities and equations (3)
Note/VNCFSTJOQBSFOUIFTFTJOEJDBUFIPXNBOZTUBOEBSETTUBUFNFOUTBQQFBSXJUIJOUIFDMVTUFS
Chapter Four 20
Chapter | Results for Mathematics
Match for Each Comparison Set to the Common Core
Standards
Categorical Concurrence Statistic
5BCMFTIPXTUIFBWFSBHFOVNCFSPGNBUDIFTQFSDPODFQUVBM
DBUFHPSZ CFUXFFO UIF $PNNPO $PSF TUBOEBSET BOE FBDI
set of comparison standards for mathematics. Generally, all
DBUFHPSJFTGPSBMMTUBOEBSETTFUTIBWFBSFMBUJWFMZIJHIOVNCFS
PGNBUDIFT"TXJUI&OHMJTIMBOHVBHFBSUTBOEMJUFSBDZ TPNF
DBUFHPSJFTIBWFWFSZIJHITUBOEBSEEFWJBUJPOT JOEJDBUJOHUIBU
SBUFSTWBSJFEXJEFMZJOUIFOVNCFSPGNBUDIFTUIFZJEFOUJmFE
#FDBVTFBTJOHMFDPSSFTQPOEFODFJOBDPOUFOUBSFBCFUXFFO
UXP TFUT PG TUBOEBSET JT DPOTJEFSFE TVGmDJFOU UP NFFU UIF
TUBOEBSETUPTUBOEBSET BMJHONFOU DSJUFSJPO $PPL
UIF DSJUFSJPO GPS $BUFHPSJDBM $PODVSSFODF JT NFU GPS FWFSZ
DPODFQUVBM DBUFHPSZ GPS FWFSZ DPNQBSJTPO TUBOEBSE TFU
"DSPTTSBUFST NPSFUIBOPOFTUBOEBSEGSPNFWFSZTFUPGUIFmWF
DPNQBSJTPO TUBOEBSET PO BWFSBHF JT NBUDIFE UP B $PNNPO
$PSFTUBOEBSE TFF5BCMF
*O"QQFOEJY$ UIFSFJTNPSFEFUBJMFEEJTDVTTJPOGPSFBDITFUPG
DPNQBSJTPOTUBOEBSETBOEIPXJUBMJHOTUPUIF$PNNPO$PSF
The precise correspondence of matches between the Common
Core standards and individual comparison sets of standards is
QSPWJEFEJOUIF5FDIOJDBM4VQQMFNFOU
Table . Average Number of Matches for Mathematics Common Core
Standards Across Five Sets of Standards
Common Core
mathematics
conceptual
category
Average number of matches
CA
MA
TCCRS
KSUS
IB
M
SD
M
SD
M
SD
M
SD
M
SD
Number and
Quantity
.
.
.
.
.
.
.
.
.
.
Algebra
.
.
.
.
.
.
.
.
.
.
Functions
.
.
.
.
.
.
.
.
.
.
Geometry
.
.
.
.
.
.
.
.
.
.
Statistics and
Probability
.
.
.
.
.
.
.
.
.
.
Total
.
.
.
.
.
.
.
.
.
.
CA = California; MA = Massachusetts; TCCRS = Texas College and Career Readiness Standards; KSUS = Knowledge and Skills for
University Success; IB = International Baccalaureate.
Table . Categorical Concurrence for Mathematics
Common Core mathematics conceptual category
CA
MA
TCCRS
KSUS
IB
Number and Quantity
Algebra
Functions
Geometry
Statistics and Probability
CA = California; MA = Massachusetts; TCCRS = Texas College and Career Readiness Standards; KSUS = Knowledge and Skills for University Success; IB =
International Baccalaureate.
Meets the criterion for Categorical Concurrence (averaged across raters, a single correspondence exists between the two sets of standards);
Does not meet the criterion for Categorical Concurrence.
Chapter Four 21
Chapter | Results for Mathematics
Depth of Knowledge
Ratings for Common Core Standards
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for each of the Common Core mathematics conceptual
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DBUFHPSZ XIJDIIBTBNPEFPGMFWFM SFDBMMBOESFQSPEVDUJPO
UIF TUBOEBSET JOWPMWF TVDI TLJMMT BT FYQMBJOJOH QSPQFSUJFT
PG JSSBUJPOBM FYQPOFOUT SBUJPOBM BOE JSSBUJPOBM OVNCFST BOE
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WFDUPST BOE NBUSJDFT 5IFTF TLJMMT NBZ CF NPSF PSJFOUFE
UPXBSE POFTUFQ SFDBMM PS QSPCMFN TPMWJOH *O UIF (FPNFUSZ
DBUFHPSZ UIFTUBOEBSETJOWPMWFTVDITLJMMTBTQSPWJOHUIFPSFNT
EFSJWJOH FRVBUJPOT BOE VTJOH FYQFSJNFOUBUJPO UP WFSJGZ
DPODFQUT TVDI BT TJNJMBSJUZ 4VDI TLJMMT NBZ MFOE UIFNTFMWFT
NPSF UPXBSE TUSBUFHJD BOE FYUFOEFE UIJOLJOH XIJDI DPVME
FYQMBJOXIZUIFNPEFSBUJOHGPSUIBUDPOUFOUTQFDJmDBSFBXBT
BUMFWFM TUSBUFHJDUIJOLJOH
Figure . Percent of Common Core Mathematics Standards
at each Depth of Knowledge Level
Level 4
Extended Thinking
5%
Level 3
Strategic Thinking
20%
Level 1
Recall and
Reproduction
21%
Table . Depth of Knowledge (DOK) Modal
Ratings for Mathematics Common Core Conceptual
Categories
Common Core mathematics conceptual category
DOK mode
Number and Quantity
Algebra
Functions
Geometry
Statistics and Probability
At the standard level, the Common Core mathematics standards
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the ELA and literacy Common Core standards with fewer at the
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TUBOEBSET BSF SBUFE BT TLJMMT BOE DPODFQUT MFWFM 0WFSBMM
BSF BU B MFWFM SFDBMM BOE SFQSPEVDUJPO BSF BU B
MFWFM TLJMMT BOE DPODFQUT BSF BU B MFWFM TUSBUFHJD
UIJOLJOH BOEBSFBUMFWFM FYUFOEFEUIJOLJOH 'JHVSF
TVNNBSJ[FTUIJTJOGPSNBUJPO%0,SBUJOHTGPSBMMTUBOEBSETBSF
QSPWJEFEJO"QQFOEJY#
Level 2
Skills and Concepts
54%
Chapter Four 22
Chapter | Results for Mathematics
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Practice within the Common Core standards were not rated
for the purposes of this study. The Mathematical Practices
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$PSF NBUIFNBUJDT TUBOEBSET 5IVT VTJOH UIF NBUIFNBUJDT
practices in the application and use of the other Common Core
mathematics standards could conceivably lead to different
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DOK Consistency of Each Comparison Set to the Common
Core Standards
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BCPWF BU BOEVOEFSUIFDPHOJUJWFEFNBOEMFWFMPGUIF$PNNPO
$PSFTUBOEBSET*OUIFmHVSF BMJOFJTESBXOBU XIJDIJT
UIFDSJUFSJPOGPSUIFOVNCFSPGTUBOEBSETGBMMJOHBCPWFPSBUUIF
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UIF%0,$POTJTUFODZTUBUJTUJD'PSUIF/VNCFSBOE2VBOUJUZ
"MHFCSB BOE4UBUJTUJDTBOE1SPCBCJMJUZDPODFQUVBMDBUFHPSJFT
BMM TFUT PG TUBOEBSET NFFUJOH UIF $BUFHPSJDBM $PODVSSFODF
DSJUFSJPO BMTP NFFU UIF %0, DSJUFSJPO 'PS (FPNFUSZ POMZ UIF
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UFOE UP CF TJNJMBS UP PS NPSF DPHOJUJWFMZ DPNQMFY UIBO UIF
Common Core standards. The California state standards and
the Massachusetts state standards are similar to or more
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DPODVSSFODF 'JHVSF JMMVTUSBUFT UIFTF mOEJOHT 5IF mHVSF
also shows that some standards sets fall just above or just
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if an alternative criterion had been selected.
Figure . Depth of Knowledge Level Comparisons of the Five Sets of Comparison
Standards to Common Core Mathematics Standards
25
50
CA
MA
TCCRS
KSUS
IB
Functions
CA
MA
TCCRS
KSUS
IB
Geometry
CA
MA
TCCRS
KSUS
IB
CA
MA
TCCRS
KSUS
IB
Statistics and
Probability
Algebra
Number and
Quantity
0
CA
MA
TCCRS
KSUS
IB
75
100
Average
Percent
% Above
% At
% Under
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Chapter Four 23
Chapter | Results for Mathematics
Breadth of Coverage
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$PWFSBHFJONBUIFNBUJDTBDSPTTUIFDPNQBSJTPOTUBOEBSETXBTDPOTJTUFOUMZTUSPOH JOEJDBUJOHUIBUNBUDIJOHDPOUFOUGPSFBDI
DPNQBSJTPOTFUPGTUBOEBSETXBTEJTQFSTFEBDSPTTUIFDMVTUFSTPGUIF$PNNPO$PSFTUBOEBSET TFF5BCMF
Table . Breadth of Coverage Criterion for Mathematics
Common Core mathematics conceptual category
CA
MA
TCCRS
KSUS
IB
Number and Quantity
Algebra
Functions
Geometry
Statistics and Probability
CA = California; MA = Massachusetts; TCCRS = Texas College and Career Readiness Standards; KSUS = Knowledge and Skills for University Success; IB =
International Baccalaureate.
means that a majority of clusters in the Common Core conceptual category have at least one matched comparison standard;
means that more than one cluster in the Common Core conceptual category have at least one matched comparison standard;
means that one or fewer than one cluster in the Common Core conceptual category have at least one matched comparison standard.
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Chapter Four 24
Chapter
| Summary and Discussion
In this chapter we review the purpose of the study, discuss the
method chosen to obtain data necessary to answer the three
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The study addresses three research questions:
1.
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the comparison standards the same as or different
from what is described in the Common Core
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2.
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$PSFTUBOEBSETBOEUPXIBUFYUFOUBSFUIFNBUDIFE
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3.
How broadly do the matched comparison standards
cover the content of the Common Core standards?
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and the comparison of the Common Core standards to
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standards. The two states deemed to have standards that
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BSF $BMJGPSOJB BOE .BTTBDIVTFUUT 5IF UXP TFUT PG DPMMFHF
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UP EFUFSNJOF SFMBUJWF DPHOJUJWF EFNBOE 5IF UIJSE NFUSJD
EFUFSNJOFT CSFBEUI PG PWFSMBQ PS DPWFSBHF GPS NBUDIJOH
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$PSFTUBOEBSETBOEPUIFSTUBOEBSETZTUFNT OPUUPFOHBHFJO
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The overall results of the study, as summarized in Table 20,
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standards and the comparison standards, with somewhat
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&-"BOEMJUFSBDZ PGBOBMZTFTBUUIFTUSBOEMFWFMNFFU
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is relatively modest, namely, one or more correspondences
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Chapter Five •
Chapter | Summary and Discussion
Table . Summary of Alignment Findings for Five Sets of Standards Compared to the Common Core Standards
Common Core
FRQWHQWVSHFLÀFDUHDV
Comparison standards
CA
MA
TCCRS
KSUS
IB
English language arts and literacy
Reading for Literature
Reading for Informational Texts
Writing
Speaking and Listening
Language
NA
Reading in History/Social Studies
NA
Reading in Science and Technical Subjects
NA
NA
Writing in History/Social Studies, Science,
and Technical Subjects
Mathematics
Number & Quantity
Algebra
Functions
Geometry
Statistics & Probability
CA = California; MA = Massachusetts; TCCRS = Texas College and Career
Readiness Standards; KSUS = Knowledge and Skills for University Success; IB =
International Baccalaureate.
Key
Categorical Concurrence met
Strong coverage
Depth of Knowledge met
Moderate coverage
Limited or no coverage
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the mathematics standards comparisons than the ELA and
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$PNNPO $PSF BMJHONFOU XPSL 1PSUFS .D.BLFO )XBOH
:BOH
'PSDPHOJUJWFDPNQMFYJUZJO&-"BOEMJUFSBDZ PGTUSBOE
level analyses indicated that the comparison standard sets
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cases, the comparison standard sets tended to be rated lower
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$PNNPO$PSFTUBOEBSET4UBUFTTIPVMEDBSFGVMMZJOUFSQSFUUIF
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Common Core ELA and literacy standards in particular will be
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curriculum materials for the Common Core standards need to
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NBUFSJBMTUPFOTVSFUIFZBSFTVGmDJFOUMZDIBMMFOHJOH5IJTJTUSVF
Chapter Five 26
Chapter | Summary and Discussion
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XIFO EFWFMPQJOH NBUFSJBMT UP UFBDI BOE BTTFTT SFBEJOH PG
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content areas.
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indicate that the comparison standard sets are at or above the
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found comparison standard sets to be below the level of the
Common Core standards. The Common Core content areas
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Functions.
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the breadth of topics set forth in the Common Core standards.
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DPWFSBHFBOEPOFTIPXFEMJNJUFEDPWFSBHF'PSNBUIFNBUJDT
mOEJOHTTVHHFTUUIBUDPNQBSJTPOTFUTTIPXTUSPOHDPWFSBHF
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the Common Core standards may not have a match, the topics
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SFnFDUFEJOUIFDPNQBSJTPOTUBOEBSET
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TUBUFT TUBOEBSET "NPOH UIF DPNQBSJTPO TUBOEBSET JO UIJT
TUVEZ UIBU BSF DPOTJEFSFE SJHPSPVT BOE DPMMFHF BOE DBSFFS
QSFQBSBUPSZ IPXFWFS UIF PWFSBMM mOEJOHT TVHHFTU B HFOFSBM
MFWFMPGBHSFFNFOUCFUXFFOUIF$PNNPO$PSFTUBOEBSETBOE
UIF DPNQBSJTPO TUBOEBSET SFHBSEJOH XIBU JT JNQPSUBOU GPS
IJHI TDIPPM TUVEFOUT UP LOPX JO &OHMJTI MBOHVBHF BSUT BOE
NBUIFNBUJDT JO PSEFS UP CF IJHIMZ DIBMMFOHFE BOE SFBEZ GPS
DPMMFHFBOEDBSFFST
5IF QVSQPTF PG UIJT TUVEZ XBT UP BTDFSUBJO BMJHONFOU OPU UP
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other set of standards. There is no absolute reason that every
set of comparison standards must match the Common Core
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to the Common Core standards in one or more areas does
not mean the comparison standards are inferior or need to
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is not necessarily the best or only measure of standards quality.
Closing Note From The Authors
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ensure reliable and valid results. This is one of the reasons we
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different method and reached a different conclusion. This study
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$PSFVTJOHUIF4VSWFZPG&OBDUFE$VSSJDVMVN 4&$ BNFUIPE
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authors conclude that the Common Core standard represent
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In our opinion, it is possible for both studies to be correct in their
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B NVDI NPSF EFUBJMFE MFWFM "T TUVEJFT PG DPOUFOU BMJHONFOU
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true in the case of the Common Core standards, which were
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entry-level postsecondary course areas. At the same time,
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of Common Core standards. In other words, it does not appear
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TUVEFOUOFFETUPTVDDFFEJOFWFSZQPTUTFDPOEBSZTFUUJOH5IF
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XPSL $POMFZ $POMFZ FU BM UIBU QPTUTFDPOEBSZ
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Chapter Five 27
Chapter | Summary and Discussion
important as the content covered in most cases.
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Common Core standards are rolled out statewide. This is true
and necessary for both ELA and mathematics. It is perhaps
more obvious that the ELA standards will be operationalized
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about how students should learn the standards. As we note in
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each of the mathematical standards. The standards authors
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school, futures that include additional postsecondary study
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Chapter Five 28
| References
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References •
| References
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3PMGIVT & %FDLFS -& #SJUF +- (SFHPSZ - A systematic comparison of the American Diploma Project English
language arts college readiness standards with those of the ACT, College Board, and Standards for Success. (Issues &
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Standards3FUSJFWFEGSPNIUUQTFQJDPOMJOFPSHmMFTQEG$$34UBOEBSETQEG
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References 30
Appendices to
Lining Up: The Relationship
between the Common Core State Standards
and Five Sets of Comparison Standards
Appendix A | Description of the
Depth of Knowledge Calculation
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Appendix A •
Appendix B | Common Core Standards
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mathematics standards.
Table B. English Language Arts and Literacy Common Core Standards Content, with Depth of
Knowledge Consensus Ratings
Reference
standard
numbera
Standard
DOK
rating
Reading Standards for Literature
.
Key Ideas and Details
.a
. Cite strong and thorough textual evidence to support analysis of what the text says explicitly as well as
inferences drawn from the text, including determining where the text leaves matters uncertain.
.b
. Determine two or more themes or central ideas of a text and analyze their development over the
course of the text, including how they interact and build on one another to produce a complex account;
provide an objective summary of the text.
. Analyze the impact of the author’s choices regarding how to develop and relate elements of a story
or drama (e.g., where a story is set, how the action is ordered, how the characters are introduced and
developed).
.
Craft and Structure
.a
. Determine the meaning of words and phrases as they are used in the text, including figurative and connotative meanings; analyze the impact of specific word choices on meaning and tone, including words
with multiple meanings or language that is particularly fresh, engaging, or beautiful. (Include Shakespeare as well as other authors.)
. Analyze how an author’s choices concerning how to structure specific parts of a text (e.g., the choice
of where to begin or end a story, the choice to provide a comedic or tragic resolution) contribute to its
overall structure and meaning as well as its aesthetic impact.
. Analyze a case in which grasping point of view requires distinguishing what is directly stated in a text
from what is really meant (e.g., satire, sarcasm, irony, or understatement).
.
Integration of Knowledge and Ideas
.a
. Analyze multiple interpretations of a story, drama, or poem (e.g., recorded or live production of a play
or recorded novel or poetry), evaluating how each version interprets the source text. (Include at least one
play by Shakespeare and one play by an American dramatist.)
. Demonstrate knowledge of eighteenth-, nineteenth-, and early-twentieth-century foundational works
of American literature, including how two or more texts from the same period treat similar themes or
topics.
.
Range of Reading and Level of Text Complexity
.a
. By the end of grade , read and comprehend literature, including stories, dramas, and poems, in the
grades –CCR text complexity band proficiently, with scaffolding as needed at the high end of the range.
By the end of grade , read and comprehend literature, including stories, dramas, and poems, at the
high end of the grades –CCR text complexity band independently and proficiently.
Reading Standards for Informational Texts
.
Key Ideas and Details
.a
. Cite strong and thorough textual evidence to support analysis of what the text says explicitly as well as
inferences drawn from the text, including determining where the text leaves matters uncertain.
.b
. Determine two or more central ideas of a text and analyze their development over the course of the
text, including how they interact and build on one another to provide a complex analysis; provide an
objective summary of the text.
.c
.b
.c
.b
a
The reference standard number refers to the numbering system that was used for the purposes of organizing ratings for this study.
Appendix B •
Common Core Standards
Table B. continued
Reference
standard
numbera
.c
Standard
DOK
rating
. Analyze a complex set of ideas or sequence of events and explain how specific individuals, ideas, or
events interact and develop over the course of the text.
.
Craft and Structure
.a
. Determine the meaning of words and phrases as they are used in a text, including figurative, connotative, and technical meanings; analyze how an author uses and refines the meaning of a key term or terms
over the course of a text (e.g., how Madison defines faction in Federalist No. ).
.b
. Analyze and evaluate the effectiveness of the structure an author uses in his or her exposition or argument, including whether the structure makes points clear, convincing, and engaging.
.c
. Determine an author’s point of view or purpose in a text in which the rhetoric is particularly effective,
analyzing how style and content contribute to the power, persuasiveness, or beauty of the text.
.
Integration of Knowledge and Ideas
.a
. Integrate and evaluate multiple sources of information presented in different media or formats (e.g.,
visually, quantitatively) as well as in words in order to address a question or solve a problem.
.b
. Delineate and evaluate the reasoning in seminal U.S. texts, including the application of constitutional
principles and use of legal reasoning (e.g., in U.S. Supreme Court majority opinions and dissents) and
the premises, purposes, and arguments in works of public advocacy (e.g., The Federalist, presidential
addresses).
. Analyze seventeenth-, eighteenth-, and nineteenth-century foundational U.S. documents of historical
and literary significance (including The Declaration of Independence, the Preamble to the Constitution,
the Bill of Rights, and Lincoln’s Second Inaugural Address) for their themes, purposes, and rhetorical
features.
.
Range of Reading and Level of Text Complexity
.a
. By the end of grade , read and comprehend literary nonfiction in the grades –CCR text complexity
band proficiently, with scaffolding as needed at the high end of the range. By the end of grade , read
and comprehend literary nonfiction at the high end of the grades –CCR text complexity band independently and proficiently.
Writing Standards
.
Text Types and Purposes
.a
. Write arguments to support claims in an analysis of substantive topics or texts, using valid reasoning
and relevant and sufficient evidence.
.b
a. Introduce precise, knowledgeable claim(s), establish the significance of the claim(s), distinguish the
claim(s) from alternate or opposing claims, and create an organization that logically sequences claim(s),
counterclaims, reasons, and evidence.
b. Develop claim(s) and counterclaims fairly and thoroughly, supplying the most relevant evidence for
each while pointing out the strengths and limitations of both in a manner that anticipates the audience’s
knowledge level, concerns, values, and possible biases.
c. Use words, phrases, and clauses as well as varied syntax to link the major sections of the text, create
cohesion, and clarify the relationships between claim(s) and reasons, between reasons and evidence, and
between claim(s) and counterclaims.
.e
d. Establish and maintain a formal style and objective tone while attending to the norms and conventions
of the discipline in which they are writing.
.f
e. Provide a concluding statement or section that follows from and supports the argument presented.
.g
. Write informative/explanatory texts to examine and convey complex ideas, concepts, and information
clearly and accurately through the effective selection, organization, and analysis of content.
.h
a. Introduce a topic; organize complex ideas, concepts, and information so that each new element builds
on that which precedes it to create a unified whole; include formatting (e.g., headings), graphics (e.g.,
figures, tables), and multimedia when useful to aiding comprehension.
.c
.c
.d
Appendix B 34
Common Core Standards
Table B. continued
Reference
standard
numbera
Standard
DOK
rating
b. Develop the topic thoroughly by selecting the most significant and relevant facts, extended definitions,
concrete details, quotations, or other information and examples appropriate to the audience’s knowledge
of the topic.
.j
c. Use appropriate and varied transitions and syntax to link the major sections of the text, create cohesion, and clarify the relationships among complex ideas and concepts.
.k
d. Use precise language, domain-specific vocabulary, and techniques such as metaphor, simile, and analogy to manage the complexity of the topic.
.l
e. Establish and maintain a formal style and objective tone while attending to the norms and conventions
of the discipline in which they are writing.
.m
f. Provide a concluding statement or section that follows from and supports the information or explanation presented (e.g., articulating implications or the significance of the topic).
.n
. Write narratives to develop real or imagined experiences or events using effective technique, wellchosen details, and well-structured event sequences.
.o
a. Engage and orient the reader by setting out a problem, situation, or observation and its significance,
establishing one or multiple point(s) of view, and introducing a narrator and/or characters; create a
smooth progression of experiences or events.
.p
b. Use narrative techniques, such as dialogue, pacing, description, reflection, and multiple plot lines, to
develop experiences, events, and/or characters.
.q
c. Use a variety of techniques to sequence events so that they build on one another to create a coherent
whole and build toward a particular tone and outcome (e.g., a sense of mystery, suspense, growth, or
resolution).
.r
d. Use precise words and phrases, telling details, and sensory language to convey a vivid picture of the
experiences, events, setting, and/or characters.
.s
e. Provide a conclusion that follows from and reflects on what is experienced, observed, or resolved over
the course of the narrative.
.
Production and Distribution of Writing
.a
. Produce clear and coherent writing in which the development, organization, and style are appropriate
to task, purpose, and audience. (Grade-specific expectations for writing types are defined in standards
– above.)
. Develop and strengthen writing as needed by planning, revising, editing, rewriting, or trying a new approach, focusing on addressing what is most significant for a specific purpose and audience. (Editing for
conventions should demonstrate command of Language standards –, up to and including grades –
on page .)
.c
. Use technology, including the Internet, to produce, publish, and update individual or shared writing
products in response to ongoing feedback, including new arguments or information.
.
Research to Build and Present Knowledge
.a
. Conduct short as well as more sustained research projects to answer a question (including a self-generated question) or solve a problem; narrow or broaden the inquiry when appropriate; synthesize multiple
sources on the subject, demonstrating understanding of the subject under investigation.
. Gather relevant information from multiple authoritative print and digital sources, using advanced
searches effectively; assess the strengths and limitations of each source in terms of the task, purpose, and
audience; integrate information into the text selectively to maintain the flow of ideas, avoiding plagiarism
and overreliance on any one source and following a standard format for citation.
.c
. Draw evidence from literary or informational texts to support analysis, reflection, and research.
.d
a. Apply grades – Reading standards to literature (e.g., “Demonstrate knowledge of eighteenth-,
nineteenth-, and early-twentieth-century foundational works of American literature, including how two or
more texts from the same period treat similar themes or topics”).
b. Apply grades – Reading standards to literary nonfiction (e.g., “Delineate and evaluate the reasoning in seminal U.S. texts, including the application of constitutional principles and use of legal reasoning
[e.g., in U.S. Supreme Court Case majority opinions and dissents] and the premises, purposes, and arguments in works of public advocacy [e.g., The Federalist, presidential addresses]”).
.i
.b
.b
.e
Appendix B 35
Common Core Standards
Table B. continued
Reference
standard
numbera
Standard
DOK
rating
.
Range of Writing
.a
. Write routinely over extended time frames (time for research, reflection, and revision) and shorter
time frames (a single sitting or a day or two) for a range of tasks, purposes, and audiences.
Speaking and Listening Standards
.
Comprehension and Collaboration
.a
. Initiate and participate effectively in a range of collaborative discussions (one-on-one, in groups, and
teacher-led) with diverse partners on grades - topics, texts, and issues, building on others’ ideas and
expressing their own ideas clearly and persuasively.
a. Come to discussions prepared, having read and researched material under study; explicitly draw on
that preparation by referring to evidence from texts and other research on the topic or issue to stimulate
a thoughtful, well-reasoned exchange of ideas.
.c
b. Work with peers to promote civil, democratic discussions and decision-making, set clear goals and
deadlines, and establish individual roles as needed.
.d
c. Propel conversations by posing and responding to questions that probe reasoning and evidence;
ensure a hearing for a full range of positions on a topic or issue; clarify, verify, or challenge ideas and
conclusions; and promote divergent and creative perspectives.
d. Respond thoughtfully to diverse perspectives; synthesize comments, claims, and evidence made on all
sides of an issue; resolve contradictions when possible; and determine what additional information or
research is required to deepen the investigation or complete the task.
. Integrate multiple sources of information presented in diverse formats and media (e.g., visually, quantitatively, orally) in order to make informed decisions and solve problems, evaluating the credibility and
accuracy of each source and noting any discrepancies among the data.
. Evaluate a speaker’s point of view, reasoning, and use of evidence and rhetoric, assessing the stance,
premises, links among ideas, word choice, points of emphasis, and tone used.
.
Presentation of Knowledge and Ideas
.a
. Present information, findings, and supporting evidence, conveying a clear and distinct perspective,
such that listeners can follow the line of reasoning, alternative or opposing perspectives are addressed,
and the organization, development, substance, and style are appropriate to purpose, audience, and a
range or formal and informal tasks.
.b
. Make strategic use of digital media (e.g., textual, graphical, audio, visual, and interactive elements) in
presentations to enhance understanding of findings, reasoning, and evidence and to add interest.
.c
. Adapt speech to a variety of contexts and tasks, demonstrating a command of formal English when
indicated or appropriate. (See grades – Language standards and on page for specific expectations.)
Language Standards
.
Conventions of Standard English
.a
. Demonstrate command of the conventions of standard English grammar and usage when writing or
speaking.
.b
a. Apply the understanding that usage is a matter of convention, can change over time, and is sometimes
contested.
.c
b. Resolve issues of complex or contested usage, consulting references (e.g., Merriam-Webster’s Dictionary of English Usage, Garner’s Modern American Usage) as needed.
.d
. Demonstrate command of the conventions of standard English capitalization, punctuation, and spelling
when writing.
.e
a. Observe hyphenation conventions.
.f
b. Spell correctly.
.
Knowledge of Language
.a
. Apply knowledge of language to understand how language functions in different contexts, to make
effective choices for meaning or style, and to comprehend more fully when reading or listening.
.b
.e
.f
.g
Appendix B 36
Common Core Standards
Table B. continued
Reference
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Standard
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rating
a. Vary syntax for effect, consulting references (e.g., Tufte’s Artful Sentences) for guidance as needed; apply an understanding of syntax to the study of complex texts when reading.
.
Vocabulary Acquisition and Use
.a
. Determine or clarify the meaning of unknown and multiple-meaning words and phrases based on
grades - reading and content, choosing flexibly from a range of strategies.
.b
a. Use context (e.g., the overall meaning of a sentence, paragraph, or text; a word’s position or function
in a sentence) as a clue to the meaning of a word or phrase.
.c
b. Identify and correctly use patterns of word changes that indicate different meanings or parts of speech
(e.g., conceive, conception, conceivable).
.d
c. Consult general and specialized reference materials (e.g., dictionaries, glossaries, thesauruses), both
print and digital, to find the pronunciation of a word or determine or clarify its precise meaning, its part
of speech, its etymology, or its standard usage.
.e
d. Verify the preliminary determination of the meaning of a word or phrase (e.g., by checking the inferred
meaning in context or in a dictionary).
.f
. Demonstrate understanding of figurative language, word relationships, and nuances in word meanings.
.g
a. Interpret figures of speech (e.g., hyperbole, paradox) in context and analyze their role in the text.
.h
b. Analyze nuances in the meaning of words with similar denotations.
.i
. Acquire and use accurately general academic and domain-specific words and phrases, sufficient for
reading, writing, speaking, and listening at the college- and career-readiness level; demonstrate independence in gathering vocabulary knowledge when considering a word or phrase important to comprehension or expression.
Reading Standards for Literacy in History/Social Studies
.
Key Ideas and Details
.a
. Cite specific textual evidence to support analysis of primary and secondary sources, connecting insights
gained from specific details to an understanding of the text as a whole.
.b
. Determine the central ideas or information of a primary or secondary source; provide an accurate summary that makes clear the relationships among the key details and ideas.
.c
. Evaluate various explanations for actions or events and determine which explanation best accords with
textual evidence, acknowledging where the text leaves matters uncertain.
.
Craft and Structure
.a
. Determine the meaning of words and phrases as they are used in a text, including analyzing how an
author uses and refines the meaning of a key term over the course of a text (e.g., how Madison defines
faction in Federalist No. ).
.b
. Analyze in detail how a complex primary source is structured, including how key sentences, paragraphs, and larger portions of the text contribute to the whole.
.c
. Evaluate authors’ differing points of view on the same historical event or issue by assessing the authors’ claims, reasoning, and evidence.
.
Integration of Knowledge and Ideas
.a
. Integrate and evaluate multiple sources of information presented in diverse formats and media (e.g.,
visually, quantitatively, as well as in words) in order to address a question or solve a problem.
.b
. Evaluate an author’s premises, claims, and evidence by corroborating or challenging them with other
information.
.c
. Integrate information from diverse sources, both primary and secondary, into a coherent understanding of an idea or event, noting discrepancies among sources.
.
Range of Reading and Level of Text Complexity
.a
. By the end of grade , read and comprehend history/social studies texts in the grades – text
complexity band independently and proficiently.
.b
Appendix B 37
Common Core Standards
Table B. continued
Reference
standard
numbera
Standard
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rating
Reading Standards for Literacy in Science and Technical Subjects
.
Key Ideas and Details
.a
. Cite specific textual evidence to support analysis of science and technical texts, attending to important
distinctions the author makes and to any gaps or inconsistencies in the account.
.b
. Determine the central ideas or conclusions of a text; summarize complex concepts, processes, or information presented in a text by paraphrasing them in simpler but still accurate terms.
.c
. Follow precisely a complex multistep procedure when carrying out experiments, taking measurements,
or performing technical tasks; analyze the specific results based on explanations in the text.
.
Craft and Structure
.a
. Determine the meaning of symbols, key terms, and other domain-specific words and phrases as they
are used in a specific scientific or technical context relevant to grades - texts and topics.
.b
. Analyze how the text structures information or ideas into categories or hierarchies, demonstrating
understanding of the information or ideas.
.c
. Analyze the author’s purpose in providing an explanation, describing a procedure, or discussing an
experiment in a text, identifying important issues that remain unresolved.
.
Integration of Knowledge and Ideas
.a
. Integrate and evaluate multiple sources of information presented in diverse formats and media (e.g.,
quantitative data, video, multimedia) in order to address a question or solve a problem.
.b
. Evaluate the hypotheses, data, analysis, and conclusions in a science or technical text, verifying data
when possible and corroborating or challenging conclusions with other sources of information.
.c
. Synthesize information from a range of sources (e.g., texts, experiments, simulations) into a coherent
understanding of a process, phenomenon, or concept, resolving conflicting information when possible.
.
Range of Reading and Level of Text Complexity
.a
. By the end of Grade , read and comprehend science/technical texts in the grades – text complexity band independently and proficiently.
Writing Standards for Literacy in History/Social Studies, Science, and Technical Subjects
.
Text Types and Purposes
.a
. Write arguments focused on discipline-specific content.
.b
a. Introduce precise, knowledgeable claim(s), establish the significance of the claim(s), distinguish the
claim(s) from alternate or opposing claims, and create an organization that logically sequences the
claim(s), counterclaims, reasons, and evidence.
b. Develop claim(s) and counterclaims fairly and thoroughly, supplying the most relevant data and
evidence for each while pointing out the strengths and limitations of both claim(s) and counterclaims in
a discipline-appropriate form that anticipates the audience’s knowledge level, concerns, values, and possible biases.
c. Use words, phrases, and clauses as well as varied syntax to link the major sections of the text, create
cohesion, and clarify the relationships between claim(s) and reasons, between reasons and evidence, and
between claim(s) and counterclaims.
.e
d. Establish and maintain a formal style and objective tone while attending to the norms and conventions
of the discipline in which they are writing.
.f
e. Provide a concluding statement or section that follows from or supports the argument presented.
.g
. Write informative/explanatory texts, including the narration of historical events, scientific procedures/
experiments, or technical processes.
.h
a. Introduce a topic and organize complex ideas, concepts, and information so that each new element
builds on that which precedes it to create a unified whole; include formatting (e.g., headings), graphics
(e.g., figures, tables), and multimedia when useful to aiding comprehension.
.c
.d
Appendix B 38
Common Core Standards
Table B. continued
Reference
standard
numbera
Standard
DOK
rating
b. Develop the topic thoroughly by selecting the most significant and relevant facts, extended definitions,
concrete details, quotations, or other information and examples appropriate to the audience’s knowledge
of the topic.
.j
c. Use varied transitions and sentence structures to link the major sections of the text, create cohesion,
and clarify the relationships among complex ideas and concepts.
.k
d. Use precise language, domain-specific vocabulary and techniques such as metaphor, simile, and analogy to manage the complexity of the topic; convey a knowledgeable stance in a style that responds to the
discipline and context as well as to the expertise of likely readers.
.l
e. Provide a concluding statement or section that follows from and supports the information or explanation provided (e.g., articulating implications or the significance of the topic).
.
Production and Distribution of Writing
.a
. Produce clear and coherent writing in which the development, organization, and style are appropriate
to task, purpose, and audience.
.b
. Develop and strengthen writing as needed by planning, revising, editing, rewriting, or trying a new approach, focusing on addressing what is most significant for a specific purpose and audience.
.c
. Use technology, including the Internet, to produce, publish, and update individual or shared writing
products in response to ongoing feedback, including new arguments or information.
.
Research to Build and Present Knowledge
.a
. Conduct short as well as more sustained research projects to answer a question (including a self-generated question) or solve a problem; narrow or broaden the inquiry when appropriate; synthesize multiple
sources on the subject, demonstrating understanding of the subject under investigation.
. Gather relevant information from multiple authoritative print and digital sources, using advanced
searches effectively; assess the strengths and limitations of each source in terms of the specific task, purpose, and audience; integrate information into the text selectively to maintain the flow of ideas, avoiding
plagiarism and overreliance on any one source and following a standard format for citation.
. Draw evidence from informational texts to support analysis, reflection, and research.
.
Range of Writing
.a
. Write routinely over extended time frames (time for reflection and revision) and shorter time frames
(a single sitting or a day or two) for a range of discipline-specific tasks, purposes, and audiences.
.i
.b
.c
a
The reference standard number refers to the numbering system that was used for the purposes of organizing ratings for this study.
Appendix B 39
Common Core Standards
Table B. Mathematics Common Core Standards Content, with Depth of Knowledge (DOK)
Consensus Ratings
Reference
standard
numbera
Standard
DOK
rating
Number and Quantity
The Real Number System
.
Extend the properties of exponents to rational exponents.
.a
. Explain how the definition of the meaning of rational exponents follows from extending the properties
of integer exponents to those values, allowing for a notation for radicals in terms of rational exponents.
For example, we define / to be the cube root of because we want (/) = (/) to hold, so (/) must
equal .
.b
. Rewrite expressions involving radicals and rational exponents using the properties of exponents.
.
Use properties of rational and irrational numbers.
.a
. Explain why the sum or product of two rational numbers is rational; that the sum of a rational number
and an irrational number is irrational; and that the product of a nonzero rational number and an
irrational number is irrational.
Quantities
.
Reason quantitatively and use units to solve problems.
.a
. Use units as a way to understand problems and to guide the solution of multi-step problems; choose
and interpret units consistently in formulas; choose and interpret the scale and the origin in graphs and
data displays.
.b
. Define appropriate quantities for the purpose of descriptive modeling.
.c
. Choose a level of accuracy appropriate to limitations on measurement when reporting quantities.
The Complex Number System
.
Perform arithmetic operations with complex numbers.
.a
. Know there is a complex number i such that i = –, and every complex number has the form a + bi with
a and b being real.
.b
. Use the relation i = – and the commutative, associative, and distributive properties to add, subtract,
and multiply complex numbers.
.c
. (+) Find the conjugate of a complex number; use conjugates to find moduli and quotients of complex
numbers.
.
Represent complex numbers and their operations on the complex plane.
.a
. (+) Represent complex numbers on the complex plane in rectangular and polar form (including real
and imaginary numbers), and explain why the rectangular and polar forms of a given complex number
represent the same number.
.b
. (+) Represent addition, subtraction, multiplication, and conjugation of complex numbers geometrically
on the complex plane; use properties of this representation for computation. For example, ( – √i) =
because ( – √i) has modulus and argument °.
.c
. (+) Calculate the distance between numbers in the complex plane as the modulus of the difference, and
the midpoint of a segment as the average of the numbers at its endpoints.
.
Use complex numbers in polynomial identities and equations.
.a
. Solve quadratic equations with real coefficients that have complex solutions.
.b
. (+) Extend polynomial identities to the complex numbers. For example, rewrite x + as (x + i)(x – i).
.c
. (+) Know the Fundamental Theorem of Algebra; show that it is true for quadratic polynomials.
a
The reference standard number refers to the numbering system that was used for the purposes of organizing ratings for this study.
(+) is an indication in the Common Core mathematics standards document to show that some mathematics standards represent advanced content and are intended to
prepare students for advanced courses (see Chapter for description).
+
is an indication in the Common Core mathematics standards document to show a modeling standard (see Chapter for description).
Appendix B 40
Common Core Standards
Table B. continued
Reference
standard
numbera
DOK
rating
Standard
Vector and Matrix Quantities
.
Represent and model with vector quantities.
.a
. (+) Recognize vector quantities as having both magnitude and direction. Represent vector quantities by
directed line segments, and use appropriate symbols for vectors and their magnitudes (e.g., v, |v|, ||v||,
v).
.b
. (+) Find the components of a vector by subtracting the coordinates of an initial point from the
coordinates of a terminal point.
.c
. (+) Solve problems involving velocity and other quantities that can be represented by vectors.
.
Perform operations on vectors.
.a
. (+) Add and subtract vectors.
.b
a. Add vectors end-to-end, component-wise, and by the parallelogram rule. Understand that the
magnitude of a sum of two vectors is typically not the sum of the magnitudes.
.c
b. Given two vectors in magnitude and direction form, determine the magnitude and direction of
their sum.
.d
c. Understand vector subtraction v – w as v + (–w), where –w is the additive inverse of w, with
the same magnitude as w and pointing in the opposite direction. Represent vector subtraction
graphically by connecting the tips in the appropriate order, and perform vector subtraction
component-wise.
.e
. (+) Multiply a vector by a scalar.
.f
a. Represent scalar multiplication graphically by scaling vectors and possibly reversing their
direction; perform scalar multiplication component-wise, e.g., as c(vx, vy) = (cvx, cvy).
.g
b. Compute the magnitude of a scalar multiple cv using ||cv|| = |c|v. Compute the direction of cv
knowing that when |c|v ≠ , the direction of cv is either along v (for c > ) or against v (for c < ).
.
Perform operations on matrices and use matrices in applications.
.a
. (+) Use matrices to represent and manipulate data, e.g., to represent payoffs or incidence relationships
in a network.
.b
. (+) Multiply matrices by scalars to produce new matrices, e.g., as when all of the payoffs in a game are
doubled.
.c
. (+) Add, subtract, and multiply matrices of appropriate dimensions.
.d
. (+) Understand that, unlike multiplication of numbers, matrix multiplication for square matrices is not a
commutative operation, but still satisfies the associative and distributive properties.
.e
. (+) Understand that the zero and identity matrices play a role in matrix addition and multiplication
similar to the role of and in the real numbers. The determinant of a square matrix is nonzero if and
only if the matrix has a multiplicative inverse.
.f
. (+) Multiply a vector (regarded as a matrix with one column) by a matrix of suitable dimensions to
produce another vector. Work with matrices as transformations of vectors.
.g
. (+) Work with × matrices as transformations of the plane, and interpret the absolute value of the
determinant in terms of area.
Algebra
Seeing Structure in Expressions
.
.a
Interpret the structure of expressions
+
. Interpret expressions that represent a quantity in terms of its context.
.b
a. Interpret parts of an expression, such as terms, factors, and coefficients.
.c
b. Interpret complicated expressions by viewing one or more of their parts as a single entity. For
example, interpret P(+r)n as the product of P and a factor not depending on P.
Appendix B 41
Common Core Standards
Table B. continued
Reference
standard
numbera
Standard
DOK
rating
. Use the structure of an expression to identify ways to rewrite it. For example, see x – y as (x) – (y),
thus recognizing it as a difference of squares that can be factored as (x – y)(x + y).
.
Write expressions in equivalent forms to solve problems
.a
. Choose and produce an equivalent form of an expression to reveal and explain properties of the
quantity represented by the expression.
.d
.b
a. Factor a quadratic expression to reveal the zeros of the function it defines.
.c
b. Complete the square in a quadratic expression to reveal the maximum or minimum value of the
function it defines.
.d
c. Use the properties of exponents to transform expressions for exponential functions. For example
the expression .t can be rewritten as (./)t ≈ .t to reveal the approximate equivalent
monthly interest rate if the annual rate is %.
. Derive the formula for the sum of a finite geometric series (when the common ratio is not ), and use
the formula to solve problems. For example, calculate mortgage payments.
.e
Arithmetic with Polynomials and Rational Functions
.
Perform arithmetic operations on polynomials
.a
. Understand that polynomials form a system analogous to the integers, namely, they are closed under
the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials.
.
Understand the relationship between zeros and factors of polynomials
.a
. Know and apply the Remainder Theorem: For a polynomial p(x) and a number a, the remainder on
division by x – a is p(a), so p(a) = if and only if (x – a) is a factor of p(x).
.b
. Identify zeros of polynomials when suitable factorizations are available, and use the zeros to construct
a rough graph of the function defined by the polynomial.
.
Use polynomial identities to solve problems
.a
. Prove polynomial identities and use them to describe numerical relationships. For example, the
polynomial identity (x + y) = (x – y) + (xy) can be used to generate Pythagorean triples.
.b
. (+) Know and apply the Binomial Theorem for the expansion of (x + y)n in powers of x and y for a
positive integer n, where x and y are any numbers, with coefficients determined for example by Pascal’s
Triangle. (The Binomial Theorem can be proved by mathematical induction or by a combinatorial
argument.)
.
Rewrite rational expressions
.a
. Rewrite simple rational expressions in different forms; write a(x)/b(x) in the form q(x) + r(x)/b(x),
where a(x), b(x), q(x), and r(x) are polynomials with the degree of r(x) less than the degree of b(x), using
inspection, long division, or, for the more complicated examples, a computer algebra system.
. (+) Understand that rational expressions form a system analogous to the rational numbers, closed
under addition, subtraction, multiplication, and division by a nonzero rational expression; add, subtract,
multiply, and divide rational expressions.
.b
Creating Equations
.
Create equations that describe numbers or relationships
.a
. Create equations and inequalities in one variable and use them to solve problems. Include equations
arising from linear and quadratic functions, and simple rational and exponential functions.
.b
. Create equations in two or more variables to represent relationships between quantities; graph
equations on coordinate axes with labels and scales.
.c
. Represent constraints by equations or inequalities, and by systems of equations and/or inequalities,
and interpret solutions as viable or nonviable options in a modeling context. For example, represent
inequalities describing nutritional and cost constraints on combinations of different foods.
. Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving
equations. For example, rearrange Ohm’s law V =IR to highlight resistance R.
.d
Appendix B 42
Common Core Standards
Table B. continued
Reference
standard
numbera
Standard
DOK
rating
Reasoning with Equations and Inequalities
.
Understand solving equations as a process of reasoning and explain the reasoning
.a
. Explain each step in solving a simple equation as following from the equality of numbers asserted at
the previous step, starting from the assumption that the original equation has a solution. Construct a
viable argument to justify a solution method.
.b
. Solve simple rational and radical equations in one variable, and give examples showing how
extraneous solutions may arise.
.
Solve equations and inequalities in one variable
.a
. Solve linear equations and inequalities in one variable, including equations with coefficients
represented by letters.
.b
. Solve quadratic equations in one variable.
.c
.d
a. Use the method of completing the square to transform any quadratic equation in x into an
equation of the form (x – p) = q that has the same solutions. Derive the quadratic formula from this
form.
b. Solve quadratic equations by inspection (e.g., for x = ), taking square roots, completing the
square, the quadratic formula and factoring, as appropriate to the initial form of the equation.
Recognize when the quadratic formula gives complex solutions and write them as a ± bi for real
numbers a and b.
.
Solve systems of equations
.a
. Prove that, given a system of two equations in two variables, replacing one equation by the sum of that
equation and a multiple of the other produces a system with the same solutions.
.b
. Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of
linear equations in two variables.
.c
. Solve a simple system consisting of a linear equation and a quadratic equation in two variables
algebraically and graphically. For example, find the points of intersection between the line y = -x and the
circle x +y = .
.d
. (+) Represent a system of linear equations as a single matrix equation in a vector variable.
.e
. (+) Find the inverse of a matrix if it exists and use it to solve systems of linear equations (using technology for matrices of dimension × or greater).
.
Represent and solve equations and inequalities graphically
.a
. Understand that the graph of an equation in two variables is the set of all its solutions plotted in the
coordinate plane, often forming a curve (which could be a line).
.b
. Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y =
g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately, e.g., using
technology to graph the functions, make tables of values, or find successive approximations. Include
cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic
functions.+
. Graph the solutions to a linear inequality in two variables as a halfplane (excluding the boundary
in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two
variables as the intersection of the corresponding half-planes.
Functions
.c
Interpreting Functions
.
Understand the concept of a function and use function notation
.a
. Understand that a function from one set (called the domain) to another set (called the range) assigns
to each element of the domain exactly one element of the range. If f is a function and x is an element of
its domain, then f(x) denotes the output of f corresponding to the input x. The graph of f is the graph of
the equation y = f(x).
Appendix B 43
Common Core Standards
Table B. continued
Reference
standard
numbera
Standard
DOK
rating
.b
. Use function notation, evaluate functions for inputs in their domains, and interpret statements that use
function notation in terms of a context.
.c
. Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of
the integers. For example, the Fibonacci sequence is defined recursively by f() = f() = , f(n+) = f(n) + f(n) for n ≥ .
.
Interpret functions that arise in applications in terms of the context
.a
. For a function that models a relationship between two quantities, interpret key features of graphs and
tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the
relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive,
or negative; relative maximums and minimums; symmetries; end behavior; and periodicity.+
. Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it
describes. For example, if the function h(n) gives the number of person-hours it takes to assemble n engines
in a factory, then the positive integers would be an appropriate domain for the function.+
.c
. Calculate and interpret the average rate of change of a function (presented symbolically or as a table)
over a specified interval. Estimate the rate of change from a graph.+
.
Analyze functions using different representations
.a
. Graph functions expressed symbolically and show key features of the graph, by hand in simple cases
and using technology for more complicated cases.+
.b
.b
a. Graph linear and quadratic functions and show intercepts, maxima, and minima.
.c
b. Graph square root, cube root, and piecewise-defined functions, including step functions and
absolute value functions.
.d
c. Graph polynomial functions, identifying zeros when suitable factorizations are available, and
showing end behavior.
.e
d. (+) Graph rational functions, identifying zeros and asymptotes when suitable factorizations are
available, and showing end behavior.
.f
e. Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude.
.g
. Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.
.h
a. Use the process of factoring and completing the square in a quadratic function to show zeros,
extreme values, and symmetry of the graph, and interpret these in terms of a context.
.i
b. Use the properties of exponents to interpret expressions for exponential functions. For example,
identify percent rate of change in functions such as y = (.)t, y = (.)t, y = (.)t, y = (.)t/, and
classify them as representing exponential growth or decay.
. Compare properties of two functions each represented in a different way (algebraically, graphically,
numerically in tables, or by verbal descriptions). For example, given a graph of one quadratic function and
an algebraic expression for another, say which has the larger maximum.
.j
Building Functions
.
.a
Build a function that models a relationship between two quantities
+
. Write a function that describes a relationship between two quantities.
.b
a. Determine an explicit expression, a recursive process, or steps for calculation from a context.
.c
b. Combine standard function types using arithmetic operations. For example, build a function that
models the temperature of a cooling body by adding a constant function to a decaying exponential, and
relate these functions to the model.
Appendix B 44
Common Core Standards
Table B. continued
Reference
standard
numbera
.d
Standard
c. (+) Compose functions. For example, if T(y) is the temperature in the atmosphere as a function of
height, and h(t) is the height of a weather balloon as a function of time, then T(h(t)) is the temperature
at the location of the weather balloon as a function of time.
DOK
rating
.e
. Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to
model situations, and translate between the two forms.+
.
Build new functions from existing functions
.a
. Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of
k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate
an explanation of the effects on the graph using technology. Include recognizing even and odd functions
from their graphs and algebraic expressions for them.
. Find inverse functions.
.b
.c
a. Solve an equation of the form f(x) = c for a simple function f that has an inverse and write an
expression for the inverse. For example, f(x) = x for x > or f(x) = (x+)/(x–) for x ≠ .
.d
b. (+) Verify by composition that one function is the inverse of another.
.e
c. (+) Read values of an inverse function from a graph or a table, given that the function has an
inverse.
.f
d. (+) Produce an invertible function from a non-invertible function by restricting the domain.
.g
. (+) Understand the inverse relationship between exponents and logarithms and use this relationship to
solve problems involving logarithms and exponents.
Linear and Exponential Models
.
Construct and compare linear and exponential models and solve problems
.a
. Distinguish between situations that can be modeled with linear functions and with exponential functions.
.b
a. Prove that linear functions grow by equal differences over equal intervals, and that exponential
functions grow by equal factors over equal intervals.
.c
b. Recognize situations in which one quantity changes at a constant rate per unit interval relative to
another.
.d
c. Recognize situations in which a quantity grows or decays by a constant percent rate per unit interval relative to another.
.e
. Construct linear and exponential functions, including arithmetic and geometric sequences, given a
graph, a description of a relationship, or two input-output pairs (include reading these from a table).
.f
. Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity
increasing linearly, quadratically, or (more generally) as a polynomial function.
.g
. For exponential models, express as a logarithm the solution to abct = d where a, c, and d are numbers
and the base b is , , or e; evaluate the logarithm using technology.
.
Interpret expressions for functions in terms of the situation they model
.a
. Interpret the parameters in a linear or exponential function in terms of a context.
Trigonometric Functions
.
Extend the domain of trigonometric functions using the unit circle
.a
. Understand radian measure of an angle as the length of the arc on the unit circle subtended by the
angle.
.b
. Explain how the unit circle in the coordinate plane enables the extension of trigonometric functions
to all real numbers, interpreted as radian measures of angles traversed counterclockwise around the unit
circle.
Appendix B 45
Common Core Standards
Table B. continued
Reference
standard
numbera
.c
Standard
DOK
rating
. (+) Use special triangles to determine geometrically the values of sine, cosine, tangent for π/, π/
and p/, and use the unit circle to express the values of sine, cosine, and tangent for x, π+x, and π–x in
terms of their values for x, where x is any real number.
.d
. (+) Use the unit circle to explain symmetry (odd and even) and periodicity of trigonometric functions.
.
Model periodic phenomena with trigonometric functions
.a
. Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency,
and midline.+
.b
. (+) Understand that restricting a trigonometric function to a domain on which it is always increasing or
always decreasing allows its inverse to be constructed.
.c
. (+) Use inverse functions to solve trigonometric equations that arise in modeling contexts; evaluate the
solutions using technology, and interpret them in terms of the context.+
.
Prove and apply trigonometric identities
.a
. Prove the Pythagorean identity sin (ș) + cos (ș) = and use it to calculate trigonometric ratios.
.b
. (+) Prove the addition and subtraction formulas for sine, cosine, and tangent and use them to solve
problems.
Geometry
Congruence
.
Experiment with transformations in the plane
.a
. Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on
the undefined notions of point, line, distance along a line, and distance around a circular arc.
.b
. Represent transformations in the plane using, e.g., transparencies and geometry software; describe
transformations as functions that take points in the plane as inputs and give other points as outputs.
Compare transformations that preserve distance and angle to those that do not (e.g., translation versus
horizontal stretch).
.c
. Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations and reflections
that carry it onto itself.
.d
. Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular
lines, parallel lines, and line segments.
.e
. Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure using,
e.g., graph paper, tracing paper, or geometry software. Specify a sequence of transformations that will
carry a given figure onto another.
.
Understand congruence in terms of rigid motions
.a
. Use geometric descriptions of rigid motions to transform figures and to predict the effect of a given
rigid motion on a given figure; given two figures, use the definition of congruence in terms of rigid
motions to decide if they are congruent.
.b
. Use the definition of congruence in terms of rigid motions to show that two triangles are congruent if
and only if corresponding pairs of sides and corresponding pairs of angles are congruent.
.c
. Explain how the criteria for triangle congruence (ASA, SAS, and SSS) follow from the definition of
congruence in terms of rigid motions.
.
Prove geometric theorems
.a
. Prove theorems about lines and angles. Theorems include: vertical angles are congruent; when a
transversal crosses parallel lines, alternate interior angles are congruent and corresponding angles are
congruent; and points on a perpendicular bisector of a line segment are exactly those equidistant from the
segment’s endpoints.
Appendix B 46
Common Core Standards
Table B. continued
Reference
standard
numbera
Standard
DOK
rating
. Prove theorems about triangles. Theorems include: measures of interior angles of a triangle sum to
°; base angles of isosceles triangles are congruent; the segment joining midpoints of two sides of a
triangle is parallel to the third side and half the length; and the medians of a triangle meet at a point.
. Prove theorems about parallelograms. Theorems include: opposite sides are congruent, opposite
angles are congruent, the diagonals of a parallelogram bisect each other, and conversely, rectangles are
parallelograms with congruent diagonals.
.
Make geometric constructions
.a
. Make formal geometric constructions with a variety of tools and methods (compass and straightedge,
string, reflective devices, paper folding, dynamic geometric software, etc.). Examples include: copying
a segment; copying an angle; bisecting a segment; bisecting an angle; constructing perpendicular lines,
including the perpendicular bisector of a line segment; and constructing a line parallel to a given line
through a point not on the line.
. Construct an equilateral triangle, a square, and a regular hexagon inscribed in a circle.
.b
.c
.b
Similarity, Right Triangles, and Trigonometry
.
Understand similarity in terms of similarity transformations
.a
. Verify experimentally the properties of dilations given by a center and a scale factor:
.b
a. A dilation takes a line not passing through the center of the dilation to a parallel line, and leaves a
line passing through the center unchanged.
.c
b. The dilation of a line segment is longer or shorter in the ratio given by the scale factor.
. Given two figures, use the definition of similarity in terms of similarity transformations to decide if they
are similar; explain using similarity transformations the meaning of similarity for triangles as the equality
of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides.
.e
. Use the properties of similarity transformations to establish the AA criterion for two triangles to be
similar.
.
Prove theorems involving similarity
.a
. Prove theorems about triangles. Theorems include: a line parallel to one side of a triangle divides the
other two proportionally, and conversely; the Pythagorean Theorem proved using triangle similarity.
.b
. Use congruence and similarity criteria for triangles to solve problems and to prove relationships in
geometric figures.
.
Define trigonometric ratios and solve problems involving right triangles
.a
. Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle,
leading to definitions of trigonometric ratios for acute angles.
.d
.b
. Explain and use the relationship between the sine and cosine of complementary angles.
.c
. Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.
.
Apply trigonometry to general triangles
.a
. (+) Derive the formula A = / ab sin(C) for the area of a triangle by drawing an auxiliary line from a
vertex perpendicular to the opposite side.
.b
. (+) Prove the Laws of Sines and Cosines and use them to solve problems.
.c
. (+) Understand and apply the Law of Sines and the Law of Cosines to find unknown measurements in
right and non-right triangles (e.g., surveying problems, resultant forces).
Circles
.
Understand and apply theorems about circles
.a
. Prove that all circles are similar.
Appendix B 47
Common Core Standards
Table B. continued
Reference
standard
numbera
Standard
DOK
rating
. Identify and describe relationships among inscribed angles, radii, and chords. Include the relationship
between central, inscribed, and circumscribed angles; inscribed angles on a diameter are right angles; and
the radius of a circle is perpendicular to the tangent where the radius intersects the circle.
.c
. Construct the inscribed and circumscribed circles of a triangle, and prove properties of angles for a
quadrilateral inscribed in a circle.
.d
. (+) Construct a tangent line from a point outside a given circle to the circle.
.
Find arc lengths and areas of sectors of circles
.a
. Derive using similarity the fact that the length of the arc intercepted by an angle is proportional to the
radius, and define the radian measure of the angle as the constant of proportionality; derive the formula
for the area of a sector.
.b
Expressing Geometric Properties with Equations
.
Translate between the geometric description and the equation for a conic section
.a
. Derive the equation of a circle of given center and radius using the Pythagorean Theorem; complete
the square to find the center and radius of a circle given by an equation.
.b
. Derive the equation of a parabola given a focus and directrix.
.c
. (+) Derive the equations of ellipses and hyperbolas given foci and directrices.
.
Use coordinates to prove simple geometric theorems algebraically
.a
. Use coordinates to prove simple geometric theorems algebraically. For example, prove or disprove that a
figure defined by four given points in the coordinate plane is a rectangle; prove or disprove that the point (,
√) lies on the circle centered at the origin and containing the point (, ).
. Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems
(e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given
point).
.c
. Find the point on a directed line segment between two given points that partitions the segment in a
given ratio.
.d
. Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using
the distance formula.+
.b
Geometric Measurement and Dimension
.
Explain volume formulas and use them to solve problems
.a
. Give an informal argument for the formulas for the circumference of a circle, area of a circle, volume of
a cylinder, pyramid, and cone. Use dissection arguments, Cavalieri’s principle, and informal limit arguments.
.b
. (+) Give an informal argument using Cavalieri’s principle for the formulas for the volume of a sphere
and other solid figures.
.c
. Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.+
.
Visualize relationships between two-dimensional and three-dimensional objects
.a
. Identify the shapes of two-dimensional cross-sections of three-dimensional objects, and identify threedimensional objects generated by rotations of two-dimensional objects.
Modeling with Geometry
.
Apply geometric concepts in modeling situations
.a
. Use geometric shapes, their measures, and their properties to describe objects (e.g., modeling a tree
trunk or a human torso as a cylinder).+
.b
. Apply concepts of density based on area and volume in modeling situations (e.g., persons per square
mile, BTUs per cubic foot).+
.c
. Apply geometric methods to solve design problems (e.g., designing an object or structure to satisfy
physical constraints or minimize cost; working with typographic grid systems based on ratios).+
Appendix B 48
Common Core Standards
Table B. continued
Reference
standard
numbera
DOK
rating
Standard
Statistics and Probability+
Interpreting Categorical and Quantitative Data
.
Summarize, represent, and interpret data on a single count or measurement variable
+
.a
. Represent data with plots on the real number line (dot plots, histograms, and box plots).
.b
. Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and
spread (interquartile range, standard deviation) of two or more different data sets.+
.c
. Interpret differences in shape, center, and spread in the context of the data sets, accounting for
possible effects of extreme data points (outliers).+
.d
. Use the mean and standard deviation of a data set to fit it to a normal distribution and to estimate
population percentages. Recognize that there are data sets for which such a procedure is not appropriate.
Use calculators, spreadsheets, and tables to estimate areas under the normal curve.+
.
Summarize, represent, and interpret data on two categorical and quantitative variables
.a
. Summarize categorical data for two categories in two-way frequency tables. Interpret relative
frequencies in the context of the data (including joint, marginal, and conditional relative frequencies).
Recognize possible associations and trends in the data.+
. Represent data on two quantitative variables on a scatter plot, and describe how the variables are
related.+
.b
.c
.d
.e
a. Fit a function to the data; use functions fitted to data to solve problems in the context of the data.
Use given functions or choose a function suggested by the context. Emphasize linear, quadratic, and
exponential models.
b. Informally assess the fit of a function by plotting and analyzing residuals.
c. Fit a linear function for a scatter plot that suggests a linear association.
.
Interpret linear models
.a
. Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context
of the data.+
.b
. Compute (using technology) and interpret the correlation coefficient of a linear fit.+
.c
+
. Distinguish between correlation and causation.
Making Inferences and Justifying Conclusions
.
Understand and evaluate random processes underlying statistical experiments
.a
. Understand statistics as a process for making inferences about population parameters based on a
random sample from that population.+
.b
. Decide if a specified model is consistent with results from a given data-generating process, e.g., using
simulation. For example, a model says a spinning coin falls heads up with probability .. Would a result of
tails in a row cause you to question the model?+
.
Make inferences and justify conclusions from sample surveys, experiments, and observational studies
.a
. Recognize the purposes of and differences among sample surveys, experiments, and observational
studies; explain how randomization relates to each.+
.b
. Use data from a sample survey to estimate a population mean or proportion; develop a margin of error
through the use of simulation models for random sampling.+
.c
. Use data from a randomized experiment to compare two treatments; use simulations to decide if
differences between parameters are significant.+
.d
. Evaluate reports based on data.+
Appendix B 49
Common Core Standards
Table B. continued
Reference
standard
numbera
Standard
DOK
rating
Conditional Probability and the Rules of Probability
.
Understand independence and conditional probability and use them to interpret data
.a
. Describe events as subsets of a sample space (the set of outcomes) using characteristics (or categories)
of the outcomes, or as unions, intersections, or complements of other events (“or,” “and,” “not”).+
.b
. Understand that two events A and B are independent if the probability of A and B occurring together is
the product of their probabilities, and use this characterization to determine if they are independent.+
.c
. Understand the conditional probability of A given B as P(A and B)/P(B), and interpret independence of
A and B as saying that the conditional probability of A given B is the same as the probability of A, and the
conditional probability of B given A is the same as the probability of B.+
. Construct and interpret two-way frequency tables of data when two categories are associated with
each object being classified. Use the two-way table as a sample space to decide if events are independent
and to approximate conditional probabilities. For example, collect data from a random sample of students
in your school on their favorite subject among mathematics, science, and English. Estimate the probability
that a randomly selected student from your school will favor science given that the student is in tenth grade.
Do the same for other subjects and compare the results.+
. Recognize and explain the concepts of conditional probability and independence in everyday language
and everyday situations. For example, compare the chance of having lung cancer if you are a smoker with
the chance of being a smoker if you have lung cancer.+
.
Use the rules of probability to compute probabilities of compound events in a uniform probability model
.a
. Find the conditional probability of A given B as the fraction of B’s outcomes that also belong to A, and
interpret the answer in terms of the model.+
.b
. Apply the Addition Rule, P(A or B) = P(A) + P(B) – P(A and B), and interpret the answer in terms of the
model.+
.c
. (+) Apply the general Multiplication Rule in a uniform probability model, P(A and B) = P(A)P(B|A) = P(B)
P(A|B), and interpret the answer in terms of the model.+
.d
. (+) Use permutations and combinations to compute probabilities of compound events and solve
problems.+
.d
.e
Using Probability to Make Decisions
.
Calculate expected values and use them to solve problems
.a
. (+) Define a random variable for a quantity of interest by assigning a numerical value to each event in
a sample space; graph the corresponding probability distribution using the same graphical displays as for
data distributions.+
.b
. (+) Calculate the expected value of a random variable; interpret it as the mean of the probability
distribution.+
.c
. (+) Develop a probability distribution for a random variable defined for a sample space in which
theoretical probabilities can be calculated; find the expected value. For example, find the theoretical
probability distribution for the number of correct answers obtained by guessing on all five questions of
a multiple-choice test where each question has four choices, and find the expected grade under various
grading schemes.+
. (+) Develop a probability distribution for a random variable defined for a sample space in which
probabilities are assigned empirically; find the expected value. For example, find a current data distribution
on the number of TV sets per household in the United States, and calculate the expected number of sets per
household. How many TV sets would you expect to find in randomly selected households?+
.
Use probability to evaluate outcomes of decisions
.a
. (+) Weigh the possible outcomes of a decision by assigning probabilities to payoff values and finding
expected values.+
.d
Appendix B 50
Common Core Standards
Table B. continued
Reference
standard
numbera
Standard
DOK
.b
a. Find the expected payoff for a game of chance. For example, find the expected winnings from a
state lottery ticket or a game at a fast-food restaurant.
.c
b. Evaluate and compare strategies on the basis of expected values. For example, compare a highdeductible versus a low-deductible automobile insurance policy using various, but reasonable, chances
of having a minor or a major accident.
.d
. (+) Use probabilities to make fair decisions (e.g., drawing by lots, using a random number generator).+
.e
. (+) Analyze decisions and strategies using probability concepts (e.g., product testing, medical testing,
pulling a hockey goalie at the end of a game).+
a
The reference standard number refers to the numbering system that was used for the purposes of organizing ratings for this study.
(+) is an indication in the Common Core mathematics standards document to show that some mathematics standards represent advanced content and are intended to
prepare students for advanced courses (see Chapter for description).
+
is an indication in the Common Core mathematics standards document to show a modeling standard (see Chapter for description).
Appendix B 51
Appendix C | Results by Individual
Comparison Standards
*OUIFTFDUJPOTUIBUGPMMPX XFQSFTFOUUIFBMJHONFOUmOEJOHT
between each set of individual comparison standards and the
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statistics and raw data.
California Standards
The 11thothHSBEF &OHMJTI MBOHVBHF BSUT TUBOEBSET BOE
UIFthothHSBEFTUBOEBSETJONBUIFNBUJDTPGUIF$BMJGPSOJB
$POUFOU 4UBOEBSET XFSF DPNQBSFE UP UIF $PNNPO $PSF
standards.
Figure C. Percentage of Common
Core Standards that Match California
Standards for ELA and Literacy
Percent
100
Matched
Not matched
78
75
50
22
25
0
Common Core Standards
(113 statements)
English Language Arts and Literacy Findings for
the California Standards
Match
3FDBMM UIBU SBUFST JEFOUJmFE VQ UP UISFF $PNNPO $PSF
TUBOEBSET BT NBUDIJOH FBDI $BMJGPSOJB TUBOEBSE 'JHVSF $
shows the percent of Common Core statements (n
that any of the nine ELA raters matched to one or more of
the California standards (n 5IF mHVSF DPMMBQTFT
mOEJOHT BDSPTT BMM FJHIU &OHMJTI MBOHVBHF BSUT &-" BOE
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$BMJGPSOJBTUBOEBSETIBWFNBUDIFTUPPGUIF$PNNPO
$PSF TUBOEBSET JO UIF 8SJUJOH 4QFBLJOH BOE -JTUFOJOH BOE
-BOHVBHFTUSBOET5IFZIBWFNBUDIFTUPPGUIF$PNNPO
$PSF TUBOEBSET JO UIF 3FBEJOH 4UBOEBSET JO 4DJFODF BOE
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strand. The data presented here is based on at least one
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PGNBUDIFTGPSBOZHJWFOTUBOEBSEWBSJFTXJEFMZ$IBQUFS
provides the mean and standard deviation for the number of
DPNQBSJTPOTUBOEBSETNBUDIJOH$PNNPO$PSFTUBOEBSETJO
FBDI TUSBOE 5IF 5FDIOJDBM 4VQQMFNFOU EJTQMBZT UIF FYBDU
standards from the Common Core and the comparison sets
that were matched.
&WFSZ TUSBOE NFFUT UIF DSJUFSJPO GPS UIF $BUFHPSJDBM
$PODVSSFODFTUBUJTUJD XIJDITQFDJmFTUIBU BDSPTTSBUFST BO
BWFSBHFPGPOFDPSSFTQPOEFODFJOBDPOUFOUBSFBJTTVGmDJFOU
Figure C. Percentage of Common Core Standards that Match California Standards for ELA and Literacy Strand
Percent
Matched
100
100
100
100
Not matched
89
80
76
75
60
50
40
20
25
47
53
24
11
0
0
0
0
Reading for
Literature
(9)
Reading for
Informational
Texts
(10)
Writing
(28)
Speaking and
Listening
(10)
Language
(17)
Reading in
History/Social
Studies (10)
Reading in
Science and
Technical
Subjects (10)
Writing in
History/Social
Studies,
Science, and
Technical
Subjects (19)
Common Core strand (number of statements)
Appendix C •
Results by Individual Comparison Standards
Table C. Summary for Alignment Between the California Standards and
Common Core Standards for English Language Arts and Literacy
Common Core ELA and literacy strand
Categorical
Concurrence
Coverage
Reading for Literature
Reading for Informational Texts
Writing
Speaking and Listening
Language
Reading in History/Social Studies
Reading in Science and Technical Subjects
Writing in History/Social Studies, Science, and Technical
Subjects
Meets the criterion for Categorical Concurrence (averaged across raters, a single correspondence exists between the two sets
of standards);
Does not meet the criterion for Categorical Concurrence;
means that a majority of topics in the Common Core category have at least one matched comparison standard;
means that in more than one topic in the Common Core category have at least one matched comparison standard;
means that in one or less than one topic in the Common Core category have at least one matched comparison standard.
Breadth of Coverage
#SFBEUI PG $PWFSBHF JT TUSPOH GPS BMM UIF &-" BOE Figure C. California Standards Depth of Knowledge Levels Under,
literacy strands (the majority of Common Core topics At, and Above the Common Core for ELA and Literacy
IBWFNBUDIJOHDPNQBSJTPOTUBOEBSETXJUIJOUIFN
This means that the California standards that match
to Common Core standards are distributed across
content topics within each Common Core strand.
5BCMF $ QSFTFOUT UIF BMJHONFOU TVNNBSZ GPS UIF
8FCC BOE $PPL BMJHONFOU TUBUJTUJDT $PPL
$PPL8JMNFT 8FCC B
Depth of Knowledge
Across all matched standards for ELA and literacy,
BOBWFSBHFPG SD PG$BMJGPSOJBTUBOEBSET
BSF BU UIF TBNF %FQUI PG ,OPXMFEHF %0, MFWFM
BT UIF $PNNPO $PSF TUBOEBSET XJUI BO BWFSBHF
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alternative criterion had been selected.
Note5PUBMQFSDFOUNBZFRVBMTMJHIUMZBCPWFPSCFMPXEVFUPSPVOEJOH
Appendix C 53
Results by Individual Comparison Standards
Mathematics Findings for the California
Standards
Match
'JHVSF$TIPXTUIFQFSDFOUPG$PNNPO$PSFTUBUFNFOUT n =
UIBUBOZPGUIFTFWFONBUIFNBUJDTSBUFSTNBUDIFEUPPOFPS
more of the California standards (n 5IFmHVSFDPMMBQTFT
mOEJOHT BDSPTT UIF mWF DPODFQUVBM DBUFHPSJFT *O 'JHVSF $
XFEJWJEFmOEJOHTCZDPODFQUVBMDBUFHPSZ"TUIFCBSHSBQIT
JOEJDBUF BIJHIQFSDFOUPGUIF$PNNPO$PSFTUBOEBSETNBUDI
$BMJGPSOJBTUBOEBSETJOFBDIDPODFQUVBMDBUFHPSZ SBOHJOHGSPN
o "HBJO UIFEBUBQSFTFOUFEIFSFJTCBTFEPOBUMFBTU
POFSBUFSNBUDIJOHBUMFBTUPOFTUBOEBSE IPXFWFSUIFOVNCFS
PG NBUDIFT GPS BOZ HJWFO TUBOEBSE WBSJFT XJEFMZ $IBQUFS
provides the mean and standard deviation for the number of
DPNQBSJTPO TUBOEBSET NBUDIJOH $PNNPO $PSF TUBOEBSET JO
FBDIDPODFQUVBMDBUFHPSZ5IF5FDIOJDBM4VQQMFNFOUEJTQMBZT
UIFFYBDUTUBOEBSETGSPNUIF$PNNPO$PSFBOEUIFDPNQBSJTPO
TFUTUIBUXFSFNBUDIFE&WFSZDPODFQUVBMDBUFHPSZNFFUTUIF
DSJUFSJPOGPSUIF$BUFHPSJDBM$PODVSSFODFTUBUJTUJD
Figure C. Percentage of Common
Core Standards that Match California
Standards, for Mathematics
Percent
100
87
Matched
Not matched
75
50
13
25
0
Common Core Standards
(192 statements)
Figure C. Percentage of Common Core Standards that Match California Standards,
by Mathematics Conceptual Category
Matched
Percent
100
91
88
Not matched
86
89
82
75
50
25
9
12
18
14
11
0
Number and
Quantity
(32)
Algebra
(34)
Functions
(45)
Geometry
(45)
Statistics and
Probability
(36)
Common Core conceptual category (number of statements)
Appendix C 54
Results by Individual Comparison Standards
Table C. Summary for Alignment Between the California Standards
and Common Core Standards for Mathematics
Common Core mathematics conceptual
category
Categorical
Concurrence
Coverage
Number and Quantity
Algebra
Functions
Geometry
Statistics and Probability
Meets the criterion for Categorical Concurrence (averaged across raters, a single correspondence exists between
the two sets of standards);
Does not meet the criterion for Categorical Concurrence;
means that a majority of topics in the Common Core category have at least one matched comparison standard;
means that in more than one topic in the Common Core category have at least one matched comparison
standard;
means that Common Core standards in one or less than one topic in the strand have at least one matched
comparison standard.
Breadth of Coverage
#SFBEUI PG $PWFSBHF JT TUSPOH GPS BMM UIF NBUIFNBUJDT
DPODFQUVBMDBUFHPSJFT UIFNBKPSJUZPG$PNNPO$PSFDMVTUFST
IBWF NBUDIJOH DPNQBSJTPO TUBOEBSET XJUIJO UIFN 5BCMF $
QSFTFOUTUIFTVNNBSJ[FEBMJHONFOUSFTVMUTGPSNBUIFNBUJDT
Depth of Knowledge
For California mathematics standards that match to Common
$PSFTUBOEBSET BOBWFSBHFPG SD GBMMBUUIFTBNF
MFWFMBTUIF$PNNPO$PSFTUBOEBSETXJUIBOBWFSBHFPG
(SD MPXFSJODPHOJUJWFEFNBOEBOE SD IJHIFS
JODPHOJUJWFEFNBOE'PVSPGUIFmWF$PNNPO$PSFDPODFQUVBM
DBUFHPSJFT TIPXO JO 'JHVSF $ NFFU UIF %0, $POTJTUFODZ
DSJUFSJPO XJUI(FPNFUSZCFJOHUIFPOFDBUFHPSZUIBUEPFTOPU
NFFU UIF DSJUFSJPO "T 'JHVSF $ TIPXT TPNF DBUFHPSJFT GBMM
DMPTF UP BOE SFTVMUT XPVME CF EJGGFSFOU JG BO BMUFSOBUJWF
criterion had been selected.
'JHVre%$BMJGPSOJB4UBOEBSET%FQUIPG,OPXMFEHF
Figure C. Percentage of California Standards Under, At, or
-FWFMT6OEFS, At, and Above, the Common Core
Above the Depth of Knowledge Level of the Common Core
Standards, for Mathematics
0
/VNCFS
and
2VBOUJUZ
"MHFCSB
Functions
25
50
75
100
AWFSBHF
Percent
"CPWF
"U
6OEFS
Geometry
4UBUJTUJDT
and
Probability
Note5PUBMQFSDFOUNBZFRVBMTMJHIUMZBCPWFPSCFMPXEVFUPSPVOEJOH
Appendix C 55
Results by Individual Comparison Standards
Massachusetts Standards
The study compared the 11thothHSBEF TUBOEBSET GSPN UIF
.BTTBDIVTFUUT $VSSJDVMVN 'SBNFXPSLT UP UIF $PNNPO $PSF
standards.
English Language Arts and Literacy Findings for
the Massachusetts Standards
Match
3FDBMM UIBU SBUFST JEFOUJmFE VQ UP UISFF $PNNPO $PSF
standards that correspond with each Massachusetts standard.
'JHVSF$TIPXTUIFQFSDFOUPG$PNNPO$PSFTUBUFNFOUT n
UIBUBOZPGUIFOJOF&-"SBUFSTNBUDIFEUPPOFPSNPSF
of the Massachusetts standards (n 5IFmHVSFDPMMBQTFT
mOEJOHT BDSPTT BMM FJHIU &OHMJTI MBOHVBHF BSUT &-" BOE
MJUFSBDZTUSBOET*O'JHVSF$ XFEJWJEFmOEJOHTCZTUSBOE"T
UIF CBS HSBQIT JOEJDBUF UIF .BTTBDIVTFUUT TUBOEBSET IBWF
NBUDIFTGPSPGUIF$PNNPO$PSFTUBOEBSETJO3FBEJOH
GPS-JUFSBUVSF BOE4QFBLJOHBOE-JTUFOJOH5IF.BTTBDIVTFUUT
TUBOEBSET IBWF NBUDIFT UP o PG UIF $PNNPO $PSF
TUBOEBSET JO UIF 3FBEJOH GPS *OGPSNBUJPOBM 5FYU 8SJUJOH BOE
-BOHVBHF TUSBOET 'PS UIF 3FBEJOH 4UBOEBSET JO )JTUPSZ
4PDJBM 4UVEJFT TUSBOE 3FBEJOH 4UBOEBSET JO 4DJFODF BOE
5FDIOJDBM 4VCKFDUT TUSBOE BOE 8SJUJOH 4UBOEBSET JO )JTUPSZ
4PDJBM 4UVEJFT 4DJFODF BOE 5FDIOJDBM 4VCKFDUT TUSBOE UIF
.BTTBDIVTFUUT TUBOEBSET IBWF NBUDIFT UP o PG UIF
Common Core standards.14JYPGFJHIUTUSBOETNFFUUIFDSJUFSJPO
GPSUIF$BUFHPSJDBM$PODVSSFODFTUBUJTUJD XIJDITQFDJmFTUIBU
BDSPTTSBUFST BOBWFSBHFPGPOFDPSSFTQPOEFODFJOBDPOUFOU
BSFB JT TVGmDJFOU 5IF UXP 3FBEJOH GPS -JUFSBDZ JO )JTUPSZ
4PDJBM4UVEJFTBOEJO4DJFODFBOE5FDIOJDBM4VCKFDUT EPOPU
meet the criterion.
5IFEBUBQSFTFOUFEIFSFJTCBTFEPOBUMFBTUPOFSBUFSNBUDIJOHBUMFBTU
POFTUBOEBSE IPXFWFSUIFOVNCFSPGNBUDIFTGPSBOZHJWFOTUBOEBSEWBSJFT
widely. Chapter 3 provides the mean and standard deviation for the number of
DPNQBSJTPOTUBOEBSETNBUDIJOH$PNNPO$PSFTUBOEBSETJOFBDITUSBOE5IF
5FDIOJDBM4VQQMFNFOUEJTQMBZTUIFFYBDUTUBOEBSETGSPNUIF$PNNPO$PSFBOE
the comparison sets that were matched.
1
Figure C. Percentage of Common
Core Standards that Match
Massachusetts Standards, for ELA
and Literacy
Percent
100
Matched
Not matched
68
75
50
32
25
0
Common Core Standards
(113 statements)
Figure C. Percentage of Common Core Standards that Match Massachusetts Standards, by ELA and Literacy
Strand
Percent
Matched
100
100
100
Not matched
94
90
80
71
75
63
60
50
40
37
29
20
25
10
0
0
6
0
Reading for
Literature
(9)
Reading for
Informational
Texts
(10)
Writing
(28)
Speaking and
Listening
(10)
Language
(17)
Reading in
History/Social
Studies (10)
Reading in
Science and
Technical
Subjects (10)
Writing in
History/Social
Studies,
Science, and
Technical
Subjects (19)
Common Core strand (number of statements)
Appendix C 56
Results by Individual Comparison Standards
Table C. Summary for Alignment Between the Massachusetts Standards
and the Common Core Standards for English Language Arts and Literacy
Categorical
Concurrence
Common Core ELA and literacy strand
Coverage
Reading for Literature
Reading for Informational Texts
Writing
Speaking and Listening
Language
Reading in History/Social Studies
Reading in Science and Technical Subjects
Writing in History/Social Studies, Science, and Technical
Subjects
Meets the criterion for Categorical Concurrence (averaged across raters, a single correspondence exists between the two
sets of standards);
Does not meet the criterion for Categorical Concurrence;
means that a majority of topics in the Common Core category have at least one matched comparison standard;
means that in more than one topic in the Common Core category have at least one matched comparison standard;
means that in one or less than one topic in the Common Core category have at least one matched comparison standard.
Breadth of Coverage
Figure C. Percentage of Massachusetts Standards Under, At, or Above
#SFBEUI PG $PWFSBHF JT TUSPOH GPS TFWFO TUSBOET GPS the Depth of Knowledge Level of the Common Core Standards, for ELA
these, the majority of Common Core topics have and Literacy
NBUDIJOH DPNQBSJTPO TUBOEBSET XJUIJO UIFN 5IF
3FBEJOH 4UBOEBSET JO )JTUPSZ4PDJBM 4UVEJFT TUSBOE
JT NPEFSBUF JO UFSNT PG DPWFSBHF 5IJT NFBOT UIBU
Common Core standards match to Massachusetts
standards in more than one topic but not a majority of
UPQJDTXJUIJOUIFTUSBOE"TVNNBSZUBCMF 5BCMF$
QSFTFOUT UIF &-" BOE MJUFSBDZ BMJHONFOU SFTVMUT GPS
UIF8FCCBOE$PPLBMJHONFOUTUBUJTUJDT $PPL
$PPL8JMNFT 8FCC B
Depth of Knowledge
Across all matched standards for ELA and literacy,
BO BWFSBHF PG SD PG .BTTBDIVTFUUT
TUBOEBSETBSFBUUIFTBNF%FQUIPG,OPXMFEHF %0,
MFWFM BT UIF $PNNPO $PSF TUBOEBSET "DDPSEJOH UP
TUVEZSBUJOHT BOBWFSBHFPG SD BSFMFTT
DPHOJUJWFMZEFNBOEJOHBOEBOBWFSBHFPG SD =
BSFNPSFDPHOJUJWFMZEFNBOEJOH
NA
NA
Note5PUBMQFSDFOUNBZFRVBMTMJHIUMZBCPWFPSCFMPXEVFUPSPVOEJOH
0GUIFTJYTUSBOETNFFUJOHUIF$BUFHPSJDBM$PODVSSFODF
DSJUFSJPO mWF NFFU UIF %0, $POTJTUFODZ DSJUFSJPO
XIJDI JT CBTFE PO BU MFBTU PG UIF NBUDIJOH
.BTTBDIVTFUUT TUBOEBSET CFJOH BU PS BCPWF UIF %0, PG UIF
DPSSFTQPOEJOH$PNNPO$PSFTUBOEBSE TFF'JHVSF$ 0OF
TUSBOEEJEOPUNFFUUIFDSJUFSJPO8SJUJOH4UBOEBSETGPS-JUFSBDZ
JO)JTUPSZ4PDJBM4UVEJFT 4DJFODF BOE5FDIOJDBM4VCKFDUT"T
'JHVSF$TIPXT TPNFTUSBOETGBMMDMPTFUPBOESFTVMUT
would be different if an alternative criterion had been selected.
Appendix C 57
Results by Individual Comparison Standards
Mathematics Findings for the Massachusetts
Standards
Match
'JHVSF$TIPXTUIFQFSDFOUPG$PNNPO$PSFTUBUFNFOUT n
UIBUIBWFNBUDIFTJOUIF.BTTBDIVTFUUTTUBOEBSET n =
5IFmHVSFDPMMBQTFTmOEJOHTBDSPTTUIFmWFDPODFQUVBM
DBUFHPSJFT *O 'JHVSF $ XF EJWJEF mOEJOHT CZ DPODFQUVBM
DBUFHPSZ "T UIF CBS HSBQIT JOEJDBUF B IJHI QFSDFOU PG UIF
Common Core standards cover the Massachusetts standards
JOFBDIDPODFQUVBMDBUFHPSZ SBOHJOHGSPNo 2 Every
DPODFQUVBM DBUFHPSZ NFFUT UIF DSJUFSJPO GPS UIF $BUFHPSJDBM
Concurrence statistic.
Figure C. Percentage of Common
Core Standards that Match
Massachusetts Standards, for
Mathematics
Percent
88
100
Matched
Not matched
75
50
5IFEBUBQSFTFOUFEIFSFJTCBTFEPOBUMFBTUPOFSBUFSNBUDIJOHBUMFBTU
POFTUBOEBSE IPXFWFSUIFOVNCFSPGNBUDIFTGPSBOZHJWFOTUBOEBSEWBSJFT
XJEFMZ$IBQUFSQSPWJEFTUIFNFBOBOETUBOEBSEEFWJBUJPOGPSUIFOVNCFSPG
DPNQBSJTPOTUBOEBSETNBUDIJOH$PNNPO$PSFTUBOEBSETJOFBDIDPODFQUVBM
DBUFHPSZ5IF5FDIOJDBM4VQQMFNFOUEJTQMBZTUIFFYBDUTUBOEBSETGSPNUIF
Common Core and the comparison sets that were matched.
2
25
12
0
Common Core Standards
(192 statements)
Figure C. Percentage of Common Core Standards that Match Massachusetts
Standards, by Mathematics Conceptual Category
Matched
Percent
Not matched
100
91
100
89
89
72
75
50
28
25
0
9
11
11
0
Number and
Quantity
(32)
Algebra
(34)
Functions
(45)
Geometry
(45)
Statistics and
Probability
(36)
Common Core conceptual category (number of statements)
Appendix C 58
Results by Individual Comparison Standards
Table C. Summary for Alignment Between the Massachusetts
Standards and Common Core Standards in Mathematics
Common Core mathematics conceptual
category
Categorical
Concurrence
Coverage
Number and Quantity
Algebra
Functions
Geometry
Statistics and Probability
Meets the criterion for Categorical Concurrence (averaged across raters, a single correspondence exists between
the two sets of standards);
Does not meet the criterion for Categorical Concurrence;
means that a majority of topics in the Common Core category have at least one matched comparison standard;
means that in more than one topic in the Common Core category have at least one matched comparison
standard;
means that in one or less than one topic in the Common Core category have at least one matched comparison
standard.
Breadth of Coverage
#SFBEUI PG $PWFSBHF JT TUSPOH GPS BMM UIF NBUIFNBUJDT
DPODFQUVBMDBUFHPSJFT UIFNBKPSJUZPG$PNNPO$PSFDMVTUFST
IBWF NBUDIJOH DPNQBSJTPO TUBOEBSET XJUIJO UIFN 5BCMF $
QSFTFOUTUIFTVNNBSJ[FEBMJHONFOUSFTVMUTGPSNBUIFNBUJDT
'JHVre%.BTTBDIVTFUUT4UBOEBSET%FQUIPG
Figure C. Percentage ofAt,
Massachusetts
Under, At,
,OPXMFEHF-FWFMT6OEFS,
and Above,Standards
the
or Above the Depth of Knowledge Level of the Common Core
For the Massachusetts standards that match to Common
Core for Mathematics
Standards, for Mathematics
Depth of Knowledge
$PNNPO $PSF TUBOEBSET BO BWFSBHF PG SD =
GBMM BU UIF TBNF MFWFM PG DPHOJUJWF EFNBOE BT UIF
$PNNPO $PSF TUBOEBSET "O BWFSBHF PG SD
PG UIF .BTTBDIVTFUUT TUBOEBSET BSF MPXFS JO
DPHOJUJWF EFNBOE UIBO UIF $PNNPO $PSF TUBOEBSET
BOEBOBWFSBHFPG SD BSFSBUFEBCPWFUIF
$PNNPO $PSF TUBOEBSET 'PVS PG UIF mWF $PNNPO
$PSFDPODFQUVBMDBUFHPSJFTNFFUUIF%0,$POTJTUFODZ
DSJUFSJPO TFF 'JHVSF $ "DDPSEJOH UP SBUJOHT UIF
(FPNFUSZDBUFHPSZEJEOPUNFFUUIFDSJUFSJPO"T'JHVSF
$TIPXT TPNFDBUFHPSJFTGBMMDMPTFUPPSBUBOE
results would be different if an alternative criterion had
been selected.
0
/VNCFS
and
2VBOUJUZ
"MHFCSB
Functions
a
25
50
75
100
AWFSBHF
Percent
"CPWF
"U
6OEFS
Geometry
4UBUJTUJDT
and
Probability
Note5PUBMQFSDFOUNBZFRVBMTMJHIUMZBCPWFPSCFMPXEVFUPSPVOEJOH
a
5IF'VODUJPOTDPODFQUVBMDBUFHPSZNFFUTUIF%0,DSJUFSJPO CVUEVFUPSPVOEJOH UIF
WBMVFBQQFBSTBUFYBDUMZ
Appendix C 59
Results by Individual Comparison Standards
Texas College and Career Readiness Standards
5IFTUVEZDPNQBSFEUIF&OHMJTIMBOHVBHFBSUT NBUIFNBUJDT
BOE DSPTTEJTDJQMJOBSZ TUBOEBSET GSPN UIF 5FYBT $PMMFHF BOE
$BSFFS 3FBEJOFTT 4UBOEBSET 5$$34 UP UIF $PNNPO $PSF
standards.
English Language Arts Findings for the TCCRS
Standards
Match
3BUFSTJEFOUJmFEVQUPUISFF$PNNPO$PSFTUBOEBSETXJUIFBDI
5$$34 TUBOEBSE 'JHVSF $ TIPXT UIF QFSDFOU PG $PNNPO
Core statements (n UIBU BOZ PG UIF OJOF &-" SBUFST
NBUDIFEUPPOFPSNPSFPGUIF5$$34TUBOEBSET n 5IF
mHVSFDPMMBQTFTmOEJOHTBDSPTTBMMFJHIU&OHMJTIMBOHVBHFBSUT
&-" BOE MJUFSBDZ TUSBOET *O 'JHVSF $ XF EJWJEF mOEJOHT
CZ TUSBOE "T UIF CBS HSBQIT JOEJDBUF JO mWF TUSBOET UIF
5$$34TUBOEBSETIBWFNBUDIFTUPPGUIF$PNNPO$PSF
TUBOEBSET 5XP BEEJUJPOBM TUSBOET IBWF NBUDIFT UP o
PG UIF $PNNPO $PSF TUBOEBSET -BOHVBHF BOE 3FBEJOH
4UBOEBSET JO )JTUPSZ4PDJBM 4UVEJFT 5IF 5$$34 TUBOEBSET
IBWF NBUDIFT UP PG UIF $PNNPO $PSF TUBOEBSET JO UIF
8SJUJOH 4UBOEBSET JO )JTUPSZ4PDJBM 4UVEJFT 4DJFODF BOE
5FDIOJDBM 4VCKFDUT TUSBOE3 Every strand meets the criterion
GPSUIF$BUFHPSJDBM$PODVSSFODFTUBUJTUJD XIJDITQFDJmFTUIBU
BDSPTTSBUFST BOBWFSBHFPGPOFDPSSFTQPOEFODFJOBDPOUFOU
BSFBJTTVGmDJFOU
5IFEBUBQSFTFOUFEIFSFJTCBTFEPOBUMFBTUPOFSBUFSNBUDIJOHBUMFBTU
POFTUBOEBSE IPXFWFSUIFOVNCFSPGNBUDIFTGPSBOZHJWFOTUBOEBSEWBSJFT
widely. Chapter 3 provides the mean and standard deviation for the number of
DPNQBSJTPOTUBOEBSETNBUDIJOH$PNNPO$PSFTUBOEBSETJOFBDITUSBOE5IF
5FDIOJDBM4VQQMFNFOUEJTQMBZTUIFFYBDUTUBOEBSETGSPNUIF$PNNPO$PSFBOE
the comparison sets that were matched.
3
Figure C. Percentage of Common
Core Standards that Match Texas
College and Career Readiness
Standards, for ELA and Literacy
Percent
92
100
Matched
Not matched
75
50
25
8
0
Common Core Standards
(113 statements)
Figure C. Percentage of Common Core Standards that Match Texas College and Career Readiness Standards, by ELA and
Literacy Strand
Percent
Matched
100
100
100
100
100
Not matched
100
90
88
68
75
50
32
25
12
0
0
0
10
0
0
0
Reading for
Literature
(9)
Reading for
Informational
Texts
(10)
Writing
(28)
Speaking and
Listening
(10)
Language
(17)
Reading in
History/Social
Studies (10)
Reading in
Science and
Technical
Subjects (10)
Writing in
History/Social
Studies,
Science, and
Technical
Subjects (19)
Common Core strand (number of statements)
Appendix C 60
Results by Individual Comparison Standards
Table C. Summary of Alignment Between the Texas College and Career
Readiness Standards and Common Core for English Language Arts and
Literacy
Common Core ELA and literacy strand
Categorical
Concurrence
Coverage
Reading for Literature
Reading for Informational Texts
Writing
Speaking and Listening
Language
Reading in History/Social Studies
Reading in Science and Technical Subjects
Writing in History/Social Studies, Science, and Technical
Subjects
Meets the criterion for Categorical Concurrence (averaged across raters, a single correspondence exists between the two sets of
standards);
Does not meet the criterion for Categorical Concurrence;
means that in a majority of topics in the Common Core category have at least one matched comparison standard;
means that in more than one topic in the Common Core category have at least one matched comparison standard;
means that in one or less than one topic in the Common Core category have at least one matched comparison standard.
Breadth of Coverage
#SFBEUIPG$PWFSBHFJTSBUFEBTTUSPOHGPSBMM&-"BOE
literacy strands (the majority of Common Core topics
IBWFNBUDIJOHDPNQBSJTPOTUBOEBSETXJUIJOUIFN
This means that the Massachusetts standards that
match to Common Core standards are distributed Figure C. Percent of Texas College and Career Readiness Standards
across content topics within each Common Core Under, At, or Above the Depth of Knowledge Level of the Common Core
Standards, for ELA and Literacy
TUSBOE 5BCMF $ QSFTFOUT UIF BMJHONFOU TVNNBSZ
GPSUIF8FCCBOE$PPLTUBUJTUJDT $PPL $PPL
8JMNFT 8FCC B
Depth of Knowledge
Across all matched standards for ELA and literacy,
BO BWFSBHF PG SD BSF BU UIF TBNF
MFWFM BT UIF $PNNPO $PSF TUBOEBSET "DDPSEJOH
UP SBUJOHT BO BWFSBHF PG SD PG UIF
TUBOEBSETBSFMPXFS BOE SD BSFIJHIFS
JO DPHOJUJWF EFNBOE 5IF %FQUI PG ,OPXMFEHF
%0, $POTJTUFODZDSJUFSJPOJTNFUGPSUXPPGFJHIU
TUSBOET UIF -BOHVBHF 4UBOEBSET BOE UIF 8SJUJOH
4UBOEBSET JO )JTUPSZ4PDJBM 4UVEJFT 4DJFODF BOE
5FDIOJDBM4VCKFDUT'PSUIFPUIFSTJY$PNNPO$PSF
TUSBOET UIFDSJUFSJPOJTOPUNFU'JHVSF$EJTQMBZT
UIF SFTVMUT HSBQIJDBMMZ "T UIF mHVSF TIPXT TPNF
TUSBOET GBMM DMPTF UP BOE SFTVMUT XPVME CF
different if an alternative criterion had been selected.
Note5PUBMQFSDFOUNBZFRVBMTMJHIUMZBCPWFPSCFMPXEVFUPSPVOEJOH
Appendix C 61
Results by Individual Comparison Standards
Mathematics Findings for the TCCRS Standards
Match
Figure C. Percentage of Common
Core Standards that Match Texas
College and Career Readiness
Standards, for Mathematics
'JHVSF $ TIPXT UIF QFSDFOU PG $PNNPO $PSF TUBUFNFOUT
(n UIBU IBWF NBUDIFT JO UIF 5$$34 NBUIFNBUJDT
standards (n 5IFmHVSFDPMMBQTFTmOEJOHTBDSPTTUIF
mWFDPODFQUVBMDBUFHPSJFT*O'JHVSF$ XFEJWJEFmOEJOHT
CZ DPODFQUVBM DBUFHPSZ "T UIF CBS HSBQIT JOEJDBUF UIF
5$$34 TUBOEBSET IBWF NBUDIFT UP B IJHI QFSDFOU SBOHJOH
GSPN o PG UIF $PNNPO $PSF TUBOEBSET JO GPVS PG mWF
DPODFQUVBMDBUFHPSJFT'PS/VNCFSBOE2VBOUJUZ UIF5$$34
TUBOEBSET IBWF NBUDIFT UP POMZ PG UIF $PNNPO $PSF
standards.&WFSZDPODFQUVBMDBUFHPSZNFFUTUIFDSJUFSJPOGPS
UIF$BUFHPSJDBM$PODVSSFODFTUBUJTUJD
Percent
100
Matched
Not matched
75
75
50
25
25
0
Common Core Standards
(192 statements)
5IFEBUBQSFTFOUFEIFSFJTCBTFEPOBUMFBTUPOFSBUFSNBUDIJOHBUMFBTU
POFTUBOEBSE IPXFWFSUIFOVNCFSPGNBUDIFTGPSBOZHJWFOTUBOEBSEWBSJFT
XJEFMZ$IBQUFSQSPWJEFTUIFNFBOBOETUBOEBSEEFWJBUJPOGPSUIFOVNCFSPG
DPNQBSJTPOTUBOEBSETNBUDIJOH$PNNPO$PSFTUBOEBSETJOFBDIDPODFQUVBM
DBUFHPSZ5IF5FDIOJDBM4VQQMFNFOUEJTQMBZTUIFFYBDUTUBOEBSETGSPNUIF
Common Core and the comparison sets that were matched.
Figure C. Percentage of Common Core Standards that Match Texas College and
Career Readiness Standards, by Mathematics Conceptual Category
Matched
Not matched
94
Not matched
94
Percent
100
66
75
50
84
78
76
34
24
25
22
16
6
0
Number and
Quantity
(32)
Algebra
(34)
Functions
(45)
Geometry
(45)
Statistics and
Probability
(36)
Common Core conceptual category (number of statements)
Appendix C 62
Results by Individual Comparison Standards
Table C. Summary for Alignment Between the Texas College
and Career Readiness Standards and Common Core Standards in
Mathematics
Common Core mathematics conceptual
category
Categorical
Concurrence
Coverage
Number and Quantity
Algebra
Functions
Geometry
Statistics and Probability
Meets the criterion for Categorical Concurrence (averaged across raters, a single correspondence exists between
the two sets of standards);
Does not meet the criterion for Categorical Concurrence;
means that in a majority of topics in the Common Core category have at least one matched comparison
standard;
means that in more than one topic in the Common Core category have at least one matched
comparison standard;
means that in one or less than one topic in the Common Core category have at least one
matched comparison standard.
Breadth of Coverage
#SFBEUI PG $PWFSBHF JT TUSPOH GPS BMM NBUIFNBUJDT
DPODFQUVBM DBUFHPSJFT JOEJDBUJOH UIBU UIF NBUDIJOH
standards are distributed across a majority of Common
Core mathematics clusters within each conceptual
DBUFHPSZ5BCMF$TVNNBSJ[FTUIFmOEJOHT
'JHVre%5FYBT$PMMFHFBOE$BSFFS3FBEJOFTT
Figure C. Percent of Texas College and Career Readiness Standards
At,
Across all matched standards in mathematics, an 4UBOEBSET%FQUIPG,OPXMFEHF-FWFMT6OEFS,
Under, At, or Above the Depth of Knowledge Level of the Common
and
Above,
the
Common
Core
For
Mathematics
BWFSBHF PG SD GBMM BU UIF TBNF MFWFM BT Core Standards, for Mathematics
Depth of Knowledge
UIF$PNNPO$PSFTUBOEBSET XJUIBOBWFSBHFPG
(SD PGUIF5FYBT$$34TUBOEBSETSBUFEMPXFSJO
DPHOJUJWF EFNBOE BOE BO BWFSBHF PG SD
SBUFE IJHIFS "MM mWF DPODFQUVBM DBUFHPSJFT NFFU UIF
%0,$POTJTUFODZDSJUFSJPO
0
25
50
75
100
/VNCFS
and
2VBOUJUZ
"MHFCSB
Functions
AWFSBHF
Percent
"CPWF
"U
6OEFS
Geometry
4UBUJTUJDT
and
Probability
Note5PUBMQFSDFOUNBZFRVBMTMJHIUMZBCPWFPSCFMPXEVFUPSPVOEJOH
Appendix C 63
Results by Individual Comparison Standards
Knowledge and Skills for University Success
&OHMJTI TUBOEBSET BOE NBUIFNBUJDT TUBOEBSET TFDUJPOT GSPN
UIF ,OPXMFEHF BOE 4LJMMT GPS 6OJWFSTJUZ 4VDDFTT ,464
4UBOEBSETXFSFDPNQBSFEUPUIF$PNNPO$PSFTUBOEBSET
English Language Arts and Literacy Findings for
the KSUS Standards
Match
'JHVSF$TIPXTUIFQFSDFOUPG$PNNPO$PSFTUBUFNFOUT n
UIBUBOZPGUIFOJOF&-"SBUFSTNBUDIFEUPPOFPSNPSF
PGUIF,464TUBOEBSET n 5IFmHVSFDPMMBQTFTmOEJOHT
BDSPTT BMM FJHIU &OHMJTI MBOHVBHF BSUT &-" BOE MJUFSBDZ
TUSBOET*O'JHVSF$ XFEJWJEFmOEJOHTCZTUSBOE"TUIFCBS
HSBQITJOEJDBUF UIF,464TUBOEBSETIBWFNBUDIFTGPS
PGUIF$PNNPO$PSFTUBOEBSETGPSUIF3FBEJOHGPS-JUFSBUVSF
TUSBOE5IF,464TUBOEBSETIBWFNBUDIFTUPoPGUIF
$PNNPO$PSFTUBOEBSETGPSTJYTUSBOET5IFZIBWFNBUDIFTUP
PGUIF$PNNPO$PSFTUBOEBSETJOUIF3FBEJOH4UBOEBSET
JO4DJFODFBOE5FDIOJDBM4VCKFDUTTUSBOE5 Every strand meets
UIF DSJUFSJPO GPS UIF $BUFHPSJDBM $PODVSSFODF TUBUJTUJD XIJDI
TQFDJmFTUIBU BDSPTTSBUFST BOBWFSBHFPGPOFDPSSFTQPOEFODF
JOBDPOUFOUBSFBJTTVGmDJFOU
5IFEBUBQSFTFOUFEIFSFJTCBTFEPOBUMFBTUPOFSBUFSNBUDIJOHBUMFBTU
POFTUBOEBSE IPXFWFSUIFOVNCFSPGNBUDIFTGPSBOZHJWFOTUBOEBSEWBSJFT
widely. Chapter 3 provides the mean and standard deviation for the number of
DPNQBSJTPOTUBOEBSETNBUDIJOH$PNNPO$PSFTUBOEBSETJOFBDITUSBOE5IF
5FDIOJDBM4VQQMFNFOUEJTQMBZTUIFFYBDUTUBOEBSETGSPNUIF$PNNPO$PSFBOE
the comparison sets that were matched.
5
Figure C. Percentage of Common
Core Standards that Match
Knowledge and Skills for University
Success Standards, for ELA and
Literacy
Percent
88
100
Matched
Not matched
75
50
25
12
0
Common Core Standards
(113 statements)
Figure C. Percentage of Common Core Standards that Match Knowledge and Skills for University Success Standards, by ELA and
Literacy Strand
Percent
Matched
100
100
96
90
94
90
Not matched
90
79
75
60
50
40
21
25
10
0
4
10
10
6
0
Reading for
Literature
(9)
Reading for
Informational
Texts
(10)
Writing
(28)
Speaking and
Listening
(10)
Language
(17)
Reading in
History/Social
Studies (10)
Reading in
Science and
Technical
Subjects (10)
Writing in
History/Social
Studies,
Science, and
Technical
Subjects (19)
Common Core strand (number of statements)
Appendix C 64
Results by Individual Comparison Standards
Table C. Summary for Alignment Between the Knowledge and Skills for
University Success Standards and the Common Core Standards in English
Language Arts and Literacy
Categorical
Concurrence
Common Core ELA and literacy strand
Coverage
Reading for Literature
Reading for Informational Texts
Writing
Speaking and Listening
Language
Reading in History/Social Studies
Reading in Science and Technical Subjects
Writing in History/Social Studies, Science, and Technical
Subjects
Meets the criterion for Categorical Concurrence (averaged across raters, a single correspondence exists between the two sets of
standards);
Does not meet the criterion for Categorical Concurrence;
means that in a majority of topics in the Common Core category have at least one matched comparison standard;
means that in more than one topic in the Common Core category have at least one matched comparison standard;
means that in one or less than one topic in the Common Core category have at least one matched comparison standard.
Breadth of Coverage
#SFBEUI PG $PWFSBHF JT SBUFE BT TUSPOH GPS BMM UIF
ELA and literacy strands (the majority of Common
$PSF UPQJDT IBWF NBUDIJOH DPNQBSJTPO TUBOEBSET
XJUIJO UIFN 5IJT NFBOT UIBU UIF ,464 TUBOEBSET
that match Common Core standards are distributed
across content topics within each Common Core Figure C. Percent of Knowledge and Skills for University Success
Standards Under, At, or Above the Depth of Knowledge Level of the
TUSBOE5BCMF$QSFTFOUTUIFBMJHONFOUTVNNBSZGPS Common Core Standards, for ELA and Literacy
UIF8FCCBOE$PPLBMJHONFOUTUBUJTUJDT $PPL
$PPL8JMNFT 8FCC B
Depth of Knowledge
"DSPTTBMMNBUDIFETUBOEBSETGPS,464JO&-"BOE
MJUFSBDZ BOBWFSBHFPG SD GBMMBUUIFTBNF
%0,MFWFMBTUIF$PNNPO$PSFTUBOEBSET XJUIBO
BWFSBHF PG SD SBUFE MPXFS JO DPHOJUJWF
EFNBOEBOEBOBWFSBHFPG SD SBUFEIJHIFS
5ISFF TUSBOET 3FBEJOH 4UBOEBSET GPS -JUFSBUVSF
-BOHVBHF 4UBOEBSET BOE 3FBEJOH 4UBOEBSET GPS
-JUFSBDZJO4DJFODFBOE5FDIOJDBM4VCKFDUT NFFUUIF
%0,$POTJTUFODZDSJUFSJPO
5ISFF TUSBOET 3FBEJOH 4UBOEBSET GPS -JUFSBUVSF
-BOHVBHF 4UBOEBSET BOE 3FBEJOH 4UBOEBSET GPS
-JUFSBDZ JO 4DJFODF BOE 5FDIOJDBM 4VCKFDUT NFFU
UIF %0, $POTJTUFODZ DSJUFSJPO XIJDI JT CBTFE PO
BUMFBTUPGUIFNBUDIJOH,464TUBOEBSETCFJOH
BUPSBCPWFUIF%0,PGUIFDPSSFTQPOEJOH$PNNPO
$PSFTUBOEBSE"T'JHVSF$TIPXT TPNFTUSBOET
GBMMDMPTFUPBOESFTVMUTXPVMECFEJGGFSFOUJGBO
alternative criterion had been selected.
Note5PUBMQFSDFOUNBZFRVBMTMJHIUMZBCPWFPSCFMPXEVFUPSPVOEJOH
Appendix C 65
Results by Individual Comparison Standards
Mathematics Findings for the KSUS Standards
Match
Figure C. Percentage of Common
Core Standards that Match
Knowledge and Skills for University
Success Standards, for Mathematics
'JHVSF $ TIPXT UIF QFSDFOU PG $PNNPO $PSF TUBUFNFOUT
(n UIBU BOZ PG UIF TFWFO NBUIFNBUJDT SBUFST NBUDIFE
UP POF PS NPSF PG UIF ,464 TUBOEBSET n 5IF mHVSF
DPMMBQTFT mOEJOHT BDSPTT UIF mWF DPODFQUVBM DBUFHPSJFT *O
'JHVSF $ XF EJWJEF mOEJOHT CZ DPODFQUVBM DBUFHPSZ "T
UIF CBS HSBQIT JOEJDBUF UIF ,464 IBWF NBUDIFT UP o
PGUIF$PNNPO$PSFTUBOEBSETJOUIF"MHFCSB 'VODUJPOT BOE
(FPNFUSZDPODFQUVBMDBUFHPSJFT5IFZIBWFNBUDIFTUP
PG UIF $PNNPO $PSF TUBOEBSET JO UIF /VNCFS BOE 2VBOUJUZ
DPODFQUVBMDBUFHPSZBOEJOUIF4UBUJTUJDTBOE1SPCBCJMJUZ
DBUFHPSZ &WFSZ DPODFQUVBM DBUFHPSZ NFFUT UIF DSJUFSJPO GPS
UIF$BUFHPSJDBM$PODVSSFODFTUBUJTUJD
Percent
100
Matched
Not matched
70
75
50
30
25
0
Common Core Standards
(192 statements)
5IFEBUBQSFTFOUFEIFSFJTCBTFEPOBUMFBTUPOFSBUFSNBUDIJOHBUMFBTU
POFTUBOEBSE IPXFWFSUIFOVNCFSPGNBUDIFTGPSBOZHJWFOTUBOEBSEWBSJFT
XJEFMZ$IBQUFSQSPWJEFTUIFNFBOBOETUBOEBSEEFWJBUJPOGPSUIFOVNCFSPG
DPNQBSJTPOTUBOEBSETNBUDIJOH$PNNPO$PSFTUBOEBSETJOFBDIDPODFQUVBM
DBUFHPSZ5IF5FDIOJDBM4VQQMFNFOUEJTQMBZTUIFFYBDUTUBOEBSETGSPNUIF
Common Core and the comparison sets that were matched.
Figure C. Percentage of Common Core Standards that Match Knowledge and
Skills for University Success Standards, by Mathematics Conceptual Category
Matched
Percent
Not matched
100
88
89
82
69
75
53
50
47
31
25
12
18
11
0
Number and
Quantity
(32)
Algebra
(34)
Functions
(45)
Geometry
(45)
Statistics and
Probability
(36)
Common Core conceptual category (number of statements)
Appendix C 66
Results by Individual Comparison Standards
Table C. Summary for Alignment Between the Knowledge
and Skills for University Success Standards and Common Core
Standards in Mathematics
Common Core mathematics conceptual
category
Categorical
Concurrence
Coverage
Number and Quantity
Algebra
Functions
Geometry
Statistics and Probability
Meets the criterion for Categorical Concurrence (averaged across raters, a single correspondence exists
between the two sets of standards);
Does not meet the criterion for Categorical Concurrence;
means that in a majority of topics in the Common Core category have at least one matched comparison
standard;
means that in more than one topic in the Common Core category have at least one matched
comparison standard;
means that in one or less than one topic in the Common Core category have at
least one matched comparison standard.
Breadth of Coverage
#SFBEUI PG $PWFSBHF JT TUSPOH GPS BMM UIF NBUIFNBUJDT
DPODFQUVBM DBUFHPSJFT UIF NBKPSJUZ PG $PNNPO $PSF
DMVTUFSTIBWFNBUDIJOHDPNQBSJTPOTUBOEBSETXJUIJOUIFN
5BCMF$QSFTFOUTUIFTVNNBSJ[FESFTVMUTGPSNBUIFNBUJDT
Depth of Knowledge
"DSPTT DPODFQUVBM DBUFHPSJFT JO NBUIFNBUJDT GPS UIPTF
,464 TUBOEBSET UIBU NBUDI $PNNPO $PSF TUBOEBSET
BO BWFSBHF PG SD GBMM BU UIF TBNF MFWFM BO
BWFSBHF PG SD BSF MPXFS BOE BO BWFSBHF PG
SD BSFIJHIFSJODPHOJUJWFEFNBOE5ISFFPGUIF
mWF $PNNPO $PSF DPODFQUVBM DBUFHPSJFT NFFU UIF %0,
$POTJTUFODZ DSJUFSJPO TFF 'JHVSF $ XJUI 'VODUJPOT
BOE (FPNFUSZ CFJOH UIF UXP DBUFHPSJFT UIBU EP OPU NFFU
UIF DSJUFSJPO "T 'JHVSF $ TIPXT TPNF DBUFHPSJFT GBMM
DMPTFUPBOESFTVMUTXPVMECFEJGGFSFOUJGBOBMUFSOBUJWF
criterion had been selected.
'JHVre%,OPXMFEHFBOE4LJMMTGPS6OJWFSTJUZ
Figure C. Percent of Knowledge and Skills for University
4VDDFTT4UBOEBSET%FQUIPG,OPXMFEHF-FWFMT
Success Standards Under, At, or Above the Depth of Knowledge
6OEFS, At, and Above, the Common Core for
Level of the Common Core Standards, for Mathematics
Mathematics
0
/VNCFS
and
2VBOUJUZ
"MHFCSB
25
50
75
100
AWFSBHF
Percent
"CPWF
"U
6OEFS
Functions
Geometry
4UBUJTUJDT
and
Probability
Note5PUBMQFSDFOUNBZFRVBMTMJHIUMZBCPWFPSCFMPXEVFUPSPVOEJOH
Appendix C 67
Results by Individual Comparison Standards
English Language Arts and Literacy Findings for
8FDPNQBSFEUIF*OUFSOBUJPOBM#BDDBMBVSFBUF *# 4UBOEBSET the IB Standards
International Baccalaureate Standards
GPS UIF %JQMPNB 1SPHSBNNF UP UIF $PNNPO $PSF TUBOEBSET
'PS &OHMJTI MBOHVBHF BSUT XF VTFE UIF DPVSTF TUBOEBSET GPS
"-BOHVBHF &YUFOEFE&TTBZ BOE5IFPSZPG,OPXMFEHF'PS
NBUIFNBUJDTXFVTFE.BUIFNBUJDBM4UVEJFT 4UBOEBSE-FWFM
)JHIFS -FWFM DPVSTF TUBOEBSET 5IF TUVEZ EJE OPU JODMVEF
BOZ DPOUFOU GSPN *# iPQUJPOTw 5IFTF BSF BEEJUJPOBM SFRVJSFE
components that each IB school selects. The number of
options varies by course and by subject. The IB options do not
IBWFTQFDJmDTUBOEBSET
Figure C. Percentage of
Common Core Standards that
Match International Baccalaureate
Standards, for ELA and Literacy
Percent
100
Matched
Not matched
66
75
50
34
Match
3FDBMMUIBUSBUFSTJEFOUJmFEVQUPUISFF$PNNPO$PSFTUBOEBSET
UIBUDPSSFTQPOEXJUIFBDI*#TUBOEBSE'JHVSF$TIPXTUIF
percent of Common Core statements (n UIBUBOZPGUIF
OJOF &OHMJTI -BOHVBHF "SUT &-" SBUFST NBUDIFE UP POF PS
more of the IB standards (n 5IFmHVSFDPMMBQTFTmOEJOHT
BDSPTT BMM FJHIU &-" BOE MJUFSBDZ TUSBOET *O 'JHVSF $ XF
EJWJEF mOEJOHT CZ TUSBOE "T UIF CBS HSBQIT JOEJDBUF UIF
*# TUBOEBSET IBWF NBUDIFT GPS PG UIF $PNNPO $PSF
TUBOEBSETJOUIF3FBEJOHGPS-JUFSBUVSFTUSBOE5IF*#TUBOEBSET
IBWF NBUDIFT UP o PG UIF $PNNPO $PSF TUBOEBSET JO
UIF8SJUJOH 4QFBLJOHBOE-JTUFOJOH BOE3FBEJOH4UBOEBSETJO
)JTUPSZ4PDJBM4UVEJFTTUSBOET5IFZIBWFNBUDIFTUPo
PGUIF$PNNPO$PSFTUBOEBSETJOUIFSFNBJOJOHGPVSTUSBOET7
4JY PG UIF FJHIU TUSBOET NFFU UIF DSJUFSJPO GPS UIF $BUFHPSJDBM
$PODVSSFODF TUBUJTUJD UIF -BOHVBHF TUSBOE BOE UIF 3FBEJOH
4UBOEBSETJO4DJFODFBOE5FDIOJDBM4VCKFDUTTUSBOEEPOPU
5IFEBUBQSFTFOUFEIFSFJTCBTFEPOBUMFBTUPOFSBUFSNBUDIJOHBUMFBTU
POFTUBOEBSE IPXFWFSUIFOVNCFSPGNBUDIFTGPSBOZHJWFOTUBOEBSEWBSJFT
widely. Chapter 3 provides the mean and standard deviation for the number of
DPNQBSJTPOTUBOEBSETNBUDIJOH$PNNPO$PSFTUBOEBSETJOFBDITUSBOE5IF
5FDIOJDBM4VQQMFNFOUEJTQMBZTUIFFYBDUTUBOEBSETGSPNUIF$PNNPO$PSFBOE
the comparison sets that were matched.
7
25
0
Common Core Standards
(113 statements)
Figure C. Percentage of Common Core Standards that Match International Baccalaureate Standards, by ELA and Literacy Strand
Percent
Matched
100
93
100
Not matched
90
70
75
53
50
47
47
30
30
25
7
0
70
70
53
30
10
0
Reading for
Literature
(9)
Reading for
Informational
Texts
(10)
Writing
(28)
Speaking and
Listening
(10)
Language
(17)
Reading in
History/Social
Studies (10)
Reading in
Science and
Technical
Subjects (10)
Writing in
History/Social
Studies,
Science, and
Technical
Subjects (19)
Common Core strand (number of statements)
Appendix C 68
Results by Individual Comparison Standards
Depth of Knowledge
0WFSBMM GPSUIPTF*#&-"BOEMJUFSBDZ
standards that match the Common
$PSF BOBWFSBHFPG SD
of the IB standards fall at the same
%FQUI PG ,OPXMFEHF %0, BT UIF
Common Core standards across all
TUSBOET "O BWFSBHF PG SD =
PG UIF *# TUBOEBSET BSF SBUFE
MPXFS BOE BO BWFSBHF PG SD
BSF SBUFE IJHIFS JO DPHOJUJWF
EFNBOE 0G UIF TJY TUSBOET UIBU
NFFUUIFDSJUFSJPOGPSUIF$BUFHPSJDBM
Concurrence statistic, four strands
NFFU UIF DSJUFSJPO GPS UIF %0,
$POTJTUFODZ TUBUJTUJD 'JHVSF $
EFQJDUT UIF SFTVMUT HSBQIJDBMMZ "T
UIF mHVSF TIPXT TPNF TUSBOET
GBMMDMPTFUPBOESFTVMUTXPVME
therefore be different if an alternative
criterion had been selected.
Table C. Summary for Alignment Between the International Baccalaureate
Standards and Common Core Standards in English Language Arts and Literacy
Common Core ELA and literacy strand
Categorical
Concurrence
Coverage
Reading for Literature
Reading for Informational Texts
Writing
Speaking and Listening
Language
Reading in History/Social Studies
Reading in Science and Technical Subjects
Writing in History/Social Studies, Science, and Technical
Subjects
Meets the criterion for Categorical Concurrence (averaged across raters, a single correspondence exists between the two sets of
standards);
Does not meet the criterion for Categorical Concurrence;
means that in a majority of topics in the Common Core category have at least one matched comparison standard;
means that in more than one topic in the Common Core category have at least one matched comparison standard;
means that in one or less than one topic in the Common Core category have at least one matched comparison standard.
Breadth of Coverage
#SFBEUIPG$PWFSBHFJTTUSPOHGPSmWFPGUIF&-"BOE
Figure C. Percent of International Baccalaureate Standards Under,
literacy strands (for these, the majority of Common At, or Above the Depth of Knowledge Level of the Common Core
$PSF UPQJDT IBWF NBUDIJOH DPNQBSJTPO TUBOEBSET Standards, for ELA and Literacy
XJUIJO UIFN 5IJT NFBOT UIBU UIF *# TUBOEBSET UIBU
match to Common Core standards are distributed
BDSPTTDPOUFOUUPQJDTXJUIJOUIPTFmWF$PNNPO$PSF
TUSBOET0OFTUSBOE 3FBEJOHGPS*OGPSNBUJPOBM5FYUT
IBT NPEFSBUF DPWFSBHF 5IJT NFBOT UIBU $PNNPO
Core standards match to IB standards in more than
one topic but not a majority of topics within the strand.
0OF TUSBOE -BOHVBHF IBT MJNJUFE DPWFSBHF UIFSF
is one topic that has Common Core standards with
NA
NBUDIFT UP UIF *# TUBOEBSET 5BCMF $ QSFTFOUT UIF
TVNNBSZPGUIFBMJHONFOUTUBUJTUJDTGPSUIF8FCCBOE
$PPLBMJHONFOUTUBUJTUJDT $PPL $PPL8JMNFT
8FCC
NA
Note5PUBMQFSDFOUNBZFRVBMTMJHIUMZBCPWFPSCFMPXEVFUPSPVOEJOH
Appendix C 69
Results by Individual Comparison Standards
Mathematics Findings for the IB Standards
Match
Figure C. Percentage of
Common Core Standards that
Match International Baccalaureate
Standards, for Mathematics
'JHVSF$TIPXTUIFQFSDFOUPG$PNNPO$PSFTUBUFNFOUT n
UIBU BOZ PG UIF TFWFO NBUIFNBUJDT SBUFST NBUDIFE UP
one or more of the IB standards (n 5IFmHVSFDPMMBQTFT
mOEJOHTBDSPTTUIFmWFDPODFQUVBMDBUFHPSJFT*O'JHVSF$
XFEJWJEFmOEJOHTCZDPODFQUVBMDBUFHPSZ"TUIFCBSHSBQIT
JOEJDBUF UIF *# TUBOEBSET IBWF NBUDIFT UP o PG UIF
$PNNPO$PSFTUBOEBSETJOGPVSPGUIFDPODFQUVBMDBUFHPSJFT
5IFZ IBWF NBUDIFT UP PG UIF $PNNPO $PSF TUBOEBSET
JO UIF (FPNFUSZ DPODFQUVBM DBUFHPSZ Every conceptual
DBUFHPSZNFFUTUIFDSJUFSJPOGPSUIF$BUFHPSJDBM$PODVSSFODF
statistic.
Percent
100
Matched
Not matched
77
75
50
23
25
0
Common Core Standards
(192 statements)
5IFEBUBQSFTFOUFEIFSFJTCBTFEPOBUMFBTUPOFSBUFSNBUDIJOHBUMFBTU
POFTUBOEBSE IPXFWFSUIFOVNCFSPGNBUDIFTGPSBOZHJWFOTUBOEBSEWBSJFT
XJEFMZ$IBQUFSQSPWJEFTUIFNFBOBOETUBOEBSEEFWJBUJPOGPSUIFOVNCFSPG
DPNQBSJTPOTUBOEBSETNBUDIJOH$PNNPO$PSFTUBOEBSETJOFBDIDPODFQUVBM
DBUFHPSZ5IF5FDIOJDBM4VQQMFNFOUEJTQMBZTUIFFYBDUTUBOEBSETGSPNUIF
Common Core and the comparison sets that were matched.
Figure C. Percentage of Common Core Standards that Match International
Baccalaureate Standards, by Mathematics Conceptual Category
Matched
Percent
97
100
Not matched
89
86
76
75
56
44
50
24
25
14
11
3
0
Number and
Quantity
(32)
Algebra
(34)
Functions
(45)
Geometry
(45)
Statistics and
Probability
(36)
Common Core conceptual category (number of statements)
Appendix C 70
Results by Individual Comparison Standards
Table C. Summary of Alignment for the International Baccalaureate
Standards and Common Core Standards in Mathematics
Common Core mathematics conceptual category
Categorical
Concurrence
Coverage
Number and Quantity
Algebra
Functions
Geometry
Statistics and Probability
Meets the criterion for Categorical Concurrence (averaged across raters, a single correspondence exists between the
two sets of standards);
Does not meet the criterion for Categorical Concurrence;
means that in a majority of topics in the Common Core category have at least one matched comparison standard;
means that in more than one topic in the Common Core category have at least one matched comparison standard;
means that in one or less than one topic in the Common Core category have at least one matched comparison
standard.
Breadth of Coverage
#SFBEUI PG $PWFSBHF JT TUSPOH GPS BMM UIF NBUIFNBUJDT
DPODFQUVBMDBUFHPSJFT UIFNBKPSJUZPG$PNNPO$PSFDMVTUFST
IBWFNBUDIJOHDPNQBSJTPOTUBOEBSETXJUIJOUIFN 5BCMF$
QSFTFOUTUIFTVNNBSJ[FEBMJHONFOUSFTVMUTGPSNBUIFNBUJDT
Depth of Knowledge
Figure
Percent of
International Baccalaureate
30.C.
International
BaccalaurFBUF4UBOEBSds
For those IB mathematics standards that match Common 'JHVre
Standards Under, At, or Above the
of Knowledge
%FQUIPG,OPXMFEHF-FWFMT6OEFS,
At,Depth
and Above,
$PSFDPOUFOU BOBWFSBHFPG SD PGTUBOEBSETGBMM
of the
Common Core Standards, for Mathematics
theLevel
Common
Core
BUUIFTBNFMFWFMPGDPHOJUJWFEFNBOEBTUIF$PNNPO$PSF
0
25
50
75
100
TUBOEBSET BDSPTT BMM NBUIFNBUJDT DPODFQUVBM DBUFHPSJFT
AWFSBHF
/VNCFS
"OBWFSBHFPG SD PGUIF*#TUBOEBSETGBMMMPXFS
Percent
and
JO DPHOJUJWF EFNBOE UIBO UIF $PNNPO $PSF TUBOEBSET
2VBOUJUZ
BOE BO BWFSBHF PG SD GBMM BCPWF UIF $PNNPO
"CPWF
"MHFCSB
$PSFTUBOEBSET5ISFFPGUIFmWF$PNNPO$PSFDPODFQUVBM
"U
DBUFHPSJFTNFFUUIF%0,$POTJTUFODZDSJUFSJPO TFF'JHVSF
6OEFS
a
XJUI'VODUJPOTBOE(FPNFUSZCFJOHUIFUXPDBUFHPSJFT Functions
UIBU EP OPU NFFU UIF DSJUFSJPO "T 'JHVSF $ TIPXT TPNF
DBUFHPSJFT GBMM DMPTF UP PS BU BOE SFTVMUT XPVME CF Geometry
different if an alternative criterion had been selected.
4UBUJTUJDT
and
Probability
Note5PUBMQFSDFOUNBZFRVBMTMJHIUMZBCPWFPSCFMPXEVFUPSPVOEJOH
a
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Appendix C 71
Appendix D| Alignment Matches for Common
Core Content-specific Areas
NBEF GPS FBDI UPQJD UIF TVCBSFBT XJUIJO B TUSBOE 5IF
tables illustrate that there is certain content within a strand
that tends to have more concentration of matches than other
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UPQJD$IBQUFSQSFTFOUFEUIFBWFSBHFOVNCFSPGNBUDIFT
per standard for each topic across all comparison sets.
Number of Alignment Matches for Common
Core English Language Arts and Literacy Topics,
by Comparison Standard Set
The tables that follow present more information about the
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&OHMJTIMBOHVBHFBSUT &-" BOEMJUFSBDZTUSBOET4QFDJmDBMMZ
the tables show the total number of matches that all raters
Table D. Number of Matches Within Each Common Core Topic in the Reading for Literature Strand
Cumulative number of matchesa
Topic
(number of statements)
CA
MA
TCCRS
KSUS
IB
All standards
Key Ideas and Details ()
Craft and Structure ()
Integration of Knowledge and Ideas ()
Range of Reading and Level of Text Complexity ()
CA = California; MA = Massachusetts; TCCRS = Texas College and Career Readiness Standards; KSUS = Knowledge and Skills for University Success; IB = International
Baccalaureate
a
These matches are cumulative across all raters, meaning that the results show all ratings, including when raters matched the same Common Core standard multiple times
within one comparison set of standards and across multiple comparison sets of standards.
Table D. Number of Matches Within Each Common Core Topic in the Reading for Informational Texts
Strand
Cumulative number of matchesa
Topic
(number of statements)
CA
MA
TCCRS
KSUS
IB
All standards
Key Ideas and Details ()
Craft and Structure ()
Integration of Knowledge and Ideas ()
Range of Reading and Level of Text Complexity ()
CA = California; MA = Massachusetts; TCCRS = Texas College and Career Readiness Standards; KSUS = Knowledge and Skills for University Success; IB = International
Baccalaureate
a
These matches are cumulative across all raters, meaning that the results show all ratings, including when raters matched the same Common Core standard multiple times
within one comparison set of standards and across multiple comparison sets of standards.
Table D. Number of Matches Within Each Common Core Topic in the Writing Strand
Topic
(number of statements)
Cumulative number of matchesa
CA
MA
TCCRS
KSUS
IB
All standards
Text Types and Purposes ()
Production and Distribution of Writing ()
Research to Build and Present Knowledge ()
Range of Writing ()
CA = California; MA = Massachusetts; TCCRS = Texas College and Career Readiness Standards; KSUS = Knowledge and Skills for University Success; IB = International
Baccalaureate
a
These matches are cumulative across all raters, meaning that the results show all ratings, including when raters matched the same Common Core standard multiple times
within one comparison set of standards and across multiple comparison sets of standards.
Appendix D •
Alignment Matches for Specific Common Core Content-specific areas
Table D. Number of Matches Within Each Common Core Topic in the Speaking and Listening Strand
Cumulative number of matchesa
Topic
(number of statements)
CA
MA
TCCRS
KSUS
IB
All standards
Comprehension and Collaboration ()
Presentation of Knowledge and Ideas ()
CA = California; MA = Massachusetts; TCCRS = Texas College and Career Readiness Standards; KSUS = Knowledge and Skills for University Success; IB = International
Baccalaureate
a
These matches are cumulative across all raters, meaning that the results show all ratings, including when raters matched the same Common Core standard multiple times
within one comparison set of standards and across multiple comparison sets of standards.
Table D. Number of Matches Within Each Common Core Topic in the Language Strand
Cumulative number of matchesa
Topic
(number of statements)
CA
MA
TCCRS
KSUS
IB
All standards
Conventions of Standard English ()
Knowledge of Language ()
Vocabulary Acquisition and Use ()
CA = California; MA = Massachusetts; TCCRS = Texas College and Career Readiness Standards; KSUS = Knowledge and Skills for University Success; IB = International
Baccalaureate
a
These matches are cumulative across all raters, meaning that the results show all ratings, including when raters matched the same Common Core standard multiple times
within one comparison set of standards and across multiple comparison sets of standards.
Table D. Number of Matches Within Each Common Core Topic in the Reading for Literacy in History/
Social Studies Strand
Topic
(number of statements)
Cumulative number of matchesa
CA
MA
TCCRS
KSUS
IB
All standards
Key Ideas and Details ()
Craft and Structure ()
Integration of Knowledge and Ideas ()
Range of Reading and Level of Text Complexity ()
CA = California; MA = Massachusetts; TCCRS = Texas College and Career Readiness Standards; KSUS = Knowledge and Skills for University Success; IB = International
Baccalaureate
a
These matches are cumulative across all raters, meaning that the results show all ratings, including when raters matched the same Common Core standard multiple times
within one comparison set of standards and across multiple comparison sets of standards.
Table D. Number of Matches Within Each Common Core Topic in the Reading for Literacy in Science
and Technical Subjects Strand
Topic
(number of statements)
Cumulative number of matchesa
CA
MA
TCCRS
KSUS
IB
All standards
Key Ideas and Details ()
Craft and Structure ()
Integration of Knowledge and Ideas ()
Range of Reading and Level of Text Complexity ()
CA = California; MA = Massachusetts; TCCRS = Texas College and Career Readiness Standards; KSUS = Knowledge and Skills for University Success; IB = International
Baccalaureate
a
These matches are cumulative across all raters, meaning that the results show all ratings, including when raters matched the same Common Core standard multiple times
within one comparison set of standards and across multiple comparison sets of standards.
Appendix D 73
Alignment Matches for Specific Common Core Content-specific areas
Table D. Number of Matches Within Each Common Core Topic in the Writing for Literacy in History/
Social Studies, Science, and Technical Subjects Strand
Cumulative number of matchesa
Topic
(number of statements)
CA
MA
TCCRS
KSUS
IB
All standards
Text Types and Purposes ()
Production and Distribution of Writing ()
Research to Build and Present Knowledge ()
Range of Writing ()
CA = California; MA = Massachusetts; TCCRS = Texas College and Career Readiness Standards; KSUS = Knowledge and Skills for University Success; IB = International
Baccalaureate
a
These matches are cumulative across all raters, meaning that the results show all ratings, including when raters matched the same Common Core standard multiple times
within one comparison set of standards and across multiple comparison sets of standards.
Appendix D 74
Alignment Matches for Specific Common Core Content-specific areas
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The tables illustrate that there are certain clusters within a
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PUIFSDMVTUFSTXJUIJOUIFTBNFDBUFHPSZ/PUFUIBUUIFOVNCFS
PGSBUFETUBUFNFOUT TIPXOJOQBSFOUIFTFT BMTPWBSJFTBDSPTT
DMVTUFS$IBQUFSQSFTFOUFEUIFBWFSBHFOVNCFSPGNBUDIFT
per standard for each cluster across all comparison sets.
Number of Alignment Matches for Common
Core Clusters, by Comparison Standard Set for
Mathematics
The tables that follow present more information about the
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$PSF NBUIFNBUJDT DPODFQUVBM DBUFHPSJFT 4QFDJmDBMMZ UIF
tables show the total number of matches that all raters made
Table D. Number of Matches Within Each Common Core Cluster in the Number and Quantity
Conceptual Category
Cluster
(number of statements)
Cumulative number of matchesa
CA
MA
TCCRS
KSUS
IB
All standards
Extend the properties of exponents to rational
exponents ()
Use properties of rational and irrational numbers
()
Reason quantitatively and use units to solve
problems ()
Perform arithmetic operations with complex
numbers ()
Represent complex numbers and their operations
on the complex plane ()
Use complex numbers in polynomial identities and
equations ()
Represent and model with vector quantities ()
Perform operations on vectors ()
Perform operations on matrices and use matrices
in applications ()
CA = California; MA = Massachusetts; TCCRS = Texas College and Career Readiness Standards; KSUS = Knowledge and Skills for University Success; IB = International
Baccalaureate
a
These matches are cumulative across all raters, meaning that the results show all ratings, including when raters matched the same Common Core standard multiple times
within one comparison set of standards and across multiple comparison sets of standards.
Appendix D 75
Alignment Matches for Specific Common Core Content-specific areas
Table D. Number of Matches Within Each Common Core Cluster in the Algebra Conceptual Category
Cluster
(number of statements)
Cumulative number of matchesa
CA
MA
TCCRS
KSUS
IB
All standards
Interpret the structure of expressions ()
Write expressions in equivalent forms to solve
problems ()
Perform arithmetic operations on polynomials()
Understand the relationship between zeros and
factors of polynomials ()
Use polynomial identities to solve problems ()
Rewrite rational expressions ()
Create equations that describe numbers or
relationships ()
Understand solving equations as a process of
reasoning and explain the reasoning ()
Solve equations and inequalities in one variable
()
Solve systems of equations ()
Represent and solve equations and inequalities
graphically ()
CA = California; MA = Massachusetts; TCCRS = Texas College and Career Readiness Standards; KSUS = Knowledge and Skills for University Success; IB = International
Baccalaureate
a
These matches are cumulative across all raters, meaning that the results show all ratings, including when raters matched the same Common Core standard multiple times
within one comparison set of standards and across multiple comparison sets of standards.
Table D. Number of Matches Within Each Common Core Cluster in the Functions Conceptual
Category
Cluster
(number of statements)
Cumulative number of matchesa
CA
MA
TCCRS
KSUS
IB
All standards
Understand the concept of a function and use
function notation ()
Interpret functions that arise in applications in
terms of the context ()
Analyze functions using different representations
()
Build a function that models a relationship
between two quantities ()
Build new functions from existing functions ()
Construct and compare linear and exponential
models and solve problems ()
Interpret expressions for functions in terms of the
situation they model ()
Extend the domain of trigonometric functions
using the unit circle ()
Model periodic phenomena with trigonometric
functions ()
Prove and apply trigonometric identities ()
CA = California; MA = Massachusetts; TCCRS = Texas College and Career Readiness Standards; KSUS = Knowledge and Skills for University Success; IB = International
Baccalaureate
a
These matches are cumulative across all raters, meaning that the results show all ratings, including when raters matched the same Common Core standard multiple times
within one comparison set of standards and across multiple comparison sets of standards.
Appendix D 76
Alignment Matches for Specific Common Core Content-specific areas
Table D. Number of Matches Within Each Common Core Cluster in the Geometry Conceptual
Category
Cluster
(number of statements)
Cumulative number of matchesa
CA
MA
TCCRS
KSUS
IB
All standards
Experiment with transformations in the plane ()
Understand congruence in terms of rigid motions
()
Prove geometric theorems ()
Make geometric constructions ()
Understand similarity in terms of similarity
transformations ()
Prove theorems involving similarity ()
Define trigonometric ratios and solve problems
involving right triangles ()
Apply trigonometry to general triangles ()
Understand and apply theorems about circles ()
Find arc lengths and areas of sectors of circles ()
Translate between the geometric description and
the equation for a conic section ()
Use coordinates to prove simple geometric
theorems algebraically ()
Explain volume formulas and use them to solve
problems ()
Visualize relationships between two-dimensional
and three-dimensional objects ()
Apply geometric concepts in modeling situations
()
CA = California; MA = Massachusetts; TCCRS = Texas College and Career Readiness Standards; KSUS = Knowledge and Skills for University Success; IB = International
Baccalaureate
a
These matches are cumulative across all raters, meaning that the results show all ratings, including when raters matched the same Common Core standard multiple times
within one comparison set of standards and across multiple comparison sets of standards.
Appendix D 77
Alignment Matches for Specific Common Core Content-specific areas
Table D. Number of Matches Within Each Common Core Cluster in the Statistics and Probability
Conceptual Category
Cluster
(number of statements)
Cumulative number of matchesa
CA
MA
TCCRS
KSUS
IB
All standards
Summarize, represent, and interpret data on a
single count or measurement variable ()
Summarize, represent, and interpret data on two
categorical and quantitative variables ()
Interpret linear models ()
Understand and evaluate random processes
underlying statistical experiments ()
Make inferences and justify conclusions from
sample surveys, experiments, and observational
studies ()
Understand independence and conditional
probability and use them to interpret data ()
Use the rules of probability to compute
probabilities of compound events in a uniform
probability model ()
Calculate expected values and use them to solve
problems ()
Use probability to evaluate outcomes of decisions
()
CA = California; MA = Massachusetts; TCCRS = Texas College and Career Readiness Standards; KSUS = Knowledge and Skills for University Success; IB = International
Baccalaureate
a
These matches are cumulative across all raters, meaning that the results show all ratings, including when raters matched the same Common Core standard multiple times
within one comparison set of standards and across multiple comparison sets of standards.
Appendix D 78