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Common Core State Standards
The Times They Are A-Changin’
Agenda
• Commonalities & Connections• Determining Differences• Impacting Instruction• Necessary Nows
COMMONALITIES & CONNECTIONS
Show-Me Standards &
Mathematics Common Core State Standards
Common Core Standards
Mathematical Content
+Mathematical Practice
College and Career Ready
Common Standards
Show-Me Standards
Knowledge (content)
+ Performance (process)
well-prepared for future education, work, and civic responsibilities
Standards for Mathematical Practice1. Make sense of
problems and persevere in solving them. (3.1, 3.2)
2. Reason abstractly and quantitatively. (3.5, 3.8)
3. Construct viable arguments and critique the reasoning of others. (1.7, 1.8, 3.3, 3.5)
4. Model with mathematics. (1.10, 3.8)
5. Use appropriate tools strategically. (1.4, 2.7)
6. Attend to precision. (2.1, 1.7)
7. Look for and make use of structure. (1.7)
8. Look for and express regularity in repeated reasoning. (1.6)
Red font indicates Show-Me Process standards that align to the CCSS Mathematical Practices Standards.
Grade Level Overview Page
Standards for Mathematical
Content
Comparing the GLEs/CLEs and CCSS
• Neither are curriculum documents• GLEs/CLEs are assessment specifications that
define assessable content, procedures, and processes for NCLB mandated assessments
• Both include content, procedures, and processes that are aligned to the Missouri Show-Me Standards
• Both are aligned to the National Council of Teachers of Mathematics K – 8 Curriculum Focal Points (2006).
• Alignment Analysis• Commonalities• CCSS not aligned to the v2.0 GLEs and
CLEs
Commonalities & Connections Documents
CCSS Mathematics K - 8 Domains 8/2011
Domain K 1 2 3 4 5 6 7 8Counting and
CardinalityK.CC.1, 2, 3, 4a, 4b, 4c, 5, 6, 7
Operations and Algebraic Thinking
K.OA.1, 2, 3, 4, 5 1.OA.1, 2, 3, 4, 5, 6, 7, 8
2.OA.1, 2, 3, 4 3.OA.1, 2, 3, 4, 5, 6, 7, 8, 9
4.OA.1, 2, 3, 4, 5 5.OA.1, 2, 3
Numbers and Operations in Base
Ten
K.NBT.1 1.NBT.1, 2a, 2b, 2c, 3, 4, 5, 6
2.NBT.1a, 1b, 2, 3, 4, 5, 6, 7, 8, 9
3.NBT.1, 2, 3 4.NBT.1, 2, 3, 4, 5, 6
5.NBT.1, 2, 3a, 3b, 4, 5, 6, 7
Numbers and Operations -
Fractions
3.NF.1, 2a, 2b, 3a, 3b, 3c, 3d
4.NF.1, 2, 3a, 3b, 3c, 3d, 4a, 4b, 4c, 5, 6, 7
5.NF.1, 2, 3, 4a, 4b, 5a, 4b, 5a, 5b, 6, 7a, 7b, 7c
Measurement and Data
K.MD.1, 2, 3 1.MD.1, 2, 3, 4 2.MD.1, 2, 3, 4, 5, 6, 7, 8, 9, 10
3.MD.1,2, 3, 4, 5a, 5b, 6, 7a, 7b, 7c, 7d, 8
4.MD.1, 2, 3, 4, 5a, 5b, 6, 7
5.MD.1, 2, 3a, 3b, 4, 5a, 5b, 5c
Geometry K.G.1, 2, 3, 4, 5, 6
1.G.1, 2, 3 2.G.1, 2, 3 3.G.1, 2 4.G.1, 2, 3 5.G1, 2, 3, 4 6.G.1, 2, 3, 4 7.G1, 2, 3, 4, 5, 6
8.G.1a, 1b, 1c, 2, 3, 4, 5, 6, 7, 8, 9
Ratios and Proportional Relationships
6.RP.1, 2, 3a, 3b, 3c, 3d
7.RP.1, 2a, 2b, 2c, 2d, 3
The Number System
6.NS.1, 2, 3, 4, 5, 6a, 6b, 6c, 7a, 7b, 7c, 7d, 8
7.NS.1a, 1b, 1c, 1d, 2a, 2b, 2c, 2d, 3
8.NS.1, 2,
Expressions and Equations
6.EE1, 2a, 2b, 2c, 3, 4, 5, 6, 7, 8, 9
7.EE.1, 2, 3, 4a, 4b
8.EE.1, 2, 3, 4, 5 ,6, 7a, 7b, 8a, 8b, 8c
Statistics and Probability
6.SP.1, 2, 3, 4, 5a, 5b, 5c, 5d
7.SP.1, 2, 3, 4, 5, 6, 7a, 7b, 8a, 8b, 8c
8.SP.1, 2, 3, 4
Functions 8.F.1, 2, 3, 4, 5
CCSS Mathematics Traditional Pathway HS Domains 8/2011
ConceptualCategory Domain Algebra I Geometry Algebra II Fourth
Course
Number and
Quantity
The Real Number System N.RN.1, 2, 3
Quantities N.Q. 1, 2, 3
The Complex Number System N.CN.1, 2, 7, (+)8, (+)9 (+)N.CN.3, 4, 5, 6
Vector and Matrix Quantities (+)N.VM.1, 2, 3, 4a, 4b, 4c, 5a, 5b, 6, 7, 8, 9, 10, 11, 12
Algebra
Seeing Structure in Expressions A.SSE.1a, 1b, 2, 3a, 3b, 3c
A.SSE.1a, 1b, 2, 4
Arithmetic with Polynomials and Rational Expressions
A.APR.1 A.APR.1, 2, 3, 4 (+)5, 6, (+)7
Creating Equations A.CED. 1, 2, 3, 4 A.CED.1, 2, 3, 4
Reasoning with Equations and Inequalities A.REI.I, 3, 4a, 4b, 5, 6, 7, 10, 11, 12
A.REI.2, 11 (+) A.REI. 8, 9
Functions and
Models
Interpreting Functions F.IF.1, 2, 3, 4, 5, 6, 7a, 7b, 7e, 8a, 8b, 9
F.IF.4, 5, 6, 7b, 7c, 7e, 8, 9
F.IF.7d
Building Functions F.BF.1a, 1b, 2, 3, 4a F.BF.1b, 3, 4a (+)F.BF.1c, 4c, 4d, 5
Linear, Quadratic and Exponential Models F.LE.1a, 1b, 1c, 2, 3, 5 F.LE.4
Trigonometric Functions F.TF.1, 2, 5, 8 (+)F.TF.3, 4, 6, 7, 9
Geometry
Congruence G.CO.1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13
Similarity, Right Triangles, and Trigonometry G.SRT.1a, 1b, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11
Circles G.C. 1, 2, 3, (+)4, 5
Expressing Geometric Properties with Equations G.GPE.1, 2, 4, 5, 6, 7 (+)G.GPE.3
Geometric Measurement and Dimension G.GMD.1, 3, 4 (+)G.GMD.2
Modeling with Geometry G.GMG.1, 2, 3
Statistics and
Probability
Interpreting Categorical and Quantitative Data S.ID.1, 2, 3, 5, 6a, 6b, 6c, 7, 8, 9
S.ID.4
Making Inferences and Justifying Conclusions S.IC.1, 2, 3, 4, 5, 6
Conditional Probabilities and the Rules of Probability S.CP.1, 2, 3, 4, 5, 6, 7, (+)8, (+)9
Using Probability to Make Decisions (+)S.MD.6, 7 (+)S.MD.6, 7 (+)S.MD.5a, 5b
CCSS/v2.0 GLEs Alignment Analysis
Domain CCSS Cluster/Standards Missouri v2.0 GLE
CCSS Alignment to v2.0 GLE/CLE
Counting and
Cardinality (CC)
K.CC1Count to 100 by ones and by tens..
N1AK *rote count to 100 and recognize numbers up to 31
Partial alignment to bold, italicized portion of GLE
N1D1 *skip count by 2s, 5s and 10s
Partial alignment to bold, italicized portion of GLE
Mathematics Commonalities
CCSS Grades K – 8 Domain and Cluster Alignments to v2.0 GLEs/CLEs
Domain K 1 2Below Grade Level
At Grade Level
Above Grade Level
Below Grade Level
At Grade Level
Above Grade Level
Below Grade Level
At Grade Level
Above Grade Level
Counting and Cardinality
N1AKN1DKN3BK
N1A1N1D1
N3BKA3AK
N1A1
Operations and Algebraic Thinking
N1CKA3AK
N2A1 N2A1A2A1A3A1
N3C2A3A2
N3B2
N1C1A2B1
N1D1 A3A2 N1D3N2A3
N1C1N3B1N3C1N1C1
CCSS/v2.0 GLEs Alignment Analysis
Domain CCSS Cluster/Standards Missouri v2.0 GLE
CCSS Alignment to v2.0 GLE/CLE
Counting and
Cardinality (CC)
K.CC2 Count forward beginning from a given number within the known sequence (instead of having to begin at 1).
Underlined portion is not aligned to any GLE/CLE.
K.CC3 Write numbers from 0 to 20. Represent a number of objects with a written numeral 0-20 (with 0 representing a count of no objects).
N1A1 *read, write, and compare whole numbers less than 100
Partial alignment to bold, italicized portion of Grade 1 GLE
N3BK *connect number words (orally) and quantities they represent
Partial alignment to bold, italicized portion of GLEBold underlined portion of the CCSS
represents content/processes/procedures that do not align with any GLEs/CLEs.
DOMAIN CCSS v2.0 GLE/CLE CCSS Content not addressed in GLEs/CLEsNumbers and Operations-
Fractions (NF)
3.NF.1, 2a, 2b, 3a, 3b, 3c, 3d
N1C3, N2A3N1B4N1A5, N1B5
3.NF1 Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction a/b as the quantity formed by a parts of size 1/b.
3.NF3b Recognize and generate simple equivalent fractions, e.g., 1/2 = 2/4, 4/6 = 2/3). Explain why the fractions are equivalent, e.g., by using a visual fraction model
3.NF3d Compare two fractions with the same numerator or the same denominator by reasoning about their size. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model.
IMPACTING INSTRUCTION
INSTRUCTIONAL FOCUS TIME IN K SHOULD FOCUS ON THESE CRITICAL AREAS:
(1) representing, relating, and operating on whole numbers, initially with sets of objects;(2) describing shapes and space. More learning time in Kindergarten should be devoted to number than other topics.
DOMAINâ
CCSSMO v2.0 GLE/CLE
that aligns to CCSS CCSS Not aligned
Counting and Cardinality (CC)
K.CC.1, 2, 3, 4a, 4b, 4c, 5, 6, 7
*N1AK, *N3BK, *A3AK*N1A1, *N1D1
K.CC.2K.CC.3K.CC.4b, 4cK.CC.7
Operations and Algebraic
Thinking (OA)
K.OA.1, 2, 3, 4, 5
*N1CK, *A3AK*N1A1
K.OA.1
Numbers and Operations in
Base Ten (NBT)
K.NBT.1 *A3AK, *M1AK, *M2AK
NONE
PLANNING FOR PD
CCSS Mathematics K - 8 Domains 7/2011
Domain K 1 2 3 4 5 6 7 8Counting and
CardinalityK.CC.1, 2, 3, 4a, 4b, 4c, 5, 6, 7
Operations and Algebraic Thinking
K.OA.1, 2, 3, 4, 5 1.OA.1, 2, 3, 4, 5, 6, 7, 8
2.OA.1, 2, 3, 4 3.OA.1, 2, 3, 4, 5, 6, 7, 8, 9
4.OA.1, 2, 3, 4, 5 5.OA.1, 2, 3
Numbers and Operations in Base
Ten
K.NBT.1 1.NBT.1, 2a, 2b, 2c, 3, 4, 5, 6
2.NBT.1a, 1b, 2, 3, 4, 5, 6, 7, 8, 9
3.NBT.1, 2, 3 4.NBT.1, 2, 3, 4, 5, 6
5.NBT.1, 2, 3a, 3b, 4, 5, 6, 7
Numbers and Operations -
Fractions
3.NF.1, 2a, 2b, 3a, 3b, 3c, 3d
4.NF.1, 2, 3a, 3b, 3c, 3d, 4a, 4b, 4c, 5, 6, 7
5.NF.1, 2, 3, 4a, 4b, 5a, 4b, 5a, 5b, 6, 7a, 7b, 7c
Measurement and Data
K.MD.1, 2, 3 1.MD.1, 2, 3, 4 2.MD.1, 2, 3, 4, 5, 6, 7, 8, 9, 10
3.MD.1,2, 3, 4, 5a, 5b, 6, 7a, 7b, 7c, 7d, 8
4.MD.1, 2, 3, 4, 5a, 5b, 6, 7
5.MD.1, 2, 3a, 3b, 4, 5a, 5b, 5c
Geometry K.G.1, 2, 3, 4, 5, 6
1.G.1, 2, 3 2.G.1, 2, 3 3.G.1, 2 4.G.1, 2, 3 5.G1, 2, 3, 4 6.G.1, 2, 3, 4 7.G1, 2, 3, 4, 5, 6
8.G.1a, 1b, 1c, 2, 3, 4, 5, 6, 7, 8, 9
Ratios and Proportional Relationships
6.RP.1, 2, 3a, 3b, 3c, 3d
7.RP.1, 2a, 2b, 2c, 2d, 3
The Number System
6.NS.1, 2, 3, 4, 5, 6a, 6b, 6c, 7a, 7b, 7c, 7d, 8
7.NS.1a, 1b, 1c, 1d, 2a, 2b, 2c, 2d, 3
8.NS.1, 2,
Expressions and Equations
6.EE1, 2a, 2b, 2c, 3, 4, 5, 6, 7, 8, 9
7.EE.1, 2, 3, 4a, 4b
8.EE.1, 2, 3, 4, 5 ,6, 7a, 7b, 8a, 8b, 8c
Statistics and Probability
6.SP.1, 2, 3, 4, 5a, 5b, 5c, 5d
7.SP.1, 2, 3, 4, 5, 6, 7a, 7b, 8a, 8b, 8c
8.SP.1, 2, 3, 4
Functions 8.F.1, 2, 3, 4, 5
Five initial domains for professional development:•Grades K – 2 Counting and Cardinality
Numbers and Operations
•Grades K – 5 Operations and Algebraic Thinking•Grades 3 – 5 Number and Operations – Fractions•Grades 6 – 7 Ratios and Proportional Reasoning•Grade 8 – Geometry
ALL professional development should incorporate the Standards for Mathematical Practice
CCSS Mathematics Traditional Pathway HS Domains 7/2011
ConceptualCategory Domain Algebra I Geometry Algebra II Fourth
Course
Number and
Quantity
The Real Number System N.RN.1, 2, 3
Quantities N.Q. 1, 2, 3
The Complex Number System N.CN.1, 2, 7, (+)8, (+)9 (+)N.CN.3, 4, 5, 6
Vector and Matrix Quantities (+)N.VM.1, 2, 3, 4a, 4b, 4c, 5a, 5b, 6, 7, 8, 9, 10, 11, 12
Algebra
Seeing Structure in Expressions A.SSE.1a, 1b, 2, 3a, 3b, 3c
A.SSE.1a, 1b, 2, 4
Arithmetic with Polynomials and Rational Expressions
A.APR.1 A.APR.1, 2, 3, 4 (+)5, 6, (+)7
Creating Equations A.CED. 1, 2, 3, 4 A.CED.1, 2, 3, 4
Reasoning with Equations and Inequalities A.REI.I, 3, 4a, 4b, 5, 6, 7, 10, 11, 12
A.REI.2, 11 (+) A.REI. 8, 9
Functions and
Models
Interpreting Functions F.IF.1, 2, 3, 4, 5, 6, 7a, 7b, 7e, 8a, 8b, 9
F.IF.4, 5, 6, 7b, 7c, 7e, 8, 9
F.IF.7d
Building Functions F.BF.1a, 1b, 2, 3, 4a F.BF.1b, 3, 4a (+)F.BF.1c, 4c, 4d, 5
Linear, Quadratic and Exponential Models F.LE.1a, 1b, 1c, 2, 3, 5 F.LE.4
Trigonometric Functions F.TF.1, 2, 5, 8 (+)F.TF.3, 4, 6, 7, 9
Geometry
Congruence G.CO.1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13
Similarity, Right Triangles, and Trigonometry G.SRT.1a, 1b, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11
Circles G.C. 1, 2, 3, (+)4, 5
Expressing Geometric Properties with Equations G.GPE.1, 2, 4, 5, 6, 7 (+)G.GPE.3
Geometric Measurement and Dimension G.GMD.1, 3, 4 (+)G.GMD.2
Modeling with Geometry G.GMG.1, 2, 3
Statistics and
Probability
Interpreting Categorical and Quantitative Data S.ID.1, 2, 3, 5, 6a, 6b, 6c, 7, 8, 9
S.ID.4
Making Inferences and Justifying Conclusions S.IC.1, 2, 3, 4, 5, 6
Conditional Probabilities and the Rules of Probability S.CP.1, 2, 3, 4, 5, 6, 7, (+)8, (+)9
Using Probability to Make Decisions (+)S.MD.6, 7 (+)S.MD.6, 7 (+)S.MD.5a, 5b
•Implementation of Mathematical Practices
•Review the “Pathways” recommended in the CCSS Appendix A and determine which ones will best benefit your students
•Carefully consider the content in each course and use names that are most appropriate.
Necessary Nows
Immediate Implementations...
• Access the Common Core State Standards and support documents/resources created by DESE at http://www.dese.mo.gov/divimprove/curriculum/common-core-math.htm
• Identify common content within the v2.0 GLEs/CLEs and CCSS that may not be included in grades or courses now and include the content in instruction and assessment.
• Make it a priority to begin implementation of all Standards for Mathematical Practice in K – 12 mathematics classes.
• Implement the Kindergarten Mathematics CCSS during the 2011 – 2012 school year
Common Core Tools…
http://commoncoretools.wordpress.com/tools/• The Illustrative Mathematics Project• Progressions for the Common Core• Technical manual for the Common Core (Jason Zimba)• Hyperlinked version of the mathematics standards• K–8 Standards by domain: Counting and Cardinality,
Operations and Algebraic Thinking, Number and Operations in Base Ten, Number and Operations—Fractions, Measurement and Data, Geometry, Ratio and Proportional Relationships, The Number System, Expressions and Equations, Statistics and Probability, Functions.
Other:Connections to mathematical practices (processes and proficiencies) -- http://www.ted.com/talks/dan_meyer_math-curriculum_makeover.html
Questions?
Be watching on the DESE website for information regarding an upcoming Mathematics CCSS webinar for additional implementation information and resources for Missouri educators.
THANKS
Trish GoddardSWRPDCMathematics Content [email protected]