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 Practice 1.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 Counting and Cardinality K.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, 55.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, 31.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, 32.G.1, 2, 33.G.1, 24.G.1, 2, 35.G1, 2, 3, 46.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 Conceptual Category Domain Algebra I GeometryAlgebra IIFourth 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 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, 4aF.BF.1b, 3, 4a(+)F.BF.1c, 4c, 4d, 5 Linear, Quadratic and Exponential Models F.LE.1a, 1b, 1c, 2, 3, 5F.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.5a, 5b

CCSS/v2.0 GLEs Alignment Analysis DomainCCSS Cluster/Standards Missouri v2.0 GLE CCSS Alignment to v2.0 GLE/CLE Counting and Cardinality (CC) K.CC1 Count 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 K12 Below 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 N1AK N1DK N3BK N1A1 N1D1 N3BK A3AK N1A1 Operations and Algebraic Thinking N1CK A3AK N2A1 A2A1 A3A1 N3C2 A3A2 N3B2 N1C1 A2B1 N1D1A3A2 N1D3 N2A3 N1C1 N3B1 N3C1 N1C1

CCSS/v2.0 GLEs Alignment Analysis DomainCCSS 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 (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 GLE Bold underlined portion of the CCSS represents content/processes/procedures that do not align with any GLEs/CLEs.

DOMAINCCSSv2.0 GLE/CLECCSS Content not addressed in GLEs/CLEs Numbers and Operations- Fractions (NF) 3.NF.1, 2a, 2b, 3a, 3b, 3c, 3d N1C3, N2A3 N1B4 N1A5, 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. DOMAIN  CCSS MO 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.2 K.CC.3 K.CC.4b, 4c K.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 Counting and Cardinality K.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, 55.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, 31.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, 32.G.1, 2, 33.G.1, 24.G.1, 2, 35.G1, 2, 3, 46.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 Conceptual Category Domain Algebra I GeometryAlgebra IIFourth 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 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, 4aF.BF.1b, 3, 4a(+)F.BF.1c, 4c, 4d, 5 Linear, Quadratic and Exponential Models F.LE.1a, 1b, 1c, 2, 3, 5F.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.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 core-math.htm 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… 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.Counting and CardinalityOperations and Algebraic ThinkingNumber and Operations in Base TenNumber and Operations— FractionsMeasurement and DataGeometryRatio and Proportional RelationshipsThe Number SystemExpressions and EquationsStatistics and ProbabilityFunctions Other: Connections to mathematical practices (processes and proficiencies) --

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 Goddard SWRPDC Mathematics Content Specialist