Common Core State Standards Math
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In this math Common Core State Standards training, participants will learn to recognize the structure of the Common Core State Standards (CCSS) in Mathematics, identify the shifts represented in the CCSS and consider implications and implementation plans.
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Common Core State Standards Math
- 1. …to the CORE! 6-12 Mathematics Teacher University May 25, 2012 Dr. Marci Shepard Orting School District Teaching, Learning & Assessment May 2012
- 2. A Picture of Our Day of Learning Dr. Marci Shepard Orting School District Teaching, Learning & Assessment May 2012
- 3. Learning Target We are building awareness and gaining familiarity with the Common Core State Standards and assessment. • Recognize the structure of the Common Core State Standards (CCSS) in Mathematics • Identify the shifts represented in the CCSS • Consider implications and implementation plans for OSD Dr. Marci Shepard Orting School District Teaching, Learning & Assessment May 2012
- 4. Common Core State Standards - Mathematics Dr. Marci Shepard Orting School District Teaching, Learning & Assessment May 2012
- 5. Placemats Dr. Marci Shepard Orting School District Teaching, Learning & Assessment May 2012
- 6. Mathematics Standards for Mathematical Practice Carry across all grade levels Describe habits of mind of a mathematically expert students Standards for Mathematical Content K-8 standards represented by grade level, organized into domains that progress over several grades 2-4 Focal points at each grade level High school standards represented by conceptual themes (Number & Quantity, Algebra, Functions, Modeling, Geometry, Statistics & Probability) Dr. Marci Shepard Orting School District Teaching, Learning & Assessment May 2012
- 7. Mathematics Standards for Mathematical Practice Carry across all grade levels Describe habits of mind of a mathematically expert students Page 6 Dr. Marci Shepard Orting School District Teaching, Learning & Assessment May 2012
- 8. Standards for Mathematical Practice Dr. Marci Shepard Orting School District Teaching, Learning & Assessment May 2012
- 9. Mathematics Standards for Mathematical Practice Carry across all grade levels Describe habits of mind of a mathematically expert students Standards for Mathematical Content K-8 standards represented by grade level, organized into domains that progress over several grades 2-4 Focal points at each grade level High school standards represented by conceptual themes (Number & Quantity, Algebra, Functions, Modeling, Geometry, Statistics & Probability) Dr. Marci Shepard Orting School District Teaching, Learning & Assessment May 2012
- 10. Content Progressions and Major Shifts Major Shifts Focus Coherence Application • Fewer big ideas -- • Articulated progressions of • Being able to - learn more topics and performances apply concepts • Learning of that are developmental and and skills to new concepts is connected to other situations emphasized progressions Dr. Marci Shepard Orting School District Teaching, Learning & Assessment May 2012
- 11. Critical Areas in Mathematics PRIORITIES in Support of Rich Instruction and Grade Expectations of Fluency and Conceptual Understanding Addition and subtraction, measurement using K–2 whole number quantities Multiplication and division of whole numbers 3–5 and fractions Ratios and proportional reasoning; early 6 expressions and equations Ratios and proportional reasoning; arithmetic 7 of rational numbers 8 Linear algebra Dr. Marci Shepard Orting School District Teaching, Learning & Assessment May 2012
- 12. High School Dr. Marci Shepard Orting School District Teaching, Learning & Assessment May 2012
- 13. Organization of the Standards Dr. Marci Shepard Orting School District Teaching, Learning & Assessment May 2012
- 14. Format of K-8 Standards Grade Level Domain Standard Cluster Dr. Marci Shepard Orting School District Teaching, Learning & Assessment May 2012
- 15. Cross-cutting Grade Level Introduction themes Critical Area of Focus Dr. Marci Shepard Orting School District Teaching, Learning & Assessment May 2012
- 16. Grade Level Overview Grade 4 Overview Mathematical Practices Operations and Algebraic Thinking 1. Make sense of problems and Use the four operations with whole numbers to solve problems. persevere in solving them Gain familiarity with factors and multiples. 2. Reason abstractly and Generate and analyze patterns. quantitatively Number and Operations in Base Ten 3. Construct viable arguments Generalize place value understanding for multi-digit whole and critique the reasoning of numbers. others Use place value understanding and properties of operations to perform multi-digit arithmetic. 4. Model with mathematics Number and Operations—Fractions 5. Use appropriate tools Extend understanding of fraction equivalence and ordering. strategically Build fractions from unit fractions by applying and extending 6. Attend to precision previous understandings of operations on whole numbers. Understand decimal notation for fractions, and compare decimal 7. Look for and make use of fractions. structure Measurement and Data 8. Look for and express Solve problems involving measurement and conversion of regularity in repeated measurements from a larger unit to a smaller unit. reasoning Represent and interpret data. Geometric measurement: understand concepts of angle and measure angles. Geometry Draw and identify lines and angles, and classify shapes by properties of their lines and angles. Dr. Marci Shepard Orting School District Teaching, Learning & Assessment May 2012
- 17. CCSS for High School Mathematics • Organized in “Conceptual Categories” ▫ Number and Quantity ▫ Algebra ▫ Functions ▫ Modeling ▫ Geometry ▫ Statistics and Probability • Conceptual categories are not courses • Additional mathematics for advanced courses indicated by (+) • Standards with connections to modeling indicated by (★) Dr. Marci Shepard Orting School District Teaching, Learning & Assessment May 2012
- 18. Format of High School Standards Domain Cluster Standard Advanced Dr. Marci Shepard Orting School District Teaching, Learning & Assessment May 2012
- 19. Format of Standards Dr. Marci Shepard Orting School District Teaching, Learning & Assessment May 2012
- 20. Conceptual Category Introduction Dr. Marci Shepard Orting School District Teaching, Learning & Assessment May 2012
- 21. Conceptual Category Overview Domain Cluster Dr. Marci Shepard Orting School District Teaching, Learning & Assessment May 2012
- 22. High School Conceptual Categories • Numbers and quantities • Algebra • Functions • Geometry • Statistics and probability Dr. Marci Shepard Orting School District Teaching, Learning & Assessment May 2012
- 23. High School Mathematical Pathways Typical in U.S. • Two main pathways: ▫ Traditional: Two algebra courses and a geometry course, with statistics and probability in each ▫ Integrated: Three courses, each of which includes algebra, geometry, statistics, and probability Typical • Both pathways: outside U.S. ▫ Complete the Common Core in the third year ▫ Include the same “critical areas” ▫ Require rethinking high school mathematics ▫ Prepare students for a menu of fourth-year courses Dr. Marci Shepard Orting School District Teaching, Learning & Assessment May 2012
- 24. Two Main Pathways Dr. Marci Shepard Orting School District Teaching, Learning & Assessment May 2012
- 25. Pathway Overview Dr. Marci Shepard Orting School District Teaching, Learning & Assessment May 2012
- 26. Course Overview: Critical Areas (units) Dr. Marci Shepard Orting School District Teaching, Learning & Assessment May 2012
- 27. Course Detail by Unit (critical area) Dr. Marci Shepard Orting School District Teaching, Learning & Assessment May 2012
- 28. Dr. Marci Shepard Orting School District Teaching, Learning & Assessment May 2012
- 29. May 2012 Dr. Marci Shepard Orting School District Teaching, Learning & Assessment May 2012
- 30. Before… Dr. Marci Shepard Orting School District Teaching, Learning & Assessment May 2012
- 31. After… Dr. Marci Shepard Orting School District Teaching, Learning & Assessment May 2012
- 32. 2010-2011 Training for PowerStandards • K-5 math • 6-8 Math • Algebra & Geometry • 9-12 ELA Communication • Instructional Council • Key Communicator • PD/Meetings Dr. Marci Shepard Orting School District Teaching, Learning & Assessment May 2012
- 33. 2011-2012 CCSS Workgroup • Overview for all • Math • ELA • Implementation planning OSPI/ESD Trainings • Marci and teachers attend 2-day math training • Marci and teachers attend 2-day ELA training Teacher University • Provided printed standards • Overview of standards and assessment Communication • Teacher University • OSD Website • Key Communicator • Twitter • Presentation to the school board • Teacher meeting with Superintendent • Instructional Council • PD/Meetings Dr. Marci Shepard Orting School District Teaching, Learning & Assessment May 2012
- 34. 2012-2013 Math Transition OPS • K-Counting and Cardinality (CC); Operations and Algebraic Thinking (OA) • 1&2-Operations and Algebraic Thinking (OA); Number and Operations in Base Ten (NBT) PtR • Number and Operations- Fractions (NF); Operations and Algebraic Thinking (OA) OMS • 6&7-Ratio and Proportion Relationship (RP); Number System (NS); Expressions and Equations (EE) • 8-Number System (NS); Expressions and Equations (EE); Functions (F) OHS • Algebra 1&Geometry-Unit 1; Unit 2; Unit 4 Dr. Marci Shepard Orting School District Teaching, Learning & Assessment May 2012
- 35. Math Transition 2013-2014 OPS • Measurement and Data (MD); Geometry (G) PtR • Number and Operations in Base Ten (NBT); Measurement and Data (MD) OMS • Geometry (G); Statistics and Probability (SP) OHS • Algebra 1-Unit 3; Unit 5 • Geometry – Unit 3, Unit 5; Unit 6 Dr. Marci Shepard Orting School District Teaching, Learning & Assessment May 2012
- 36. Full Implementation 2014-2015 Math Transition • All domains Dr. Marci Shepard Orting School District Teaching, Learning & Assessment May 2012
- 37. ELA Transition 2012-2013 ELA teachers (K-5 & 6-12) • Foundational Skills (K-5) • Reading Standards – Literary and Informational • Language Standards #4-6 – Vocabulary Acquisition and Use • And… Other content area teachers (6-12) • College and Career Readiness (CCR) Anchor Standards for Reading & Reading Standards for Literacy in the content areas • Emphasis on #10 – Text Complexity • Emphasis on #4 – Academic Vocabulary Dr. Marci Shepard Orting School District Teaching, Learning & Assessment May 2012
- 38. 2013-2014 ELA Transition ELA teachers (K-5 & 6-12) • Writing Standards • Language Standards #1-3 – Conventions of Standard English • Speaking and Listening Standards • And… Other content area teachers (6-12) • College and Career Readiness (CCR) Anchor Standards for Writing & Writing Standards for Literacy in the content areas • Emphasis on #1 – Arguments focused on discipline-specific content • Reading #10 – Balance of informational and literary texts Dr. Marci Shepard Orting School District Teaching, Learning & Assessment May 2012
- 39. Full Implementation 2014-2015 Math Transition • All domains ELA Transition ELA teachers • All reading, writing, language and speaking & listening standards 6-12 Other content area teachers • All CCR Reading standards • All CCR Writing standards Dr. Marci Shepard Orting School District Teaching, Learning & Assessment May 2012
- 40. Technology and Multi-Media Skills 2012-2013 Develop a K-12 skills continuum Dr. Marci Shepard Orting School District Teaching, Learning & Assessment May 2012
- 41. Full Implementation 2014-2015 Math Transition • All domains ELA Transition ELA teachers • All reading, writing, language and speaking & listening standards 6-12 Other content area teachers • All CCR Reading standards • All CCR Writing standards Technology/Multi-media Skills All teachers • Incorporate technology and multi-media to gather, research, develop and publish information Dr. Marci Shepard Orting School District Teaching, Learning & Assessment May 2012
- 42. Recommended PD 2012-2013 K-5 • 1-2 days release time for CCSS mathematics shift • PLC Facilitators meet 5 times (4 reading topics and 1 language) then lead learning in PLCs • IA’s join PLCs when it’s a literacy focus 6-12 • 1-2 days release time for ELA and Math teachers All teachers (TU): • CCR Reading – focus on text complexity and academic vocabulary Dr. Marci Shepard Orting School District Teaching, Learning & Assessment May 2012
- 43. Recommended PD 2013-2014 K-5 • 1-2 days release time for CCSS mathematics shift • PLC Facilitators meet times (4 writing topics, 1 language and 1 speaking & listening) then lead learning in PLCs • IA’s join PLCs when it’s a literacy focus 6-12 • 1-2 days release time for ELA and Math teachers All teachers: • CCR writing – focus on arguments and balance of literary & information texts Dr. Marci Shepard Orting School District Teaching, Learning & Assessment May 2012
- 44. 2012-2013 2013-2014 2014-2015 ELA Teachers Foundational Skills (K-5) Writing Standards • All reading, K-5 & Reading Standards – Literary and Informational Language Standards #1-3 – Conventions of Standard writing, language 6-12 Language Standards #4-6 – Vocabulary Acquisition and English and speaking & Use Speaking and Listening Standards listening And “other content area teachers” And “other content area teachers” standards Other Content • College and Career Readiness (CCR) Anchor • College and Career Readiness (CCR) Anchor • All CCR Reading Teachers Standards for Reading & Reading Standards for Standards for Writing & Writing Standards for standards Literacy in the content areas Literacy in the content areas • All CCR Writing • Emphasis on #10 – Text Complexity • Emphasis on #1 – Arguments focused on standards • Emphasis on #4 – Academic Vocabulary discipline-specific content • Emphasis on Reading #10 – Balance of informational and literary texts Math OPS OPS • All domains • K-Counting and Cardinality (CC); Operations and • Measurement and Data (MD); Geometry (G) Algebraic Thinking (OA) PtR • 1&2-Operations and Algebraic Thinking (OA); • Number and Operations in Base Ten (NBT); Number and Operations in Base Ten (NBT) Measurement and Data (MD) PtR OMS Number and Operations-Fractions (NF); Operations and • Geometry (G); Statistics and Probability (SP) Algebraic Thinking (OA) OHS OMS • Algebra 1-Unit 3; Unit 5 6&7-Ratio and Proportion Relationship (RP); Number • Geometry – Unit 3, Unit 5; Unit 6 System (NS); Expressions and Equations (EE) 8-Number System (NS); Expressions and Equations (EE); Functions (F) OHS Algebra 1&Geometry-Unit 1; Unit 2; Unit 4 Technology and Develop a K-12 skills continuum • Incorporate Multi-Media technology and Skills multi-media to gather, research, develop and Dr. Marci Shepard Orting School District Teaching, Learning & Assessment May 2012 publish information
- 45. OSD Website Dr. Marci Shepard Orting School District Teaching, Learning & Assessment May 2012
- 46. Dr. Marci Shepard Orting School District Teaching, Learning & Assessment May 2012
- 47. Wrap up: Go-around and share one word… I’m feeling _________________ to the CORE! Dr. Marci Shepard Orting School District Teaching, Learning & Assessment May 2012
Notas do Editor
- Handouts: Content Progressions & Shifts slideMathematical Practices slideMath Practices descriptionsThis slide up as groups report.
- Handouts: Content Progressions & Shifts slideMathematical Practices slideMath Practices descriptionsThis slide up as groups report.
- Handouts: Content Progressions & Shifts slideMathematical Practices slideMath Practices descriptionsThis slide up as groups report.
- These critical areas in K-8 mathematics are intended to establish a firm foundation for high school algebraGreat implications on instructional practice – many instructional materials are surface and don’t provide the depth of practiceApproach mathematics in a different way – dive deep into a core area to develop habits of mind in those areas versus rushing through materialsWhat does critical area mean? Focus DAILY on the 2-4 focal point areas.
- HS
- Each K-8 grade is made up of domains, clusters and standards.Domain names are in the shaded band; overarching ideas that continue across multiple grades; illustrates a progression of increasing complexity Clusters are underneath in bold with the standards numbered under each of the clusters; describes the big idea of a group of related standardsStandards are numbered and describe what students should know and be able to do at each grade level
- (Each grade in K-8 begins with an Introduction.These introductions identify the critical areas, which cut across topics, in the gradeThe numbered description of each critical area illustrates the focus for the learning.
- The second page of each grade is an Overview. It identifies the domains and clusters in that grade also reminding readers of the mathematical practices.
- High school has an added level in the hierarchy – the Conceptual Category. These Conceptual Categories are: Number and Quantity, Algebra, Functions, Geometry, Statistics and Probability and Modeling. Modeling actually does not have Standards; it is embedded within the other Conceptual Categories. Standards connected to Modeling are indicated by asterisks. Conceptual Categories are not courses. Standards marked with a plus sign are standards that are necessary for advanced mathematics. This means that any student who intends to pursue advanced mathematics needs these experiences.
- Within each Conceptual Category the structure parallels K-8. There are Domains or big ideas. The bolded statements are the Clusters. The Standards are numbered and further describe the Cluster. An added element is the (+) standards which identify standards that are needed for advanced study. They are not intended to be required for all students.
- Like the K-8 grade level introduction, the Conceptual Category Introduction describes the mathematics within the Conceptual Category and places that mathematics within the K-16 perspective.
- The Conceptual Category Overview serves as an outline of the conceptual category, listing the domains with their clusters, and reminding readers of the mathematical practices.
- An Achieve committee organized the high school standards into course sequences.
- Each Pathway prepares students for a menu of fourth-year courses such as:Pre-calculus (or AP Calculus)AP StatisticsDiscrete MathematicsAdvanced Quantitative ReasoningAnd courses designed for particular career technical pathways
- Each of the Pathways has an overview that details the content addressed in each course. The columns represent each course with the related domains, clusters and standards.
- The critical areas are fleshed out as the units within each course. The overview By the end of the third course in each pathway, all of the critical areas have been addressed.
- Unit details are elaborated with the addition of unit overviews containing instructional notes. These notes are seen in italics and further clarify the related clusters and standards.