Common Core State Standards for Mathematics Overview Review of Common Core State Standards and Timelines Math Standards and Practices Next Steps and Resources

CCSS Implementation Process Awareness Transition Implementation AWARENESS AND DISSEMINATION Building Readiness for the New Standards SY 2010-11 TRANSITION Moving to the New Standards SY 2011-12, 2012-13 IMPLEMENTATION Putting Standards Into Practice SY 2013-14 INTENT: To illustrate the phases of implementation of Common Core Standards. Direct participants to the acronyms handout. CCSS (Common Core State Standards) is one of many acronyms that they will need to get used to. They may also see these referred to elsewhere as CCCS (California’s Common Core Standards) The state has established a timeline for the transition to Common Core. That doesn’t mean we are all in the same place on this journey, however. Thinking about your own system, where are you in this transition? California’s CCSS: Toolkit adapted by the Stanislaus County Office of Education

States Adopting Common Core Standards © Copyright 2010. National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved. INTENT: To provide information on the states that have adopted the CCSS As of August 2012, only four and a half* states have not adopted the CCSS (Alaska, Texas, Wisconsin, Nebraska, Virginia). This list includes the District of Columbia and the U.S. Virgin Islands. *Minnesota has adopted ELA but not math. Address the issue that this is grass roots effort initiated by the National Governors Association and Council of Chief State School Officers. It has been expedited by the inclusion of adoption as a requirement to compete for race to the top funds, but is not otherwise a federal initiative. California’s CCSS: Toolkit adapted by the Stanislaus County Office of Education

Why? To ensure that our students are… meeting college and career expectations (Text Complexity needs to be increased K-12); provided a vision of what it means to be an academically literate person in the twenty-first century; prepared to succeed in our global economy and society; and provided with rigorous content and applications of higher knowledge through higher order thinking skills. INTENT: To provide a background on why the new standards were written The standards were written to ensure that our students are: [click] meeting college and career expectations; While reading demands in college, workforce training programs, and life in general have held steady or increased over the last half century, K–12 texts have actually declined in sophistication, and relatively little attention has been paid to students’ ability to read complex texts independently. Furthermore, students in college are expected to read complex texts with substantially greater independence (i.e., much less scaffolding) than students in typical K–12 programs. [click] provided a vision of what it means to be an academically literate person in the twenty-first century; [click] prepared to succeed in our global economy and society; and Students must be prepared for both our domestic economy and, more so than ever before, for our global economy. [click] provided with rigorous content and applications of higher knowledge through higher order thinking skills. This means our students must master ever more rigorous content and be prepared to apply that content to succeed. 2011 © CA County Superintendents Educational Services Association California’s CCSS: Toolkit adapted by the Stanislaus County Office of Education

Benefits Internationally benchmarked Evidence and research-based Expectations clear to students, parents, teachers, and the general public Consistent expectations for all INTENT: To provide the benefits of the CCSS The standards were written to ensure that our students are: [click] Internationally benchmarked Competition. The CCSS are internationally benchmarked and will help ensure our students are globally competitive. [click] Evidence and research-based Preparation. The CCSS define the K-12 expectations for college and career readiness. They will help prepare students with the knowledge and skills needed to succeed in education and training after high school. If evidence could not be found that a standard is critical to college and careers, it did not make the final cut. Collaboration. The standards create a foundation to work collaboratively across states and districts, pooling resources and expertise, to create curricular tools, professional development, common assessments and other materials. [click] Expectations clear to students, parents, teachers, and the general public Clarity. The standards are focused, coherent, and clear. Clearer standards help students (and parents and teachers) understand what is expected of them. [click] Consistent expectations for all Equity. Expectations are consistent for all. California’s CCSS: Toolkit adapted by the Stanislaus County Office of Education

INTENT: To depict California’s timeline for the transition. This was taken from the CDE website. Updated 10/2012 California’s CCSS: Toolkit adapted by the Stanislaus County Office of Education

Underlying Frameworks National Council of Teachers of Mathematics 5 Process Standards Problem Solving Reasoning and Proof Communication Connections Representations Participants will probably be familiar with the process standards, so don’t spend time here. NCTM (2000). Principles and Standards for School Mathematics. Reston, VA: Author.

Underlying Frameworks Strands of Mathematical Proficiency Strategic Competence Adaptive Reasoning Conceptual Understanding Productive Disposition Procedural Fluency Mention that these build upon and expand NCTM Process Standards. Briefly mention inter-related nature of these proficiencies, then move to next slide that defines each of these proficiencies. Adding It Up:Helping Children Learn Mathematics National Research Council NRC (2001). Adding It Up. Washington, D.C.: National Academies Press.

Common Core State Standards Mathematics Standards Lead writers: Phil Daro, Bill McCallum, Jason Zimba, Writing teams Review teams Two rounds of public review and feedback 85% of State Standards must be CCSS California Standards indicated in standards Review information briefly. Although national professional organizations like NCTM, NCSM, MAA, ASSM and AMTE were not formally involved in the writing process, they had considerable input: Many of their members were members of the writing and review teams. The organizations provided formal review and feedback on each draft of the standards, as well as having input in between.

What’s different about CCSS? These Standards are not intended to be new names for old ways of doing business. They are a call to take the next step. It is time for states to work together to build on lessons learned from two decades of standards based reforms. It is time to recognize that standards are not just promises to our children, but promises we intend to keep. http://www.youtube.com/watch?v=BNP5MdDDFPY — CCSS (2010, p.5) Too often in the past, important components of NCTM Standards, such as the process standards, were voluntary for teachers to implement. Now, with CCSS, standard assessments are part of state’s adoptions of the standards. And, because those assessments will address all aspects of the standards, implementing these more challenging aspects of the standards will be mandatory, not volutary.

Two Types of Math Standards Math Content Standards Standards for Math Practice Vary by grade level and conceptual category Describe what students should know, understand, and be able to do at that grade level. Same eight standards common to all grade levels K-12 Capture: Mathematical processes Habits of mind and thinking skills specific to math INTENT: To signal transition to discussion of CCSS for Mathematics Common Core State Standards for Mathematics come in two categories. The Math Content Standards are different for each grade level and conceptual category and describe what students should know, understand, and be able to do at that grade level. Note that “conceptual categories” apply to high school only. The Standards for Mathematical Practice are the same eight standards at every grade level and describe the processes and habits of mind that students will engage in as they go about the business of learning mathematics. California’s CCSS: Toolkit adapted by the Stanislaus County Office of Education

Standards for Mathematical Practice Make sense of problems and persevere in solving them Reason abstractly and quantitatively Construct viable arguments and critique the reasoning of others Model with mathematics Use appropriate tools strategically Attend to precision Look for and make use of structure Look for and express regularity in repeated reasoning INTENT: To understand the Standards for Mathematical Practice as outlined in the CCSS These describe the varieties of expertise that educators should seek to develop in their students. Explain that there is a strong emphasis on student problem solving, reasoning and “practicing” mathematics. They carry across all grade levels; whether a student is in grade K or grade 12, the Standards for Mathematical Practice are the same. What will change is the level of sophistication with which students engage in the practices. Tools listed under # 5 practice include: paper and pencil, concrete models, ruler, protractor, calculator, spreadsheet, computer algebra system, statistical package, dynamic geometry software and digital content located on a website. HANDOUTS: CCSS for Mathematics spiral booklet 2011 © CA County Superintendents Educational Services Association California’s CCSS: Toolkit adapted by the Stanislaus County Office of Education

The Standards for Mathematical Practice #2 - Reason abstractly and quantitatively http://illustrativemathematics.org/standards/practice Insidemathematics.org (MARS Tasks) http://insidemathematics.org/index.php/exemplary-lessons-integrating-practice-standards Mathematics Practice 2 First Link: These videos show a student solving a problem using an approach that reflects the knowledge and skill described in 4.OA.3 and another student both solving the same problem but using the knowledge and skill described in 8.EE.8. In both cases, the students move fluidly between the context and the mathematics and back again. Second Link: Although the Common Core identifies eight standards of mathematical practice and Inside Mathematics highlights the ways in which all eight are evident in many different classrooms, teachers commonly engage their students in multiple practices simultaneously. These single clips demonstrate the students’ capacities in several practices.

Big Picture in Mathematics Standards of Mathematical Practice Grades K-5 Grades 6-8 8th Grade Options Core Standards to prepare for Algebra 1 Algebra 1 High School Math CCSS Grade Level Standards

Domains and Conceptual Categories Distribution INTENT: To understand how domains and conceptual categories are distributed across the grade levels This diagram illustrates how the domains are distributed across the CCSS. This diagram does not show how a domain may impact multiple domains in future grades. An example is K-5 Measurement and Data, which splits into Statistics and Probability and Geometry in grade 6. Likewise, Operations and Algebraic Thinking in K-5 provides a foundation for Ratios and Proportional Relationships, The Number System, Expressions and Equations, and Functions in grades 6-8. Findell & Foughty (2011) College and Career-Readiness through the Common Core State Standards for Mathematics California’s CCSS: Toolkit adapted by the Stanislaus County Office of Education

Design and Organization Critical areas at each grade level INTENT: To understand how focus was built into the Common Core State Standards for Mathematics Each grade level has 2-4 critical areas that are described on the introduction pages for each grade level. Note that these pages are not included in California’s version, not because they weren’t adopted on per se, but because they weren’t “acted on” by the Board of Education when the standards were adopted. California viewed these introductions as the kind of information that we typically include in our math curriculum framework. The content will likely be acted on with the adoption of the next framework which is expected in November 2013. We included the pages in our standards booklet because the information is critical to successful implementation of the Standards. For grades K-8, ask participants to find the introduction page for their grade level, or choose a specific grade level for all participants to view. Explain that each grade level has 2-4 critical areas. (2 critical areas for Kinder; 3 critical areas for grades 4, 5, 8; 4 critical areas at grades 1, 2, 3, 6, 7). They bring focus to the standards at each grade by grouping and summarizing the big ideas that educators can use to build their curriculum and to guide instruction.

Format of the Overview Domains: Overarching ideas that connect topics across the grades INTENT: To understand the structure of the CCSS for Mathematics Have participants turn to booklet p.18 of the CCSS for Mathematics spiral booklet. Point out the grade level and explain that the standards are organized into Domains and Clusters. The domains are: Operations and Algebraic Thinking Number and Operations in Base Ten Number and Operations – Fractions Measurement and Data Bulleted under each Domain are the Clusters. For example, there are between one and four clusters for each domain in grade 3. Note that Mathematical Practice Standards are on every overview page. Have participants turn to their specific grade level or conceptual cluster overview page (see below) and examine the domains, cluster headings, and mathematical practices. Note that Advanced Placement Probability and Statistics and Calculus do not have overview pages. HANDOUTS: CCSS for Mathematics Clusters: Illustrate the progression of increasing complexity from grade to grade California’s CCSS: Toolkit adapted by the Stanislaus County Office of Education

Format of the Standards INTENT: To understand the structure of the CCSS for Mathematics Inform participants that we will be looking at how to read the standards. Standards are located under the Domain and Cluster and define what each student should understand and be able to do. Clusters are groups of related standards. Note that standards from different clusters may sometimes be closely related because mathematics is a connected subject. Domains are larger groups of related standards. Standards from different domains may sometimes be closely related. Have participants locate booklet p. 20 in the CCSS for Mathematics handout and point out the Number and Operations Cluster, Use place value understanding and properties of operations to perform multi-digit arithmetic. Ask them to compare the cluster in their document to the cluster on the screen. Difference: Standard 1.1 is bold, italicized, and underlined. HANDOUTS: CCSS for Mathematics © Copyright 2010. National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved. California’s CCSS: Toolkit adapted by the Stanislaus County Office of Education

Smarter Balanced Assessments 2014 – First Smarter Balanced Assessment Performance Tasks Technology Enhanced / Constructed Responses http://sampleitems.smarterbalanced.org/itempreview/sbac/index.htm

Appendix A: Designing High School Mathematics Courses Based on the Common Core State Standards. There are 4 pathways outlined in Appendix A: The traditional approach (Algebra1, Geometry, Algebra II) The integrated approach (Mathematics I, II and III courses) The “compacted” traditional approach (completed grade 7&8 mathematics and Algebra 1 by the end grade 8). The “compacted” integrated approach (completed grade 7&8 mathematics and Mathematics I by the end of grade 8). High School: Traditional Pathway Two Algebra courses and a Geometry course, with some data, probability and statistics throughout each course. (More traditional approach) High School: Integrated Pathway A sequence of 3 courses each of which treats aspects of algebra, geometry and data, and probability, and statistics. (More integrated approach) Overview of Appendix A (page 2) Introduction to the 4 pathways and instructional implications (page 3-5) How to read the pathways (page 6-7) Pathways (traditional and integrated: pages 8-79) Compressed pathways introduction (pages 80-81) Pathways (compressed traditional and integrated: pages 82-146) Additional mathematics courses (page 147) References (page 148) 4/23/2017 24

High School Two Mathematics Pathways Courses in higher level mathematics: Precalculus, Calculus*, Advanced Statistics, Discrete Mathematics, Advanced Quantitative Reasoning, or courses designed for career technical programs of study. Algebra II Mathematics III Geometry Mathematics II INTENT: To understand two of the model course pathways for high school Distribute Pathways booklet to those who, by a show of hands, indicate they will likely need more in-depth information about high school math pathways. These should include middle school or high school math teacher leaders, administrators, curriculum coordinators, and district leaders. Briefly orient participants to the contents of the booklet. There are two mathematics pathways suggested in the Common Core documents. They can be found in Appendix A of the CCSS for Mathematics. [click] Traditional Pathway: An approach typically seen in the U.S. that consists of two Algebra courses and a Geometry course, with some data, probability, and statistics included in each course [click] Integrated Pathway: An approach typically seen internationally that consists of a sequence of three courses, each of which includes Algebra, Geometry, Probability, and Statistics [click] Both pathways lead to courses in higher level mathematics MATERIALS: Secondary Mathematics Course Pathways Resources booklet HS Algebra I Mathematics I TRADITIONAL Pathway (Typical in U.S.) 2 Algebra courses, 1 Geometry course, with Probability and Statistics interwoven INTEGRATED Pathway (Typical outside of U.S.) 3 courses that attend to Algebra, Geometry, and Probability and Statistics each year California’s CCSS: Toolkit adapted by the Stanislaus County Office of Education

Getting to Calculus Sooner: Two Compacted Pathways Jan. 16th document has additional information about this…Will have a better idea in March 2013 (Framework). Traditional Compacted Pathway: complete content of 7th, 8th, and HS Algebra I in grades 7 (Compacted 7th Grade) and 8 (8th Grade Algebra I) enabling them to finish Algebra II by the end of the sophomore year. Integrated Compacted Pathway: complete content of 7th, 8th, and Mathematics I in grades 7 (Compacted 7th Grade) and 8 (8th Grade Mathematics I), enabling them to complete Mathematics III by the end of the sophomore year INTENT: To understand the accelerated pathways for middle school found in Appendix A of the CCSS for Mathematics. [click] A “compacted” version of the Traditional pathway where no content is omitted, in which students would complete the content of 7th grade, 8th grade, and the High School Algebra I course in grades 7 (Compacted 7th Grade) and 8 (8th Grade Algebra I), which will enable them to reach Calculus or other college-level courses by their senior year. While the K-7 CCSS effectively prepare students for algebra in 8th grade, some standards from 8th grade have been placed in the Accelerated 7th Grade course to make the 8th Grade Algebra I course more manageable. [click] A “compacted” version of the Integrated pathway where no content is omitted, in which students would complete the content of 7th grade, 8th grade, and the Mathematics I course in grades 7 (Compacted 7th Grade) and 8 (8th Grade Mathematics I), which will enable them to reach Calculus or other college-level courses by their senior year. While the K-7 CCSS effectively prepare students for algebra in 8th grade, some standards from 8th grade have been placed in the Accelerated 7th Grade course to make the 8th Grade Mathematics I course more manageable. [click] Both pathways will prepare students for precalculus in their junior year and Calculus in their senior year. NOTES: The grade 8 CCSS course is not a remedial course. It is a course that contains rich mathematics and is not aligned to the California Algebra Readiness Program currently designed for grades 8 and above. The SMARTER Balanced Consortium is creating assessments for the 8th grade CCSS Course and not the 8th grade Algebra 1 Course that was designed by California. California’s CCSS: Toolkit adapted by the Stanislaus County Office of Education

2013 Mathematics Framework In July 2012, SBE approved the guidelines that will direct the work of the Mathematics Framework committee. The direction to the committee includes: A discussion of options for middle school acceleration to support Algebra I or Integrated Mathematics I prior to ninth grade, consistent with other Common Core states. Will be finalized in March 2013 Framework. Guidance on assessing students’ readiness for Algebra I or Integrated Mathematics I. Suggested courses for both Traditional (Algebra I, Geometry, Algebra II) and Integrated (Integrated Mathematics I, II, III) high school mathematics pathways consistent with other Common Core states. Handout The Algebra I course will be composed of the Common Core State Standards in place of the unique California Grade 8 Algebra I standards. The content of the CCSS-based Algebra I course will be the same regardless of the grade level at which it is taught. INTENT: To understand the guidelines that will direct the work of the Mathematics Framework Committee For more information about the 2013 Mathematics Framework, visit http://www.cde.ca.gov/ci/ma/cf/index.asp California’s CCSS: Toolkit adapted by the Stanislaus County Office of Education

Implementing CCSS Challenge: Recognizing that CCSS are not “business as usual” and decisions need to be made. Providing assistance to teachers in the Mathematical Practices. Textbooks materials available on a limited basis before the first assessments. The where not to start— Aligning grade by grade de-emphasizes the standards progressions across grades, which are key aspects of the standards. Even though many states did such alignments as part of their adoption process, that does not mean that districts or schools should do that as well. Instead, a good starting point is to lead with the mathematical practices.

Senate Bill 1200 (Hancock) Authorizes the state board to modify California’s Common Core Standards on or before March 20, 2013 such that: One set of standards is adopted at each grade level The content standards for algebra 1 are based upon the common core academic content standards for mathematics Modifications to the common core academic content standards in mathematics will be incorporated into the curriculum framework for mathematics Intent: Provide information about SB-1200 (Hancock) Academic content standards For the full text of the bill, visit http://www.leginfo.ca.gov/pub/11-12/bill/sen/sb_1151-1200/sb_1200_bill_20120824_amended_asm_v92.html The bill also requires: The Superintendent to consult a specified group of experts in mathematics for purposes of developing the recommendations. A minimum of 2 public hearings in order for the public to provide input on the Superintendents recommendations. The adoption of the College and Career Readiness Anchor Standards. California’s CCSS: Toolkit adapted by the Stanislaus County Office of Education

Getting Started with CCSS Suggested First Implementation Steps: Mathematical practices Progressions within and among content clusters and domains – alignment of instructional materials Assessments – SBAC Decision about Pathways Prepare to look critically at Instructional Materials