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**Transitioning to the Common Core Trinity County Office of Education**

August 15, 2012 Mathematics TIME: 1 minute (for Slides 1 to 2) INTENT: To provide: 1) an overview of California’s Common Core State Standards for English Language Arts & Literacy in History/Social Studies, Science, and Technical Subjects (CCSS for ELA) and California’s Common Core State Standards for Mathematics (CCSS for Mathematics); and 2) cover the basic design, benefits, and major shifts in the new common core state standards AUDIENCE: Educators including district and site administrators, teachers, paraprofessionals, etc. MODULE TIME: 3 hours Welcome and Agenda – 1 minute (Slides 1-2) CCSS Overview – 15 minutes (Slides 3-8) ELA & Literacy in History/Social Studies, Science, and Technical Subjects – 109 minutes (Slides 9-39) Mathematics – 45 minutes (40-57) Assessment and Closing – 10 minutes (Slides 58-63) HANDOUTS: CCSS KWL Chart CCSS for ELA CCSS for ELA College and Career Readiness (CCR) Anchor Standards CCSS for Mathematics Common Core Standards for California: Organization The 3 Big Buckets of Writing VIDEOS: Shampton_CCS_Goals.mp4 ACTIVITY MATERIALS (may require preparation in advance): CCR Anchor Standards cards (copy and cut cards in advance) California’s Common Core State Standards: Toolkit | Overview

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**Agenda Welcome and Agenda Review Warm-Up Activity Introduction - CCSS**

CCSS Math – Standards Design CCSS Math – Practice and Instruction CCSS Math – Materials and Alignment Assessment Planning for Implementation TIME: 1 minute (CONTINUED for Slides 1 to 2) INTENT: To provide an overview of the module content ___________________________________________________________________________________ Review the slide. California’s Common Core State Standards: Toolkit | Overview

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**Binder Resources CISC Math Powerpoint**

Standards for Mathematical Practice Facilitating Mathematical Thinking with Effective Questions Questions for Planning and Observation SBAC Powerpoint Sample SBAC Assessment Items Article: “Teaching in Grades 3 and 4: How is each Common Core State Standard different from each old objective?” Article: “10 Practical Tips for Making Fractions Come Alive and Make Sense” California Common Core State Standards – Math

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**Handouts Standards for Mathematical Practice (laminated)**

Facilitating Mathematical Thinking with Effective Questions (laminated) Activity Worksheets: Table Pattern Task, Grade Level Tasks, Next Steps CCSS Standards Implementation Worksheet

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**English Learners and the Common Core State Standards**

The toolkit is an introduction and guide to initial implementation. Additional intentional support for English learners is critical. Work grounded in the revised English Language Development (ELD) standards will be necessary. TIME: 3 minutes (for Slide 3) INTENT: To explain that while it is not explicitly addressed in the toolkit, intentional work in support of English learners is required ___________________________________________________________________________________ Address with participants that work beyond the scope of this document will be necessary to ensure that English learners successfully master the Common Core State Standards. The California English Language Development (ELD) Standards are being revised and aligned to the Common Core State Standards for English Language Arts and to reflect current research in English language development instruction. Future work should be grounded in these revised ELD standards. INSTRUCTOR NOTE: This toolkit provides an introduction and guide to initial implementation of the CCSS. It does not explicitly address the instructional needs of English learners. However, experts in the education of English learners were involved in the development of the CCSS for English language arts. These individuals assisted in shaping the standards in general and had a significant impact on the language and vocabulary standards. While this toolkit does address some instructional strategies that may be appropriate for English learners, more work specific to their needs will be necessary. California’s Common Core State Standards: Toolkit | Overview

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**KWL Chart What I already KNOW about the Common Core State Standards**

What I WOULD like to learn about the Common Core State Standards What I LEARNED about the Common Core State Standards TIME: 12 minutes (for Slides 4 to 8) INTENT: To provide a reflection of what participants know and would like to learn about CCSS ___________________________________________________________________________________ Ask participants to locate the CCSS KWL Chart handout. Explain the KWL Chart: K stands for what participants already Know W stands for what participants Would like to learn L stands for what participants have Learned Ask participants to complete the first two columns on their own. You may want to ask participants to share what they would like to learn with the whole group. This will let you, as the Instructor, know the needs of your group and be able to best address them during the presentation. HANDOUTS: CCSS KWL Chart 2011 © CA County Superintendents Educational Services Association California’s Common Core State Standards: Toolkit | Overview

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States that Adopted © Copyright National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved. TIME: 12 minutes (CONTINUED for Slides 4 to 8) INTENT: To provide information on the states that have adopted the CCSS ___________________________________________________________________________________ As of November 2011, only five states have not adopted the CCSS. This list includes the District of Columbia and the U.S. Virgin Islands. California’s Common Core State Standards: Toolkit | Overview

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**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. TIME: 12 minutes (CONTINUED for Slides 4 to 8) 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 Common Core State Standards: Toolkit | Overview

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**Benefits Internationally benchmarked Evidence and research-based**

Expectations clear to students, parents, teachers, and the general public Consistent expectations for all TIME: 12 minutes (CONTINUED for Slides 4 to 8) 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. 2011 © CA County Superintendents Educational Services Association California’s Common Core State Standards: Toolkit | Overview

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**Heart and Soul ELA College and Career Readiness Anchor Standards**

Mathematics Standards for Mathematical Practice TIME: 12 minutes (CONTINUED for Slides 4 to 8) INTENT: To understand two very important parts of the CCSS: 1) CCR Anchor Standards and 2) Standards for Mathematical Practice ___________________________________________________________________________________ The CCR Anchor Standards and Standards for Mathematical Practice are the heart and soul of the CCSS. This training is designed to deepen participants understanding of these standards. 2011 © CA County Superintendents Educational Services Association California’s Common Core State Standards: Toolkit | Overview

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**Lexile Framework © for Reading Study Summary of Text Lexile Measures**

Interquartile Ranges Shown (25% - 75%) 1600 1400 1200 Text Lexile Measure (L) TIME: 10 minutes (CONTINUED for Slides 20 to 24) ___________________________________________________________________________________ Click through the Lexile measures for the various text types. [click] High School Literature [click] College Literature [click] High School Textbooks [click] College Textbooks [click] Military [click] Personal Use [click] Entry-Level Occupations [click] SAT 1, ACT, AP Point out that some career and personal use texts have a higher lexile than college texts. Note for participants the readability level for entry level positions. (Provide examples from personal experience.) [click] Tell participants 1200 is considered the minimum lexile reading level needed for every citizen to achieve. 1000 800 600 High School Literature College Literature High School Textbooks College Textbooks Military Personal Use Entry-Level Occupations SAT 1, ACT, AP* * Source of National Test Data: MetaMetrics California’s Common Core State Standards: Toolkit | Overview

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**5th Grade Collaborative Conversations**

Engage effectively in collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners, building on others’ ideas and expressing one’s own clearly. Come to discussions prepared, having read or studied required material; explicitly draw on that preparation and other information known about the topic to explore ideas under discussion. Follow agreed-upon rules for discussions and carry out assigned roles. Pose and respond to specific questions by making comments that contribute to the discussion and elaborate on the remarks of others. Review the key ideas expressed and draw conclusions in light of information and knowledge gained from discussions. TIME: 5 minutes (CONTINUED for Slides 36 to 37) ___________________________________________________________________________________ Here is a sample Speaking and Listening standard for 5th grade. This is similar to the norms that are set in academic and professional communities. Each aspect of this statement supports the key foundations for effective and productive collaborative discussion. Note the appropriateness of the standard for a wide variety of academic and work environments students will enter into. 2011 © CA County Superintendents Educational Services Association California’s Common Core State Standards: Toolkit | Overview

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**Integrating Media Sources**

Reading Standards for Informational Text, Grade 6 7. Integrate information presented in different media or formats (e.g., visually, quantitatively) as well as in words to develop a coherent understanding of a topic or issue. Writing Standards, Grade 6 6. Use technology, including the Internet, to produce and publish writing as well as to interact and collaborate with others; demonstrate sufficient command of keyboarding skills to type a minimum of three pages in a single sitting. TIME: 5 minutes (CONTINUED for Slides 38 to 39) ___________________________________________________________________________________ Tell participants that research and media skills are blended into the Standards as a whole. Paraphrase the following paragraph from the CCSS Introduction, p. 4: To be ready for college, workforce training, and life in a technological society, students need the ability to gather, comprehend, evaluate, synthesize, and report on information and ideas, to conduct original research in order to answer questions or solve problems, and to analyze and create a high volume and extensive range of print and nonprint texts in media forms old and new. The need to conduct research and to produce and consume media is embedded into every aspect of today’s curriculum. In like fashion, research and media skills and understandings are embedded throughout the Standards rather than treated in a separate section.1 As demonstrated in these Grade 6 examples, the use of media sources is integrated across the strands. Take a moment to read the example standards. These are only a few examples from Grade 6. It is important to note that there are numerous examples of integration of media sources within each grade level across the strands. 1National Governors Association Center for Best Practices and Council of Chief State School Officers (2010). Common Core State Standards for ELA. 2011 © CA County Superintendents Educational Services Association California’s Common Core State Standards: Toolkit | Overview

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**Standards for Mathematical Practice**

“The Standards for Mathematical Practice describe varieties of expertise that mathematics educators at all levels should seek to develop in their students. These practices rest on important ‘processes and proficiencies’ with longstanding importance in mathematics education.” National Governors Association Center for Best Practices and Council of Chief State School Officers (2010) Common Core State Standards for Mathematics TIME: 8 minutes (CONTINUED for Slides 40 to 43) INTENT: To introduce participants to the CCSS for Mathematics Standards for Mathematical Practice and understand the two frameworks from which the standards were written ___________________________________________________________________________________ Read the quote. Emphasize that the Standards for Mathematical Practice are the processes and proficiencies that mathematics educators are seeking to develop in their students. The new Standards for Mathematical Practice were based partly on two frameworks: National Council of Teachers of Mathematics (NCTM)—Principles and Standards for School Mathematics National Research Council—Adding It Up: Helping Children Learn Mathematics California’s Common Core State Standards: Toolkit | Overview

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**Underlying Frameworks National Council of Teachers of Mathematics**

Five Process Standards Problem Solving Reasoning and Proof Communication Connections Representations TIME: 8 minutes (CONTINUED for Slides 40 to 43) ___________________________________________________________________________________ Explain that the Principles and Standards for School Mathematics1 focus on five process standards. [click] Problem Solving: Problem solving should be an integral part of mathematics, not just an isolated piece of the mathematics program. By solving mathematical problems, students acquire ways of thinking, habits of persistence and curiosity, and confidence in unfamiliar situations that serve them well both inside and outside the classroom. [click] Reasoning and Proof: Mathematical reasoning and proof offer powerful ways of developing and expressing insights about a wide range of phenomena. People who reason and think analytically tend to note patterns, structure, or regularities in both real-world and mathematical situations. [click] Communication: Mathematical communication is a way of sharing ideas and clarifying understanding. When students are challenged to communicate the results of their thinking to others orally or in writing, they learn to be clear, convincing, and precise in their use of mathematical language. [click] Connections: Mathematics is an integrated field of study. When students connect mathematical ideas, their understanding is deeper and more lasting, and they come to view mathematics as a coherent whole. They see mathematical connections in the rich interplay among mathematical topics, in contexts that relate mathematics to other subjects, and in their own interests and experiences. [click] Representations: Mathematical ideas can be represented in a variety of ways: pictures, concrete materials, tables, graphs, number and letter symbols, spreadsheet displays, etc. The ways in which mathematical ideas are represented is fundamental to how people understand and use these ideas. 1 National Council of Teachers of Mathematics (2000). Principles and Standards for School Mathematics. National Council of Teachers of Mathematics (2000) Principles and Standards for School Mathematics California’s Common Core State Standards: Toolkit | Overview

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**Underlying Frameworks Strands of Mathematical Proficiency**

Conceptual Understanding Strategic Competence Productive Disposition Procedural Fluency Adaptive Reasoning TIME: 8 minutes (CONTINUED for Slides 40 to 43) ___________________________________________________________________________________ Adding it Up was written by the National Research Council. Five mathematical proficiencies are identified in this document: [click] Adaptive reasoning- capacity for logical thought, explanation, and justification [click] Strategic Competence: ability to formulate, represent, and solve mathematical problems [click] Conceptual Understanding: comprehension of mathematical concepts, operations, and relations [click] Productive Disposition: belief in one’s own efficacy to do mathematics; mathematics is useful [click] Procedural Fluency: skills in carrying out procedures Research shows that each of these strands is equally important. Pose the question, “What does the graphic communicate about the nature of the five strands?” Possible answers: They are all equally important. In order for the rope to be strong, each strand must be strong, etc. National Research Council (2001) Adding It Up California’s Common Core State Standards: Toolkit | Overview

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**Part 1: Standards for Mathematical Practice**

Make sense of problems and persevere in solving them …start by explaining the meaning of a problem and looking for entry points to its solution Reason abstractly and quantitatively …make sense of quantities and their relationships to problem situations Construct viable arguments and critique the reasoning of others …understand and use stated assumptions, definitions, and previously established results in constructing arguments Model with mathematics …can apply the mathematics they know to solve problems arising in everyday life, society, and the workplace TIME: 7 minutes (for Slides 44 to 46) INTENT: To understand the Standards for Mathematical Practice as outlined in the CCSS ___________________________________________________________________________________ Have participants locate the CCSS for Mathematics handout and turn to the Standards for Mathematical Practice found on pp.1-2. Briefly discuss each of the Standards for Mathematical Practice. HANDOUTS: CCSS for Mathematics 2011 © CA County Superintendents Educational Services Association California’s Common Core State Standards: Toolkit | Overview

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**Part 2: Standards for Mathematical Practice**

Use appropriate tools strategically …consider the available tools when solving a mathematical problem Attend to precision …communicate precisely using clear definitions and calculate accurately and efficiently Look for and make use of structure …look closely to discern a pattern or structure Look for and express regularity in repeated reasoning …notice if calculations are repeated, and look for both general methods and for shortcuts TIME: 7 minutes (CONTINUED for Slides 44 to 46) INTENT: To understand the Standards for Mathematical Practice as outlined in the CCSS ___________________________________________________________________________________ Continued from previous slide. Briefly discuss Standards 5-8. HANDOUTS: CCSS for Mathematics 2011 © CA County Superintendents Educational Services Association California’s Common Core State Standards: Toolkit | Overview

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**Standards for Mathematical Practice**

Locate the CCSS for Mathematics and read the first three words for each mathematical practice and notice the similarities. What do they begin with? Mathematically proficient students… TIME: 7 minutes (CONTINUED for Slides 44 to 46) INTENT: To understand that the Standards for Mathematical Practice focus on developing mathematically proficient students ___________________________________________________________________________________ Have participants locate the CCSS for Mathematics handout and read the first three words for each mathematical practice and notice the similarities. Then, ask [click] “What do they begin with?” [click] “Mathematically Proficient Students…” HANDOUTS: CCSS for Mathematics Briars & Mitchell (2010) Getting Started with the Common Core State Standards California’s Common Core State Standards: Toolkit | Overview

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**Standards for Mathematical Practice**

Locate and read the handout, Standards for Mathematical Practice. Discuss the importance of the verbs in the practices and how they define the habits of mind demonstrated by a mathematically proficient student. TIME: 10 minutes (CONTINUED for Slides 12 to 13) INTENT: To allow participants an opportunity to review the Eight Standards for Mathematical Practice ___________________________________________________________________________________ It is likely that participants will have interacted with the Standards for Mathematical Practice before this, but give them some time to review. Make sure they focus on the key verbs of the Standards for Mathematical Practice as they help define what mathematically proficient students do. HANDOUTS: CCSS for Mathematics Standards for Mathematical Practice California’s Common Core State Standards: Toolkit | Instructional Materials, K-5 | ELA and Mathematics

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**Standards for Mathematical Practice**

The Eight Standards for Mathematical Practice place an emphasis on student demonstrations of learning that describe the thinking processes, habits of mind, and dispositions that students need to develop. TIME: 2 minutes (for Slide 47) INTENT: To understand that the Standards for Mathematical Practice describe two types of student learning: 1) thinking process and habits of mind; and 2) mathematical content ___________________________________________________________________________________ The Standards for Mathematical Practice describe the thinking processes, habits of mind, and dispositions that students need to develop a deep, flexible, and enduring understanding of mathematics. For example, in Standards for Mathematical Practice 1, students will need to engage in tasks that have them analyze givens, constraints, relationships, and goals. They need to monitor and evaluate their progress and be able to change course if necessary. adapted from Briars & Mitchell (2010) Getting Started with the Common Core State Standards California’s Common Core State Standards: Toolkit | Overview

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**Domains Distribution (K-8)**

TIME: 5 minutes (for Slides 48 to 49) INTENT: To understand how the domains build upon each other from grade level to grade level and the focus of each domain ___________________________________________________________________________________ Explain the big ideas of each domain. Counting and Cardinality (K only): Students count a number of objects to find the total number in set and compare numbers. Counting and Cardinality begin in Pre-K with the foundations and continues through Kindergarten. Number and Operations in Base Ten (K-5): Students learn to understand place value, beginning with decomposing and composing numbers in Kindergarten, and move on to understanding and becoming proficient with operations. Ratio and Proportional Relationships (6-7): Students develop and understanding of and apply proportional relationships; understand ratio concepts and use ratio reasoning to solve problems in real world situations. Number and Operations in Fractions (3-5): Students develop an understanding of fractions, their equivalence, and their ordering. The Number System (6-8): Students apply and extend previous understanding of operations and fractions to perform operations on rational numbers. Operations and Algebraic Thinking (K-5): Students solve problems involving addition, subtraction, multiplication, and division; students generate and analyze patterns. Expressions and Equations(6-8): Students create and solve algebraic equations and expressions. Functions (8): Students define, evaluate, and compare functions; use functions to model relationships. Geometry (K-5): Students reason with shapes and their attributes, draw and identify lines and angles, and graph points on the coordinate plane. Geometry (6-8): Students solve real world problems involving area, surface area, and volume. Measurement and Data (K-5): Students describe and compare measurable attributes, measure and estimate lengths, and solve problems involving measurements of time, volume, and mass, and convert measurements units within a measurement system. Statistics and Probability (6-8): Students use random sampling to draw inferences about a population; investigate chance processes and develop, use, and evaluate probability models. Findell & Foughty (2011) College and Career-Readiness through the Common Core State Standards for Mathematics California’s Common Core State Standards: Toolkit | Overview

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**Focusing Attention Within Number and Operations**

K-5 6-8 High School Operations and Algebraic Thinking Expressions and Equations Algebra Number and Operations - Base Ten The Number System TIME: 5 minutes (CONTINUED for Slides 48 to 49) INTENT: To understand that the Standards for Mathematical Practice use mathematical progression to help ensure success as students progress through grade levels, practices, and content ___________________________________________________________________________________ The content of the K-5 domains and the 6-8 domains lead students to be ready for algebra. The big ideas have been backward mapped and build upon each other as students move up the grades. This is the critical nature of mathematical progressions. Number and Operations - Fractions Briars & Mitchell (2010) Getting Started with the Common Core State Standards California’s Common Core State Standards: Toolkit | Overview

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**California Grade 8 Options**

Goal for 8th grade students is Algebra 1. Two sets of standards for 8th grade Standards for Algebra 1 (CA addition to the CCSS) 8th grade Common Core Standards for Mathematics 8th grade Common Core Finalize preparation for students in high school. TIME: 5 minutes (for Slide 50) INTENT: To understand the CCSS grade 8 options ___________________________________________________________________________________ In California, the goal for 8th grade students is Algebra 1. The CCSS has standards for grades K-8 organized by domain, and the courses/clusters begin in grade 9. Each state was able to add an additional 15% to the original CCSS. California added a grade 8 Algebra 1 Course. As a result, there are 2 options for grade 8 students in California. While it is the goal for California 8th graders to take Algebra, students can take the grade 8 course as outlined by the national document or they can take the Algebra 1 course that California designed for 8th grade students. Each option will prepare students for college and career. INSTRUCTOR NOTE: 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. K-7 standards as augmented prepare students for either set of standards. 2011 © CA County Superintendents Educational Services Association California’s Common Core State Standards: Toolkit | Overview

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**Mathematics Standards for High School**

Arranged by conceptual categories (not by course): Number and Quantity (p. 49) Algebra (p. 52) Functions (p. 56) Modeling (p. 60) Geometry (p. 62) Statistics and Probability (p. 67) TIME: 10 minutes (for Slides 51 to 54) INTENT: To understand that the CCSS for high school mathematics are organized into conceptual categories; this differs from how the previous standards are organized ___________________________________________________________________________________ Currently, in most districts, 9th grade students are enrolled in Geometry or Algebra 1, and 10th grade students are enrolled in Geometry or Algebra II, etc. [click] The CCSS advocates for a more integrated model where content from several conceptual categories is combined into similar big ideas or key concepts and taught in an integrated fashion (to be discussed later in the presentation). Have participants locate the CCSS for Mathematics handout and follow along: [click] Number and Quantity: the real number system, quantities; the complex number system; and vector and matrix quantities [click] Algebra: seeing structure in expressions; arithmetic with polynomials and rational expressions; creating equations; and reasoning with equations and inequalities [click] Functions: interpreting functions; building functions; linear, quadratic, and exponential models; and trigonometric functions [click] Modeling: Modeling links classroom mathematics and statistics to everyday life, work, and decision-making. Modeling is the process of choosing and using appropriate mathematics and statistics to analyze empirical situations, to understand them better, and to improve decisions. Modeling is best interpreted not as a collection of isolated topics but rather in relation to other standards. Making mathematical models is a Standard for Mathematical Practice, and specific modeling standards appear throughout the high school standards indicated by a star symbol (★). The star symbol sometimes appears on the heading for a group of standards; in that case, it should be understood to apply to all standards in that group. [click] Geometry: congruence; similarity, right triangles, and trigonometry; circles; expressing geometric properties with equations; geometric measurement and dimension; modeling with geometry [click] Statistics and Probability: interpreting categorical and quantitative data; making inferences and justifying conclusions; conditional probability and rules of probability; using probability to make decisions HANDOUTS: CCSS for Mathematics adapted from Foster (2011) Assessment for Learning California’s Common Core State Standards: Toolkit | Overview

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**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 TIME: 10 minutes (CONTINUED for Slides 51 to 54) INTENT: To understand two of the model course pathways for high school ___________________________________________________________________________________ There are two mathematics pathways: [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 Inform participants that the pathways can be found in Appendix A of the CCSS for Mathematics. 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 adapted from 2011 © CA County Superintendents Educational Services Association California’s Common Core State Standards: Toolkit | Overview

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**Getting to Calculus Sooner: Two Compacted Pathways**

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 Both prepare students for Precalculus in their junior year and Calculus in their senior year. TIME: 10 minutes (CONTINUED for Slides 51 to 54) ___________________________________________________________________________________ There are two ADDITIONAL mathematics pathways: [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. California’s Common Core State Standards: Toolkit | Overview

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**Format of the Overview Domains:**

Overarching ideas that connect topics across the grades TIME: 8 minutes (for Slides 55 to 57) INTENT: To understand the structure of the CCSS for Mathematics ___________________________________________________________________________________ Have participants turn to p. 24 of the CCSS for Mathematics handout. 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 © Copyright National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved. California’s Common Core State Standards: Toolkit | Overview

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**Format of the Standards**

TIME: 8 minutes (CONTINUED for Slides 55 to 57) ___________________________________________________________________________________ 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 p. 14 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 National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved. California’s Common Core State Standards: Toolkit | Overview

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**Format of the Standards California’s 15% Addition**

TIME: 8 minutes (CONTINUED for Slides 55 to 57) INTENT: To understand how the standards that CA added to the CCSS are represented. ___________________________________________________________________________________ Each state was allowed to add 15% to the original CCSS. Notice that Standard 1.1 is bold, underlined, and italicized. [click] This is an example of a standard that California added to the CCSS document. All standards that California added are bold, italicized, and underlined. © Copyright National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved. California’s Common Core State Standards: Toolkit | Overview

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**Assessment: What We Know**

Assessments will begin in California is a governing state in the SMARTER Balanced Assessment Consortium. Assessments will include: Computer Adaptive Assessments (interim & summative) Performance Assessments (interim & summative) Selected Response Constructed Response Extended Performance Assessments TIME: 10 minutes (CONTINUED for Slides 58 to 63) INTENT: To provide an overview of the broad features of SMARTER Balanced Assessment Consortium’s (SBAC’s) assessment plan ___________________________________________________________________________________ There are still many unanswered questions about what the 2014 assessments will look like. Here is what we know: Although originally associated with PAARC, California has recently signed on with SBAC and has opted to take a governing role. This means California educators will take a strong role in developing the assessments. Unlike current CST assessments, the new CCSS assessments will be computer-based and be adaptive. Adaptive means that the questions will adjust in difficulty level as the student answers. This will prevent frustration and burnout as students take the test—and thus give a more accurate read of their proficiency levels. In addition to end of the year summative assessment, SBAC will provide item banks and performance assessments for districts to locally administer benchmarks. Performance assessments will be both single period and extended—over several days and incorporating speaking and listening tasks. California’s Common Core State Standards: Toolkit | Overview

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**Common Core State Standards Implementation Considerations**

All Teachers Scaffold comprehension of increasingly complex texts Integrate media sources into instructional activities Support/monitor informal talk ELA Teachers Teach more informational text Teach how a wide variety of forms fall into three overarching modes of writing: Argument, Expository, and Narrative Science and History Teachers Teach Reading and Writing skills in their content areas explicitly Mathematics Teachers Teach the habits of mind that students need to develop a deep, flexible, and enduring understanding of mathematics TIME: 10 minutes (CONTINUED for Slides 58 to 63) INTENT: To provide a summary of the overview of implementation considerations ___________________________________________________________________________________ [click] ALL teachers will need to: Pay attention to text complexity – not just the reading levels, possibly learning new ways to determine the complexity of the text book and other supplemental readings that are assigned. Find ways in which video, computer animations, audio, and other technologies will add to lessons both in presentations and in how students share their learning. Create opportunities for students to talk to one another using academic vocabulary and develop ways to monitor these conversations and teach students to monitor their own conversations. [click] ELA teachers will need to figure out which genres fall into which “buckets” at which grade levels, and this will have to be agreed on at the school or district level. [click] Science and History teachers will need to learn how to incorporate reading and writing strategies into their content lessons. [click] Mathematics teachers will need to teach the habits of mind that students need to develop a deep, flexible, and enduring understanding of mathematics. California’s Common Core State Standards: Toolkit | Overview

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**Reflection Locate the KWL chart you began earlier in the training.**

Complete the third column. Discuss with a partner. TIME: 10 minutes (CONTINUED for Slides 58 to 63) INTENT: To reflect on the CCSS ___________________________________________________________________________________ Refer participants back to the CCSS KWL Chart they began earlier and have them complete the third column. Then, ask participants to discuss their KWL Chart with a partner. HANDOUTS: CCSS KWL Chart California’s Common Core State Standards: Toolkit | Overview

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**Toolkit Modules Module 1: Overview (3 hours)**

Module 2: Content and Curriculum (90 minutes each) ELA, K-12 Additional Mini-Modules (60 minutes): Informational Text; Writing; Text Complexity; Collaboration, Research, and Use of Media Mathematics, K-8 Mathematics, 6-12 Module 3: Instruction (3 hours each) ELA and Mathematics, K-5 ELA only: Additional Mini-Modules (60 minutes): Informational Text; Writing; Text Complexity; Collaboration, Research, and Use of Media ELA, 6-12 Module 4: Instructional Materials (3 hours each) ELA, 6-12 (3 hours) TIME: 10 minutes (CONTINUED for Slides 58 to 63) INTENT: To provide additional information on the remaining Toolkit Modules ___________________________________________________________________________________ Review the slide. INSTRUCTOR NOTE: It is highly recommended that the modules be completed in the order presented. California’s Common Core State Standards: Toolkit | Overview

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**Effective Instruction**

“A long line of students has established that the single most important school influence on student learning is the quality of the teacher.” as presented by Linda Darling-Hammond (2007) How would you describe a classroom where effective instruction and learning is taking place? TIME: 8 minutes (CONTINUED for Slides 3 to 7) ___________________________________________________________________________________ Read the quote aloud. [click] Ask participants how they would describe a classroom where effective instruction and learning is taking place. Have participants discuss the question with a partner. INSTRUCTOR NOTE: Linda Darling-Hammond is a Professor of Education at Stanford University. She is a former president of the American Educational Research Association and member of the National Academy of Education. Her research, teaching, and policy work focus on issues of school restructuring, teacher quality, and educational equity. From , she served as Executive Director of the National Commission on Teaching and America’s Future, a blue-ribbon panel whose 1996 report, What Matters Most: Teaching for America’s Future, led to sweeping policy changes affecting teaching and teacher education. California’s Common Core State Standards: Toolkit | Instruction, K-5 | ELA and Mathematics

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**California Standards for the Teaching Profession**

Engaging and supporting all students Connect to students’ prior knowledge Use a variety of instructional strategies Promote autonomy, interaction, and choice Engage students in critical thinking/problem solving Engage students in reflecting on their learning Understanding and organizing content Organize curriculum to support understanding Interrelate ideas and information TIME: 8 minutes (CONTINUED for Slides 3 to 7) ___________________________________________________________________________________ There must be a common understanding regarding the expectations for instruction. In 1997, California established the California Standards for the Teaching Profession (CSTP) to provide a common language and vision of teaching. “Teaching is more than methodology.”1 It is a complex process centered around student learning. Briefly discuss two of the four standards (continues on the next slide). [click] Engaging/Supporting: Critical thinking and problem solving are an essential part of the CCSS. [click] Understanding/Organizing Content: With an emphasis on application of knowledge in the CCSS, it will be essential that we have a deep understanding of our content area so we can help students make connections. INSTRUCTOR NOTE: Two standards are not referenced here: CSTP 2: Creating and Maintaining Effective Environments and CSTP 6: Developing as a Professional Educator. 1California Department of Education and California Commission on Teacher Credentialing (2007). California Standards for the Teaching Profession. California’s Common Core State Standards: Toolkit | Instruction, K-5 | ELA and Mathematics

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**California Standards for the Teaching Profession**

Planning instruction Establish clear goals for student learning Design short- and long-term plans Modify plans according to student needs Assessing student learning Collect and use multiple sources of information Use results to guide instruction Involve students in assessing their own learning TIME: 8 minutes (CONTINUED for Slides 3 to 7) ___________________________________________________________________________________ Continue to briefly discuss the remaining two standards. [click] Planning Instruction: With an emphasis on critical thinking and application, we will need to make decisions to allow students sufficient time to learn and apply their new learning. [click] Assessing Student Learning: Assessing student understanding before, during and after instruction will ensure that we are adjusting our instruction to meet their learning needs. INSTRUCTOR NOTE: Two standards are not referenced here: CSTP 2: Creating and Maintaining Effective Environments and CSTP 6: Developing as a Professional Educator. California’s Common Core State Standards: Toolkit | Instruction, K-5 | ELA and Mathematics

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**Learning Pyramid Passive Learning Active Learning**

TIME: 8 minutes (CONTINUED for Slides 3 to 7) ___________________________________________________________________________________ The CSTPs tell us what we need to do as teachers, but how do we do it? What are the most effective methods of teaching? The CCSS do not dictate curriculum or teaching methods. The Learning Pyramid that illustrates students’ retention rates based on the methods used for instruction. All of the methods discussed are strategies that may be appropriate at one point or another. [click] (top) Lecture, Reading, Audio-Visual, Demonstration (passive) [click] (bottom) Discussion Group, Practice by Doing, Teach Others/Immediate Use (active) Discuss which have the greatest impact on student learning. Active Learning adapted from Ntl Institute for Applied Behavioral Science (n.d.) California’s Common Core State Standards: Toolkit | Instruction, K-5 | ELA and Mathematics

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**Rigor/Relevance Framework®**

International Center for Leadership in Education (n.d.) TIME: 10 minutes (CONTINUED for Slides 8 to 18) INTENT: To lay the groundwork of “why” we need the CCSS ___________________________________________________________________________________ In addition to actively engaging students in the learning process, we need to help students think critically. Ask participants to locate the Rigor/Relevance Framework handout. In order to prepare our students for a global economy, we need to teach them how to apply and adapt their learning to predictable and unpredictable situations that arise in the future. We are preparing them for jobs of the future that do not exist as of yet. Incorporating more rigorous and relevant instruction in classrooms is necessary for the development of 21st century thinking skills. The Rigor/Relevance Framework was created by the International Center for Leadership in Education founded by Dr. Willard Dagget. “It is a tool to examine curriculum, instruction, and assessment.”1 The Framework shows the relationship between the Knowledge Taxonomy (Bloom’s) and the Application Model. Both are equally important in developing rigorous and relevant instruction. HANDOUTS: Rigor/Relevance Framework 1International Center for Leadership (n.d.). Rigor/Relevance Framework. California’s Common Core State Standards: Toolkit | Instruction, K-5 | ELA and Mathematics

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**Quadrant D: Adaptation**

Students think in complex ways and apply acquired knowledge and skills, even when confronted with perplexing unknowns, to find creative solutions and take action that further develops their skills and knowledge. Evaluation 6 D Adaptation International Center for Leadership in Education (n.d.) Synthesis 5 Analysis 4 TIME: 10 minutes (CONTINUED for Slides 8 to 18) ___________________________________________________________________________________ Quadrant D learning is characterized by Adaptation—students think in complex ways and apply the knowledge and skills they have acquired to predictable and unpredictable situations.1 Instruction focuses on higher level thinking skills on the Knowledge Taxonomy and the application of knowledge, skills, and understanding in real world situations—a big part of the CCSS. [click] Application: Can the student use the information in a new way? (choose, demonstrate, dramatize, employ, illustrate, interpret, operate, schedule, sketch, solve, use, write) [click] Analysis: Can the student distinguish between the different parts? (appraise, compare, contrast, criticize, differentiate, discriminate, distinguish, examine, experiment, question, test) [click] Synthesis: Can the student create a new product or point of view? (assemble, construct, create, design, develop, formulate, write) [click] Evaluation: Can the student justify a stand or decision? (appraise, argue, defend, judge, select, support, value, evaluate) 1International Center for Leadership (n.d.). Rigor/Relevance Framework. Application 3 3 Apply knowledge across disciplines 4 Apply to real-world predictable situation 5 Apply to real-world unpredictable situation California’s Common Core State Standards: Toolkit | Instruction, K-5 | ELA and Mathematics

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Quadrant D Verbs evaluate validate justify rate referee infer rank dramatize argue conclude Products evaluation newspaper estimation trial editorial radio program Play collage machine adaptation poem debate invention TIME: 10 minutes (CONTINUED for Slides 8 to 18) ___________________________________________________________________________________ Here are some of the verbs and products that can be associated with Quadrant D learning. [click] “The Verb List can be used either to create a desired level of expected student performance or to evaluate the level of existing curriculum, instruction, or assessment.”1 As we take a closer look at the CCSS, look for these verbs, as well as the verbs associated with the other quadrants. [click] The Products list suggests ways in which students may demonstrate Quadrant D learning. 1International Center for Leadership (n.d.). Rigor/Relevance Framework. California’s Common Core State Standards: Toolkit | Instruction, K-5 | ELA and Mathematics

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**Quadrant C: Assimilation**

Students extend and refine their knowledge so that they can use it automatically and routinely to analyze and solve problems and create solutions. Evaluation 6 C Assimilation International Center for Leadership in Education (n.d.) Synthesis 5 Analysis 4 TIME: 10 minutes (CONTINUED for Slides 8 to 18) ___________________________________________________________________________________ Quadrant C is high on the Knowledge Taxonomy and is low on Application model. “Students extend and refine their acquired knowledge to be able to use that knowledge automatically and routinely to analyze and solve problems.”1 Quadrant C is where students would make relevant connections within the discipline. This quadrant represents deep understanding in a content area which is a goal of the CCSS. [click] Application: Can the student use the information in a new way? (choose, demonstrate, dramatize, employ, illustrate, interpret, operate, schedule, sketch, solve, use, write) [click] Analysis: Can the student distinguish between the different parts? (appraise, compare, contrast, criticize, differentiate, discriminate, distinguish, examine, experiment, question, test) [click] Synthesis: Can the student create a new product or point of view? (assemble, construct, create, design, develop, formulate, write) [click] Evaluation: Can the student justify a stand or decision? (appraise, argue, defend, judge, select, support, value, evaluate) 1International Center for Leadership (n.d.). Rigor/Relevance Framework. Application 3 1 Knowledge in one discipline 2 Apply Knowledge in one discipline California’s Common Core State Standards: Toolkit | Instruction, K-5 | ELA and Mathematics

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Quadrant C Verbs sequence annotate examine report criticize paraphrase calculate expand summarize classify diagram Products essay abstract blueprint inventory report plan chart questionnaire classification diagram discussion collection annotation TIME: 10 minutes (CONTINUED for Slides 8 to 18) ___________________________________________________________________________________ Here are some verbs and products that would be associated with Quadrant C learning. [click] Verbs List [click] Products List California’s Common Core State Standards: Toolkit | Instruction, K-5 | ELA and Mathematics

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**Quadrant B: Application**

Students use acquired knowledge to solve problems, design solutions, and complete work. B Application Application 3 International Center for Leadership in Education (n.d.) Comprehension 2 TIME: 10 minutes (CONTINUED for Slides 8 to 18) ___________________________________________________________________________________ Quadrant B is low on the Knowledge Taxonomy and high on Application. “Students use acquired knowledge to solve problems, design solutions, and complete work. The highest level of application is to apply appropriate knowledge to new and unpredictable situations.”1 [click] Awareness: Can the student recall or remember the information? (define, duplicate, list, memorize, recall, repeat. [click] Comprehension: Can the student explain ideas or concepts? (classify, describe, discuss, explain, identify, locate, recognize, report, select, translate, paraphrase) [click] Application: Can the student use the information in a new way? (choose, demonstrate, dramatize, employ, illustrate, interpret, operate, schedule, sketch, solve, use, write) 1International Center for Leadership (n.d.). Rigor/Relevance Framework. Awareness 1 3 Apply knowledge across disciplines 4 Apply to real-world predictable situation 5 Apply to real-world unpredictable situation California’s Common Core State Standards: Toolkit | Instruction, K-5 | ELA and Mathematics

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Quadrant B Verbs apply sequence demonstrate interview construct solve calculate dramatize interpret illustrate Products scrapbook summary interpretation collection annotation explanation solution demonstration outline TIME: 10 minutes (CONTINUED for Slides 8 to 18) ___________________________________________________________________________________ Here are some verbs and products that would be associated with Quadrant B learning. [click] Verbs List [click] Products List California’s Common Core State Standards: Toolkit | Instruction, K-5 | ELA and Mathematics

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**Quadrant A: Acquisition**

Students gather and store bits of knowledge/info rmation and are expected to remember or understand this acquired knowledge. A Acquisition Application 3 International Center for Leadership in Education (n.d.) Comprehension 2 TIME: 10 minutes (CONTINUED for Slides 8 to 18) ___________________________________________________________________________________ Quadrant A is low on the Knowledge Taxonomy and low on Application. “Students gather and store bits of knowledge and information. Students are primarily expected to remember or understand this acquired knowledge.”1 [click] Awareness: Can the student recall or remember the information? (define, duplicate, list, memorize, recall, repeat. [click] Comprehension: Can the student explain ideas or concepts? (classify, describe, discuss, explain, identify, locate, recognize, report, select, translate, paraphrase) [click] Application: Can the student use the information in a new way? (choose, demonstrate, dramatize, employ, illustrate, interpret, operate, schedule, sketch, solve, use, write) 1International Center for Leadership (n.d.). Rigor/Relevance Framework. Awareness 1 1 Knowledge in one discipline 2 Apply knowledge in discipline California’s Common Core State Standards: Toolkit | Instruction, K-5 | ELA and Mathematics

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Quadrant A Verbs name label define select identify list memorize recite locate record Products definition worksheet list quiz test workbook true-false reproduction recitation TIME: 10 minutes (CONTINUED for Slides 8 to 18) ___________________________________________________________________________________ Here are some verbs and products that are associated with Quadrant A learning. [click] Verbs List [click] Products List California’s Common Core State Standards: Toolkit | Instruction, K-5 | ELA and Mathematics

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**Rigor/Relevance Framework® Teacher/Student Roles**

Student Think C B A D Student Think & Work Teacher Work Student Work RELEVANCE Low High R I G O R International Center for Leadership in Education (n.d.) TIME: 10 minutes (CONTINUED for Slides 8 to 18) ___________________________________________________________________________________ The four quadrants of the Rigor/Relevance Framework engage students and teachers in different roles. In Quadrant A, “teachers expend energy to create and assess learning activities—provide information, create worksheets, and grade student work. The student is often the passive learner.”1 In Quadrant B, “the emphasis is on the student doing real-world work. This student work is often more complicated than Quadrant A work and requires more time.” 1 In Quadrant C, “students are expected to think in complex ways—to analyze, compare, create and evaluate.”1 In Quadrant D, learning “is more demanding and requires students to think and work. Roles shift from the teacher-centered instruction in Quadrant A to student-centered instruction in Quadrants B, C, and D.”1 As we think about preparing our students for the 21st Century, we want to actively engage them in more rigorous and relevant instruction, spending more time in Quadrants B, C, and D. In a moment, we will begin to take a closer look at instruction in the English Language Arts classroom. Then we will take a closer look at math instruction. 1International Center for Leadership (n.d.). Rigor/Relevance Framework. California’s Common Core State Standards: Toolkit | Instruction, K-5 | ELA and Mathematics

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**TEACHER RESPONSIBILITY STUDENT RESPONSIBILITY**

The Gradual Release of Responsibility Structure for Successful Instruction TEACHER RESPONSIBILITY Focus Lesson “I do it” Guided Instruction “We do it” TIME: 40 minutes (CONTINUED for Slides 30 to 42) INTENT: To provide a visual representation of the instructional model – Gradual Release of Responsibility (GRR) that is a research-based model in which responsibility for task completion gradually shifts over time from teacher to student ___________________________________________________________________________________ Ask the following: How many of you are familiar with this model? How often do you use it? Think/Pair/Share your experience with this instructional model. Collaborative “You do it together” Independent “You do it alone” STUDENT RESPONSIBILITY Fisher & Frey (2008) Better Learning Through Structured Teaching California’s Common Core State Standards: Toolkit | Instruction, K-5 | ELA and Mathematics

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**The “Sudden” Release of Responsibility**

TEACHER RESPONSIBILITY Focus Lesson “I do it” TIME: 40 minutes (CONTINUED for Slides 30 to 42) INTENT: To provide a visual representation of a “non-example” of Gradual Release of Responsibility ___________________________________________________________________________________ Good instruction is NOT a “SUDDEN RELEASE” of responsibility. Have someone give an example of a “SUDDEN RELEASE” of responsibility. Independent “You do it alone” STUDENT RESPONSIBILITY Fisher & Frey (2008) Better Learning Through Structured Teaching California’s Common Core State Standards: Toolkit | Instruction, K-5 | ELA and Mathematics

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**The “Good Enough” Release of Responsibility**

TEACHER RESPONSIBILITY Focus Lesson “I do it” Guided Instruction “We do it” TIME: 40 minutes (CONTINUED for Slides 30 to 42) INTENT: To provide a visual representation of a “not quite good enough” example of Gradual Release of Responsibility, one that many of us still believe to be “good enough” ___________________________________________________________________________________ The Model of Direct Instruction is often seen as GOOD ENOUGH, but it is lacking an important element. In the past instruction may have looked liked this, but research has supported the power of collaboration in the learning process. Independent “You do it alone” STUDENT RESPONSIBILITY Fisher & Frey (2008) Better Learning Through Structured Teaching California’s Common Core State Standards: Toolkit | Instruction, K-5 | ELA and Mathematics

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**A Model for Student Success The Gradual Release of Responsibility**

TEACHER RESPONSIBILITY Focus Lesson Guided Instruction “I do it” “We do it” “You do it together” Collaborative Independent “You do it alone” STUDENT RESPONSIBILITY TIME: 40 minutes (CONTINUED for Slides 30 to 42) INTENT: To provide a visual representation of The Gradual Release of Responsibility ___________________________________________________________________________________ So the Model for Student Success is… [click] The Gradual Release of Responsibility Ask participants to discuss with a partner the differences between the “Good Enough Model” on the previous slide and this model. Call the group back together and ask, “What does ‘The Gradual Release of Responsibility’ look like in the classroom?” Fisher & Frey (2008) Better Learning Through Structured Teaching California’s Common Core State Standards: Toolkit | Instruction, K-5 | ELA and Mathematics

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**CCSS for Mathematics Provide focus and coherence**

Organized around mathematical principles Stress conceptual understanding of key ideas as well as skills Prepare students for college and career What are the implications for instruction? TIME: 5 minutes (CONTINUED for Slides 43 to 47) INTENT: To provide some background on the CCSS for Mathematics ___________________________________________________________________________________ The intent of the standards is to provide grade level focus areas so teachers and students can go deeper with the content, rather than just “cover” topics. The CCSS is organized around the big ideas of mathematics, so content flows in progressions. There is a balanced emphasis on conceptual understanding and procedural fluency. The overall goal is to prepare students for college and career. [click] What are the implications for instruction? California’s Common Core State Standards: Toolkit | Instruction, K-5 | ELA and Mathematics

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**Influence on Student Learning**

“…teachers themselves need to understand the standards. Teachers must have deep and appropriate content knowledge to reach that understanding; they must be adaptable, with enough mastery to teach students with a range of abilities; and they must have the ability to inspire at least some of their students to the highest levels of mathematical achievement.” Ewing (n.d.) The Common Core Math Standards “…teachers themselves need to understand the standards. Teachers must have deep and appropriate content knowledge to reach that understanding; they must be adaptable, with enough mastery to teach students with a range of abilities; and they must have the ability to inspire at least some of their students to the highest levels of mathematical achievement.” Ewing (n.d.) The Common Core Math Standards TIME: 5 minutes (CONTINUED for Slides 43 to 47) ___________________________________________________________________________________ Read the quote on the slide. [click] “teachers must have deep and appropriate content knowledge,” “they must be adaptable,” and “they must have the ability to inspire.” The CCSS for Mathematics clearly show that teachers of math in all grades must have much deeper content knowledge to teach math effectively. The emphasis on real-world problem solving and connections between concepts and skills will require us to engage in the same mathematics our students will be doing. INSTRUCTOR NOTE: John Ewing is the President of Math for America, a nonprofit organization with a mission to improve mathematics education in US public secondary schools by recruiting, training, and retaining outstanding mathematics teachers. California’s Common Core State Standards: Toolkit | Instruction, K-5 | ELA and Mathematics

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**Standards for Mathematical Practice Seek to Develop in Students**

NCTM Process Standards Problem Solving Reasoning and Proof Communication Representation Connections Strands of Math Proficiency Adaptive Reasoning Strategic Competence Conceptual Understanding Procedural Fluency Productive Disposition Strands of Math Proficiency Adaptive Reasoning Strategic Competence Conceptual Understanding Procedural Fluency Productive Disposition TIME: 5 minutes (CONTINUED for Slides 43 to 47) ___________________________________________________________________________________ In the Overview Module, we were introduced to the Standards for Mathematical Practice which are consistent expectations across all grade levels K-12. They are based on National Council of Teachers of Mathematics’ (NCTM) Process Standards (Principles and Standards for School Mathematics, NCTM, 2000). [click] Problem solving should be an integral part of mathematics. By solving mathematical problems students acquire ways of thinking, habits of persistence and curiosity, and confidence in unfamiliar situations. [click] Reasoning and proof – People who reason and think analytically tend to note patterns, structure, or regularities in both real-world and mathematical situations. [click] Communication – When students are challenged to communicate the results of their thinking to others orally or in writing, they learn to be clear, convincing, and precise in their use of mathematical language. [click] Representations of mathematical ideas are represented in a variety of ways: pictures, concrete materials, tables, graphs, …are fundamental to how people understand and use those ideas. [click] Connections of mathematical ideas allow for deeper and more lasting understanding. National Research Council’s (NRC) Strands of Mathematical Proficiency (Adding It Up, NRC, 2001) [click] Adaptive Reasoning: capacity for logical thought, explanation, and justification [click] Strategic Competence: ability to formulate, represent, and solve mathematical problems [click] Conceptual Understanding: comprehension of mathematical concepts, operations, and relations [click] Productive Disposition: belief in one’s own efficacy to do mathematics; mathematics as useful [click] Procedural Fluency: skills to carry out procedures [click] Productive Disposition plays a significant role in the Standards for Mathematical Practice. California’s Common Core State Standards: Toolkit | Instruction, K-5 | ELA and Mathematics

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**Standards for Mathematical Practice**

Overarching habits of mind of a productive mathematical thinker Reasoning and explaining Modeling and using tools Seeing structure and generalizing 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics. 5. Use appropriate tools strategically. 1. Make sense of problem and persevere in solving them. 6. Attend to precision. TIME: 5 minutes (CONTINUED for Slides 43 to 47) ___________________________________________________________________________________ William McCallum, one of the writers of the CCSS for Mathematics, has paired the Standards for Mathematical Practice in the following way. Review the slide. When we look at the Standards for Mathematical Practice, we can see how these standards support the kinds of thinking and work described in Quadrants B, C, and D. This organization of the standards helps us consider the implications the CCSS will have on instruction. In addition to teaching content, we need to plan instruction to help students make sense of problems and persevere in solving them—a challenge we’ve always been faced with in mathematics, but now it is a standard we need to help students achieve. In our lesson plans, we need to create opportunities for students to engage in reasoning and explaining or using multiple representations and tools to model problems. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning adapted from McCallum (2011) Standards for Mathematical Practice California’s Common Core State Standards: Toolkit | Instruction, K-5 | ELA and Mathematics

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**Create a Frayer Model Poster**

Essential Characteristics Teaching Methods Examples of What Students Will Be Doing Non-examples of What Students Will Be Doing Standards for Mathematical Practice TIME: 30 minutes (for Slides 48 to 49) INTENT: To look deeply at one of the Standards for Mathematical Practice and to preview the other seven ___________________________________________________________________________________ The Frayer Model is a word categorization activity that helps learners develop their understanding of concepts. There are many variations of the Frayer Model, but most include the Essential Characteristics of the concept as well as Examples and Non-Examples of the concept. The use of examples and non- examples is a concept attainment strategy. Essential Characteristics: The major characteristics or elements of the Standards for Mathematical Practice Teaching Methods: Think about the CSTPs discussed earlier and the primary methods you currently use to facilitate demonstration of the Standards for Mathematical Practice. Examples of Student Actions: What would it look like if students were engaged in this Standards for Mathematical Practice? Think about the kinds of thinking and work in the four quadrants of the Rigor/Relevance Framework. Non-examples of what students will be doing: What would it look like if students were not engaged in Standards for Mathematical Practice? What would they be doing instead? [click] Review the activity instructions. Assign a practice to each table. Refer them to p. 47 of the CCSS for Mathematics handout. Remind the group assigned to SMP 4, Modeling with Mathematics, to refer to pp Encourage them to include the basic modeling cycle on their poster. HANDOUTS: CCSS for Mathematics SUPPLIES: Chart paper Markers Work with a table group on one of the Standards for Mathematical Practice. Create a Frayer Model Poster connecting student actions and teacher actions. California’s Common Core State Standards: Toolkit | Instruction, K-5 | ELA and Mathematics

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**Frayer Model Poster Carousel**

Display your poster. Examine the poster to the right of your group’s poster. Look for evidence of the “processes and proficiencies.” Rotate to the right and continue until you have finished examining all posters. Be ready to share out any questions or “ahas.” TIME: 30 minutes (CONTINUED for Slides 48 to 49) ___________________________________________________________________________________ Have participants locate the Standards for Mathematical Practice handout. Review the slide. Have participants record key ideas they want to remember about each practice on the handout. HANDOUTS: Mathematics: Standards for Mathematical Practice Standards for Mathematical Practice (note-taking) California’s Common Core State Standards: Toolkit | Instruction, K-5 | ELA and Mathematics

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**Research-Informed Best Practices**

Access prior knowledge and address students’ misconceptions Provide routines and structures that help struggling learners organize critical content Engage students with challenging tasks that involve active meaning making Use formative assessment and provide timely, specific feedback Provide on-going cumulative distributed practice Promote learners’ beliefs about their own intelligence (growth mindset vs. fixed mindset) adapted from Briars (2011) Intensified Algebra Access prior knowledge and address students’ misconceptions Provide routines and structures that help struggling learners organize critical content Engage students with challenging tasks that involve active meaning making Use formative assessment and provide timely, specific feedback Provide on-going cumulative distributed practice Promote learners’ beliefs about their own intelligence (growth mindset vs. fixed mindset) adapted from Briars (2011) Intensified Algebra TIME: 30 minutes (for Slides 50 to 56) INTENT: To review best instructional practices in mathematics ___________________________________________________________________________________ The strategies listed are well established research results that have been shown to increase student learning in mathematics. We want to continue to use these best practices in our classrooms. [click] In particular, we want to focus on the third bullet, since this is often neglected in classrooms as we try to “cover” content and “simplify” the content for lower-performing students. With an emphasis on rigor and relevance in mathematics, one of the ways we can start transitioning to the CCSS is to engage students in problem solving. California’s Common Core State Standards: Toolkit | Instruction, K-5 | ELA and Mathematics

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**Cognitively-Guided Instruction Process**

Start the study of a new concept with a rich problem or hypothesis Use your understanding of student thinking to guide further instruction Invite your students to engage in the problem TIME: 30 minutes (CONTINUED for Slides 50 to 56) INTENT: To introduce the Cognitively-Guided Instruction process as a strategy for engaging students in the Standards for Mathematical Practice ___________________________________________________________________________________ With a focus on real-world applications, we’d liked to introduce the Cognitively-Guided Instruction Process as a strategy for engaging students in the Standards for Mathematical Practice. Cognitively Guided Instruction (CGI) is an approach to teaching mathematics where teachers utilize what they know about their student’s understanding of mathematics to select problems, pose those problems, question students, and facilitate discussion and sharing. CGI focuses on student thinking and analysis through the use of word problems, combined with the math process standards: problem solving, reasoning and proof, communication, connections, and representation. As we solve the Table Pattern Task described on the next slide, consider how the CGI process connects to the Standards for Mathematical Practice. Question, justify, and critique thinking Communicate multiple representations of solutions. Gendron (2011) So, What’s New in the Common Core State Standards? California’s Common Core State Standards: Toolkit | Instruction, K-5 | ELA and Mathematics

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Table Pattern Task A catering manager wants to know how many people can sit around the tables he uses for parties. The number of people who can sit around the tables will depend on the shape of the table and the number that are put together. How can the manager determine how many people can sit around any number of tables of any shape? TIME: 30 minutes (CONTINUED for Slides 50 to 56) INTENT: To introduce the Cognitively-Guided Instruction process as a strategy for engaging students in the Mathematical Practice ___________________________________________________________________________________ Read the problem. [click] Show a triangular table with three people. Ask, “How many people can sit around two of these tables?” [click] Show two tables. Ask, “How many people can sit at three tables?” [click] Show three tables. Ask, “What if the table was a quadrilateral with four sides?” [click] Show the quadrilaterial table. “How many people can sit around two tables?” [click] Show the two quadrilaterial tables. “How many people can sit around three tables?” [click] Show the two quadrilaterial tables. “How many people can sit around four tables?” [click] Show the three quadrilaterial tables. Ask, “What if I had eight-sided tables? How many people can sit around those?” Have participants locate the Table Pattern Task handout and pattern blocks. Explain that the caterer has a variety of table shapes, and our goal is to help him/her determine how many people can sit around any number of tables of any shape. Tell participants to read the problem. Model how to use the CGI process with this task. Invite students to engage in the problem: What do you know about the problem? What do you need to find out? What might be one way to get started with the problem? Communicate multiple representations of solutions: What strategies could you use to organize your thinking? How could you explain what you know right now? What patterns do you notice as the number of tables increases? How does the number of people change as the number of tables increases? HANDOUTS: Table Pattern Task ACTIVITY MATERIALS (may require preparation in advance): Pattern Blocks California’s Common Core State Standards: Toolkit | Instruction, K-5 | ELA and Mathematics

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Table Pattern Task Find an algebraic rule to describe the relationship between the number of tables, n, and the number of people, p, for tables with any number of sides, s. Explain your thinking. TIME: 30 minutes (CONTINUED for Slides 50 to 56) INTENT: To introduce the Cognitively-Guided Instruction process as a strategy ___________________________________________________________________________________ Tell participants that now that they’ve had a chance to explore the problem, think about how they might generalize their findings into an algebraic rule. Have them work with a partner to share their thinking and describe the relationship between the number of people, tables, and sides. Facilitate their work by circulating and asking questions that engage participants in the process (question, justify, critique thinking): What is the relationship between the number of tables and sides? Number of tables and people? What patterns do you notice as the number of tables increase? As the number of sides increase? Have you tried looking at tables with 5 sides or 6 sides? Have one or two participants share their solutions. Ask the audience whether the solution makes sense and what questions they have regarding the strategy or solution. California’s Common Core State Standards: Toolkit | Instruction, K-5 | ELA and Mathematics

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**Debrief the CGI Process**

Table Pattern Task Start the study of a new concept with a rich problem or hypothesis Question, justify, and critique thinking Use your understanding of student thinking to guide further instruction Communicate multiple representations of solutions. Invite your students to engage in the problem Use results to plan next steps Asked questions to unpack the problem TIME: 30 minutes (CONTINUED for Slides 50 to 56) INTENT: To debrief the task in terms of Cognitively-Guided Instruction and the Standards for Mathematical Practice ___________________________________________________________________________________ Ask participants to think about the Learning Pyramid they saw earlier. The Table Pattern Task engaged us in “doing math” with a partner and discussing ideas at your table and with the whole group, so we were actively engaged in the bottom layers of the pyramid. [click] The CGI Process begins with a rich problem or task. Ask, “When we think about the Rigor/Relevance Framework, in which quadrant does this task fall?” (Pair share or choral response - B or D) Ask, “How did the facilitator invite you to engage in the problem?” Have participants pair share or volunteer to share whole group. [click] Asked questions while presenting the task in chunks, first with triangular tables, then with quadrilateral tables, etc., to make sure we understood the problem). [click] Tell participants that the facilitator continued to ask questions to consider possible strategies and relationships. Ask, “What did the facilitator do to engage you in the process of step 4 (question, justify, critique thinking)? [click] Circulated and asked us to explain what we knew while we worked; asked us to present our solutions and explain our reasoning; asked the audience to ask questions about the solution/strategy. [click] Tell participants that in the final step, we plan instruction according to student needs. Have them recall the CSTPs introduced earlier and how this process aligns with them (CSTP 1: Engage students in critical thinking and problem solving; CSTP 5: Assess and use results to plan instruction. Asked questions to check for understanding during and after the task Asked questions about strategies and relationships Gendron (2011) So, What’s New in the Common Core State Standards? California’s Common Core State Standards: Toolkit | Instruction, K-5 | ELA and Mathematics

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**Table Pattern Task and Standards for Mathematical Practice**

Standard for Mathematical Practice 3: Construct viable arguments and critique the reasoning of others. How did the teacher facilitate the task to support Standard 3? As a student, what did you do to demonstrate proficiency of Standard 3? What other Standards for Mathematical Practice were addressed by this task? TIME: 30 minutes (CONTINUED for Slides 50 to 56) ___________________________________________________________________________________ Ask, “How did the CGI process engage students in the Standards for Mathematical Practice?” Tell participants that many practices may have been addressed by this problem. [click] To begin with, let’s start looking at Practice 3 because the Table Pattern Task provides an opportunity to make conjectures, and the cooperative approach to the problem provides an opportunity to critique the reasoning of others. [click] How did the teacher facilitate the task to support Standard 3? Lower level questioning to gain entry to the problem Questions to think about how to organize thinking/work Questioning to consider possible strategies Pattern blocks/handout to model the problem Peer support to discuss the problem/strategize together [click] What did the student do? (Questions for Planning and Observation, North Bay Mathematics Project) Make conjectures, then explore the problem to support or disprove their conjectures and then refine or change their conjectures? Construct their justification? Use objects? Drawings? Diagrams? Examples and counter examples? Have opportunities to explain their conclusions and communicate their reasoning with others? Have opportunities to ask useful questions to seek clarity? Follow the arguments of others looking for flaws and explaining them? [click] What other Standards for Mathematical Practice were addressed by this task? Have participants locate the Facilitating Mathematical Thinking with Effective Questions handout which can be used as a resource to facilitate problem solving. HANDOUTS: Facilitating Mathematical Thinking with Effective Questions California’s Common Core State Standards: Toolkit | Instruction, K-5 | ELA and Mathematics

65
**Modifying the Table Pattern Task**

How might we vary the task for different grade levels? Using the CCSS for Mathematics handout, work with grade-level partners to provide some examples. TIME: 30 minutes (CONTINUED for Slides 50 to 56) INTENT: To consider how the task might be modified for different grade levels ___________________________________________________________________________________ OPTIONAL SLIDE: Omit if short on time. The CGI Process engages students in a rich task. Depending on the grade level, we could generate different goals for our students. For example, we wouldn’t ask a fourth grader to generate a three variable rule. Have participants locate the CCSS for Mathematics handout and turn to their grade level. Have pairs or small groups of participants decide on how they would modify this task to meet the needs and goals of their students. 3.OA.9 Identify arithmetic patterns… (p.13) 4.OA.5 Generate a number or shape pattern…(p.17) 5.OA.3 Generate two numerical patterns…(p.21) 6.EE.9 Use variables to represent two quantities…(p.27) 7.EE.4 Use variables to represent quantities…(p.31) A-CED.2* Create equations in two or more variables …(p.54) HANDOUTS: CCSS for Mathematics California’s Common Core State Standards: Toolkit | Instruction, K-5 | ELA and Mathematics

66
**Students’ Beliefs About Their Intelligence**

Fixed Mindset Avoid learning situations if they might make mistakes Try to hide, rather than fix, mistakes or deficiencies Growth Mindset Work to correct mistakes and deficiencies View effort as positive; increase effort when challenged TIME: 10 minutes (for Slides 57 to 62) INTENT: To understand that teaching a growth mindset helps students develop a productive disposition ___________________________________________________________________________________ Review the slide. A student’s mindset influences his/her motivation. Briars (2011) Implementing the More Challenging Aspects of Common Core State Standards California’s Common Core State Standards: Toolkit | Instruction, K-5 | ELA and Mathematics

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**Students Can Develop Growth Mindsets**

Explicit instruction about the brain, its function, and that intellectual development is the result of effort and learning has increased students’ achievement in middle school mathematics. Teacher praise influences mindsets: Fixed: Praise refers to intelligence Growth: Praise refers to effort, engagement, perseverance TIME: 10 minutes (CONTINUED for Slides 57 to 62) ___________________________________________________________________________________ Ask, “How many of you can think of a student who had a fixed mindset? A growth mindset? Many unmotivated students have a fixed mindset. We need to help students develop a growth mindset so they will put in the effort. Review the slide. Briars (2011) Implementing the More Challenging Aspects of Common Core State Standards California’s Common Core State Standards: Toolkit | Instruction, K-5 | ELA and Mathematics

68
**Expectancy: Can I Do This?**

Attribute successes to high effort or effective strategy Attribute failures to low effort or ineffective strategy Avoid saying, “You’re smart” Discuss the different views of intelligence Be explicit about what sorts of effort lead to success Design instruction to support successful learning experiences TIME: 10 minutes (CONTINUED for Slides 57 to 62) ___________________________________________________________________________________ Review the slide. Possible talking points: Telling a student s/he is “smart” reinforces a belief that success is based primarily on ability rather than practice and persistence. Saying you’re smart reinforces a fixed mindset because you are or you aren’t. Efforts that lead to success are taking notes, demonstrating problem-solving strategies, mathematical discourse, asking for help, and/or teaching others. Strategies for designing instruction to support success are connecting to existing understandings, providing balanced instruction, academic language support, structured peer support, and differentiated instruction. Ask, “When you think about the Table Pattern Task, how was a growth mindset supported?” Participants should pair share at their tables. If time allows, call on one or two individuals to share out. Dweck (2006) Presentation on Intelligence Theory California’s Common Core State Standards: Toolkit | Instruction, K-5 | ELA and Mathematics

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**Value: Is This Important?**

“How many of us have used the “it’s on the test” to emphasize the importance of a skill or assignment?” TIME: 10 minutes (CONTINUED for Slides 57 to 62) ___________________________________________________________________________________ Once we address “Can I Do This?,” we need to address “Is This Important?” Many of us have used the “it’s on the test” as a reason to emphasize the importance to students of a skill or assignment. Sometimes this rationale is effective because it addresses a student’s short-term goal of passing the class or receiving a good grade, but the research connecting rigor, relevance, and relationships other critical reasons why a student sees something as important. California’s Common Core State Standards: Toolkit | Instruction, K-5 | ELA and Mathematics

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**Value: Is This Important?**

Connect classroom activities to personal short-term goals. Connect classroom activities to personal long-term goals. Place classroom activities in personally meaningful contexts. TIME: 10 minutes (CONTINUED for Slides 57 to 62) ___________________________________________________________________________________ Review the slide as follows: [click] Other personal short-term goals besides grades include: goals—personal pride, peer and parental approval, recognition, autonomy (“I get to decide what I do”). [click] Personal long-term goals connect to possible careers or jobs, including post-secondary education. Long- and short-term goals may be addressed in personal conversations with students. However, instruction that is more relevant or personally meaningful not only increases student interest, but also deepens learning through application and students are better able to retain skills and knowledge (retention through connections—Quadrant B, C, D learning). [click] Personally meaningful contexts include applying mathematics to situations they can relate to (concrete realia, referencing local places or people, interdisciplinary connections with classes they are currently taking, etc.) If time allows, tell participants to think of some skills or concepts they have taught in which content was put into a context to which students could relate. Have them discuss with their table, and then call on several tables to share out. California’s Common Core State Standards: Toolkit | Instruction, K-5 | ELA and Mathematics

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**Growth Mindset and Productive Disposition**

“Just as students must develop a productive disposition towards mathematics such that they believe that mathematics makes sense and that they can figure it out, so too must teachers develop a similar productive disposition.” National Research Council (2001) Adding It Up “Just as students must develop a productive disposition toward’s mathematics such that they believe that mathematics makes sense and that they can figure it out, so too must teachers develop a similar productive disposition.” National Research Council (2005) Adding It Up TIME: 10 minutes (CONTINUED for Slides 57 to 62) ___________________________________________________________________________________ Review the slide. [click] …”so too must teachers develop a similar productive disposition.” California’s Common Core State Standards: Toolkit | Instruction, K-5 | ELA and Mathematics

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**Best Practices for the Common Core**

Engage students with challenging tasks that involve active meaning making Quadrant B, C, and D learning opportunities Cognitively-Guided Instruction with a focus on the Standards for Mathematical Practice Questioning to facilitate thinking and learning Promote learners’ beliefs about their own intelligence (growth mindset vs. fixed mindset) Design instruction to support student success Explicitly reinforce high effort and students’ use of effective strategies Repackage content using real-world connections, puzzles, and games Model a productive disposition TIME: 6 minutes (CONTINUED for Slides 63 to 66) INTENT: To summarize the module and highlight best practices ___________________________________________________________________________________ Review the slide as follows: [click] First big idea: Engage students with challenging tasks that involve active meaning making. [click] Second big idea: Promote learners’ beliefs about their own intelligence (growth mindset vs. fixed mindset California’s Common Core State Standards: Toolkit | Instruction, K-5 | ELA and Mathematics

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**Reflection Think about what you learned today.**

Decide on one thing you will do differently to start transitioning to the Common Core State Standards. Share your ideas with a partner. TIME: 6 minutes (CONTINUED for Slides 63 to 66) INTENT: To reflect and plan next steps toward transitioning to the CCSS ___________________________________________________________________________________ Have participants reflect on today’s learning. Ask them to decide on one thing they will do differently to start transitioning to the CCSS. Have participants share their ideas with a partner. If time allows, ask for volunteers to share out. California’s Common Core State Standards: Toolkit | Instruction, K-5 | ELA and Mathematics

74
**Effective Instruction**

“A long line of students has established that the single most important school influence on student learning is the quality of the teacher.” as presented by Linda Darling-Hammond (2007) How would you describe a classroom where effective instruction and learning is taking place? TIME: 8 minutes (for Slides 3 to 6) INTENT: To set the stage. ___________________________________________________________________________________ Read the quote. [click] How would you describe a classroom where effective instruction and learning is taking place? Have participants discuss the question with a partner. INSTRUCTOR NOTE: Linda Darling-Hammond is a Professor of Education at Stanford University. She is a former president of the American Educational Research Association and member of the National Academy of Education. Her research, teaching, and policy work focus on issues of school restructuring, teacher quality, and educational equity. From , she served as Executive Director of the National Commission on Teaching and America’s Future, a blue-ribbon panel whose 1996 report, What Matters Most: Teaching for America’s Future, led to sweeping policy changes affecting teaching and teacher education. California’s Common Core State Standards: Toolkit | Instruction, | ELA

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**Update Supplemental Instructional Materials**

Recent legislation (SB 140) authorizes the CDE to approve supplemental instructional materials to provide a bridge between the common core academic content standards and the instructional materials currently being used. TIME: 5 minutes (for Slide 3) INTENT: To review the legislation supporting supplemental instructional materials. ___________________________________________________________________________________ SB 140 (Lowenthal) – Instructional Materials Signed by the Governor on October 8th, 2011 Chaptered by the Secretary of State as Chapter 623, Statutes of 2011 Purpose is to develop a list of supplemental instructional materials (SIMS) aligned with CCSS On/before July 1, 2012 For use in K-7 in mathematics and K-8 for ELA SBE must approve or reject the list by September 30, 2012 SIMs provide a bridge between the common core academic content standards and the instructional materials currently being used. There will be two types of materials: 1) those connected to current programs and 2) those that stand alone (not connected to a specific program). CDE Process CDE review of SIMs currently in first phase Process reviews standards maps and adopted materials of participating publishers for alignment to CCSS Proposed evaluation criteria for SIMs was submitted by CDE to State Board of Education (SBE) at the January board meeting Additional updated information is available on the CDE Superintendent’s Supplemental Materials Review Web page at California’s Common Core State Standards: Toolkit | Instructional Materials, K-5 | ELA and Mathematics

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**Step 1: Select a Standard**

Examples of Grade Level Shifts Concept 1997 Standard CCSS Compose simple shapes to form larger shapes (e.g., 2 triangles to form a rectangle) Grade 2 Kindergarten Introduction of fractions as numbers Grade 3 Add and subtract simple fractions Grade 4 Introduction of Integers Grade 6 Dividing fractions by fractions Grade 5 TIME: 60 minutes (CONTINUED for Slides 14 to 23) INTENT: To provide an overview of Step 1 ___________________________________________________________________________________ The first step is to Select a Standard. This chart provides examples of concepts that have either shifted to an earlier grade, such as “composing simple shapes to form larger shapes…” or to a later grade, such as “introduction of fractions as numbers…” adapted from © 2001 California County Superintendents Educational Services Associations, Mathematics General California’s Common Core State Standards: Toolkit | Instructional Materials, K-5 | ELA and Mathematics

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**Step 1: Select a Standard Model**

Concept: Add and Subtract Fractions Domain: Number and Operations – Fractions 4.NF Standard: 3b. Decompose a fraction into a sum of fractions with the same denominator in more than one way, recording each decomposition by an equation. Justify decompositions, e.g., by using a visual fraction model. Examples: 3/8 = 1/8 + 1/8 + 1/8 3/8 = 1/8 + 2/ /8 = /8 = 8/8 + 8/8 + 1/8 TIME: 60 minutes (CONTINUED for Slides 14 to 23) INTENT: To provide a model of Step 1 ___________________________________________________________________________________ For our purposes today, we are are selecting the concept of adding and subtracting fractions. Adding and Subtracting Simple Fractions: We choose this concept because it is an example of a grade level shift. This concept is taught in 3rd grade in the current standards and will be taught in 4th grade in the CCSS. Regarding this choice of standard, using the CCSS for Mathematics, we selected standard 4NF.3b in grade 4. We choose this standard because it is new to the grade level and because of its complexity, detail, and level of application that it requires. Next, we will align the standard. HANDOUTS: CCSS for Mathematics Examples of Grade Level Shifts California’s Common Core State Standards: Toolkit | Instructional Materials, K-5 | ELA and Mathematics

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**Step 2: Align the Standard Model**

Look for instruction and resources that align to the standard. Determine the resources with which you will start. Analyze the instruction, identify the alignment in the instructional design, rigor, and/or focus of the materials. TIME: 60 minutes (CONTINUED for Slides 14 to 23) INTENT: To provide a model of Step 2 ___________________________________________________________________________________ The second step is to align the current instructional materials to the standard. [click] First, demonstrate looking for instructional materials and resources that align to the standard. [click] Next, think aloud about which resources you might start with, using the Teachers Editions as the minimum requirement. Student materials and ancillary resources should also be reviewed along with any other instructional materials. [click] Then, analyze aloud the materials to identify alignment and gaps in the instructional design, rigor, and/or focus. Allow time for participants to practice aligning a standard on their own. INSTRUCTOR NOTE: Advanced preparation is recommended prior to modeling Step 2. HANDOUTS: CCSS for Mathematics California’s Common Core State Standards: Toolkit | Instructional Materials, K-5 | ELA and Mathematics

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**Step 3: Identify Next Steps**

With your group, identify the next steps necessary to analyze the alignment between the CCSS and current instructional materials. Record the next steps on chart paper. Be prepared to share with the whole group. TIME: 60 minutes (CONTINUED for Slides 14 to 23) INTENT: To identify the next steps needed to analyze alignment in instruction or resources in current instruction ___________________________________________________________________________________ Review the slide. Guide the group to consider their next steps in their teaching practice – what else do they need to know in order to be prepared to implement the standards? What questions or concerns do they have about what they learned in this process? Call the group back together to share out with the whole group. SUPPLIES: Chart paper Markers California’s Common Core State Standards: Toolkit | Instructional Materials, K-5 | ELA and Mathematics

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**Part 1: Connecting to Standards for Mathematical Practice Instructional Materials**

With your table group, locate and read the Questions for Planning and Observation handout. Discuss how these questions might support the effective implementation of these practices and what, if any, additional questions you might add. TIME: 60 minutes (CONTINUED for Slides 14 to 23) INTENT: To have participants interact with a set of questions specially created to elicit student behaviors that focus on the Standards for Mathematical Practice ___________________________________________________________________________________ Have participants read through the questions. Remind them that these questions focus on student actions for each Standards for Mathematical Practice. Have them discuss how these might be used to support the Standards for Mathematical Practice and add any other questions they might have. HANDOUTS: Questions for Planning and Observation California’s Common Core State Standards: Toolkit | Instructional Materials, K-5 | ELA and Mathematics

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**Part 2: Connecting to Standards for Mathematical Practice Instructional Materials**

Follow along as the instructor models the Task Analysis Templates and Samples. With a partner, look through your instructional materials and locate places that could be used to support the effective implementation of the Standards for Mathematical Practice. Consider: Lesson Sections Sample Problems/Tasks Assessment Items Other Ancillary Materials TIME: 60 minutes (CONTINUED for Slides 14 to 23) INTENT: To have participants explore their current instructional materials to find places/problems/tasks that help support the attainment of the Standards for Mathematical Practice ___________________________________________________________________________________ Ask participants to locate the Task Analysis Templates and Task Analysis Samples. Using one of the Task Analysis Template Samples provided, explain the process of finding a rich task, describing expected student actions, and relating them to a specific practice. The modifications section can be used if additional prompts or changes can be made to further enhance the task. HANDOUTS: Task Analysis and Task/Practice Samples and Templates California’s Common Core State Standards: Toolkit | Instructional Materials, K-5 | ELA and Mathematics

82
**Describe the expected student behaviors. **

Part 3: Connecting to Standards for Mathematical Practice Instructional Materials Using the Task Analysis Template, “Finding and Enhancing Tasks Already Aligned to CCSS Standards for Mathematical Practice in the Text,” find a specific problem/task that reflects a CCSS mathematical practice. Describe the expected student behaviors. Be prepared to share with the whole group. TIME: 60 minutes (CONTINUED for Slides 14 to 23) ___________________________________________________________________________________ Review the slide. After participants have had time to explore their materials and complete their own template, have them share out a specific task. It is important that they be as specific as possible about the expected student action and how it relates to the Standards for Mathematical Practice. HANDOUTS: Task Analysis and Task/Practice Samples and Templates California’s Common Core State Standards: Toolkit | Instructional Materials, K-5 | ELA and Mathematics

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**Part 4: Connecting to Standards for Mathematical Practice Instructional Materials**

With a partner, identify a “routine” problem from a lesson in your instructional materials using the Task/Practice Sample, “Extending a Textbook Problem to Access a Mathematical Practice.” Using the Standards for Mathematical Practice, describe how you might extend the problem to better access a SPECIFIC practice. TIME: 60 minutes (CONTINUED for Slides 14 to 23) ___________________________________________________________________________________ Using one of the Task/Practice samples, explain the process of finding a “typical” task and extending it to reflect one practice, then extending it again for a different practice. Review the slide. Inform participants that it is important for them to pick a problem that is typical of most lessons. Make sure they extend the problem to reflect just one practice. Share out some of their examples. INSTRUCTOR NOTE: A number of schools and districts across the country are beginning to implement CCSS by trying out a kind of “pilot” unit or selecting specific mathematical practices to try in a specific area of mathematics curriculum. This allows them to explore different ways the mathematical practices can be used, and helps them to see how current materials do or do not support the mathematical practices. It also begins to suggest the kinds of supplemental materials that may be needed. HANDOUTS: Task Analysis and Task/Practice Samples and Templates California’s Common Core State Standards: Toolkit | Instructional Materials, K-5 | ELA and Mathematics

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**Be ready to share out both problems.**

Part 5: Connecting to Standards for Mathematical Practice Instructional Materials Using the same problem, discuss how you would extend it again to access a DIFFERENT Standards for Mathematical Practice. Be ready to share out both problems. TIME: 60 minutes (CONTINUED for Slides 14 to 23) ___________________________________________________________________________________ Review the slide. Tell participants that they will now take the same problem and extend it again to reflect a different Standards for Mathematical Practice. This will focus them on student actions. INSTRUCTOR NOTE: Guide the participants to continue to examine how they can use different Standards for Mathematical Practice to fully teach a concept and application. Task Practice Templates are available for participants to choose more of the concepts and skills that they find most critical to teach. This activity is a precursor to beginning to use the Standards for Mathematical Practice with current instructional materials. HANDOUTS: Task Analysis and Task/Practice Samples and Templates California’s Common Core State Standards: Toolkit | Instructional Materials, K-5 | ELA and Mathematics

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Reflection How might the information from this activity change the way you utilize instructional materials to effectively incorporate Standards for Mathematical Practice in your instruction? Which problems/tasks will you choose to implement and why? Which Standards for Mathematical Practice are addressed in these tasks? TIME: 10 minutes (for Slide 24) ___________________________________________________________________________________ Have participants complete a module reflection form and discuss. Share out if there is time. HANDOUTS: Reflection Questions California’s Common Core State Standards: Toolkit | Instructional Materials, K-5 | ELA and Mathematics

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Alignment Process Aligning Current Instructional Materials to the Common Core State Standards Select the Standard Align the Standard Identify Next Steps TIME: 2 minutes (for Slide 4) INTENT: To provide a quick overview of the process that we have outlined to do this analysis ___________________________________________________________________________________ Review the slide. These are the three steps we have identified to help us transition to the CCSS. Let participants know that you will model each of the steps, and then have them complete the process on their own. Because the standards are so closely articulated from grade to grade, it is important that the instruction from grade to grade is equally aligned. We recommend that cross-grade level groups work on the same standard simultaneously. California’s Common Core State Standards: Toolkit | Instructional Materials, | ELA

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**Step 1: Select a Standard**

Start with Standards that are completely new to a grade Standards that are significantly different in rigor or complexity Decide on a comprehensive approach Review one of these standards from each strand OR Review one whole strand at a time TIME: 20 minutes (for Slides 5 to 6) INTENT: To provide an overview of Step 1 ___________________________________________________________________________________ The first step is to select a standard. [click] Start with a standard that is new or significantly different. [click] Then, decide on a comprehensive approach – either review one of these standards from each strand or one whole strand at a time. Next, I will model this process. California’s Common Core State Standards: Toolkit | Instructional Materials, | ELA

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**Step 2: Aligning the Standard to Your Current Instructional Materials**

Look for instructional materials and resources in your current adoption that align to the standard. Brainstorm which materials and resources you will start with. “Dig in” to identify alignment or gaps in the instructional design, rigor, and/or focus of the materials. TIME: 30 minutes (for Slides 7 to 8) INTENT: To provide an overview of Step 2 ___________________________________________________________________________________ The second step is to align the current instructional materials to the standard. [click] First, look for instructional materials and resources that align to the standard. [click] Next, brainstorm which resources you might start with, using the Teacher’s Edition as the minimum requirement. Student materials and ancillary resources should also be reviewed along with any other instructional materials. [click] Then, “dig in” to the materials to identify alignment and gaps in the instructional design, rigor, and/or focus. INSTRUCTOR NOTE: Participants should look for evidence of alignment of the standards to the lessons and resources in their instructional materials. California’s Common Core State Standards: Toolkit | Instructional Materials, | ELA

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**Step 3: Identify Next Steps**

With your group, identify the next steps necessary to analyze the alignment between the CCSS and current instructional materials. Record the next steps on chart paper. Be prepared to share with the whole group. TIME: 20 minutes (for Slide 10) INTENT: To identify the next steps needed to analyze alignment in instruction or resources in current instruction ___________________________________________________________________________________ Review the slide. Guide the group to consider their next steps in their teaching practice – what else do they need to know in order to be prepared to implement the standards? What questions or concerns do they have about what they learned in this process. Call the group back together to share out. California’s Common Core State Standards: Toolkit | Instructional Materials, | ELA

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Reflect, Discuss, Share Examine standards that will clearly require collaboration. Develop ideas for ways in which teachers will work together across content areas. Consider ways that collaboration can be sustained in planning, teaching, and assessment of student work. Share out main ideas and where to start. TIME: 30 minutes (for Slide 12) INTENT: To help teachers consider how instructional materials from other content areas must be used in partnership with teachers in other departments to meet the CCSS ___________________________________________________________________________________ Review the slide. Inform participants that the last 10 minutes of this activity should be used to compile and record on chart paper your main ideas for each bullet. When 10 minutes remain, let participants know it is time to chart. HANDOUTS: CCSS for ELA CCSS for ELA: Anchor Standards SUPPLIES: Chart paper Markers California’s Common Core State Standards: Toolkit | Instructional Materials, | ELA

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**Connecting to Current Practice**

Think-Pair-Share How do the new standards correspond to what you already include in your curriculum? Think back to the last informational text passage, writing, or speaking assignment you gave your students. What might you do differently next time to help students transition to the CCSS? TIME: 4 minutes (for Slide 29) ___________________________________________________________________________________ Have participants reflect on their current practices and what they might start doing now to transition to the CCSS. California’s Common Core State Standards: Toolkit | Content and Curriculum, K-12 | ELA

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Next Steps What can be done as an individual teacher, a department, a site, and/or a district to support the transition to teaching the CCSS? Choose a perspective and write down three ideas: TIME: 10 minutes (for Slides 13 to 14) INTENT: To provide participants with time to reflect and plan next steps toward transitioning to the CCSS ___________________________________________________________________________________ Review the slide. Encourage participants to record and commit to next steps. Note that Teacher leaders/Administrators may want to anticipate the challenges their teachers may express and think about how they might provide support. Ask participants to share their idea(s) in a small group. If time allows, conduct a whole-group debrief by charting responses. Ask participants to choose one of their own ideas and one of the “group responses” to incorporate as next steps. California’s Common Core State Standards: Toolkit | Instructional Materials, | ELA

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**For Further Investigation**

California’s Common Core State Standards Common Core State Standards Initiative Illustrativemathematics.org commoncoretools.me map.mathshell.org ime.math.arizona.edu/progressions TIME: 10 minutes (CONTINUED for Slides 13 to 14) ___________________________________________________________________________________ Review the slide. California’s Common Core State Standards: Toolkit | Instructional Materials, | ELA

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**Math Standards Summary (key concepts/skills) of Standard:**

1 2 3 4 5 6 7 8 9 10 TIME: 23 minutes (CONTINUED for Slides 11 to 19) ACTIVITY (handout) ___________________________________________________________________________________ Summaries might include: 1 = ask/answer questions 2 = determine main idea; analyze development; provide summary 3 = analyze interactions; identify key steps 4 = determine meaning of unknown words 5 = analyze use of text features; analyze text structures 6 = acknowledge differences in points of view; evaluate different points of view 7 = draw information from several sources; compare and contrast various mediums 8 = describe how reasons support specific points; distinguish among fact, opinion, reasoned judgment 9 = integrate information from several texts; analyze seminal U.S. documents and how they address related themes and concepts 10 = read and comprehend literary nonfiction; read and comprehend history/social studies texts; read and comprehend science and technical subject texts. If time permits, have participants share out. California’s Common Core State Standards: Toolkit | Content and Curriculum, K-12 | ELA

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Common Core State Standards—Mathematics Introduction/Overview 1 Cathy Carroll

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