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© ASCD 2013 | Common Core State Standards Bill and Melinda Gates/ASCD Grant: Virtual Learning Networks: Mathematics Webinar 1: Demonstrating Mathematical Understanding Teacher Networks: Building Capacity for Powerful Instruction January 2014

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© ASCD 2013 | Common Core State Standards Virtual Convening Agenda WELCOME! Introduction of ASCD Faculty Member and attendees Reminder of VLN Goals Today’s Problem of Practice Possible Next POP for Webinar 2? ASCD/Gates Grant: Virtual Learning Networks

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© ASCD 2013 | Common Core State Standards Virtual Convening Agenda WELCOME! Introduction of ASCD Faculty Member and attendees Overview of the ASCD/Gates Grant Eliciting Problems of Practice Next steps ASCD/Gates Grant: Virtual Learning Networks

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© ASCD 2013 | Common Core State Standards Nanci Smith ASCD/Gates Grant: Virtual Learning Networks

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© ASCD 2013 | Common Core State Standards Poll 1: Who are you? ASCD/Gates Grant: Virtual Learning Networks

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© ASCD 2013 | Common Core State Standards Poll 2: What do you do in education? ASCD/Gates Grant: Virtual Learning Networks

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© ASCD 2013 | Common Core State Standards Virtual Convening Agenda WELCOME! Introduction of ASCD Faculty Member and attendees Reminder of VLN Goals Today’s Problem of Practice Possible Next POP for Webinar 2? ASCD/Gates Grant: Virtual Learning Networks

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© ASCD 2013 | Common Core State Standards Two Years Five Webinars per year Content specific Host by ASCD faculty member Synchronous Recorded and archived on EduCore ASCD/Gates Grant: Virtual Learning Networks

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© ASCD 2013 | Common Core State Standards Goals: 1. Cultivate “Constructivist Community” 2. Help understand and facilitate the implementation of the CCSS-M 3. Develop a virtual team to support each other 4. Exchange resources ASCD/Gates Grant: Virtual Learning Networks

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© ASCD 2013 | Common Core State Standards Phase One 1 Virtual Convening 4 Webinars Structured around “Problem of Practice” Challenges identified by participants in implementing CCSS in their classrooms Collaboration with trusted experts Helpful feedback in a timely manner ASCD/Gates Grant: Virtual Learning Networks

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© ASCD 2013 | Common Core State Standards ASCD Edge ASCD proprietary social networking platform Share comments and resources Share video, audio, photos Share upcoming events, updates, alerts PLEASE!!! Join the conversation. Blog on the Edge. Respond to postings. Ask questions! Share ideas. ASCD/Gates Grant: Virtual Learning Networks

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© ASCD 2013 | Common Core State Standards ascdedge.ascd.org

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© ASCD 2013 | Common Core State Standards Virtual Convening Agenda WELCOME! Introduction of ASCD Faculty Member and attendees Reminder of VLN Goals Today’s Problem of Practice Possible Next POP for Webinar 2? ASCD/Gates Grant: Virtual Learning Networks

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© ASCD 2013 | Common Core State Standards Something To Try First… WHICH ONE DOES NOT BELONG AND WHY? Short Answer Question 1: Please type your response in the question box!

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© ASCD 2013 | Common Core State Standards Today’s Problem of Practice How do we get students to engage with math like a mathematician through the Common Core? ASCD/Gates Grant: Virtual Learning Networks

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© ASCD 2013 | Common Core State Standards Key Instructional Shifts: Mathematics Focus: Focus on where standards focus - Deep not wide! Coherence: Think across grades and link to major topics - Progressions ASCD/Gates Grant: Virtual Learning Networks

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© ASCD 2013 | Common Core State Standards Key Instructional Shifts: Mathematics, Cont. Rigor: Require fluency, application, deep understanding – A balance of conceptual understanding and skill. Math Practices College and Career Readiness ASCD/Gates Grant: Virtual Learning Networks

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© ASCD 2013 | Common Core State Standards Key Instructional Shifts: Mathematics Today’s POP looks more deeply at: Rigor: Require fluency, application, deep understanding – A balance of conceptual understanding and skill. Math Practices ASCD/Gates Grant: Virtual Learning Networks

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© ASCD 2013 | Common Core State Standards ASCD/Gates Grant: Virtual Learning Networks Rigor - Balance of Conceptual Understanding and Skills Source: From “Balance of Conceptual Understanding and Skills,” by the Hunt Institute.

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© ASCD 2013 | Common Core State Standards ASCD/Gates Grant: Virtual Learning Networks Rigor - Balance of Conceptual Understanding and Skills Conceptual Understanding: 3.NF.1 Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction a/b as the quantity formed by a parts of size 1/b. Procedural Skill and Fluency: 5.NBT.5 Fluently multiply multi-digit whole numbers using the standard algorithm. Application: 7.NS.3 Solve real-world and mathematical problems involving the four operations with rational numbers.

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© ASCD 2013 | Common Core State Standards Green Flags and Red Flags Adapted from Leading the Change to Common Core State Standards: Essential Tools for School and District Leaders by Sue Z. Beers and Judy F. Carr, © 2012 by ASCD. All rights reserved Teacher-Controlled Actions ASCD/Gates Grant: Virtual Learning Networks

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© ASCD 2013 | Common Core State Standards ASCD/Gates Grant: Virtual Learning Networks Rigor - Balance of Conceptual Understanding and Skills Equal intensity Speed not an issue Authentic, real-life practice and extended application Little or no formative assessment Timed tests as only mastery assessment Tricks and mnemonic devices

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© ASCD 2013 | Common Core State Standards ASCD/Gates Grant: Virtual Learning Networks Rigor - Balance of Conceptual Understanding and Skills Deep conceptual understanding and assessment Feedback and next steps tied to standards Justification Strategies without fluency and conceptual understanding Accepting steps without reasoning Weak explanation

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© ASCD 2013 | Common Core State Standards ASCD/Gates Grant: Virtual Learning Networks Rigor - Balance of Conceptual Understanding and Skills Fluency with number facts Efficiency and accuracy Judicious use of technology that does not impede fluency Over use of tables and aids (including calculators) No fluency expectations, or fluency achieved only outside of the classroom

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© ASCD 2013 | Common Core State Standards Poll Question 3: What Green Flags are strongest in your class, school or district? ASCD/Gates Grant: Virtual Learning Networks a. Speed not an issue b. Authentic, real-life practice and extended application c. Deep conceptual understanding and assessment d. Fluency with number facts e. Use of technology that does not impede fluency

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© ASCD 2013 | Common Core State Standards Poll Question 4: What Green Flags need more attention in your class, school or district? ASCD/Gates Grant: Virtual Learning Networks a. Speed not an issue b. Authentic, real-life practice and extended application c. Deep conceptual understanding and assessment d. Fluency with number facts e. Use of technology that does not impede fluency

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© ASCD 2013 | Common Core State Standards But, what about student- controlled actions? Standards for Mathematical Practices ASCD/Gates Grant: Virtual Learning Networks

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© ASCD 2013 | Common Core State Standards ASCD/Gates Grant: Virtual Learning Networks Mathematical Practices Standards 1.Make sense of complex problems and persevere in solving them. 2.Reason abstractly and quantitatively 3.Construct viable arguments and critique the reasoning of others. 4.Model with mathematics. 5.Use appropriate tools strategically. 6.Attend to precision 7.Look for and make use of structure 8.Look for and express regularity in repeated reasoning.

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© ASCD 2013 | Common Core State Standards ASCD/Gates Grant: Virtual Learning Networks Mathematical Practices Standards 1.Make sense of complex problems and persevere in solving them. Key Ideas Before: Explain the problem; organize information; make a plan During: Persevere!; monitor progress; check reasonableness; create new plans After: Check my answer and method; reflect on what worked Student Actions Display sense-making behaviors Show patience and listen to others Turn and talk for first steps and/or generate solution plan Analyze information in problems Use and recall multiple strategies Self-evaluate and redirect Assess reasonableness of process and answer Nanci Smith, 2014

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© ASCD 2013 | Common Core State Standards ASCD/Gates Grant: Virtual Learning Networks Mathematical Practices Standards 2.Reason abstractly and quantitatively Key Ideas Contextualize and Decontextualize Reasoning Habits include 1) creating an understandable representation of the problem solved, 2) considering the units involved, 3) attending to the meaning of quantities, and 4) using properties to help solve problems. Student Actions Represent abstract and contextual situations symbolically Interpret problems logically in context Estimate for reasonableness Make connections including real life situations Create and use multiple representations Visualize problems Put symbolic problems into context Nanci Smith, 2014

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© ASCD 2013 | Common Core State Standards ASCD/Gates Grant: Virtual Learning Networks Mathematical Practices Standards 3.Construct viable arguments and critique the reasoning of others. Key Ideas Construct arguments: justify and generalize; use examples and non- examples; use multiple representations including manipulatives and drawings Critique reasoning: listen well; identify mistakes; ask questions to clarify thoughts and ideas Student Actions Questions others Use examples and non-examples Support beliefs and challenges with mathematical evidence Forms logical arguments with conjectures and counterexamples Use multiple representations for evidence Listen and respond to others well Uses precise mathematical vocabulary Nanci Smith, 2014

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© ASCD 2013 | Common Core State Standards ASCD/Gates Grant: Virtual Learning Networks Mathematical Practices Standards 4.Model with mathematics. Key Ideas Understand and express how math models the real world Represent Math through: concrete models symbols pictures oral real-world language situations Student Actions Connect math (numbers and symbols) to real-life situations Symbolize real-world problems with math Make sense of mathematics Apply prior knowledge to solve problems Choose and apply representations, manipulatives and other models to solve problems Use strategies to make problems simpler Use estimation and logic to check reasonableness of an answer Nanci Smith, 2014

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© ASCD 2013 | Common Core State Standards ASCD/Gates Grant: Virtual Learning Networks Mathematical Practices Standards 5.Use appropriate tools strategically. Key Ideas Recongnize that math tools are not all material tools but include mental strategies. Know HOW to use math tools. Know WHEN to use math tools. Know WHICH tool to use. Reason about the effectiveness of tools. Student Actions Choose appropriate tool(s) for a given problem Use technology to deepen understanding Identify and locate resources Defend mathematically choice of tool Nanci Smith, 2014

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© ASCD 2013 | Common Core State Standards ASCD/Gates Grant: Virtual Learning Networks Mathematical Practices Standards 6.Attend to precision Key Ideas Speak, read, write and listen mathematically. Calculate accurately and efficiently. Use correct notation, vocabulary and units of measure. Answer what a question asks. Student Actions Communicate (oral and written) with precise vocabulary Carefully formulate questions and explanations (not retelling steps) Decode and interpret meaning of symbols Pay attention to units, labeling, scale, etc. Calculate accurately and effectively Express answers within context when appropriate Nanci Smith, 2014

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© ASCD 2013 | Common Core State Standards ASCD/Gates Grant: Virtual Learning Networks Mathematical Practices Standards 7.Look for and make use of structure Key Ideas The structure of numbers and operations make sense and I can use those structures to solve problems. Access the organization of numbers and space to solve problems. Student Actions Look for, identify, and interpret patterns and structures Make connections to skills and strategies previously learned to solve new problems and tasks Breakdown complex problems into simpler and more manageable chunks Use multiple representations for quantities View complicated quantities as both a single object or a composition of objects Nanci Smith, 2014

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© ASCD 2013 | Common Core State Standards ASCD/Gates Grant: Virtual Learning Networks Mathematical Practices Standards 8.Look for and express regularity in repeated reasoning. Key Ideas Look for and use patterns. Use repeated reasoning to solve similar problems. Create “shortcuts” and strategies based on patterns. Student Actions Design and state “shortcuts” Generate “rules” from repeated reasoning or practice (e.g. integer operations) Evaluate the reasonableness of intermediate steps Make generalizations Nanci Smith, 2014

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© ASCD 2013 | Common Core State Standards Classroom Challenge: Interpreting Algebraic Expressions Found on EduCore ™ ! ASCD/Gates Grant: Virtual Learning Networks

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© ASCD 2013 | Common Core State Standards Classroom Challenge: Interpreting Algebraic Expressions Found on EduCore ™ ! ASCD/Gates Grant: Virtual Learning Networks

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© ASCD 2013 | Common Core State Standards Interpreting Algebraic Expressions ASCD/Gates Grant: Virtual Learning Networks

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© ASCD 2013 | Common Core State Standards Short Answer #2 Short Answer #2 Which Practices did the students exhibit and when? ASCD/Gates Grant: Virtual Learning Networks

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© ASCD 2013 | Common Core State Standards Virtual Convening Agenda WELCOME! Introduction of ASCD Faculty Member and attendees Reminder of VLN Goals Today’s Problem of Practice Next steps ASCD/Gates Grant: Virtual Learning Networks

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© ASCD 2013 | Common Core State Standards Continue the learning: Archived webinar on Mathematical Understandings: -development/webinars/nanci- smith-webinar.aspx -development/webinars/nanci- smith-webinar.aspx -development/webinars/nanci- smith-webinar.aspx ASCD/Gates Grant: Virtual Learning Networks

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© ASCD 2013 | Common Core State Standards ASCD/Gates Grant: Virtual Learning Networks Short Answer #3 Short Answer #3 On what topics or Problems of Practice would you like next month’s Webinar to focus?

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© ASCD 2013 | Common Core State Standards Next Steps: Post, Post, Post!! Please use Edge to communicate! Let’s get a real dialogue going. ASCD/Gates Grant: Virtual Learning Networks

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© ASCD 2013 | Common Core State Standards Our Webinars are scheduled for: Thursday, December 12 th Friday, January 17 th Friday, February 21 st Friday, March 28 th Monday, May 5 th Be Sure to Join on Edge!! ASCD/Gates Grant: Virtual Learning Networks

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© ASCD 2013 | Common Core State Standards Questions? Comments? Concerns? Quips? Quotes? Qualms? Or Conundrums? Be Sure to Join on Edge!! Invite Others. ASCD/Gates Grant: Virtual Learning Networks

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© ASCD 2013 | Common Core State Standards Thank you! Connect with me on: ASCD Edge: Nanci Smith & VLN Mathematics Group ASCD/Gates Grant: Virtual Learning Networks

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