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1 National Council of Supervisors of Mathematics Illustrating the Standards for Mathematical Practice: Reasoning and Explaining The National Council of Supervisors of Mathematics The Common Core State Standards Illustrating the Standards for Mathematical Practice: Reasoning about Problems and Unpacking Others Reasoning www.mathedleadership.org

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2 National Council of Supervisors of Mathematics Illustrating the Standards for Mathematical Practice: Reasoning and Explaining Module Evaluation Facilitator: At the end of this Powerpoint, you will find a link to an anonymous brief e- survey that will help us understand how the module is being used and how well it worked in your setting. We hope you will help us grow and improve our NCSM resources!

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3 National Council of Supervisors of Mathematics Illustrating the Standards for Mathematical Practice: Reasoning and Explaining Common Core State Standards Mathematics Standards for Content Standards for Practice

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4 National Council of Supervisors of Mathematics Illustrating the Standards for Mathematical Practice: Reasoning and Explaining Todays Goals To explore the mathematical standards for Content and Practice To consider how the Common Core State Standards (CCSS) are likely to impact your mathematics program and plan next steps In particular, participants will Examine opportunities to develop skill in reasoning about problems and unpacking othersreasoning

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5 National Council of Supervisors of Mathematics Illustrating the Standards for Mathematical Practice: Reasoning and Explaining 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. (CCSS, 2010)

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6 National Council of Supervisors of Mathematics Illustrating the Standards for Mathematical Practice: Reasoning and Explaining Standards for Mathematical Practice 1.Make sense of 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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7 National Council of Supervisors of Mathematics Illustrating the Standards for Mathematical Practice: Reasoning and Explaining Structuring the Practices

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8 National Council of Supervisors of Mathematics Illustrating the Standards for Mathematical Practice: Reasoning and Explaining Standards for Mathematical Practice What implications might the Standards for Mathematical Practice have on your classroom? 1. Individually review the Standards for Mathematical Practice. 2.Choose a partner at your table and discuss a new insight you had into the Standards for Mathematical Practice. 3.Then discuss the following question.

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9 National Council of Supervisors of Mathematics Illustrating the Standards for Mathematical Practice: Reasoning and Explaining Buttons Task Gita plays with her grandmothers collection of black and white buttons. She arranges them in patterns. Her first 3 patterns are shown below. Pattern #1 Pattern #2 Pattern #3 Pattern #4 1.Draw pattern 4 next to pattern 3. 2.How many white buttons does Gita need for Pattern 5 and Pattern 6? Explain how you figured this out. 3.How many buttons in all does Gita need to make Pattern 11? Explain how you figured this out. 4.Gita thinks she needs 69 buttons in all to make Pattern 24. How do you know that she is not correct? How many buttons does she need to make Pattern 24?

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10 National Council of Supervisors of Mathematics Illustrating the Standards for Mathematical Practice: Reasoning and Explaining Buttons Task 1.Individually complete parts 1 - 3. 2.Then work with a partner to compare your work and complete part 4. Look for as many ways to solve parts 3 and 4 as possible. 3.Consider each of the following questions and be prepared to share your thinking with the group: a)What mathematics content is needed to complete the task? b)Which mathematical practices are needed to complete the task?

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11 National Council of Supervisors of Mathematics Illustrating the Standards for Mathematical Practice: Reasoning and Explaining The Nature of Tasks Used in the Classroom … Tasks as they appear in curricular materials Student learning Will Impact Student Learning!

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12 National Council of Supervisors of Mathematics Illustrating the Standards for Mathematical Practice: Reasoning and Explaining But, WHAT TEACHERS DO with the tasks matters too! Stein, Grover & Henningsen (1996) Smith & Stein (1998) Stein, Smith, Henningsen & Silver (2000) The Mathematical Tasks Framework Tasks as they appear in curricular materials Student learning Tasks as they appear in curricular materials Student learning Tasks as set up by teachers Tasks as enacted by teachers and students

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13 National Council of Supervisors of Mathematics Illustrating the Standards for Mathematical Practice: Reasoning and Explaining www.InsideMathematics.org A re-engagement lesson using the Buttons Task Francis Dickinson San Carlos Elementary Grade 5 http://www.insidemathematics.org/index.php/classroom-video-visits/public- lessons-numerical-patterning/218-numerical-patterning-lesson- planning?phpMyAdmin=NqJS1x3gaJqDM-1-8LXtX3WJ4e8

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14 National Council of Supervisors of Mathematics Illustrating the Standards for Mathematical Practice: Reasoning and Explaining Learner A Pictorial Representation What does Learner A see staying the same? What does Learner A see changing? Draw a picture to show how Learner A sees this pattern growing through the first 3 stages. Color coding and modeling with square tiles may come in handy. Verbal Representation Describe in your own words how Learner A sees this pattern growing. Be sure to mention what is staying the same and what is changing.

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15 National Council of Supervisors of Mathematics Illustrating the Standards for Mathematical Practice: Reasoning and Explaining Learner B Pictorial Representation What does Learner B see staying the same? What does Learner B see changing? Draw a picture to show how Learner B sees this pattern growing through the first 3 stages. Color coding and modeling with square tiles may come in handy. Verbal Representation Describe in your own words how Learner B sees this pattern growing. Be sure to mention what is staying the same and what is changing.

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16 National Council of Supervisors of Mathematics Illustrating the Standards for Mathematical Practice: Reasoning and Explaining Buttons Task Revisited Which of the Standards of Mathematical Practice did you see the students working with? Cite explicit examples to support your thinking. What did Mr. Dickinson gain from using the same math task two days in a row, rather than switching to a different task(s)? How did the way the lesson was facilitated support the development of the standards of practice for students? What implications for teachers implementing CCSS does this activity suggest to you?

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17 National Council of Supervisors of Mathematics Illustrating the Standards for Mathematical Practice: Reasoning and Explaining Again, WHAT TEACHERS DO with the tasks matters too! Stein, Grover & Henningsen (1996) Smith & Stein (1998) Stein, Smith, Henningsen & Silver (2000) The Mathematical Tasks Framework Tasks as they appear in curricular materials Student learning Tasks as they appear in curricular materials Student learning Tasks as set up by teachers Tasks as enacted by teachers and students

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18 National Council of Supervisors of Mathematics Illustrating the Standards for Mathematical Practice: Reasoning and Explaining Planning to Support Students Opportunity to Learn Select a typical task (or a related set of problems) from your instructional materials and design a lesson so that it offers more opportunities for students to develop both the content and practice standards.

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19 National Council of Supervisors of Mathematics Illustrating the Standards for Mathematical Practice: Reasoning and Explaining Next Steps and Resources Review the implications you listed earlier and discuss with your table group one or two next steps you might take as a district, school, and classroom teacher.

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20 National Council of Supervisors of Mathematics Illustrating the Standards for Mathematical Practice: Reasoning and Explaining Todays Goals To explore the mathematical standards for Content and Practice To consider how the Common Core State Standards (CCSS) are likely to impact your mathematics program and plan next steps In particular, participants will Examine opportunities to develop skill in reasoning about problems and unpacking othersreasoning

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21 National Council of Supervisors of Mathematics Illustrating the Standards for Mathematical Practice: Reasoning and Explaining End of Day Reflections 1. Are there any aspects of your own thinking and/or practice that our work today has caused you to consider or reconsider? Explain. 2.Are there any aspects of your students mathematical learning that our work today has caused you to consider or reconsider? Explain.

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22 National Council of Supervisors of Mathematics Illustrating the Standards for Mathematical Practice: Reasoning and Explaining Join us in thanking the Noyce Foundation for their generous grant to NCSM that made this series possible! http://www.noycefdn.org/

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23 National Council of Supervisors of Mathematics Illustrating the Standards for Mathematical Practice: Reasoning and Explaining Project Contributors Geraldine Devine, Oakland Schools, Waterford, MI Aimee L. Evans, Arch Ford ESC, Plumerville, AR David Foster, Silicon Valley Mathematics Initiative, San José State University, San José, California Dana L. Gosen, Ph.D., Oakland Schools, Waterford, MI Linda K. Griffith, Ph.D., University of Central Arkansas Cynthia A. Miller, Ph.D., Arkansas State University Valerie L. Mills, Oakland Schools, Waterford, MI Susan Jo Russell, Ed.D., TERC, Cambridge, MA Deborah Schifter, Ph.D., Education Development Center, Waltham, MA Nanette Seago, WestEd, San Francisco, California Hope Bjerke, Editing Consultant, Redding, CA

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24 National Council of Supervisors of Mathematics Illustrating the Standards for Mathematical Practice: Reasoning and Explaining Help Us Grow! The link below will connect you to a anonymous brief e- survey that will help us understand how the module is being used and how well it worked in your setting. Please help us improve the module by completing a short ten question survey at: http://tinyurl.com/samplesurvey1

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