1. 1 National Council of Supervisors of Mathematics Illustrating the Standards for Mathematical Practice: Modeling and Using Tools The National Council of Supervisors of Mathematics The Common Core State Standards Illustrating the Standards for Mathematical Practice: Modeling with Mathematics and Using Representational Tools www.mathedleadership.org

2. 2 National Council of Supervisors of Mathematics Illustrating the Standards for Mathematical Practice: Modeling and Using Tools 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!

3. 3 National Council of Supervisors of Mathematics Illustrating the Standards for Mathematical Practice: Modeling and Using Tools Common Core State Standards Mathematics Standards for Content Standards for Practice

4. 4 National Council of Supervisors of Mathematics Illustrating the Standards for Mathematical Practice: Modeling and Using Tools 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 modeling real-world problems with mathematics using appropriate tools and representations

5. 5 National Council of Supervisors of Mathematics Illustrating the Standards for Mathematical Practice: Modeling and Using Tools 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)

6. 6 National Council of Supervisors of Mathematics Illustrating the Standards for Mathematical Practice: Modeling and Using Tools 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.

7. 7 National Council of Supervisors of Mathematics Illustrating the Standards for Mathematical Practice: Modeling and Using Tools Structuring the Practices

8. 8 National Council of Supervisors of Mathematics Illustrating the Standards for Mathematical Practice: Modeling and Using Tools 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.

9. 9 National Council of Supervisors of Mathematics Illustrating the Standards for Mathematical Practice: Modeling and Using Tools The Nature of Tasks Used in the Classroom … Tasks as they appear in curricular materials Student learning Will Impact Student Learning!

10. 10 National Council of Supervisors of Mathematics Illustrating the Standards for Mathematical Practice: Modeling and Using Tools Maria and Wayne Task Maria saved $24. She saved 3 times as much as Wayne. How much money did Wayne save? Work the task. What representations and strategies did you use to solve the task?

11. 11 National Council of Supervisors of Mathematics Illustrating the Standards for Mathematical Practice: Modeling and Using Tools Maria saved $24. She saved 3 times as much as Wayne. 1. In what way(s) did the set-up of the task differ from the traditional way we experienced the task? 2. Why do you think Ms. Sherman might have set up the task the way she did? 3. What standards for mathematical practice might be addressed through her delivery? Teacher Set Up Task as Set Up

12. 12 National Council of Supervisors of Mathematics Illustrating the Standards for Mathematical Practice: Modeling and Using Tools 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

13. 13 National Council of Supervisors of Mathematics Illustrating the Standards for Mathematical Practice: Modeling and Using Tools www.InsideMathematics.org Four boys discuss their understanding of the task. 1.What representational tools do the boys use to engage in the task? 2.What mathematics do they use to model the real-world problem? 3.How does their conversation demonstrate any of the Standards for Mathematical Practice?

14. 14 National Council of Supervisors of Mathematics Illustrating the Standards for Mathematical Practice: Modeling and Using Tools Closer Look at Content 4.OA.2 Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison. 1.What made the content of this problem so difficult and led students into thinking the problem might be 3 x 24? 2.What about student approaches reassures you? 3.What about their thinking on this standard needs refinement?

15. 15 National Council of Supervisors of Mathematics Illustrating the Standards for Mathematical Practice: Modeling and Using Tools Closer Look at Practices Model with mathematics. Use appropriate tools strategically. How does the revised task support the students development of expertise regarding these practices?

16. 16 National Council of Supervisors of Mathematics Illustrating the Standards for Mathematical Practice: Modeling and Using Tools Adapted from Lesh, R., Post, T., & Behr, M. (1987). Representations and Translations among Representations in Mathematics Learning and Problem Solving. In C. Janvier, (Ed.), Problems of Representations in the Teaching and Learning of Mathematics (pp. 33-40). Hillsdale, NJ: Lawrence Erlbaum. Geometric/ Graphical Verbal - Written and Oral Tabular Contextual Symbolic Pictures Oral Language Manipulative Models Real-World Situations Written Symbols Representation Stars Elementary Secondary

17. 17 National Council of Supervisors of Mathematics Illustrating the Standards for Mathematical Practice: Modeling and Using Tools One More Look 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.

18. 18 National Council of Supervisors of Mathematics Illustrating the Standards for Mathematical Practice: Modeling and Using Tools 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.

19. 19 National Council of Supervisors of Mathematics Illustrating the Standards for Mathematical Practice: Modeling and Using Tools 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 modeling real-world problems with mathematics using appropriate tools and representations

20. 20 National Council of Supervisors of Mathematics Illustrating the Standards for Mathematical Practice: Modeling and Using Tools 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.

21. 21 National Council of Supervisors of Mathematics Illustrating the Standards for Mathematical Practice: Modeling and Using Tools Join us in thanking the Noyce Foundation for their generous grant to NCSM that made this series possible! http://www.noycefdn.org/

22. 22 National Council of Supervisors of Mathematics Illustrating the Standards for Mathematical Practice: Modeling and Using Tools 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

23. 23 National Council of Supervisors of Mathematics Illustrating the Standards for Mathematical Practice: Modeling and Using Tools 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