1. National Council of Supervisors of Mathematics CCSS Standards of Mathematical Practice: Reasoning and Explaining The Common Core State Standards Illustrating the Standards for Mathematical Practice: Mathematical Modeling and Constructing Viable Arguments www.mathedleadership.org The National Council of Supervisors of Mathematics

2. National Council of Supervisors of Mathematics CCSS Standards of Mathematical Practice: Reasoning and Explaining Common Core State Standards Mathematics Standards for Content Standards for Practice

3. National Council of Supervisors of Mathematics CCSS Standards of Mathematical Practice: Reasoning and Explaining Today’s Goals To explore the Standards for Content and Practice. Consider how the CCSS Standards are likely to impact your mathematics program and to plan next steps. In particular participants will: Examine opportunities to develop skill in mathematical modeling and constructing viable arguments.

4. National Council of Supervisors of Mathematics CCSS Standards of 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)

5. National Council of Supervisors of Mathematics CCSS Standards of 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.

6. National Council of Supervisors of Mathematics CCSS Standards of Mathematical Practice: Reasoning and Explaining Standards for Mathematical Practice 1.Individually review the Standards for Mathematical Practice. 2.Choose a partner at your table and discuss a new insight you had into the practices, then discuss the following question: What implications might the standards of mathematical practice have on your classroom?

7. National Council of Supervisors of Mathematics CCSS Standards of Mathematical Practice: Reasoning and Explaining Common Core State Standards 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.

8. National Council of Supervisors of Mathematics CCSS Standards of Mathematical Practice: Reasoning and Explaining Common Core State Standards for Mathematical Practice In our work today, we will examine the eight Standards for Mathematical Practice through a classroom vignette. Consider: What is the nature of mathematical tasks in these classrooms? What do you hear or see in a mathematics classroom that is working to build the Standards for Mathematical Practice?

9. National Council of Supervisors of Mathematics CCSS Standards of Mathematical Practice: Reasoning and Explaining Common Core Standards of Mathematical Practice Teacher Goals: –Students will make mathematical sense of the tables and discover the mathematical reasoning. –Students will go beyond the notion that the table is either right or wrong to evaluate both mathematical sense and correct modeling. Outline: 1.Gym Task (Formative Assessment) 2.Video Rental Task (Classroom Vignette) 3.Carnival Task (Culminating Activity)

10. National Council of Supervisors of Mathematics CCSS Standards of Mathematical Practice: Reasoning and Explaining www.Inside Mathematics.org http://www.insidemathematics.org/index.php/classroom-video-visits/public- lessons-comparing-linear-functions/264-comparing-linear-functions- introduction?phpMyAdmin=NqJS1x3gaJqDM-1-8LXtX3WJ4e8http://www.insidemathematics.org/index.php/classroom-video-visits/public- lessons-comparing-linear-functions/264-comparing-linear-functions- introduction?phpMyAdmin=NqJS1x3gaJqDM-1-8LXtX3WJ4e8

11. National Council of Supervisors of Mathematics CCSS Standards of Mathematical Practice: Reasoning and Explaining Using Formative Assessment to Plan Instruction 1.Carlo thinks he will go to the gym about 20 times a month. Calculate how much each of these options would cost Carlo for one month. Which of these options is the least expensive for Carlo? Pay as you go Pay only $6 each time you work out Regular deal Pay $50 a month and $2 each time you work out All-in-one price! Pay just $100 per month for unlimited use of our great facilities

12. National Council of Supervisors of Mathematics CCSS Standards of Mathematical Practice: Reasoning and Explaining Using Formative Assessment to Plan Instruction Consider the summary of 6 th grade results of the Gym task. What are some possible next steps to deal with misconceptions or misunderstandings documented in the table?

13. National Council of Supervisors of Mathematics CCSS Standards of Mathematical Practice: Reasoning and Explaining Exploring Standards for Mathematical Practice in a Classroom 2.Create verbal and tabular representations of the 3 DVD rental plans below. Do the three plans ever cost the same? Movie Buster $3 per movie rented Online Flix $12 per month plus $1 per movie rented Mail Flix $18 per month regardless of the number of movies rented

14. National Council of Supervisors of Mathematics CCSS Standards of Mathematical Practice: Reasoning and Explaining Exploring Standards for Mathematical Practice in a Classroom In what ways did the teacher give students opportunities to make sense of the task and build perseverance in his launch of the task? launch What evidence do you see that students are building this standard of practice?

15. National Council of Supervisors of Mathematics CCSS Standards of Mathematical Practice: Reasoning and Explaining Using Student Work to Develop Standards for Mathematical Practice Examine the tables generated by Student H on the following slide. Given this work, what conclusions has the student made? What mistakes (if any) are evident in the tables? Do the tables make mathematical sense, and do they match the plans?

16. National Council of Supervisors of Mathematics CCSS Standards of Mathematical Practice: Reasoning and Explaining Using Student Work to Develop Standards for Mathematical Practice Movies 1234567 $3$6$9$12$15$18$21 Money 1234567 $13$14$15$16$17$18$19 1234567 $18$36$54$72$90$108$126 Movie Buster Online Flix Mail Flix Student H

17. National Council of Supervisors of Mathematics CCSS Standards of Mathematical Practice: Reasoning and Explaining Using Student Work to Develop Standards for Mathematical Practice As you watch the video consider:video What evidence do you see that suggests students are developing competency with Standards 1 and/or 3 for Mathematical Practice? In what ways did interactions between students support their ability to develop competency with Standards 1 and/or 3 for Mathematical Practice?

18. National Council of Supervisors of Mathematics CCSS Standards of Mathematical Practice: Reasoning and Explaining Sharing Student Work to Develop Standards for Mathematical Practice # of Movies MBOFMF 001218 132518 263818 395118 4126418 5157718 6 9018 Examine the table generated by Student A at the right. Given this work, what conclusions has the student made? What mistakes (if any) are evident in the tables?

19. National Council of Supervisors of Mathematics CCSS Standards of Mathematical Practice: Reasoning and Explaining Using Student Work to Develop Standards for Mathematical Practice As you watch the video consider:video What evidence do you see that suggests students are developing competency with Standards 1 and/or 3 for Mathematical Practices? In what ways did interactions between students support their ability to develop competency with Standards 1 and/or 3 for Mathematical Practices?

20. National Council of Supervisors of Mathematics CCSS Standards of Mathematical Practice: Reasoning and Explaining Considering Next Steps 3. Create verbal, graphical, and tabular representations of the carnival ticket plans below. Will any of the three plans ever cost the same? Dollar Deal No Entrance Fee, $1.00 per ticket Bracelet Unlimited tickets with a $12.00 bracelet Discounted Plan $4.00 Entrance Fee, with discounted tickets ($0.50/ticket)

21. National Council of Supervisors of Mathematics CCSS Standards of Mathematical Practice: Reasoning and Explaining Planning and Teaching to Develop Standards for Mathematical Practice How does the use of the three sequenced tasks support students in developing Standards for Mathematical Practice? In what ways might the task(s) have contributed to or undermined students’ developing competency with Standards for Mathematical Practice? What instructional decisions did the teacher make that seemed to support the development of Standards for Mathematical Practice for students?

22. National Council of Supervisors of Mathematics CCSS Standards of Mathematical Practice: Reasoning and Explaining Leading to Develop Standards for Mathematical Practice Reflect on the status of your district/site in developing Standards for Mathematical Practice with respect to: Students Instructional decisions in classrooms The nature of instructional and assessment materials Collegial conversations Professional development

23. National Council of Supervisors of Mathematics CCSS Standards of Mathematical Practice: Reasoning and Explaining Next steps and resources Review the implications you listed earlier, then discuss with your table group one or two next steps you might take as a district, school, and teacher.

24. National Council of Supervisors of Mathematics CCSS Standards of Mathematical Practice: Reasoning and Explaining Today’s Goals To explore the Standards for Content and Practice. Consider how the CCSS Standards are likely to impact your mathematics program and to plan next steps. In particular participants will: Examine opportunities to develop skill in mathematical modeling and constructing viable arguments.

25. National Council of Supervisors of Mathematics CCSS Standards of 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.