The Standards for Mathematical Practice

1. Building More Awareness & Ideas for Implementation! Jim Mirabelli � Mathematics Assessment Specialist Indiana Department of Education January 2012 The Standards for Mathematical Practice

2. �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) Practice the Practices Everyday!

3. CCSS Mathematical Practices Make sense of problems and persevere in solving them Reason abstractly and quantitatively Construct viable arguments and critique the reasoning of others Model with mathematics Use appropriate tools strategically Attend to precision Look for and make use of structure Look for and express regularity in repeated reasoning

4. Grouping the Standards for Mathematical Practice (McCallum, 2011)

5. Implementation of Standards for Mathematical Practice: General Guidelines

6. Math Website Resources

7. Divide and conquer How is the information similar/different than my current practice? How can I use this information? One Approach to Reviewing these Resources��

8. �The Standards for Mathematical Practice should be embedded in classroom instruction, discussions, and activities���students should have opportunities to work on carefully designed, standards-based mathematical tasks that can vary in difficulty, context, and type. � ��.assessment as well as curriculum and classroom activities must include a balance of mathematical tasks that provide opportunities for students to develop the kinds of expertise described in the practices.� �Connecting content and practices happens in the context of working on problems. � �The Standards for Mathematical Practice interact and overlap with each other and several may be used together in solving a given problem. They are not a checklist.� PARCC Model Content Frameworks: Key Understandings

9. �Students learn and use strategies for finding products and quotients that are based on the properties of operations; for example, to find 4�?�7 they may recognize that 7 = 5�?�2 and compute 4�?�5 ? 4�?�2. This is an example of seeing and making use of structure (MP.7). Such reasoning processes amount to brief arguments that students may construct and critique (MP.3).� PARCC Model Content Frameworks: A 3rd Grade Example (Pg 16)

10. �Students will analyze a number of situation types for multiplication and division, including arrays and measurement contexts. Extending their understanding of multiplication and division to these situations requires that they make sense of problems and persevere in solving them (MP.1), look for and make use of structure (MP.7) as they model these situations with mathematical forms (MP.4), and attend to precision (MP.6) as they distinguish different kinds of situations over time (MP.8). � PARCC Model Content Frameworks: A 3rd Grade Example (Pg 16)

11. PARCC Model Content Frameworks: Examples from CCSS Pg 89

12. PARCC Model Content Frameworks: Examples from CCSS Pg 89

13. �Area, surface area, and volume present modeling opportunities (MP.4) and require students to attend to precision with the types of units involved (MP.6).� A sample task: Create a miniature golf design for one hole. Your design must contain at least one triangle and one quadrilateral. Use a metric ruler to label the measurements of your design. Find the perimeter and area of your design. Students must: Create a design using knowledge of shapes Apply math to real world � shapes, perimeter, and area Be precise with measurements, labels, calculations PARCC Model Content Frameworks: A 6th Grade Example (Pg 29)

14. �Students think with precision (MP.6) and reason quantitatively (MP.2) when they use variables to represent numbers and write expressions and equations to solve a problem (6.EE.6�7). � An Example: A train travels at a constant speed of 35 miles per hour. Write an equation that represents the distance this train travels over time. Make a table showing 5 different pairs of distances and times for this train. Model this situation using a graph. Things to think about: Describe this situation to a friend. What does 35 miles per hour mean? Table of values: 35 miles in 1 hour, then 70 miles in 2 hours, etc. Precision with use of variables. Let D = the distance traveled in miles by the train. Let t = the time the train travels in hours. Check equations � does it make sense? Revise if needed. Precision with titles and labels when creating table and graph PARCC Model Content Frameworks: A 6th Grade Example (Pg 29)

15. PARCC Model Content Frameworks: High School Thoughts Connecting the SMP with math content (see examples in CF) Modeling and rich applications Star symbol ( ) in CCSS Review Appendix D in the Content Frameworks www.mathmodels.org http://map.mathshell.org/materials/index.php

16. 16 PARCC Timeline

17. PARCC Next Steps�����..

18. Math Practice 1

19. Math Practice 2

20. Math Practice 2

21. Math Practice 3

22. Math Practice 4

23. Math Practice 4

24. Math Practice 4

25. Math Practice 4

26. Math Practice 5

27. Math Practice 6

28. Math Practice 7

29. Math Practice 8

30. Indiana TimelineISTEP+ Grades 3-8 and ECAs 30

31. MP3 � Construct viable arguments and critique the reasoning of others Students: Understand and use prior learning in constructing arguments Teacher: Provides opportunities for students to listen to or read the conclusions and arguments of others How can you use this information to improve your current practice? http://www.relnei.org/events.webinararchives.php Oct. 2011 Webinar featuring Dr. �Skip� Fennell �Look For�s complete list in IDOE � Assessment Information for Teachers Community on LC Math Practice �Look For�s

32. Awareness Gained? Ideas for implementing Math Practices? Start small � pick one resource Read, discuss, implement, discuss, revise Divide and conquer Are You Overwhelmed Yet?

33. QUESTIONS? 33