1. MATHEMATICAL PRACTICES Nicole Janz February 17, 2014

2. After Lunch Brain Warm Up  Heads Up

3. Professional Learning Norms 1. Be Respectful of others in your words and actions 2. Stay on Topic 3. Minimize sidebar conversations 4. Begin and end on time 5. Monitor “air time” 6. Put cell phone on “vibe” 7. Pull your own “happiness wagon”

4. Desired Outcome:  Deepen understanding of the Common Core State Standards for mathematical content and mathematical practices

5. Agenda:  Content vs. Practices  Overview of Practices  Kindergarten Classroom  Third Grade Classroom  First Grade Classroom  Math Performance Task  Structure and Routine of a Lesson  Why use Mathematical Task?  Closing Circle

7. Content Standards and Mathematical Practice Standards Content Standards: CCSS for Mathematics What ? Mathematical Practice Standards How ? Balanced Math

16. Wow…Connections…Questions

17. Kindergarten Mathematics Common Core Content Standards K.OA.3 - Decompose numbers less than or equal to 10 into pairs in more than one way, e.g., by using objects or drawings, and record each decomposition by a drawing or equation (e.g., 5 = 2 + 3 and 5 = 4 + 1). K.MD.3 - Classify objects into given categories; count the numbers of objects in each category and sort the categories by count. ELA standard K.RL.10. Common Core Mathematical Practices Math Practice 1 Math Practice 7 Math Practice 8

18. Stand Up...Hand Up…Pair Up… Students stand up, put their hands up, and quickly find a partner with whom to share or discuss 1.Teacher says, when I say go, you will “stand up, hand up, and pair up” Teacher pauses, them says, “Go!” 2.Students stand up and keep one hand high in the air until they find the closest partner who’s not a teammate. Students do a “high five” and put their hands down. 3.Teacher may ask a question or give an assignment, and provides think time. 4.Partners interact using: Rally Robin or Timed Pair Share Kagan, Spencer, and Miguel Kagan. Kagan Cooperative Learning. Moorabbin, Vic.: Hawker Brownlow Education, 2009. Print.

19. Wow…Connections…Questions

20. Third Grade Mathematics Common Core Content Standards 3.OA.2 - Interpret whole-number quotients of whole numbers, e.g., interpret 56 ÷ 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares, or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each. For example, describe a context in which a number of shares or a number of groups can be expressed as 56 ÷ 8. Common Core Mathematical Practices Math Practice 1 Math Practice 5 Math Practice 6

21. Inside-Outside Circle Students rotate in concentric circles to face new partners for sharing, quizzing, or problem solving. 1.Students form pairs. One student from each pair moves to form one large circle in the class facing outward. 2.Remaining students find and face their partners. 3.Inside circle ask a question. Outside circle students answer. Inside circle students praise or coach. 4.Partners switch roles 5.Inside circle students rotate clockwise to a new partner. Kagan, Spencer, and Miguel Kagan. Kagan Cooperative Learning. Moorabbin, Vic.: Hawker Brownlow Education, 2009. Print.

22. Brain Break  Heads Up

23. Wow…Connections…Questions

24. First Grade Mathematics Common Core Content Standards 1.OA.2 - Solve word problems that call for addition of three whole numbers whose sum is less than or equal to 20 1.OA.4 - Understand subtraction as an unknown-addend problem 1.OA.5 - Relate counting to addition and subtraction (e.g., by counting on 2 to add 2). Common Core Mathematical Practices Math Practice 1 Math Practice 2 Math Practice 4

25. One Stray One teammate “strays” from her team to a new team to share or gather information. 1.A number is randomly called and that student from each team stands up. The remaining three teammates remain seated but raise their hands. 2.Teacher calls, “Stray.” 3.Standing students stray to a team that has their hands up 4.Team lower their hands when a new member joins them. Kagan, Spencer, and Miguel Kagan. Kagan Cooperative Learning. Moorabbin, Vic.: Hawker Brownlow Education, 2009. Print.

26. What is conceptual understanding? Students demonstrate conceptual understanding in mathematics when they provide evidence that they can recognize, label, and generate examples of concepts; use and interrelate models, diagrams, manipulatives, and varied representations of concepts; identify and apply principles; know and apply facts and definitions; compare, contrast, and integrate related concepts and principles; recognize, interpret, and apply the signs, symbols, and terms used to represent concepts. Conceptual understanding reflects a student's ability to reason in settings involving the careful application of concept definitions, relations, or representations of either. © Balka, Hull, and Harbin Miles

29. Small Group Problem Solving 1. Reader/Task Focuser- Reread the Problem and help group maintain focus 2. Reporter – Report Solution Path to the Class 3. Recorder – Write on Poster 1. Time Keeper – Monitor Time

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45. http://www.parcconline.org/parcc- assessment

46. Gradual Release of Responsibility Whole Class Cooperative Groups/Teams PartnerIndependent

48. What Mathematical Practices did you use in completing this task?

51. Components of Responsive Classroom  Morning Meeting  Rule Creation  Interactive Modeling  Positive Teacher Language  Logical Consequences  Guided Discovery  Academic Choice  Classroom Organization  Working with Families  Collaborative Problem Solving  Closing Circle

52. Closing Circle  To end the day on a calm and positive note  To practice the habit of reflection  To foster students’ awareness of valuable aspects of school, of themselves, and of classmates  To build and reinforce a sense of community

53. Closing Circle