1. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Module Analysis Grade 5—Module 3

2. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Session Objectives 2 Analyze and walk through Grade 5—Module 3. Understand how topics break into concepts and how lessons are formed from concepts. Examine the flow and format of lessons. Examine how rigorous problem solving is presented in the modules. Watch a video clip of key concepts being taught to students.

3. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units AGENDA 3

4. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Walk Through and Analyze Module Components 4 Table of Contents Overview Topics and Daily Lesson Plans Module Assessments Fluency Progression

5. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Walk Through and Analyze Module Components 5 Module Overview What is this module about? What is the purpose of the Overview?

6. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Walk Through and Analyze Module Components 6 Overview of Module Topics and Focus Lesson Chart How many topics are covered in the module? What standards are covered in the module? How many days of instruction are needed for the module? How many lessons comprise the module? When do you administer the assessments for the module?

7. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units 7 The Overview of Module Topics and Focus Lessons chart lists the teaching sequence towards attaining mastery of the standards highlighted in each lesson. Teaching sequences are the appropriate sequential order for developing mathematics skills. Teachers “build a ladder” to help students: develop conceptual understanding synthesize and apply knowledge from earlier concepts Walk Through and Analyze Module Components

8. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Walk Through and Analyze Module Components 8 Fluency – New and Familiar Fluency activities promote automaticity of skills, allowing students to reserve cognitive resources for higher level thinking.

9. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units The Common Core Approach to Differentiating Instruction 9 The Common Core State Standards for Mathematics require that “all students must have the opportunity to learn and meet the same high standards if they are to access the knowledge and skills necessary in their post school lives.”

10. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units The Common Core Approach to Differentiating Instruction 10 Structure provided by Universal Design for Learning (UDL) Asks teachers to consider: multiple means of representation multiple means of action and expression multiple means of engagement

11. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units The Common Core Approach to Differentiating Instruction 11 Charts provide suggested scaffolds for: English Language Learners Students with Disabilities Students Performing Above Grade Level Students Performing Below Grade Level

12. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units 12 Scaffolds Identify accommodations that are already being used during math instruction in your class/school/district. Walk Through and Analyze Module Components

13. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units The Common Core Approach to Differentiating Instruction 13 Marginal Notes to Teachers in Lessons

14. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Walk Through and Analyze Module Components 14 Scaffolds Look through the marginal notes on scaffolding for Topic A. Find an example you like to share with a partner at your table.

15. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Walk Through and Analyze Module Components 15 Topic Opening: Focus standard(s), instructional days, and coherence links Introductory paragraph Concept chart (one lesson per concept) Mathematical Practices Brought to Life

16. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Walk Through and Analyze Module Components 16 Topic A - Suggested Lesson Structure

17. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Walk Through and Analyze Module Components 17

18. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Walk Through and Analyze Module Components 18

19. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Walk Through and Analyze Module Components Conceptual Development 19

20. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units 20 Reflection: What do you notice about the layout of the Concept Development section of the lesson? Walk Through and Analyze Module Components

21. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Walk Through and Analyze Module Components 21

22. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units 22 Each lesson contains daily assessments: Activity Sheets Exit tickets Homework Walk Through and Analyze Module Components

23. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units 23 Each module has an accompanying section for Supplementary Materials: Assessment Tasks Exit Tickets for each lesson Mid-Module Assessment Task End-of-Module Assessment Task Cross Modular Assessment Task Fluency Progressions Bank of activities to assist with planning Intentionally organized to revisit previously learned skills to develop automaticity, to build for the day’s concept or to anticipate future concepts Walk Through and Analyze Module Components

24. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units 24 What are the strengths of the Module in implementing the CCLS for Mathematics? How does it compare with instructional materials that you have used in the past? Reflection

25. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Key Points 25 A Story of Units includes 5-7 modules for each grade level. A curriculum map and grade level overviews are provided in A Story of Units: A Curriculum Overview for Grades P-5. Topics break into concepts and concepts become lessons. The concepts may be displayed in the classroom as the learning objectives for the lessons.

26. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units AGENDA 26

27. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Analyze Lesson Components of the Module 27

28. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Analyze Lesson Components of the Module 28

29. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Turn and Talk 29 What is another possible order for the lesson components? What is the rationale for structuring the lesson in such an order?

30. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Analyze Lesson Components of the Module 30 Another lesson structure may follow this order: Exploration and Application Problems leading into the Concept Development (35 minutes) Student Debrief (10 minutes) Fluency Practice (15 minutes)

31. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Lesson Analysis 31 Pick one lesson from Grade 5—Module 3 to analyze. As you analyze the lesson, use the Lesson Analysis portion of the Session 2 Reflections Handout to record your observations.

32. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Lesson Analysis – Turn and Talk 32 What is the Suggested Lesson Structure for the lesson that you chose to review and analyze? Does the lesson you selected progress from concrete to pictorial to abstract sequence? If not, which level of concept development is the focus of your lesson and why?

33. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Lesson Analysis – Turn and Talk 33 What do you notice about the fluency portion of the lesson? How is the concept developed in the lesson? Describe the Application part of the lesson. What is the Student Debrief? Why is the Student Debrief important?

34. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Lesson Analysis continued 34 What type of assessment(s) are included in the lesson? Where is there evidence of scaffolding in the lesson you selected to review and analyze? (i.e., for diverse learners including ELLS, SWDs, advanced learners, and struggling learners)

35. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Key Points 35 The Distribution of Instructional Minutes diagram displays the 3 components of rigor. The Suggested Lesson Structure pie chart shows the breakdown of a lesson based upon a 60 minute class. The Publishers’ Criteria emphasize that materials must reflect the Standards’ balanced approach to mathematics, stressing both conceptual understanding as well as procedural skill and fluency. There is a balance of activities and tasks and a balance of how time is spent.

36. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units AGENDA 36

37. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units A Look At Rigorous Problems in the Module 37 Daily Assessments Worksheets Exit Tickets Homework Assignments Daily assessments provide valuable data to inform teachers and direct instruction. Students have daily opportunities to apply conceptual understanding learned during lessons and are held accountable for independent work.

38. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units A Look At Rigorous Problems in the Module 38 Assessment Tasks Mid-Module Assessments End-of-Module Assessments Cross-Modular Assessments

39. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units A Look At Rigorous Problems in the Module 39 Homework Sheets Build upon what students learn in the lesson for the day Provide opportunities for students to check their understanding and confirm they can solve problems independently

40. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units 40 Select one of the homework problem sheets from G5—M3. You may remove the page from your binder and place it inside of your personal board. Examine the problem then use a dry erase marker to solve the problem. A Look At Rigorous Problems in the Module

41. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units 41 Where is there evidence of the Mathematical Content Standards and Standards for Mathematical Practice in these problems? Where is there evidence of the components of rigor (fluency, conceptual understanding and application)? Examining Homework Problems

42. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units 42 Students are exposed to a variety of problems that are really apt to produce a variety of responses. A Look At Rigorous Problems in the Module

43. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Key Points 43 Rigorous problems that produce a variety of student responses are embedded throughout the module. For these problems, answers alone are insufficient. Students must be able to thoroughly explain their thought processes. Possible student work may include bar diagrams, number sentences, area models, paragraphs, etc.

44. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units AGENDA 44

45. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Video of Fractions as Division Concept 45 Guiding Questions: How did the teacher help students develop conceptual understanding? Which Standards for Mathematical Practice did the students demonstrate as they engaged in the lesson? Where did you see evidence of the three components of rigor in the video?

46. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Interpret a Fraction as Division 46 This video is posted in the video library on EngageNY: http://engageny.org/video-library

47. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Video of Fractions as Division Concept 47 Guiding Questions: How did the teacher help students develop conceptual understanding? Which Standards for Mathematical Practice did the students demonstrate as they engaged in the lesson? Where did you see evidence of the three components of rigor in the video?

48. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Biggest Takeaways 48 Turn and talk with a partner at your table about your biggest takeaways from this session.

49. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Key Points 49 A Story of Units: A Curriculum Overview for Grades P-5 provides a curriculum map and grade level overview. The Standards come to life through the lessons. Modules contain topics, topics break into concepts, and concepts become lessons. Rigorous problems are embedded throughout the module. The lesson format supports all Instructional Shifts. G5—M3 exemplifies the key components of each module in the curriculum.

50. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Next Steps 50 How can you transfer what you know about the structure of a module and its key components to next steps in the planning process? What is your plan for sharing Grade 5—Module 3 with other administrators/teachers? What is your plan for redelivery of this session?

51. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM Module Analysis Follow Up

52. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Objectives 52 Share understandings of Grade 2—Module 3 and Grade 5—Module 3 Compare and contrast Grade 2—Module 3 and Grade 5—Module 3 Analyze to find the key components of modules that can be extended to all modules in A Story of Units

53. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Team Time – Share 53 What are the strengths of the module? What questions do you have about the module? How is conceptual understanding developed from simple to complex in G2—M3 and G5— M3?

54. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Team Time – Compare 54 What are the similarities in the structure of G2—M3 and G5—M3? How are the two modules different?

55. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Team Time – Takeaways 55 What are consistent themes across G2—M3 and G5—M3 that are aligned with the CCLS and the major documents? How will knowledge of these modules prepare you for understanding future modules?