A Story of Units

1. A Story of Units Module Focus

2. Session Objectives • Identify key components of the module structure and of each lesson within A Story of Units. • Articulate the instructional focus of Module 1, thereby preparing participants to teach and/or prepare their colleagues to teach this module. • Examine lesson components including Fluency Practice, Application Problems, Concept Development with Problem Sets, and Student Debrief with Exit Tickets.

3. AGENDA • Review of Module Structure • Examination of Module Overview, Assessments, and Topic Openers • Lesson Study • Coherence Across the Module

5. Review of Module Structure

6. AGENDA • Review of Module Structure • Examination of Module Overview, Assessments, and Topic Openers • Lesson Study • Coherence Across the Module

7. Module Overview • Read the descriptive narrative. • Make note of important information that will help educators understand the content and prepare to implement this module.

8. Module Overview • How does this Module compare to your past experiences with this content? • How does each component of the Module Overview prepare you to implement this material in your classroom? • Turn and talk with others at your table about your observations.

9. Module Overview • Focus Standards • Foundational Standards • Mathematical Practices • Terminology • Tools and Representations

10. Standards for Mathematical Practice Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique 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.

11. Module Assessments • Take 5 minutes to work on the designated Assessment. • How does this task measure the skills and understanding that are addressed in this module?

12. Topic Openers • Read the descriptive narrative. • Make note of important information that will help educators implement these lessons.

13. Topic Openers • How does each topic contribute to the overall instructional goal of the module? • How are the Topic Openers useful as a planning tool? • What is the relationship between the Topic Opener and the other components of the module?

14. AGENDA • Review of Module Structure • Examination of Module Overview, Assessments, and Topic Openers • Lesson Study • Coherence Across the Module

15. Lesson Study • Examine the development and function of each lesson component. • Fluency Practice • Application Problems • Concept Development • Student Debrief • How do the lesson components work together to achieve rigor and lead toward the culminating assessment?

16. Lesson Study: Fluency Practice • Daily, substantial, sustained, and supported by the lesson structure • 10-20 minutes of easy-to-administer activities • Energetic activities that allow students to see measureable progress • Promotes automaticity – allows students to reserve their cognitive energy for higher-level thinking • Supports conceptual understanding and application as well as the mathematical practices

17. Lesson Study: Fluency Practice • Fluency activities serve a variety of purposes: • Maintenance: Staying sharp on previously learned skills • Preparation: Targeted practice for the current lesson • Anticipation: Building skills to prepare students for the in-depth work of future lessons • In fluency work, all students are actively engaged with familiar content. This provides a daily opportunity for continuous improvement and individual success.

18. Lesson Study: Fluency Practice

19. Lesson Study: Fluency Practice • In what skills should students be fluent in order to achieve success in this module? • At your table, examine the Fluency Practices in this lesson, considering their specific function within the lesson.

20. Lesson Study: Application Problems • Application involves using relevant conceptual understandings and appropriate strategies even when not prompted to do so. • Time allotted to application varies, but is commonly 5-10 minutes of the lesson. • The Read, Draw, Write (RDW) process is modeled and encouraged through daily problem solving.

21. Lesson Study: Application Problems Lesson 2: Amy is baking muffins. Each baking try can hold 6 muffins. If Amy bakes 4 trays of muffins, how many muffins will she have all together? The corner bakery has made 10 times as many muffins as Amy baked. How many muffins did the bakery produce? Bonus: If the corner bakery packages the muffins in boxes of 100, how many boxes of 100 could they make?

22. Lesson Study: Concept Development • Constitutes the major portion of instruction and generally comprises at least 20 minutes of the total lesson time.  • Builds toward new learning through intentional sequencing within the lesson and across the module. • Often utilizes the deliberate progression from concrete to pictorial to abstract, whichcompliments and supports an increasingly complex understanding of concepts. • Accompanied by thoughtfully sequenced problem sets and reproducible student sheets.

23. Lesson Study: Concept Development

24. Lesson Study: Concept Development

25. Lesson Study: Concept Development • Complete the problem set. • What do you notice about the sequence of problems?

26. Lesson Study: Student Debrief • Includes sample dialogue or suggested lists of questions to invite the reflection and active processing of the totality of the lesson experience. • Encourages students to articulate the focus of the lesson and the learning that has occurred. • Promotes mathematical conversation with and among students. • Allows student work to be shared and analyzed. • Closes the lesson with daily informal assessment known as Exit Tickets.

27. Lesson Study: Student Debrief

28. Lesson Study: Student Debrief

29. Balanced, Rigorous Instruction

30. Biggest Takeaways • How does this lesson compare to your past experiences with mathematics instruction? • Turn and talk with a partner at your table about your biggest takeaways from this session.

31. Key Points • Modules Overviews and Topic Openers provide essential information about the instructional path of the module and are key tools in planning for successful implementation. • Each of the lesson components are necessary in order to achieve balanced, rigorous instruction and to bring the Standards to life. • The Exit Ticket is an essential piece of the Student Debrief and provides daily formative assessment. • Opportunities to nurture the Standards for Mathematical Practice are embedded throughout the lesson.

32. AGENDA • Review of Module Structure • Examination of Module Overview, Assessments, and Topic Openers • Lesson Study • Coherence Across the Module

33. Progression Study • Read the selected portion of the Progression. • Highlight the information relevant to the content of this module.

34. Progression Study • How does this module implement the expectations described in the Progression?

35. Coherence Within the Module • Analyze the progression of each lesson component across the sample of lessons provided. • What does the sequence of Fluency Practicesaccomplish as a whole? • How does the sequence of Application Problems connect to topic/module? • How does the sequence of Concept Development and Student Debrief build toward mastery of the topic/module?

36. Coherence Within the Module • Analyze the progression of each lesson component across the sample of lessons provided. • What does the sequence of Fluency Practicesaccomplish as a whole? • How does the sequence of Application Problems connect to topic/module? • How does the sequence of Concept Development and Student Debrief build toward mastery of the topic/module?

37. Coherence Within the Module • Analyze the selected Problem Sets. • In what ways were the writers intentional in the design of this Problem Set? • How do the Problem Sets build toward the Assessment?

38. Coherence Within the Module • Analyze the selected Problem Sets. • In what ways were the writers intentional in the design of this Problem Set? • How do the Problem Sets build toward the Assessment?

39. Biggest Takeaways • Turn and talk with a partner at your table about your biggest takeaways from this session.

40. Key Points • The base-10 system allows for consistency across all units. • Consistency applies to rounding, as the methods used in Grade 3 rounding are applied to Grade 4 rounding of larger units. • “10 times as much” builds on the understanding of bundling groups of 10. • “Bundling” and “unbundling” from Grade 2 progresses to the addition and subtraction algorithms.

41. Next Steps • 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 this module with other administrators/teachers? • What is your plan for redelivery of this session?