1. Lesson Design: An Overview of Key Tools for Flexible Math Instruction Think about Ms. Christiansen—the teacher in the video. What helps a teacher plan for and facilitate this kind of lesson?

2. Key Themes Multiplicity and Flexibility

3. Multiplicity “Multiplicity” has to do with having knowledge of a variety of teaching and learning topics: curriculum, instructional models, lesson types, engaging learners, assessment strategies, representing mathematical ideas,...

4. Flexibility Flexibility has to do with the ability to use the knowledge of techniques, strategies, and ways of thinking in ways to provide several avenues of access to learning or a special approach that improves access for everyone.

5. Considerations for Designing Lessons Basic Principles and Best Practices Tools for Flexible Math Instruction Types of Math Lessons “Layers” of Planning

6. Basic Principles Begin with Concrete Representation Develop Understanding Encourage Communication Make Connections Take Time to Motivate Children Provide Opportunities for (Meaningful) Practice

7. Best Practice: Interlocking Ideas Student-Centered Experiential Holistic Authentic Expressive Reflective Social Collaborative Democratic Cognitive Developmental Constructivist Challenging

8. Tools for Flexible Math Instruction Multiple Means of Engagement Multiple Means of Representation Multiple Means of Communication Multiple Means of Assessment

9. Multiple Means of Engagement Such as:

10. Multiple Means of Representation Such as:

11. Multiple Means of Communication Such as:

12. Multiple Means of Assessment Such as:

13. Types of Math Lessons Before Teachers begin planning for lessons, they must know what “type” of lesson they will be teaching. The type of lesson influences many decisions a teacher makes in planning for teaching: The instructional model that guides the lesson The type of mathematical task Mathematical representations of ideas Grouping Assessment

14. Introductory Lesson: The first time a concept, skill, procedure has been taught.

15. Maintenance/Extension Lesson: A continuation or practice of a previous lesson’s concept, skill, or procedure—perhaps taking it to a deeper level or making connections.

16. Review Lesson: A concept/skill/procedure that was taught previously, but the students need to revisit.

17. “Layers” of Planning Planning for the Year Planning for the Term Planning of a Unit Planning for the Week Planning for the Day

18. Planning for the Year Tasks What is the purpose of the class? Do you need to write a course description? What are the main teaching units within the curriculum for the grade level or course? What guides the curriculum? [school, district, or state curriculum guides; department?] Approximately when will you teach each unit? How do you plan to determine end-of-term student grades? Useful Resources:

19. Planning for a Term Tasks Given the main teaching units for the year, what units will be focused on during each marking term? How much time will each unit need? Will some units cross disciplines or involve team teaching? Will any special activities be part of certain units—guest speakers, field trips? What do students already know? What school activities might impact the amount of time you have for each term? Useful Resources:

20. Planning for a Unit Tasks What are the overarching learning goals for the unit (the “big ideas”)? What are the specific student-centered objectives that define and clarify each learning goal? What else would students like to learn or know? What task ideas does the textbook offer related to each learning goal/objective? Do you have task ideas for each of the unit objectives you identified? What is a tentative sequence of the tasks ? What assessment strategies will be important for monitoring student progress and informing your teaching? (formative assessment) What ideas do you have for assessing cumulative student progress towards the learning goals for the unit? (summative assessment) Useful Resources:

21. Planning for the Week The weekly planning could be considered a “thumb- nail” sketch of lessons for the week. Tasks How will you organize your plan book? What activities do you know must be scheduled around within the week? [such as SEP’s, unit test, field trip in another class, fire drills,... ] Useful Resources:

22. Planning the Day’s Lesson: Components to Consider Activity Title Grade Level Core Standard and Objective Specific Lesson Objective Intended Learning Outcomes Lesson Type Instructional Model Connections Key Terms/Symbols Key Questions Materials Warm-Up Invitation to Learn Instructional Procedures Adaptations and Differentiation Assessment Closure