A Story of Functions

1. A Story of Functions A Close Look at Grade 9 Module 5

2. Session Objectives • Understand the mathematical concepts developed within Grade 9 Module 5. • Practice collecting evidence of effective instruction using transcripts of classroom instruction. • Discuss feedback strategies for supporting scaffolding and accommodation techniques for special populations

3. What’s In a Module? • Teacher Materials • Module Overview • Topic Overviews • Daily Lessons • Assessments • Student Materials • Daily Lessons with Problem Sets • Copy Ready Materials • Exit Tickets • Fluency Worksheets / Sprints • Assessments

4. Types of Lessons • Problem Set Students and teachers work through examples and complete exercises to develop or reinforce a concept. • Socratic Teacher leads students in a conversation to develop a specific concept or proof. • Exploration Independent or small group work on a challenging problem followed by debrief to clarify, expand or develop math knowledge. • Modeling Students practice all or part of the modeling cycle with real-world or mathematical problems that are ill-defined.

5. What’s In a Lesson? • Teacher Materials Lessons • Student Outcomes and Lesson Notes (in select lessons) • Classwork • General directions and guidance, including timing guidance • Bulleted discussion points with expected student responses • Student classwork with solutions (boxed) • Exit Ticket with Solutions • Problem Set with Solutions • Student Materials • Classwork • Problem Set

11. What are students coming in with? • G9-M1 Relationships Between Quantities and Reasoning with Equations and Their Graphs • G9-M2 Descriptive Statistics • G9-M3 Linear and Exponential Functions • G9-M4 Polynomial and Quadratic Expressions, Equations and Functions

13. Turn and Talk • What difficulties would you anticipate with student understanding of the mathematics in this section? • What scaffolds would be effective for addressing those difficulties?

18. Lesson Transcript Activity

19. Round Robin Activity • In your table groups, share the observations you made using the CCSS Instructional Practice Guide. • Each group member shares one observation and the supporting evidence. Then the group member to his/her right shares. • Continue this process until all • observations have been shared.

22. Turn and Talk • What difficulties would you anticipate with student understanding of the mathematics in this section? • What scaffolds would be effective for addressing those difficulties?

26. Key Points – Module 5 Lessons • Reinforce the notion that we are modeling with functions – • Push students to recognize when they are or are not given enough information to be sure that the function will be an accurate representation of the data or information described. • Use precision when speaking and encourage students to do the same by questioning them for accuracy and precision. • Remain aware of the discrete vs. continuous domain in the context of the situation. • Approach Lesson Summaries as opportunities for students to consolidate their knowledge – ask& scaffold, don’t tell.

27. End-of-Module Assessment Work with a partner to determine the types of accommodations and/or scaffolding that the assessment items may require.

28. Scoring the Assessment

29. Key Points – End-of-Module Assessment • Shorter modules, like G9-M5 do not have Mid-Module Assessments, only an End-of-Module Assessment designed to assess all standards of the module. • Recall, as much as possible, assessment items are designed to asses the standards while emulating PARCC Type 2 and Type 3 tasks. • Recall, rubrics are designed to inform each district / school / teacher as they make decisions about the use of assessments in the assignment of grades.

30. Biggest Takeaway What are your biggest takeaways from the study of Module 5? How can you support successful implementation of these materials at your schools given your role as a teacher, trainer, school or district leader, administrator or other representative?