1. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Functions A Close Look at Grade 9 Module 5

2. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Functions Opening Exercise Critique the following problem from G9-M5 Lesson 6:

3. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Functions A Close Look at Grade 9 Module 5

4. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Functions Participant Poll Classroom teacher Math trainer Principal or school leader District representative / leader Other

5. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Functions Session Objectives Experience the instructional approaches to teaching the content of Grade 9 Module 5 lessons. Articulate how the lessons promote mastery of the focus standards and how the module addresses the major work of the grade. Make connections from the content of previous modules and grade levels to the content of this module.

6. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Functions Agenda Orientation to Materials (if needed) Examination and exploration of: Topic A Topic B End of Module Assessment

7. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Functions Session Objectives Examination of the development of mathematical understanding across the module using a focus on Concept Development within the lessons. Introduction to mathematical models and instructional strategies to support implementation of A Story of Ratios. Consideration of scaffolding to provide multiple entry points for students at all levels.

8. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Functions Session Objectives Examination of the development of mathematical understanding across the module using a focus on Concept Development within the lessons. Introduction to mathematical models and instructional strategies to support implementation of A Story of Ratios. Consideration of scaffolding to provide multiple entry points for students at all levels.

9. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Functions A Story of Ratios Scaffolding Mathematics Instruction Key Points Amplify Language Move from Concrete to Representation to Abstract Give Specific Guidelines for Speaking, Reading, Writing, or Listening

10. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Functions Amplify Language Give clear mathematical definitions Explain multiple meanings Maintain consistency and point out interchangeable terminology

11. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Functions Move from Concrete to Representation to Abstract Use familiar contexts Visually organize thinking Provide multiple representations

12. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Functions Give Guidelines for Speaking, Reading, Writing, or Listening Provide structured opportunities to speak and write in English Give explicit instructions in student-friendly language Use visuals or examples in giving instructions.

13. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Functions Key Points Amplify Language Move from Concrete to Representation to Abstract Give Guidelines for Speaking, Reading, Writing, or Listening

14. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Functions 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?

15. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Functions Turn and Talk How does this task align with the Universal Design for Learning (UDL) in providing multiple options for: Representation: the “what of learning” Action/Expression: the “how” of learning Engagement: the “why” of learning

16. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Functions 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

17. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Functions Types of Lessons 1.Problem Set Students and teachers work through examples and complete exercises to develop or reinforce a concept. 2.Socratic Teacher leads students in a conversation to develop a specific concept or proof. 3.Exploration Independent or small group work on a challenging problem followed by debrief to clarify, expand or develop math knowledge. 4.Modeling Students practice all or part of the modeling cycle with real-world or mathematical problems that are ill-defined.

18. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Functions 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

19. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Functions Agenda Orientation to Materials (if needed) Examination and exploration of: Topic A Topic B End of Module Assessment

20. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Functions Flow of Module 5 A Synthesis of Modeling with Equations and Functions Topic A: Elements of Modeling Analyzing a Graph Analyzing a Data Set Analyzing a Verbal Description Topic B: Completing the Modeling Cycle Modeling a Context from a Graph Modeling from a Sequence Modeling a Context from Data Modeling a Context from a Verbal Description

21. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Functions 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

22. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Functions Topic A – Lesson 1: Analyzing a Graph Example 1 Exercises 1-6 Problem Set

23. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Functions Topic A – Lesson 2: Analyzing a Data Set Opening Exercise 1 Exercise 2 Problem Set – Problem 4

24. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Functions Topic A – Lesson 3: Analyzing a Verbal Description Exercise 1 Exercise 2 Exercise 3 Exercise 4

25. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Functions Key Points – Topic A The lessons in Topic A serve to consolidate student knowledge about linear, exponential and quadratic functions.

26. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Functions Agenda Orientation to Materials (if needed) Examination and exploration of: Topic A Topic B End of Module Assessment

27. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Functions Topic B – Lesson 4: Modeling a Context from a Graph Example 1 Exercise 2 Exit Ticket: Why might we want to represent a graph of a function in analytical form? Why might we want to represent a graph as a table of values?

28. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Functions Topic B – Lesson 5: Modeling a Context from a Sequence Opening Are there functions that could model this data well? If a student has up to 30 min of actual gym time during practice, how many exercises in the circuit would she be able to complete? Do we believe in patterns? Problem Set – Problems 2-4

29. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Functions Opening Exercise Critique the following problem from G9-M5 Lesson 6:

30. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Functions Topic B – Lessons 6-7: Modeling a Context from Data Lesson 6 Example 1 and Exercises 1-3 Lesson 6 Exit Ticket Lesson 7 is designed to use the regression analysis of a Ti- 84 to find equations that model data Lesson 7 Exercise 2 Lesson 7 Exit Ticket

31. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Functions Topic B – Lessons 8-9: Modeling a Context from a Verbal Description Lesson 8: Example 1-2 Lesson 8: Problem Set: #1 Lesson 8: Problem Set: #2 Lesson 9: Exit Ticket Lesson 9: Problem Set #2

32. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Functions 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.

33. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Functions Agenda Orientation to Materials (if needed) Examination and exploration of: Topic A Topic B End of Module Assessment

34. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Functions End-of-Module Assessment Work with a partner on this assessment

35. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Functions Scoring the Assessment

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

37. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Functions 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?