A Story of Functions

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

2. Session Objectives Experience and model the instructional approaches to teaching the content of the lessons of the first module. Articulate how the topics and 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 grade levels to the content of this module.

3. Agenda • Module Overview • Focus Standards for Topics A and B • In-Depth Examination of Module 1 Topics A and B: Lessons 1-9 • Demonstration Lessons • Exploring Topics A and B • Preview Topic C • Closure and Reflection

4. Grade 9 Module 1 Overview Insert Table of Contents

5. What’s in G9-M1 Topic A: Explore the main functions of the year (linear, exponential and quadratic) through graphing stories (making graphs of situations) Topic B: Study the structure of expressions, define what it means for expressions to be equivalent, re-write various polynomial expressions in equivalent forms using the properties of equality and the distributive property. Topic C: Precisely explain each step in the process of solving an equation, inequality or system of two linear equations or inequalities Topic D: The modeling cycle – solving problems using equations and inequalities in one variable, systems of equations in two variables

6. Todays Focus: Topics A and B Which standards for mathematical practices will be the focus of these lessons?

7. Focus Standards for Topics A and B • A.SSE.2 • Lesson 6: Numerical Expressions—The 4-Number Game • Exit Ticket • Consider the expression: • Draw a picture to represent the expression. • Write an equivalent expression by applying the Distributive Property.

8. Focus Standards for Topics A and B N-Q.1 A.CED.2

9. Focus Standards for Topics A and B Grade 9 M1 L3 Problem Set

10. Types of Lessons • Problem Set Students and teachers work through examples and complete exercises to develop or reinforce a concept or procedure. • 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 problems that are ill-defined and have a real world context.

11. Lesson Organization • Student • Classwork • Problem Set • Teacher • Student Outcomes • Lesson Notes (in select lessons) • Classwork • General directions and guidance, including timing guidance • Discussion points with expected student responses • Student classwork with solutions • Scaffolding Boxes • Exit Ticket • Problem Set (with solutions)

12. Exploration Lesson: Graphs of Quadratic Functions G9-M1-L2 Student Materials Example 2 G9-M1-L2 Student Materials Example 3

13. Reflecting on Lesson 2 What were the focus standards in this lesson? What teaching and learning strategies helped to make this content accessible to all learners? How does the teacher version support student engagement and learning? Which SMPs do students engage in during this lesson?

14. Exploration Lesson: Two Graphing Stories Lesson 5 Example 1 Problem Set #1 and #2

15. Reflecting on Lesson 5 What were the focus standards in this lesson? How does the teacher version support student engagement and learning? What teaching and learning strategies helped to make this content accessible to all learners? Which SMPs do students engage in during this lesson?

16. Socratic Lesson: Algebraic Expressions LESSON 7 Exercises 5-8 Exit Ticket

17. Reflecting on Lesson 7 What were the focus standards in this lesson? How does the teacher version support student engagement and learning? What teaching and learning strategies helped to make this content accessible to all learners? Which SMPs do students engage in during this lesson?

18. Standards for Mathematical Practice • Three Components of Rigor • Fluency • Conceptual Understanding • Application • FOCUS QUESTION: How do the SMPs support these three components. Find specific instances within the lessons.

19. What’s Left in Topics A and B Teacher pp. xx to xx Teacher pp. xx to xx Teacher pp. xx to xx Lessons 1, 3 and 4—Graphing Stories Lesson 6—Algebraic Expressions Lessons 8 and 9—Generating Polynomials

20. Lessons 1, 3, and 4: Graphing Stories Lesson 1—Graphs of Piece-wise Defined Linear Functions Lesson 3—Graphs of Exponential Functions Lesson 4—Typical Water Usage at a School

21. Lesson 6: Algebraic Expressions Leela is convinced that Do you think she is right? Exercise 1: The Four Number Game Exercise 3: The Four Number Game with Variables Exercise 4: Combining Like Terms IS the Distributive Property Exercise 5-7: Geometric Models

22. Lesson 8-9: Generating Polynomials Generating polynomials based on base-10 or base-n arithmetic provides a strong connection to work in elementary grades and makes meaning out of operations on polynomials The properties of real numbers provide a justification for the equivalency of statement like the one shown below:

23. Preview Topic C

24. Lesson 10 and 11: Solutions

25. Lessons 12 and 13: Solving Equations

26. Lessons 12 and 13: Solving Equations

27. Biggest Takeaway What are your biggest takeaways from this session? How can you support successful implementation of these materials at your schools given your role as a teacher, school leader, administrator or BOCES representative?

28. Key Points • Lessons 1-5 are meant to introduce, not “cover”, the various functions to be covered in the year. • Students walk away from these lessons firmly connected to the idea that graphs (and equations) are used for modeling real life situations. • The lessons serve to require students to be ever aware that variables are merely placeholders for numbers. • Timing of lessons cannot possibly meet the needs of all student populations. Teachers should preview the lesson and make conscious choices about how much time to devote to each portion. • While many exercises support the mathematical practices in and of themselves, the discussions and dialog points are often critical for both their content and for enacting the mathematical practices. • Study carefully the Lesson Notes on physics and quadratic functions.

29. A Story of Functions G9-M1 Mid-Module Assessment

30. Find Your Partners • A—your assessment buddy • B—someone from your school or school district • C—someone with a different job than you have • D—someone with the same job as you have • not from your same school or district

31. Session Objective Identify critical aspects of instruction that prepare students to reason and/or conduct modeling included on the mid-module assessment.

32. Agenda Take the mid-module assessment Score the mid-module assessment Map skills and concepts on the assessment back to the standards and the lessons

33. Mid-Module Assessment Work with a partner on this assessment pp. xx-xx

34. Scoring the Assessment

35. Connecting Standards, Assessment and Lessons Select 1-2 questions and answer the following questions. What focus standards does this question address? What foundational standards must be in place for success? What mathematical practice standards does this question address? Which lessons will help prepare my students for success on this assessment?

36. Biggest Takeaway

37. Key Points • The assessments in Module 1 are designed to take 2 days per assessment. • As much as possible, assessment items are designed to asses the standards while emulating PARCC Type 2 and Type 3 tasks.