Module 3B for Middle/High School Teachers

1. Module 3B for Middle/High School Teachers Florida Standards for Mathematics: Focus on Practice Standards

2. Transitioning to Florida Standards: Project Overview • Project is Race to the Top funded until June 2014 • All charter schools eligible to participate • Develop and deliver targeted training and technical assistance specific to charter schools in two major areas: 1) Implementation of the Florida Standards 2) Access and use of a Local Instructional Improvement System (LIIS) to analyze student achievement data to drive instruction and increase student academic achievement • No cost to charter schools

3. Project Activities • Professional development for teachers, administrators, and governing board members (Delivered regionally) • Data Literacy and Use • Florida Standards (English Language Arts & Literacy, Math) • Value-Added Model (VAM) • Training of Trainers Model for Teacher Leaders • K-5 (Up to 5 Teachers & 1 Administrator Per School) • 6-12 (Up to 5 Teachers & 1 Administrator Per School) • Training for charter school teams (Delivered regionally) • Self-assessment tool • Creating a Florida Standards Implementation Plan • Progress monitoring templates

4. Professional Development Session Alignment Set 1 Data Use Governing Board Data Use ELA Math School Leaders Module 3 PARCC Data Use ELA Math Teachers Leadership Teams Session 1 Session 2 Module 6 Florida Standards Math Module 7 ELA & Data Use

5. Professional Development Session Alignment Set 2 Governing Board Florida Standards School Leaders Assessments Data Analysis VAM Data Use ELA Math Data & ELA Data & Math Teachers Leadership Teams Session 3 Session 4 Session 5 Session 6 Module 6 Florida Standards Math Module 7 ELA & Data Use Module 8 Math & Data Use Module 5 Florida Standards ELA

6. Travel Notes • Mileage to/from the trainings will be reimbursed to the school at $.445/mile (documentation with map and mileage required) • Parking and tolls will also be reimbursed with receipt • Reimbursement is limited to two cars per school • Forms and directions to request reimbursement are available under “Resources” on www.flcharterccrstandards.org • There are specific instructions included with the form to help fill it out correctly • Reimbursements for substitutes are NOT an eligible expense

7. Focus on Standards for Mathematical Practice Outcomes By the end of this session you will have: • Gained an initial understanding of the Florida Standards for Math and the embedded changes and instructional shifts. • Explored all eight of the Standards for Mathematical Practice and identified how they are related. • Explored how practices can be clustered and examined why Practice 1: “Make sense of problems and persevere in solving them” and Practice 6: “Attend to precision” are considered the two “umbrella” standards that describe the habits of mind of successful mathematical thinkers.

8. Focus on Standards for Mathematical Practice Outcomes (cont'd) By the end of this session you will have: • Identified evidence of the Practices, with focus on Practices 1 and 6, in Florida Standards aligned mathematics tasks. • Discussed descriptors for all eight Practices, and created formal grade level descriptions for Practice 1 and Practice 6. • Explored how specific instructional strategies (e.g., questioning, engaging students in mathematical discourse, and requiring multiple representations) can help students meet the major learning goals identified as part of Florida’s “New Way to Work.” • Identified relevant resources for implementing the Florida Standards for Math and created a peer support network.

9. You Are Here Module 4 Data Use Module 1 Data Use Module 2 ELA Module 3 Math Module 8 Math & Data Use Module 7 ELA & Data Use Module 5 ELA Module 6 Math

10. 8 Components of Full Florida Standards Implementation

11. Today’s Agenda Welcome and Introductions • Pre-Assessment • Establishing a Positive Working Environment • Overview of the Florida Standards for Math • Understanding the Standards for Mathematical Practice: Developing Mathematical Expertise Lunch • Supporting Students to Make Sense of Problemsand Persevere in Solving Them • Attending to Precision in Every Lesson • Teaching the Standards for Mathematical Practice • The Right Support at the Right Time • Next Steps • Post-Assessment Wrap Up

12. Introductory Activity Pre-Assessment Guide Page 5

13. Section 1 Establishing a Positive Working Environment

14. Activity 1: Setting Norms for Productive Work How can we work well together? • In a conversation, what is something that encourages you to speak your mind? • What is something that deters you from expressing your ideas? Guide Page 7

15. Important Point Alignment to the Content Standards but not the Practice Standards DOES NOT EQUAL Florida Standards Aligned

16. Section 2 Overview of the Florida Standards for Math

17. Activity 2a: What Do We Know? Quick Write: What do you know about the Florida Standards for Math? Discuss: What does your group know about the Florida Standards for Math? Guide Page 9

18. Coherence What’s in the Florida Standards for Math? • The Standards for Mathematical Content • The Standards for Mathematical Practice Rigor Focus What’s New About the Florida Standards for Math?

19. Fewer standards allow for focusing on the major work for each grade Focus

20. Coherence The Standards are designed around coherent progressions and conceptual connections. Create equations that describe numbers or relationships. Analyze proportional relationships and use them to solve real-world and mathematical problems. Understand the connections between proportional relationships, lines, and linear equations. Guide Page 10

21. Coherence The Standards are designed around coherent progressions and conceptual connections.

22. Coherence The Standards are designed around coherent progressions and conceptual connections. • Expressing Geometric Properties with Equations G-Gpe • Translate between the geometric description and the equation for a conic section  • Use coordinates to prove simple geometric theorems algebraically

23. The major topics at each grade level focus equally on: Rigor • Conceptual Understanding • More than getting answers • Not just procedures • Accessing concepts to solve problems • Procedural Skill • and Fluency • Speed and accuracy • Used in solving more complex problems • Comes after conceptual understanding • Application of Mathematics • Using math in real-world scenarios • Choosing concepts without prompting Much more on this in the next Florida Standards for Math Sessions: Modules 6 & 8

24. Activity 2b: Then, Now and in the Future Teaching Mathematics Guide Page 11

25. Florida’s Instructional Shifts “A New Way to Work” Before planning units: Refer to the way the standards have been “chunked” within the course description Identify the major learning goals for the unit Create progress scales for each goal Develop lesson plans and formative assessments to differentiate instruction Much more on this in Modules 6 & 8

26. Phil Daro Phil Speaks

27. Teaching Mathematics Guide Page 11

28. Change Isn’t Easy Stages of Change Achievethecore.org Guide Page 12

29. Let’s Take A Break… Be back in 10 minutes…

30. Section 3 Understanding the Standards for Mathematical Practice: Developing Mathematical Expertise Guide Pages 14-23

31. SMP 1: Make sense of problems and persevere in solving them

32. SMP 1: Make sense of problems and persevere in solving them Mathematically proficient students:

33. SMP 1: Make sense of problems and persevere in solving them Farmer Lebowski has some chickens and some cows in her yard. Together, the animals have a total of 90 heads and 286 legs. How many chickens and how many cows are in the yard? Find a way to solve this problem that does not involve algebra.

34. SMP 1: Make sense of problems and persevere in solving them Instructional Supports • Don’t be afraid to challenge students! • Ask clarifying questions such as: What is the problem asking? How could you start the problem? What tools might be helpful? How can you check this? Does your answer make sense? How could you make this easier to solve?

35. SMP 1: Make sense of problems and persevere in solving them Instructional Supports • Create ‘I Can’ statements for your students so they know what is expected.

36. SMP 2: Reason abstractly and quantitatively

37. SMP 2: Reason abstractly and quantitatively Mathematically proficient students: • Make sense of quantities and relationships • Represent a problem symbolically • Consider the units involved • Understand and use properties of operations Decontextualize Contextualize

38. SMP 2: Reason abstractly and quantitatively Eighth graders are going on a field trip. There are 167 students going. How many buses are needed for the trip if each bus can hold 48 students?

39. SMP 2: Reason abstractly and quantitatively Instructional Supports • Don’t be afraid to challenge students! • Ask clarifying questions such as: What does the number___ represent in the problem? How can you represent the problem with symbols and numbers? Does your answer fit what the problem is asking?

40. SMP 2: Reason abstractly and quantitatively Instructional Supports • Create ‘I Can’ statements for your students so they know what is expected.

41. SMP 3: Construct viable arguments and critique the reasoning of others “(Students) make conjectures and build a logical progression of statements to explore the truth of their conjectures.” “Students at all grades can listen or read the arguments of others, decide whether they make sense, and ask useful questions to clarify or improve the arguments.” Mathematics Standards

42. SMP 3: Construct viable arguments and critique the reasoning of others Two more points… Mathematically proficient students: • Use definitions and previously established results in constructing arguments • Make conjectures and attempts to prove or disprove through examples and counterexamples Continuous

43. SMP 3: Construct viable arguments and critique the reasoning of others • In 2009, the maintenance budget for a school was $30,000 of a total budget of $500,000. In 2010, the figure was $31,200 of a total budget of $520,000. Inflation between 2009 and 2010 was 8 percent. • Parents complain that the money spent on maintenance has increased. • The maintenance manager for the school complains that the money for maintenance has decreased. • The Principal maintains that, in fact, there has been no change in spending patterns at the school. • Is it possible that everybody's opinion could be valid? Why or why not? Where do you stand?

44. SMP 3: Construct viable arguments and critique the reasoning of others Instructional Supports • Don’t be afraid to challenge students! • Create tasks that directly involve argumentation and critique. • Ask questions such as: How can you prove that your answer is correct? What examples could prove or disprove your argument? How is your answer different from _____’s answer? What questions do you have for_____?

45. SMP 3: Construct viable arguments and critique the reasoning of others Instructional Supports • Create ‘I Can’ statements for your students so they know what is expected.

46. SMP 4: Model with mathematics What does it mean to model with mathematics?

47. SMP 4: Model with mathematics Mathematically proficient students: • Apply reasoning to create a plan or analyze a real world problem • Apply formulas/equations • Make assumptions and approximations to make a problem simpler • Check to see if an answer makes sense and change a model when necessary • Use all kinds of physical models, images and drawings, graphs, tables, equations, etc.

48. SMP 4: Model with mathematics On its menu, a restaurant has 3 different appetizers, 4 different entrées, and 2 different desserts. How many distinct meals of 1 appetizer, one entrée, and 1 dessert could you make from this menu? Show how you know.

49. SMP 4: Model with mathematics Instructional Supports • Don’t be afraid to challenge students! • Do not interpret the standard too narrowly. • Provide a problem and explicitly ask students to write the equation or number sentence called for in the situation. • Provide a model and ask students to create a situation that matches. • Apply a C-R-A sequence when helping students to progress their thinking.

50. SMP 4: Model with mathematics Instructional Supports • Create ‘I Can’ statements for your students so they know what is expected.