THE CCLS AND CIE IN Mathematics 2012-2013 SETTING UP THE YEAR K-5

1. THE CCLS AND CIE IN Mathematics 2012-2013SETTING UP THE YEAR K-5 CFN 609 Karen Cardinali, Achievement Coach

2. Pd schedule Institute for Learning, University of Pittsburgh Professional Development Support. Series of 2 focused and iterative workshops Dates: December ?, March 4th Topics to be covered:  • Examining our vision of CCSS-aligned instruction • Deepening our understanding of the content standards related to fractions and ratios and proportional relationships within the context of a lesson. • Learning about assessing and advancing questions • Learning and applying accountable Talk Moves to the share, discuss and analyze phase of a lesson • Understanding  performance-based assessment & practice creating instruction tasks (Strategies for modifying textbook tasks to increase the cognitive demand of the tasks.) • Facilitator moves

3. AGENDA PROBLEM OF THE DAY ACTIVITY # 1: TEACHER TEAMS AND THE QUALITY REVIEW RUBRIC ACTIVITY # 2: THE CITYWIDE EXPECTATIONS AND GUIDANCE DOCUMENTS BREAK ACTIVITY # 3: ADJUSTING SCOPE AND SEQUENCE TO ALIGN TO THE MAJOR WORK OF THE GRADE IDENTIFYING GAPS. LUNCH ACTIVITY # 4: COMMON CORE ALIGNED UNITS OF STUDY ACTIVITY # 5: IMPROVING TEACHER PRACTICE THROUGH PLANNING DANIELSON COMPONENTS 1E, 3B ANB 3D REFLECTIONS AND ACTION PLAN

4. A mathematician’s birthday party… • The host had a bag with 5 birthday hats. • 3 were red; 2 were blue. • He asked for volunteers to play the game. • They stood in a line; each person faced forward. • The host pulled a hat from the bag and placed one hat on each players head.

5. Player 3 was at the back of the line; he could see the heads of players 2 and 1. • Player 2 could see the head of player 1. • Player 1 could not see anyone’s head, but stared straight ahead. • Each player could not see the hat on his own head.

6. The goal of the game was for each player to guess the color of the hat on his own head without peeking

7. Player 3 went first, and said, “ I don’t know the color of my hat.” Player 2 thought for a moment, and then said, “ I don’t know the color of my hat.” Player 1 said, “ I know the color of my hat.” How can this be?

8. A mathematician’s Birthday Party… • Solve on your own. Please do not talk to a neighbor. • After 5 minutes, you will be asked to share your strategy with a neighbor • After 5-7 minutes of sharing, you will be asked to reflect on where you are in the problem solving process.

9. Recording Sheet

10. Problem solving in mathematics Where are you in the problem solving process? What is your emotional state? Did communicating with your neighbor help you? Hinder you?

11. Problem solving in Mathematics At your table (in small groups) share your strategy and create a group solution. Be ready to share your solution with the rest of the community.

12. Mathematical Practices • Make sense of problems and persevere in solving them • Reason abstractly and quantitatively • Construct viable arguments and critique the reasoning of others • Model with mathematics • Use appropriate tools strategically • Attend to precision • Look for and make use of structure • Look for and express regularity in repeated reasoning

13. Creating Effective Mathematics lessons There’s a strong relationship between: • The development of mathematical models and modeling and Problem solving; • The development of mathematical models and modeling and reasoning; and • The development of mathematical models and modeling and a student’s ability to create a viable argument.

14. Activity 1: Quality review RubricIndicators 1.1, 1.2, 1.3, 2.2, 4.2, 5.1 Highlight any words or key phrases through out the well- developed columns that you think are connected to the work of teacher teams or that reflect or are evidence of the work being done in teacher teams. What structures need to be in place to reach these expectations? What would/could evidence that your school was well developed in this area look like? Be specific

15. Recording sheet

16. Citywide Expectations for Mathematics 2012-2013 UNITS OF STUDY 1. In grades PK-5, students will experience four Common Core-aligned units of study: two in math and two aligned to the literacy standards in ELA, social studies, and/or science.

17. Content oF the units Each unit will provide points of access for all students and culminate in a performance task aligned to the Common Core. Schools may choose to upgrade existing units, engaging in cycles of inquiry and looking closely at student work to make adjustments to curriculum, assessment, and instruction. Oneof each teacher’s Common Core-aligned units of study in 2012-13 should focus on Mathematical Practices 3 and/or 4 and the selected domain of focus. The other unit may center on standards in the same domain or on other major work of the grade as well as the above mentioned and other relevant Standards for mathematical practice.

18. Domains of Focus Pre-K-K- Operations and Algebraic Thinking 1-2-Number and Operations in Base Ten 3-Operations and Algebraic Thinking 4-5-Number and Operations—Fractions Standards for Mathematical Practice MP.3 Constructing Viable arguments and critique the Reasoning of others and MP.4 Modeling with Mathematics

19. Snapshot of Grade 5 standards Domain Cluster Standard

20. Math Content Emphases:Major work of the Grade • Major clusters – areas of intensive focus, where students need fluent understanding and application of the core concepts (approximately 70%). • Supporting clusters – rethinking and linking; areas where some material is being covered, but in a way that applies core understandings (approximately 20%). • Additional Clusters – expose students to other subjects, though at a distinct, level of depth and intensity (approximately 10%). Math Content Emphases http://engageny.org/resource/math-content-emphases Model Content Framework http://www.parcconline.org

21. Supporting… Connections at a single grade level can be used to improve focus, by tightly linking secondary topics to the major work of the grade. For example, in grade 3, bar graphs are not “just another topic to cover.” Rather, the standard about bar graphs asks students to use information presented in bar graphs to solve word problems using the four operations of arithmetic. Instead of allowing bar graphs to detract from the focus on arithmetic, the standards are showing how bar graphs can be positioned in support of the major work of the grade. In this way coherence can support focus. -K–8 Publishers’ Criteria for the Common Core State Standards for Mathematics

22. Major Work of Grade 5 Domain Cluster

23. “In depth” Opportunitieshttp://www.parcconline.org/model-content-frameworks-mathematics • 5.NBT.1 The extension of the place value system from whole numbers to decimals is a major intellectual accomplishment involving understanding and skill with base-ten units and fractions. • 5.NBT.6 The extension from one-digit divisors to two-digit divisors requires care. This is a major milestone along the way to reaching fluency with the standard algorithm in grade 6 (6.NS.2). • 5.NF.2 When students meet this standard, they bring together the threads of fraction equivalence (grades 3–5) and addition and subtraction (grades K–4) to fully extend addition and subtraction to fractions.

24. Parcc Model Content Frameworks for Mathematicshttp://www.parcconline.org/ The Model Content Frameworks for Grade 5 highlight examples of key content dependencies, examples of key instructional emphases, opportunities for in-depth work on key concepts, and connections to the mathematical practices.  While they provide additional context to the grade 5 standards, the frameworks are not meant to replace engaging with the standards themselves.  For this reason, readers are advised to have a copy of the Common Core State Standards to use in conjunction with the Model Content Frameworks.  The Model Content Frameworks for Grade 5 include the following components.  Click the links below to read more about grade 5. Examples of Key Advances from Grade 4 to Grade 5 Fluency Expectations or Examples of Culminating Standards Examples of Major Within-Grade Dependencies Examples of Opportunities for Connections among Standards, Clusters or Domains Examples of Opportunities for In-Depth Focus Examples of Opportunities for Connecting Mathematical Content and Mathematical Practices Content Emphases by Cluster

25. recommendations for using the cluster‐level emphases. DO: • Use the guidance to inform instructional decisions regarding time and other resources spent on clusters of varying degrees of emphasis. •  Allow the focus on the major work of the grade to open up the time and space to bring the Standards for Mathematical Practice to life in mathematics instruction through sense‐making, reasoning, arguing and critiquing, modeling, etc. •  Evaluate instructional materials taking the cluster‐level emphases into account. The major work of the grade must be presented with the highest possible quality; the supporting work of the grade should indeed support the major focus, not detract from it. • Set priorities for other implementation efforts taking the emphases into account, such as staff development; new curriculum development; or revision of existing formative or summative testing at the school level. -Content Emphases by cluster, DOE

26. Do NoT: • Neglect any material in the standards. (Instead, use the information provided to connect Supporting Clusters to the other work of the grade.) •  Sort clusters from Major to Supporting, and then teach them in that order. To do so would strip the coherence of the mathematical ideas and miss the opportunity to enhance the major work of the grade with the supporting clusters. •  Use the cluster headings as a replacement for the standards. All features of the standards matter — from the practices to surrounding text to the particular wording of individual content standards. Guidance is given at the cluster level as a way to talk about the content with the necessary specificity yet without going so far into detail as to compromise the coherence of the standards. Content Emphasis by Cluster- DOE

27. Standards for Mathematical Practice • Make sense of problems and persevere in solving them • Reason abstractly and quantitatively • Construct viable arguments and critique the reasoning of others • Model with mathematics • Use appropriate tools strategically • Attend to precision • Look for and make use of structure • Look for and express regularity in repeated reasoning

28. What are some of the components that support a common core aligned unit of study that meet the needs of all students?

29. Units include • Content and skills students need to know and be able to perform that align to three to six primary standards to be assessed by a culminating task; • A pre-assessment that helps to surface students’ understanding of the concepts and where understanding ends/breaks down. The pre-assessment should delineate the linguistic and content needs of ELLs; • Formative assessments/checkpoints throughout the unit; • A series of learning experiences that build students toward accomplishing the goals of the unit and that reveal a conceptual progression and connection to relevant previously learned and future concepts; • A culminating task that assesses the unit’s primary standards; • A mix of explicit teaching and student investigation; • Explicit teaching of academic vocabulary; • Access for all students through multiple means of representation, action and expression, and engagement (refer to http://www.cast.org/udl/index.html); • Instructional supports, as needed, for ELLs (refer to these ELA and Math resources).

30. CIE expectations 2. In grades PK-8, schools will use guidance from the DOE to review their scope and sequence and: Reorganize math content to teach fewer topics and allow for more time to focus on the major work of the grade.

31. DOE Guidance Documents • 1. Core Curriculum Alignment Guidance for Everyday Mathematics (k-5) • 2. Scope and Sequence Samples (K-8) • http://schools.nyc.gov/Academics/CommonCoreLibrary/CommonCoreClassroom/Mathematics/default.htm

32. DOE Guidance Documents • These documents provide a CCLS-aligned scope and sequence for Mathematics that take into account the differences in and transition from the New York State Standards to the CCLS. • The scope and sequence is aligned to the Common Core and demonstrates a focus on the major work of the grade which the State has indicated will be the focus of next year’s 3-8 State exams. • This scope and sequence represents one way that a school may choose to organize and teach the full range of the standards before the state test. It is not based on any additional information about the changes in next year’s tests.

33. Scope and Sequence Grade 5

34. Concepts that should be omitted or Bridged

35. Unit standards

36. Take a moment… This is one key piece to use when planning

37. New York state: Story OF UNITSK-5 Curriculum MapS

38. Overview of Grade 5 standards

39. The goal of the Story of Units is to enable students to successfully progress through a sequence of increasingly complex math concepts. The curriculum embodies the instructional shifts and mathematical practices prioritized by the CCLS and will enable students and teachers to successfully implement the new standards. - Common Core

40. State resources: Something to watch Curriculum ExemplarsThe curriculum exemplars provide valuable support for implementing the Common Core State Standards. http://engageny.org/resource/curriculum-exemplars/ Grade 1, 2, 7 Modules Story of units for K-5 Power point version and video

41. Alignment?

42. Take a moment…

43. Activity 2: Look over guidance documents and discuss:In order to teach a sequence of instruction that fully addresses the standards represented… • How can your teacher teams use these documents as a support when refining existing pacing and scope and sequence? • What supports do teacher teams need in order to make use of this guidance? • If this work is underway, how might you go deeper, incorporating elements of the instructional shifts and the mathematical practices?

44. Curriculum Specific Guidance Core Curriculum alignment Guidance: Grade 3

45. Grade 3 EDM alignmentwww.mheonline.com/emcrosswalk Password: CCSS2007support

46. Whole Group TalkEDM(K-5) or Other • How can these documents be used in your teacher teams? • Elementary Schools using other curricula: What aspects of this document might you pull into planning with your curriculum. • How can it be used in collaboration with the other documents?

47. In 2012-2013 the DOE is asking that Teachers focus their Pedagogical growth on Instructional Shifts that: Require fluency, application and conceptual understanding. These shifts focus on the ability to think with mathematics and mathematically, particularly targeting the ability to transfer understanding from one context to another, to select the right mathematical tools and to be able to make mathematical arguments and explain why certain decisions were made proposing solutions to “real-world” problems.

48. curricula have not always been balanced in their approach to these three aspects of rigor… “…Curricula have not always been balanced in their approach to these three aspects of rigor. Some curricula stress fluency in computation, without acknowledging the role of conceptual understanding in attaining fluency. Some stress conceptual understanding, without acknowledging that fluency requires separate classroom work of a different nature. Some stress pure mathematics, without acknowledging first of all that applications can be highly motivating for students, and moreover, that a mathematical education should make students fit for more than just their next mathematics course. At another extreme, some curricula focus on applications, without acknowledging that math doesn’t teach itself”. -K–8 Publishers’ Criteria for the Common Core State Standards for Mathematics

49. Crosswalk of Common Core Instructional Shifts: Mathematics Refresh and review the instructional shifts.

50. Key FLuencies