Mathematics

1. Mathematics Principal’s Conference Summer 2012 CFN 609

2. Session Agenda and outcomes • Know and understand the City-wide Instructional Expectations in Mathematics. • Clarify “The Major Work of the Grade” • http://engageny.org/resource/math-content-emphases/ • Become familiar with the Supporting Guidance Documents the DOE has created for Mathematics. • http://schools.nyc.gov/Academics/CommonCoreLibrary/CommonCoreClassroom/Mathematics/default.htm • Consider the context of individual schools/grade teams/math departments and come up with a plan for the utilization or extension of the guidance document(s) for 2012-13 planning. • Compare and Analyze Current vs. Common Core-aligned 3-8 assessments in relation to the Instructional Shifts. • http://www.p12.nysed.gov/apda/common-core-sample-questions/

3. Citywide Expectations for Mathematics 2012-2013 • 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. B. In grades 6-12, students will experience eight Common Core-aligned units of study: two in math, two in ELA, two in social studies, and two in science.

4. 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. One of 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.

5. 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 6-7-Ratios and Proportional Relationships 8-Expressions and Equations Standards for Mathematical Practice MP.3 Constructing Viable arguments and critique the Reasoning of others and MP.4 Modeling with Mathematics

6. Snapshot from Grade 5 STandards Domain Standards Cluster

7. Standards for Mathematical Practice • Make sense and 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

8. 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.

9. Crosswalk of Common Core Instructional Shifts: Mathematics

10. CIE expectations C. 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.

11. As the new state curriculum is completed: • The DOE has assessed the need for additional curriculum resources and determined how to use the DOE’s Core Curriculum to best support schools. At the same time, the writers of the Common Core are establishing criteria for full curricular programs and textbooks aligned to the new standards in mathematics. • During this period of transition toward a fully CCLS-aligned Curriculum, the DOE has created and posted Common Core-aligned tasks and instructional supports on the Common Core Library and has provided a flexible set of supports so that educators can choose which supports make sense based on their school’s current curriculum and context.

12. DOE Guidance Documents • 1. Core Curriculum Alignment Guidance for Everyday Mathematics (k-5) • 2. Scope and Sequence Samples (K-8) • 3. Mathematics Overviews for Impact Math (6-8) • http://schools.nyc.gov/Academics/CommonCoreLibrary/CommonCoreClassroom/Mathematics/default.htm

13. Major Work of the Grade Before we dig into the supports that the DOE has created for K-8 schools, let’s begin by reviewing the concept of “major work of the grade”. Math Content Emphases http://engageny.org/resource/math-content-emphases Model Content Framework http://www.parcconline.org/model-content-frameworks-mathematics

14. Math Content Emphases:Major work of the Grade Explanations of terms used: • 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%).

15. Major Work of Grade 5 Domain Cluster

16. Grade 5 STandards Domain Cluster Standards

17. “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.

18. 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

19. 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

20. 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.

21. Scope and Sequence Grade 5

25. Activity # 1In order to teach a sequence of instruction that fully addresses the standards represented… • How might your teacher teams use this document as a support when refining existing pacing and scope and sequence? • What supports will teacher teams need in order to make use of this guidance? • What are the structures at your school that currently exist or need to be developed to support teachers and teacher leaders with fulfilling this expectation? • If this work is underway, how might you go deeper, incorporating elements of the instructional shifts and the mathematical practices?

26. Key Advances from the Previous Grade :http://www.parcconline.org/model-content-frameworks-mathematics Highlight some of the major grade-to-grade steps in the progression of increasing knowledge and skill detailed in the standards. Examples of key advances are highlighted to stress the need to treat topics in ways that take into account where students have been in previous grades and where they will be going in subsequent grades. EX Grade 5: Students extend their grade 4 work in finding whole-number quotients and remainders to the case of two-digit divisors (5.NBT.6). EX Grade 5:  Students use their understanding of fraction equivalence and their skill in generating equivalent fractions as a strategy to add and subtract fractions, including fractions with unlike denominators.

27. Fluency Expectations or Examples of Culminating standards: Highlights individual standards that set expectations for fluency or that represent culminating masteries. Fluency standards are highlighted to stress the need to provide sufficient supports and opportunities for practice to help students meet these expectations. Culminating standards are highlighted to help give a sense of where important progressions are headed. EX: 5.NBT.5 Students fluently multiply multi-digit whole numbers using the standard algorithm.  Fluency is not meant to come at the expense of understanding but is an outcome of a progression of learning and sufficient thoughtful practice. It is important to provide the conceptual building blocks that develop understanding in tandem with skill along the way to fluency; the roots of this conceptual understanding often extend one or more grades earlier in the standards than the grade when fluency is finally expected.

28. Key FLuencies

29. Curriculum Specific Guidance Core Curriculum alignment Guidance: Grade 3 Mathematics Overviews for Impact Math: Grade 8

30. ACTIVITY #2: Other resources:EDM(K-5) and Impact Support(6-8) • Table facilitator will briefly highlight aspects of these documents for you. Take a few quiet minutes to look them and the “talking points” over. Discuss in partners or as a table how these documents can be used at your school. Use talking points to highlight specific areas of focus for your school. • Elementary Schools using other curricula may want to gather separately and continue conversations on how to use the scope and sequence documents (Grade 5).

31. Core Curriculum Alignment Guidance Document Grade 3

32. Grade 3 EDM alignment

33. Talking Points for Elementary • How might teacher teams use this document as a support when refining existing pacing and scope and sequence? • What supports will teacher teams need in order to make use of this guidance? • If this work is underway, how might teacher teams go deeper? What are your next steps? • How might we utilize the DOE bundles? • How will we incorporate the 2 common core aligned units with Performance tasks? • Can daily math routines support the instructional shifts and how might they show up in our plan? • How can we be sure to keep the focus on rich tasks and developing connected units of study where students get to explore mathematics deeply? • How can we keep an emphasis on changing pedagogy, developing classrooms where students see math as connected, engage in deep explorations as opposed to skill lesson by skill lesson. • How can we keep the instructional shifts alive when curriculum planning? Particularly focus, Fluency and Deep Understanding? • What logistics need to be set? Year long pacing, expected start and end dates, common assessments, benchmark assessments?

34. Core Curriculum Alignment Guidance 6-8

36. Talking Points for Middle School • How might your teacher teams use this document as a support when refining existing pacing and scope and sequence? • What supports will teacher teams need in order to make use of this guidance? • If this work is underway, how might you go deeper? What are your next steps? • How might we utilize the DOE bundles? • How will we incorporate the 2 common core aligned units with Performance tasks? • How can we be sure to keep the focus on rich tasks and developing connected units of study where students get to explore mathematics deeply? • How can we keep an emphasis on changing pedagogy, developing classrooms where students see math as connected, engage in deep explorations as opposed to skill lesson by skill lesson. Can we balance the two? • How can we keep the instructional shifts alive when curriculum planning? Particularly focus, Fluency and Deep Understanding? • What logistics need to be set? Year long pacing, expected start and end dates, common assessments, benchmark assessments?

37. Share Which talking point or idea regarding reworking the current scope and sequence focused your conversation? How is this pertinent to where your school is currently in regard to mapping out the year in Mathematics? Plans? Immediate changes? Current structures that will support this work?

38. Current vs Common Core-aligned 3-8 State Assessments Guiding Questions: • How will the common core aligned state ELA and Math Tests in 2012-2013 differ from current state tests? • Given the change in assessments and the demands of the common core, how might instruction need to shift to ensure our students are prepared?

39. Crosswalk of Common Core Instructional Shifts: Mathematics

40. Activity #3Comparison of test Items Read and work on the 2009-2010 and 2012-12013 test items yourself, make notes about the rigor you observe. Discuss with Partner: • What do you notice about the math problems on the old test? New test? • What tells us the new items are more rigorous than the old ones? • To what extent do the test items reflect the shifts articulated in the crosswalk document?

41. Analyzing changes to NYS math TestS: Grade 3

43. Analyzing changes to NYS math TestS: Grade 6

45. Changes and Indications of the Shifts

46. Implications… • What would our students need to know and be able to do to respond to these kinds of tasks and assessment items? • How do these problems represent the instructional shifts of fluency, application and deep understanding? • What are the implications for classroom practice?

47. NY State Curriculum Map Materials The New York State Education Department has awarded Common Core two contracts to develop Pre-Kindergarten-5th grade mathematics curriculum aligned to the NY State’s Common Core Learning Standards (CCLS). The organization has been in the field for more than a year conducting professional development and has learned a great deal about how to most effectively bring CCSS-based instruction into the classroom "Teachers will be able to follow or build on the curricular materials produced by these three vendors.  The materials will provide a carefully sequenced road map for districts to adopt or adapt”- John B King http://engageny.org/wp-content/uploads/2012/07/Year-Long-Curriculum-Map-PK-5-Academic-Year-Distribution.pdf http://engageny.org/resource/year-long-draft-curricular-maps-in-ela-and-mathematics/

48. EDUCATION DEPARTMENT AWARDS 
CONTRACTS FOR DEVELOPMENT OF
ENGLISH LANGUAGE ARTS AND MATH CURRICULA • The new curricula will all be available on EngageNY.org. The site currently hosts a number of ELA and Math exemplars. Work on these contracts will begin upon approval by the office of the state Comptroller. All modules, grades P-5, will be completed by the summer 2013. King said vendors will work closely with NYS teachers and Administrators to develop curricula. • King said SED recently issued an RFP for curriculum models and associated professional development for Grades 6-12 aligned to the New York State P-12 Common Core Learning Standards in ELA and Mathematics.  The award of the contracts is anticipated later this spring.

49. Year Long Curriculum Maps in MathEngageNY.Org

50. Doe Guidance/NYS guidance/Major work of the grade